In this talk I will describe the application of state of the art image based modelling to several seemingly different areas of biology. I show examples from biomedical (lymphatic, vascular and lung system) and agricultural problems of plant soil interaction. I will describe the workflow from imaging (X-ray CT, XRF, SEM-EDX, histology), image reconstruction, image segmentation, computation and...
There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The...
Akt/PKB (Protein Kinase B) is a major crosstalk node in the mammalian cell. Located as the juncture of several key signalling pathways, it is involved in many cellular processes, such as glucose metabolism, cell growth and the suppression of apotosis. Dysregulated Akt signalling is implicated in a range of human disorders, from diabetes to cancer.
Initially, Akt is synthesised in the...
In many biological applications, it is useful to model chemical reactions at the level of individual molecules whilst not running costly Brownian dynamics models. Modelling chemical reactions as interactions at a distance can lead to errors if multiple species and time scales are important to the kinetics (for example, catalytic reactions). Multiple time scale analysis of equivalent mean-field...
Retinal vasculature is essential for adequate oxygen supply to the inner layers of the retina, the light sensitive tissue in the eye. In embryonic development, formation of the retinal vasculature via angiogenesis is critically dependent on prior establishment of a mesh of astrocytes, which are a type of brain glial cell. Astrocytes emerge from the optic nerve head and then migrate over the...
Atherosclerotic plaque growth is characterised by a process of chronic, non-resolving inflammation that leads to the accumulation of cellular debris and extracellular fat in the inner artery wall. In advanced plaques, smooth muscle cells (SMCs) are recruited from deeper in the artery wall to synthesise a fibrous tissue cap that sequesters the thrombogenic plaque content from the bloodstream....
It is well known that growth and survival of cancer stem cells (CSCs) is highly influenced by tumour microenvironmental factors and molecular signalling, initiated by cytokines and growth factors. IL-6 is a key regulator of a number of cellular processes including proliferation, survival, differentiation, migration and invasion and it is also commonly overexpressed in many cancers. Recent...
Oscillation of lateral asymmetry diorphism is first found in scale eating cichlid, Perrisodus microlepis. Fraction of their lefty morph oscillates around 0.5 in about 5 year period. Other fish or aquatic invertebrates also reveal lateral asymmetry dimorphism and oscillation of morph fractions. One of key factors of oscillation is cross predation dominance: lefty predator eats more righty...
Two consumer species that share a single resource species can indirectly interact each other, even without direct interactions. A typical indirect interaction is exploitative resource competition that results from a depression of resource biomass by consumption, which can be referred to as “biomass-mediated indirect effect”. Another type of indirect interaction is called “trait-mediated...
Vector-borne diseases cause worldwide concern with hundreds of millions of new cases and over a million deaths reported annually. Mathematical models are a key tool in the study of the spread of diseases such as malaria and dengue. In particular, transmission models have been successful at determining the most promising intervention strategies, despite the fact that many of these models assume...
Information analysis of amplicon sequencing of fecal samples from HIV positive individuals suggested an enrichment of a particular bacterial species in the gut microbiota, as referred to dysbiosis. Although a sufficient number of samples has already accumulated for both HIV positive and negative subjects, time-series datasets are rarely available. Hence difficulty remains in tracing the...
Tissue development requires cells of different types to organise themselves into the appropriate patterns and structures to produce viable, functional tissue. Similar processes occur in tissue repair (e.g. wound healing) or when tissues are grown in vitro (tissue engineering). Understanding how this organisation is coordinated is therefore an important basic problem in biology and medicine.
I...
The fall armyworm (Spodoptera frugiperda) is a pest insect which has the propensity to destroy a wide variety of common crops. It ranges over Eastern and Central North America and, since 2016, has been invasive in Africa resulting in significant economic damage. The fall armyworm is susceptible to Bt derived insecticides, making Bt modified crops a viable method for controlling this species....
A biochemical system is a biological system consisting of a collection of chemical compounds interacting with each other. One way to model and analyze a biochemical system is by using S-systems, which are coupled ordinary differential equations based on power-law formalism. In this work, we do a parameter estimation on an S-system model called HS96. This model, proposed by Hlavacek and...
Understanding how 3D organ morphology is achieved during development is one of the ultimate goals in biology. This is important not only for pure scientific interests but also for potential medical applications for controlling and designing functional organs. To achieve these goals, it is essential to clarify the quantitative relationships between microscopic molecular/cellular activities and...
It has long been debated whether introduction of two (or more) natural enemies results in more efficient pest control than that of either one enemy. Intra-guild predation (IGP) among two natural enemies sharing a single pest has been recognized as an important factor to reduce efficiency of pest control. While the classical theoretical model of IGP showed that introduction of two natural...
Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. We use experimental data on the gaits...
Tissue engineering aims to grow artificial tissues to replace those that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected three dimensional printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to...
Climate change is known to significantly affect the dynamics of vector-borne diseases, such as malaria. In particular, the species involved in the transmission dynamics of malaria are affected by various abiotic conditions, such as temperature, precipitation, humidity and vapor pressure . A number of models, typically statistical (using data and statistical approaches to correlate some...
The number of HIV+ individuals who develop end stage renal disease (ESRD) and require life-long dialysis treatment has been continually rising in some regions around the world. A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to disease and to project the future prevalence of HIV+ ESRD. The goals of this study are...
I will discuss mathematical and computational methods for spatio-temporal modelling in molecular and cell biology, including all-atom and coarse-grained molecular dynamics (MD), Brownian dynamics (BD), stochastic reaction-diffusion models and macroscopic mean-field equations.
Microscopic (BD, MD) models are based on the simulation of trajectories of individual molecules and their localized...
Mathematical modelling of the stochastic evolutionary process of carcinogenesis can be used to derive and to optimize the timing of clinical screens so that the probability is maximal that an individual is screened within a certain "window of opportunity" for intervention when early cancer development may be observed. By using data from epidemiological studies with long-term patient follow-up,...
Age plays an important role on immunity across the lifespan, as both very young and very old individuals are at higher risk of severe infection. CD8 T cells are important for controlling a number of viral and bacterial infections, and both the number and phenotype of CD8 T cells change with age. Various mathematical and experimental methods have been used to analyse T cell kinetics, and most...
In this talk, we consider the dynamics of a Lotka-Volterra prey-predator model by a class of delay differential equations. The number of prey varies due to a general nonlinear predators' consumption rate with delays. Under the assumption that the consumption rate is monotonically increasing with respect to the number of prey, we investigate the effect of the nonlinearity and delays on the...
Many biological systems rely on both long range and short range signals in order to produce proper cell patterns during development. These patterns, such as alternating cell fates, are defined by different gene and protein expression levels. However, the relative contribution of these two signalling modes in establishing proper patterns is not well understood. Using vulval development of two...
Patients diagnosed with glioblastoma multiforme (GBM) are expected to survive only 14 months and die due to the pressure that the tumour builds in the brain as well as the formation of peritumoural edema (PTE). With the view to investigating the early stages of brain tumour development, and how it impacts the healthy brain environment, we develop a mechanistic model of GBM onset. The model is...
An important aspect in the study of reproduction is how sperm are guided toward an egg for fertilization. One such mechanism is the process of chemotaxis, in which the sperm detect changes in concentration (namely of Ca+) in the fluid environment and utilize these changes to alter the waveform of their flagellar beat. This change in beat form results in changes to the swimming path....
The Hassell equation is a classic discrete-time population model which has been widely used to model population dynamics of species with seasonal reproduction. This equation is a generalization of the Beverton-Holt equation with an additional exponent, and can describe various types of reproduction curves exhibiting from exact-compensation (contest competition) to over-compensation (scramble...
Sexual dimorphism (SD), sexual differences in traits, represents one of the most remarkable source of biodiversity in the world. In most of species, two sexes play different roles in reproduction and thus are imposed by selection pressures in different forms and strengths. This explains the generality of this phenomenon and the extensive applicability of SD theory in nature. In this talk, I...
Glioblastoma Multiforme (GBM) is the most aggressive primary brain tumour, with a median life expectancy of only 15 months with treatment. Although surgical resection is a standard-of-care procedure, the migratory nature of the tumour cells limits its efficacy as not all tumour cells can be removed. The tumour will usually re-establish itself along the resection cavity wall, known as a local...
Insects use two main modes of segment determination during development: the ancestral short-germband mode (eg. Gryllus bimaculatus) where new segments are added sequentially, and the more derived long-germband mode (eg. Drosophila melanogaster), where all segments are determined simultaneously. In dipteran insects (flies, midges and mosquitoes), which use the long-germband mode of...
Many human papillomavirus (HPV) vaccination programs currently administer three vaccines - a bivalent, a quadrivalent and a nonavalent vaccine - for a two-dose course. In this talk a model will be presented to explore optimal vaccination strategies using the three vaccines, which differ in protection breadth, cross-protection, and type-specific efficacy. Assuming the HPV infection prevalence...
Patch dynamics is a numerical multiscale solver which constructs a macroscale solution of a microscale system by solving the original microscale problem, but only within discrete patches. These patches are spread across the domain of the system and are separated by the desired macroscale spacing, thus providing a description of the system at the macroscale. The space between the patches is...
The prevention of diseases such as malaria require certain T cells to find all pathogens in the liver within a certain period of time (e.g., within 48 hours, which is the time required for liver-stage development of parasites in rodent malaria). This motivates the fundamental question of how many T cells are required to ensure complete coverage of the liver within a specified time, to a high...
Clinical trials of the four-dose RTS,S/AS01 vaccine for P. falciparum malaria demonstrated a protective effect in young children and, beginning in 2018, the vaccine will be evaluated through a large-scale pilot implementation program in Ghana, Kenya and Malawi. Recent evidence from a phase 2a challenge study indicates that varying the timing and amount of the fourth dose could further...
Introduced species are a critical threat to Australian ecosystems and species. Particularly noxious examples include the European carp, feral cats, and a variety of weeds. A central aspect of introduced species management is eradication – if they can be completely removed from a region, the impact can be nullified. A central problem population eradications is knowing whether the species has...
Peripheral nerve damage afflicts 1 M people p.a. in Europe and the USA [1]. In the most severe cases, patients experience major loss of function. The gold-standard treatment for patients with severe cases is surgery using a graft based on a healthy section of nerve taken from the patient, however, only 50% of patients experience functional recovery [2].
After a nerve is severed, the distal...
CD8+ T cells can kill Plasmodium parasites in the liver of the mammalian host; a protective effect that can be harnessed for malaria vaccination. We have previously used intra-vital imaging to measure the interaction of CD8+ T cells in the liver and Plasmodium infected hepatocytes. We have previously observed that CD8+ T cells in the liver undertake LFA-1 dependent crawling motility in the...
Syphilis, a major sexually-transmitted disease, continues to pose major public health burden in both under-developed and developed nations of the world. This study presents a new two-group sex-structured model for assessing the community-level impact of treatment and condom use on the transmission dynamics and control of syphilis. Rigorous analysis of the model shows that it undergoes the...
Overpopulated mammal populations cause damage to agricultural crops in Japan. We need to keep population sizes at appropriate levels. When we determine management plans, we have to deal with various uncertainties such as population size, population growth rate, and agricultural damages caused by mammals due to lack of sufficient data. It is important to reduce those uncertainties and allocate...
Stochastic simulations are essential to the study of biological cells, yet there is no computational framework allowing for detailed spatial simulations of genetic regulatory network within large populations of cells.
We fill this gap by developing a parallel simulation framework capable of spatially resolved stochastic simulation of cell-cell signalling in multicellular systems. We use an...
Phosphatidylinositol (3,4,5)-trisphosphate (PtdInsP3) is known to propagate as waves on the plasma membrane and is related to the membrane protrusive activities in Dictyostelium and mammalian cells. While there have been a few attempts to study their three dimensional dynamics, most of these studies focused on the dynamics extracted in one dimensional sections along the membrane in a single...
In this study, we propose a new Bayesian approach to calculate the expected extinction time of a species based on historical sighting record data. Unlike other work, our model allows comprehensively for uncertainties, provides the expected extinction time and the probability of extinction. It is extremely difficult to determine whether a species is extinct based on historical sighting...
From the foraging strategies of large organisms, to T-cells hunting pathogens, to proteins examining strands of DNA, carefully optimised search processes are a phenomenon that pervades throughout nature at many scales. Often these search processes do not proceed in isolation, but instead many instances proceed in parallel, competing for space and resources. In this talk I shall discuss...
Network of transport is found in a wide range of living system. The typical examples are vascular network in vertebrates and tracheal network in vascular plants, and mycelial network in fungi. Such a network structure is found in self-organized colony of unicellular bacteria: a biofilm that is a sheet-like aggregate of many bacteria and sticky polysaccharides secreted from the bacteria....
The collective migration of cells during embryogenesis is key to the development of vertebrates, and improper migration can lead to severe developmental diseases and deformities. As a simple model for such cell migration we study the particle based Vicsek model in an open channel geometry where cells continuously enter and leave the domain. This results in two distinct types of motion – one...
During the adaptive immune response, T and B lymphocytes receive and integrate signals from different sources that determine the strength and type of response they follow. Here we asked how reducing stimulation strength through the CD40 receptor could lead to an accelerated division-linked B cell differentiation, as noted in an earlier study [Hawkins et al., Nat Comms 2014]. We observed...
Variation of calcium concentration in hepatocytes (liver cells) is known to modulate diverse cellular functions, including bile secretion, glucose and energy metabolism and vesicular trafficking. A major question in the study of calcium signalling in hepatocytes is how these distinct cellular processes are controlled and organised via coordinated spatial and temporal calcium...
In order to explore the role of initial geometry in wound closure, we developed a new two-dimensional wound healing assay which we refer to as a sticker assay. Stickers are produced and attached to a tissue culture plate before cells are seeded into the centre of a dish. The stickers are then removed to leave a wound in the dish, which is an area with no cells. We performed a number of...
The illegal trade of wildlife is estimated to run into hundreds of millions of dollars. It is an international problem that exploits both enforcement loopholes and corruption, and it is a direct threat to the survival of plant and animal species. Smugglers transport wildlife and their derivatives from sources to destinations across the globe. They are able to choose the route they take to move...
The three-dimensional structure of eukaryotic genomes is non-random, dynamic, highly regulated, and can be observed to change according to external signals and differentiation state. Disruptions can lead to disease, in which incorrect genomic contacts are responsible for mis-regulation of gene expression. However, the underlying mechanisms that organise the genome are still largely unknown....
Wolff’s law states that bone morphology evolves according to their external mechanical loading. Following this law, researchers have tried to simulate bone shape formation, especially for trabecular bone, using topology optimization [1]. Less attention has been given to the bone outer shape, composed of cortical bone. However, trabecular bone and cortical bone are both mainly formed by...
In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analysis was carried out using varieties of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure...
Tumour associated macrophages have long been implicated in the progression of primary solid malignancies including prostate cancer. Metastatic prostate cancer typically manifests in the bone where it induces painful osteogenic lesions that are incurable. Bone is naturally rich in myeloid derived macrophages whose temporal polarization into pro- (M1) and anti-inflammatory (M2) phenotypes is...
Severe diseases arising as sequelae of superficial skin and throat infections with group A Streptococcus (GAS) are important causes of morbidity and mortality worldwide. The observed high level of heterogeneity in GAS prevalence across various temporal and spatial settings suggests potentially complex dynamics of population transmission. One of the most visible indicators of heterogeneity is...
Calcium signalling is a ubiquitous mechanism that many cell types use to control a plethora of biological processes. In particular, calcium plays a large role in fertility both for egg and sperm cells. In this presentation, we will focus on the acrosome reaction, which is a calcium-modulated vesicle release that must occur for sperm to successfully fertilize the egg. We will discuss the...
Illegal exploitation of wildlife is one of the biggest threats to biodiversity, affecting over 2,000 species. Traditionally, actions to reduce poaching have focussed on increasing the efficacy and capacity of law enforcement. However, recently, non-governmental agencies (NGOs) are heavily investing in alternative interventions to reduce consumer demand for poached wildlife products. But which...
The cellular cytoskeleton ensures the dynamic transport, localization and anchoring of various proteins and vesicles. In the development of egg cells into embryos, messenger RNA (mRNA) is transported along microtubule filaments and must accumulate at the cortex of the egg cell on a certain time and spatial scale. We present two equivalent methods of deriving the effective transport properties...
A leg wound which does not heal because of problems with the veins in the leg is called a venous leg ulcer (VLU). Chronic VLUs are the most common chronic wounds in western countries and their treatment is both costly and time consuming. In this work, we present a mathematical model of the healing of a VLU which incorporates the key biological features of this wound type. We have modelled the...
The advances in cell imaging technology has allowed for deeper understanding of the movement mechanisms of immune cells. Experimental evidence suggests that cytotoxic T lymphocytes and dendritic cells undergo and unrestricted search motion until they switch to a more restricted motion induced by activation by tumour antigens. This change in movement is not often considered in the existing...
Currently, high-resolution point cloud data can be acquired easily and cost-effectively. For example, a pipeline using Structure from Motion (SfM) and Multi-View Stereo (MVS), which is a promising technique to reconstruct a 3D surface as point cloud data from a series of 2D images taken from different angles, has been implemented in several libraries and software products. In this study, we...
CD8+ T (CTL) cells play a pivotal role in protection from viral infection. Better understanding of the heterogeneous phenotypes of T cell subsets evolving during an immune response is timely needed for development of T cell based vaccines that can provide long-term immune protection. Viruses causing chronic infections such as HIV and HCV, trigger a T cell response characterised by functional...
Many T cell receptors have long, unstructured cytoplasmic tails that contain tyrosine sites. These sites can serve as regulators of receptor activation when phosphorylated or dephosphorylated, while also serving as docking sites for cytosolic enzymes. We coarse-grain the effective interaction between two tails, and develop a mesoscopic particle-based stochastic reaction-diffusion model to...
Equine Infectious Anemia Virus (EIAV), a retrovirus that establishes a persistent lifelong infection in horses and ponies, and which can be transmitted by vectors (biting flies), is endemic in regions with warm climates. With the advent of global warming, research have shown that vector-borne diseases may be on the rise. This study seeks to understand how climate change will affect the EIAV...
In the course of animal development, the shape of macroscopic tissues emerges from collective cell dynamics. The challenge faced by researchers in the field is to understand the mechanism by which morphogenetic processes of each individual cell (i.e., when, where, and how much individual cells grow, divide, move, and die) collectively lead to the development of a large tissue with its correct...
Unlike any great apes, humans have expanded into a wide variety of habitats during the course of evolution, beginning with the transition by australopithecines from forest to savanna habitation. Novel environments are likely to have imposed hominids a demographic challenge due to such factors as higher predation risk and scarcer food resources. In fact, recent studies have found a paucity of...
Autophagy is an intracellular degradation process mediated by the autophagosome. The membrane dynamics of autophagosome formation is unique and complicated, which involves development of a small membrane cisterna into a cup-shaped structure and a double membrane spherical structure by closing the edge [1].
In this presentation, we discuss the mechanism of autophagosome formation from a...
Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that...
Clinical methods for assessing tumour response to neoadjuvant therapy largely rely on monitoring the temporal changes in tumour size. Our goal is to predict tumour response to neoadjuvant therapy in breast cancer using a mathematical model that utilizes non-invasive imaging data obtained from individual patients. Previously, a mechanically-coupled, reaction-diffusion model with logistic growth...
Bursting is a type of electrical activity seen in many neurons and endocrine cells where episodes of action potential firing are interspersed by silent phases. Pancreatic $\beta$-cells show so-called square-wave bursting when stimulated by glucose, which causes ${\text Ca^{2+}}$ oscillations and pulsatile insulin secretion. $\beta$-cells are electrically coupled within pancreatic islets, and...
Two ecotypes of the marine snail species Littorina saxatilis have, as a result of strong natural selection, maintained different shell shapes in distinct, adjacent environments. Being able to quantify and compare the underlying growth structure for the two ecotypes should provide a better insight into the reasons behind the variability of shell shapes, and connect this to the genetics and...
Scratch assays are standard in vitro experimental methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and imaging of the recolonisation of the scratched region is performed to quantify cell migration rates. Typically, scratch assays are modelled by continuum reaction diffusion equations depicting cell migration by diffusion and carrying...
The swimming motion of microorganisms such as sperm and cilia can be modelled by several methods, all of which entail solving equations of fluid-structure interaction. Among them, the Method of Regularized Stokeslets (MRS) and the Rotne-Prager-Yamakawa tensor have the advantage of not requiring a 3D Eulerian grid and using the fundamental solutions to the underlying equations instead. However,...
Mathematical models for the Ebola Virus Disease (EVD) were, until recently, mostly based on the fast/direct transmission route, which involves contact with blood or body fluid and objects that have been contaminated by body fluid. The fact that in almost all outbreaks of the EVD in Africa, the index case became infected through contact with infected animals, such as fruit bats and primates,...
In this research, we proposed an infectious disease spread model of influenza which was individually based and stochastic. We first described the method to build a realistic model, or to estimate realistic parameter values, based on observed data. An appropriate model has to be individually based and stochastic if we take advantage of small unit data (in this case, every day class unit data)....
In this presentation, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author’s knowledge. I consider a hybrid...
Glioblastoma multiforme (GBM) is a rare brain cancer with a median survival of only around 15 months. Intratumoural heterogeneity and extensive infiltration into the brain tissue contribute to poor prognosis and probable recurrence. Predicting the timing of post-treatment recurrence is often limited if using only MRI imaging measurements, as a diverse range of treatment outcomes can result...
The inter-follicular epidermis (IFE) forms the outer-most layer of the skin. Many individual components fundamental to healthy IFE structure are known: proliferation occurs only in a basal layer; above this layer cells differentiate into keratinocytes forming further distinct layers before they are shed from the surface. However, a definitive understanding of how the balance between...
Large-game hunting in human hunter-gatherers is a counter-intuitive behaviour. Despite low daily success rates and large proportions of sharing, hunter-gatherers invest in large-game hunting over the less-wasteful strategy of small-game hunting. Where investment in small-game hunting could provide a more reliable and consistent source of direct benefit to one’s offspring, large-game hunting is...
Conservation management decisions are often implemented at the scale of human communities, rather than the scale of the most relevant ecological dynamics. Research frequently points out the loss in efficiency that results from such "scale mismatches". However, the scale of management is influenced by socio-economic constraints on management actors - not all people want to cooperate with each...
In this talk, we will present a mathematical model of 2009 A/H1N1 influenza considering age structure in the Republic of Korea and suggest vaccination strategies for mitigating the epidemics. There were 750,000 confirmed cases of 2009 A/H1N1 influenza from May 2009 and August 2010. Because influenza viruses are spread through close contact, contact pattern plays an important role for the...
Nanoparticles provide a promising approach for the targeted delivery of therapeutic, diagnostic and imaging agents in the body. However, it is not yet fully understood how the physicochemical properties of the nanoparticles influence cellular association and uptake. Cellular association experiments are routinely performed in an effort to determine how nanoparticle properties impact the rate of...
Private assessment in indirect reciprocity is a natural assumption because individuals can assess others privately in this situation. However, only few studies have considered private assessment because of analytical difficulty that it present. Here, we develop an analytical method using solitary observation to solve private assessment in indirect reciprocity problem without any approximation....
Cells are often grown within collagen gels in vitro for applications in tissue engineering. The behaviour of these cells is regulated by their mechanical environment; however, the forces exerted by cells in turn affect the mechanical behaviour of the gel. We aim to better understand the interactions between the cells and the gel using mathematical modelling.
We have developed a...
Using a data base on Dengue incidence available for four different states of the country we develop mathematical models that describe the recurrent dynamics of cases at different geographical/regional levels. We present preliminary results.
Species interactions are important to determine structure and stability of ecological communities. In particular, a variety of indirect effects appear between species which do not interact directly. However, indirect effects do also appear between species that directly interact. For example, plant species sharing a common herbivore may engage in both interference competition directly with...
Xeniid corals, a family of soft corals (Alcyonacea), include species displaying a unique pulsing behaviour. Within a colony, each individual polyp pulses by actively contracting and passively expanding eight tentacles, increasing the local mixing and enhancing nutrient and gas exchange. Using the immersed boundary method with finite elements (IBFE), we constructed a 3D model of a pulsing...
Introduction: Glioblastoma (GBM) is a very aggressive primary brain cancer, noted for its diffuse infiltration into surrounding normal–appearing brain. This particular nature makes GBM notoriously difficult to treat, as these diffusely invading cells cannot be resected surgically, are difficult to target with radiation therapy, and thus must be targeted with chemotherapy. However, this too...
Networks representing the spread of infectious diseases in populations have been widely studied. Here, we formulate an SEIR model using an edge-based approach on a static random network with arbitrary degree distribution. The corresponding basic reproduction number and final epidemic size are computed. The SEIR model is used to investigate the stochasticity of the SEIR dynamics. Assuming...
When one makes his/her decision, he/she often refers to others’ opinions. We describe this situation by a network model with the nodes representing individuals and the links representing references between them. Our question is how people’s reference structure self-organizes, when each individual tries to provide correct answers by referring to more accurate agents.
To answer these questions,...
Mechanically-induced buckling underlies the shape and function of a number of biological processes, such as brain tissue folding, intestinal crypt fission, and seashell formation. Unlike many typical engineering systems in which buckling is induced by an external compressive load, mechanical instability in biology is driven often by internal growth. In these contexts, it is just as important...
The differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells), or chondrogenesis, is a key step in the tissue engineering of articular cartilage. Chondrogenesis is regulated by transforming growth factor-beta (TGF-β), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix (ECM). Tissue engineering applications require the...
One of the fundamental problems in biology would be the method by which organisms can regulate a distribution in response to global information. For example, a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual is aware of the overall situation without a leader. Slow or rapid self-organized pattern formations with time...
Circadian clocks control 24-hour rhythms in the human body, including glucose and insulin dynamics. Glucose tolerance changes depending on the time of day and misalignment between environmental stimuli such as light and food and internal circadian clocks, e.g., as observed in shiftwork, is associated with metabolic disturbances and diabetes. The mechanisms of these are poorly understood. A...
The walls of our blood vessels are under a constant mechanical load, introduced by the blood pulsating through our vessels. Recent years have seen a substantial increase in the understanding of the interplay between the dynamics of blood flow (haemodynamics) and vessel (vascular) morphology. Alterations in the homeostatic distribution of mechanical forces exerted by blood on the vessel wall is...
Macroecological patterns, such as the species area relationship (SAR), relative species abundance (RSA), and endemic area relationship (EAR) provide us useful information of ecosystem structures that can be applied to, for example, ecosystem conservations. To understand these patterns across spatial scales is one of the central challenges recent years. To tackle the challenge, we develop a...
The Human African Trypanosomiasis (HAT) parasite, which causes African Sleeping Sickness, is transmitted by the tsetse fly as a vector. It has several possible hosts, including humans and domestic animals. Because domestic animals can be a host for the parasite, it has long been assumed that keeping domestic animals near human populations increases the spread of the disease. However, several...
With a five dimensional system of ordinary differential equations based on the SIR model, we consider the dynamics of epidemics in a community which consists of residents and visitors/tourists over a short period of time. The total population size of the community is taken to be constant, ignoring its change due to any birth and death in the period under consideration. Also, the resident and...
Direct-Acting antivirals (DAAs) target intracellular viral replication and have realized high effectiveness for hepatitis C virus (HCV) patients. Now, many kinds of DAA drugs have discovered and the HCV treatment is improving day by day. A popular strategy of HCV treatment is combination of double or triple DAA drugs with different action mechanisms. Mathematical model is used to analyze the...
Life-histories in organisms faced with various selection pressures such as heterogeneity, intra- and inter-specific competitions, and variable environment. Ecologists have thought that evolution maximizes different objects from each pressure. For example, in the absence of the competitions, conventional Darwinism asserts that the adaptive life history maximizes the population growth. On the...
Chemical reactions are traditionally modelled using deterministic methods such as ordinary differential equations. In biology, we also consider the effect of diffusion upon a reactive system. For small biological systems, it is necessary to use stochastic models. In this talk, we choose to use an agent-based model commonly known as Smoluchowski kinetics.
In the Smoluchowski model, two...
Reproducibility of results is a key part of the scientific method; in general, scientific communication aims to describe a result in enough detail that readers and reviewers are able to contextualise the result within their own knowledge, and to reproduce it themselves given the appropriate skills and resources. In the field of computational biology, readers and reviewers face special...
We present an optimal impulse control problem related to anti-cancer therapeutics. Our model takes into account both the instantaneous toxicities of the treatments and the adverse effects of targeted and non-targeted antineoplastic therapies.
Rabies is a fatal zoonotic disease and remains to be a priority health concern in the Philippines. Dogs remain to be the principal carrier of rabies and despite the fatality of rabies, it is a vaccine-preventable disease. Currently, the Philippine health officials have been conducting mass dog vaccination campaigns with the goal of having a rabies-free Philippines by the year 2020. However,...
Recent studies have shown that pathogens can alter the behaviour of hosts or vectors to improve their transmission power. This happens not only in animal pathosystems but in plant pathosystems. While animal pathogens can alter the behaviour of both hosts and vectors in ways that increase frequency of host-host or host-vector encounters, in plant pathosystems the host does not have mobility, so...
p53, a cellular damage response regulator, is mutated in 50% of all cancers. We have constructed a mathematical model showing how different p53 dynamics after UV radiation and $\gamma$-irradiation exposure allows cells to respond properly to both slowly and quickly detected damage. We extend this model with an apoptosis module accounting for the transcription-dependent and -independent...
In Noor Asih et al. (2016) already given mathematical modelling as the dynamic of HPV infection on cervical cancer. Also given five scenarios for the existence of equilibrium points and their local stability. From the analysis of the system it is found the basic reproduction number is depends on the infection rate, the number of new virion that produce by infected cells, the death rate of...
Avian malaria is a mosquito-borne parasitic disease of birds caused by protists of the genera Plasmodium, most notably Plasmodium relictum. This disease has been identified as a primary cause of the drastic decline and extinctions of endemic birds on Pacific Islands. In this work, we formulate an epizootiological model of the transmission dynamics of avian malaria between a generic bird...
Bond graphs are an energy-based framework for modelling physical systems while adhering to thermodynamic and physical constraints, and they have recently been extended and applied to biochemical and electrophysiological systems. Here we describe a bond graph model of the cardiac action potential and use it to explore the issue of drift in mathematical models of electrophysiology, which is a...
Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. But how robust are these methods to future information? If additional species are added to the original set of trees, will the expanded consensus tree simply be an expansion of the original consensus tree? In this talk I will formalise and answer this...
Interspecies comparisons of physiological energetics are possible only through the prism of a formal metabolic approach such as the Dynamic Energy Budget (DEB) theory which uniformly describes how individuals of different species acquire and utilise energy. We used the DEB theory to infer the energy budgets of three commercial tuna species (skipjack, Pacific bluefin, and Atlantic bluefin)...
IUCN criteria are the most authoritative and objective to assess the conservation status of animal species. Although IUCN criteria are purely descriptive in nature, they can be interpreted as e.g. the relative size of the annual population growth factor (λ, the dominant eigenvalue of a projection matrix). This enables quantitative assessment based on demographic data (survival and...
The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem, including for biological systems. Such landscapes may refer to a true energy function for cases such as protein folding or to a phenomenological metaphor in the case of Waddington’s epigenetic landscape. In many situations, constructing a landscape comes...
Maintaining physiological levels of oxygen (O$_2$) and carbon dioxide (CO$_2$) in the blood is crucial for survival and is achieved by sophisticated neural control mechanisms affecting both the breathing pattern and heart rate. Neural activity, originated in the brainstem, drives the respiratory muscles, providing air flow into and out of the lungs where gas exchange takes place and also...
Hematopoietic system is maintained by hematopoietic stem cells (HSCs) with dual abilities of long-term self-renewal and differentiation to all types of blood cells. Recently, using a single-cell transplantation system and mice expressing a fluorescent protein, myeloid-restricted progenitors with long-term repopulating activity (MyRPs) were found. Moreover, by using paired daughter cell assay,...
We propose a structured integro-difference equation model for an invasive marine species with a pelagic larval stage and examine the role of dispersal heterogeniety on the spreading speed. The spread of the green crab up the northwest coast of the Atlantic is used as a case study. We find that the relationship between spreading speed and demographic and dispersal parameters is similar to...
Motivated by in vitro time-lapse images of ovarian cancer spheroids inducing mesothelial cell clearance, the traditional agent–based model of cell migration, based on simple volume exclusion, was extended to include the possibility that a cell seeking to move into an occupied location may push the resident cell, and any cells neighbouring it, out of the way to occupy that location. In...
Obesity is the result of caloric imbalance and is mediated by genetic, behavioural, and environmental factors. Healthy lifestyle habits, including healthy eating and physical activity, can lower the risk of becoming obese and developing related diseases. The prevalence of obesity among Korean adolescents aged 13 to 18 years increased from 13.65% in 2007 to 19.3% in 2016 for boys.
We analyze...
Recent advances in understanding of complex interactions between the processes that maintain and control the physiological state of brain parenchyma open new possibilities and deliver new challenges for modelling studies on topic. Now it is clear that any significant deviation from normal conditions as well as natural alternations of activity of cortical neurons (say, during sleep-wake...
A deterministic model of biochemical reaction networks is not always appropriate. Gene expression, for example, often involves a small number of molecules which means that noise can significantly influence the dynamics. By discretising space into voxels and letting the molecule dynamics be governed by the reaction-diffusion master equation, it is possible to model the reaction and diffusion of...
The demographic hypothesis of cumulative cultural evolution claims that population size has been a crucial determinant of the rate of cumulative cultural evolution in humans rather than other factors such as environmental risk. The original version of this hypothesis does not distinguish the role of population size from that of social connectedness, i.e. the degree to which individuals in a...
The temporal and spectral characteristics of tonic-clonic seizures are investigated by using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs....
Projection matrix models are known to provide us with a plenty of population statistics, such as population growth rate, steady size-class distribution, and sensitivity and elasticity for population growth rate. Hundreds of academic papers using the model have been published these last forty years and a database on many of their matrices is now available on the internet (COMPADRE and COMADRE),...
Many large-scale high-throughput experiments use DNA barcodes—short DNA sequences prepended to DNA libraries—for identification of individuals in pooled biomolecule populations. However, DNA synthesis and sequencing errors confound the correct interpretation of observed barcodes and can lead to significant data loss or spurious results. Widely-used error-correcting codes borrowed from computer...
Specific biomarkers can be identified in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) breast scans and quantified using pharmacokinetic models that return estimates of parameters related to tissue physiology including vessel perfusion and permeability ($K^{trans}$), the extravascular-extracellular volume fraction ($v_e$), the plasma volume fraction ($v_p$), and the efflux...
Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature cell proliferation is typically modelled using a classical logistic equation...
In this research, we study feedback control problem in the context of deterministic epidemic models. Feedback control is obtained by solving Hamilton-Jacobi-Bellman(HJB) equation, which is employed to overcome limitations of previous work. There are three key factors in the implementation of this methodology, decoupling value function and control variables, truncation of unbounded domain, and...
Stochastic evolutionary game dynamics in finite populations has recently been examined not only for symmetric games [1] but also for bimatrix games [2]. While in these studies the fixation probabilities of pure strategies are investigated, this study examines the evolutionary dynamics of two-player 2 by 2 bimatrix games with mixed-strategies in finite populations under weak selection. The game...
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviours. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A...
Improving crop yield is essential to meet increasing global food demands. Crop yields depend on the coordinated acquisition of carbon and nitrogen by the leaves and roots respectively and the use of these nutrients within each part of the plant. Changes in environmental conditions cause fluctuations in carbon and nitrogen availability. This leads to crosstalk between the signalling pathways...
The Hybrid Agent–based Library (HAL) is a Java Library made of simple, efficient, generic components which can be used to model complex spatial systems. HAL's components can broadly be classified into: on and off lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and collecting data. These components were...
The aim of this research was to explore the potential of profile likelihoods for identifiability analysis in the context of real enzyme kinetics data, collected ourselves.
Parameter identifiability concerns the question of whether the type of experimental data we have collected properly determines the parameters of our mathematical models. Identifiability issues arise because not all biological...
In genetics, enhancer regions are short non-coding strands of DNA belonging to a class of elements known as cis-regulatory. These regions, typically in intergenic regions, encompass binding sites for proteins (transcription factors) that regulate gene expression. Changes to the DNA sequence in these enhancer regions are thought to provide a mechanism to explain changes of gene expression even...
We consider a setup in which $n$ particles are initially released into a domain and diffuse freely. Part of the boundary consists of absorbing "escape" regions, where the particles can escape the domain, and reflecting regions. The rest of boundary consists of "capture" regions (receptors), that can switch between being reflecting and absorbing. Specifically, after capturing a particle, the...
Carnitine is a fundamental compound for humans. Mainly introduced via nutrition, but also synthetized in the body, this metabolite allows the transport of long-chain fatty acids in the mitochondria, where they can undergo β -oxidation. Lately, the attention on carnitine and acyl-carnitine, carnitine derivatives, has increased since it has been proposed that insulin resistance may be linked to...
Primates exhibit an array of mating behaviours and arrangements, from monogamy to promiscuity, or mate-guarding to multiple-mating. We have previously explored the role of adult sex ratio in determining the likelihood of males choosing either promiscuity or monogamy, but many questions remain open. In particular, do (and, if so, how do) longevity and life history contribute to the choice of...
The unmarried rate of Japanese people is rising year by year, and countermeasures are required. We modelled male and female marriage decision-making models based on male’s willingness to cooperate on housework and childcare. We assume that male marriage utility function decreases as male’s willingness to cooperate on housework and childcare increases, while female marriage utility function...
True slime mold Physarum polycepharum is a large uni-cellular amoeba-like organism and it can sense environmental information and change its behaviours. Large true slime mold extends its frontal parts for foraging. To study its exploration strategy, we observed how physarum spreads in a binary-tree-shaped maze. We found that slime mold changes its searching strategies when its total mass...
Asthma is a chronic lung disease of reversible airway constriction. Imaging experiments show that during an asthma attack, the asthmatic's lung exhibits what is known as clustered ventilation defects, which is the hallmark trait of asthma. This phenomenon is when there are some regions of the lung where the airways are closed, and some regions where they are open. These clusters vary from...
Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people globally. The accumulation of AD associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium signals by disrupting calcium regulatory mechanism within neurons. These disruptions can cause changes in homeostasis levels that can have detrimental effects on cell function and survival. Although...
Biofilms are sessile communities of bacteria housed in a self-produced adhesive matrix consisting of extracellular polymeric substances (EPS), including polysaccharides, proteins, lipids, and DNA. [1]. Biofilm provokes chronic bacterial infection, infection on medical devices, deterioration of water quality, and the contamination of food [2]. On the other hand, biofilm can be used for...
The occurrence of distant metastases greatly reduces or even removes the possibilities of curative treatment for cancer patients. The development of tools for predicting and diagnosing the onset of secondary tumours has long been a significant subject of cancer research effort. Moreover, it is widely known that while in some tissues cancer cells exhibit higher proliferation, in others they are...
Intracellular phase transitions are an emerging mechanism for cell organization. These membrane-less compartments are formed via liquid-liquid demixing and subsequent concentration of cellular components in a specific region. By undergoing these localized phase separations, cells are able to create dynamic compartments that help maintain the regulation of biomolecular interactions and...
Tissue engineering is a rapidly growing field, attracting a huge concentration of research effort. An important subfield of tissue engineering focuses on the use of bioreactors, devices that attempt to simulate a physiological environment in order to promote the growth of functional cell or tissue in vivo. In this talk we present a mathematical model to simulate both nutrient transport and...
Cancer is one of the leading causes of morbidity and mortality worldwide. Many of the disease related events, such as metastatic progression, treatment resistance, and overall survival, generate much uncertainty and are oftentimes viewed as random. Applying current modelling techniques and methodologies to existing data can produce a forecasting framework that can be leveraged to predict these...
The human species is unique in its tendency towards monogamy, a trait which can be traced back to hunter-gathering societies. Traditional explanations for this evolution have focused on the presence of paternal care and the needs of our offspring. However, recent research has challenged this claim, contending that the significant effects of mating competition on male choice result in...
The human brain consists of folds (gyri) and valleys (sulci) that vary dramatically in their size, extent, and shape across individuals. There is considerable debate among biologists as to how the folding patterns develop and if the folding patterns can be used to diagnose disease. In this presentation, I will discuss some of the mathematical and modelling approaches my research group is...
Empty homes, called Akiya in Japanese, due to an aging population and declining birthrate is very serious problem in the aging society of modern Japan. The current proportion of empty home in Japan is 13.5%, but it is expected to be increased up to 30.2% nationwide in 2033, implying that Akiya will have a serious impact on the economy as well as the national finance. Indeed, Detroit city in...
An endoplasmic reticulum (ER) is a tubular organelle observed in cells of eukaryote including the plants and animals. Interacting with flow of actin cytoskeleton, the net-like pattern organized by ER in plant cells is continuously moving.
For the understanding of this system, we constructed a mathematical model based on a partial differential equation (PDE). By combining two spatially...
Calcium is a universal messenger that participates in a great variety of physiological functions including muscle contraction, neuronal plasticity and immune responses. There is now compelling evidence that transient changes in the intracellular calcium concentration are key for achieving such versatility.
To date, most of these findings have been obtained from constant stimulation or step...
We constructed a dynamical model of a salivary gland acinar cell with the objective of investigating the role of two plasma membrane (PM) anion exchangers, the Ae2 (Slc4a2) and Ae4 (Slc4a9), in primary fluid secretion. Transepithelial chloride (Cl$^-$) movement drives water transport in salivary gland acinar cells. Basolateral PM mechanisms accumulate Cl$^-$ to levels well above its...
The vector-borne Dengue fever poses a major health issue in tropic environments, which includes areas such as far-north Queensland. Historically, attempts at curtailing the spread of dengue have focused on controlling the size and spread of mosquito populations that carry the virus. Several factors make this an astronomically difficult task to accomplish on any reasonable scale, however, and...
Tuberculosis (TB) is one of the top 10 causes of death worldwide, and the WHO’s EndTB strategy requires developing an effective vaccine. The H56 vaccine is a candidate currently in phase I/IIa trials as a boost to Bacillus Calmette-Guérin (BCG, the TB vaccine that is currently used in most countries world-wide). We build a multi-compartment, hybrid multi-scale model to 1) improve our...
The mammalian circadian rhythm is governed by the principal clock which is located in the suprachiasmatic nucleus (SCN). This clock is composed of tens of thousands of neurons and their connection to one another is essential to important roles of SCN: synchronization, entrainment to light, etc. Previous studies about the SCN network used the maximal information coefficient (MIC) statistic to...
A mathematical standard structure of a binary digit of memory in a cell is presented. This is based on a kind of frequency model with scale effect. This model has ability of "on-off" switching property, and moreover, this is affected by scale effect to make the memorable ability be reinforced. This property is derived from multiple covalent modification cites inducing important enzyme...
Physiological levels of oxygen and carbon dioxide in the blood are tightly regulated by varying the pattern of breathing, but this can be achieved with different combinations of amplitude and frequency. Why a specific combination of amplitude and frequency of breathing is observed remains a mystery. The aim of this study is to explore the hypothesis that the particular combination realised is...
Barreto et al. (2017) studied the rock-paper-scissors games (or cyclic competition games) by the dynamics of phenotypic and genotypic frequencies corresponding to three morphs of lizards. In their model they show that both dynamics have equal internal equilibrium but the genotypic model has wider parameter range for its stability compared to the phenotypic model.
Here, first of all, we...
The activated sludge process (ASP) is the most widely used process for the biological treatment of both domestic and industrial wastewaters. Wastewater treatment plants (WWTPs) based on the ASP are in widespread use in both developed and developing countries.
The ASP uses microorganisms which grow by consuming organic pollutants that are present in the wastewater. This produces new organisms...
Species eradications and reintroductions are drastic management actions that alter ecosystem structure with the end goal of conserving or restoring one or more species of interest. Because of the complexity of ecosystem food webs, these actions can have unintended consequences on other parts of the ecosystem. Even with the best available data, predicting future trajectories of the ecosystem...
The placement of stomata on the leaf surface is regulated by a number of things: coordinated asymmetric cellular division, genetic regulation, and distribution of extracellular signalling molecules.
It has been noted that the number of stomata per non-stomatal epidermal cell can vary between plants which have the same spatial distribution of stomata, which suggests that in some circumstances...
Since many kinds of Direct Acting Antivirals (DAA) have become the main treatment instead of interferon-α (IFN-α) against hepatitis C virus (HCV), combinations of these DAA are now standard treatment strategies. These treatments are very effective, however, at the same time, this provokes the problems which drug combination is more or most effective for each patient. Therefore, we established...
One of the challenging questions in Ecology is how spatial structure influences the formation of biodiversity patterns. Here, we explore networks that represent population connectivity including cases where dispersal is symmetric and asymmetric, looking for the relationship between population connectivity network structure and biodiversity patterns therein. In this metapopulation system, we...
There are large differences between men and women of child-bearing age in the expression level of 5 key enzymes in one-carbon metabolism almost certainly caused by the sex hormones. These male-female differences in one-carbon metabolism are greatly accentuated in during pregnancy. Thus, understanding the origin and consequences of sex differences in one-carbon metabolism is important for...
Many species of animals, plants, cyanobacteria, and fungi are reported to have circadian clocks, that is, gene regulatory and biochemical network in a cell exhibiting endogenous oscillatory dynamics with a period close to 24 hours. There is diversity in the members of the circadian system, but all clocks share similar features such as temperature-compensated circadian period. Therefore,...
Human papillomavirus, or HPV, is a sexually transmissible virus infection, which is necessary risk factor for developing cervical cancer, most common type of cancer in working age women in Moldova. We observe both behavioural change (increase in sexual partner acquisition rates) and demographical change (population ageing and massive emigration, but still very young), which both corresponding...
The spatio-temporal intra- and interspecific competition of two diffusing similar populations is considered. The growth of both populations is either logistic or shows an Allee effect. Conditions of spatial segregation without mixing are investigated. Furthermore, the impact of density-dependent environmental noise on the occurring stationary fronts is studied. A special focus is set on the...
Fluorescent cell cycle labelling in cell biology experiments provides real time information about the location of individual cells, as well as the phase of the cell cycle of individual cells. We develop a stochastic, lattice-based random walk model of a two-dimensional scratch assay where the total population is composed of three distinct subpopulations which we visualise as red, yellow and...
Using a simple lattice model describing infectious tree disease dynamics on a homogeneous landscape we can observe an Epiphytotic phase transition from local confinement of the pathogen to a global epidemic through the forest. The phase transition can be understood in terms of the forest tree density and the pathogen virulence. One interesting application of the model involves capturing the...
Pattern formation by Delta-Notch interaction has been well studied experimentally and theoretically. The Delta-Notch system is observed in various pattern formation process such as somitogenesis, neuroendocrine cell differentiation in lung, T cell differentiation and blood vessel development. Recent studies have shown endothelial cell proliferation and movement happen during this process....
Seasonality and contact patterns due to environmental fluctuations and social behaviour affect the dynamics of disease outbreaks. Recent studies applied to deterministic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to stochastic epidemic models with periodic environments to...
Tethered enzymatic reactions are a key component in signalling transduction pathways. It is found that many surface receptors rely on the tethering of cytoplasmic kinase to initiate and integrate signalling. A key factor to such reaction is the molecular reach; however, the role of it is incompletely understood. To date, a large number of compartment-based ODE and stochastic models have been...
Asymmetric cell division is one of the widespread mechanisms for generating cell diversity, for which a mother cell creates a polarity in both membrane and cytosol. In both experiment and theoretical approaches, PAR polarity of C. elegans embryo has been extensively well-studied and it was found that Anterior-Posterior (AP) polarity of cell membrane proteins plays a crucial role in...
Tuberculosis remains a widespread and deadly disease, infecting approximately two billion people worldwide. Gaining a better understanding of the immune response to Mycobacterium tuberculosis is crucial, and the increased prevalence of multi-drug resistant strains, the current complexity and length of treatment, and the inherent difficulties of experimental work each highlight the need for...
In silico prediction of the relationships between the protein structure and its physiological activity is an important research topic for drug design. Broad picture of my research is to construct a topological model to clarify the antibody-antigen recognition system, since immunotherapy is applied to wide range of severe diseases such as cancer [1].
To achieve the goal, we focus on a...
Infection with the bacteria Mycobacterium tuberculosis (Mtb) causes a dynamic immune response that spans multiple organs across multiple time scales. The infection may start with just a few Mtb infecting a few macrophages within the lungs, but sites of infection quickly experience local immune responses, and soon after draining lymph nodes become involved to mount an even greater defense....
Recently, it has been shown that intracellular transport of assembled intermediate filament proteins is one major determinant of their organization in cells. Based on experimental data, mathematical models of the spatio-temporal distribution of intermediate filaments in cells are developed to investigate the contributions of different types of transport such as retrograde flow of actin and...
It is an interesting topic to predict how dynamics change in disease progression. Our goal is to predict dynamics of the vital cells in the human immune system using the hierarchical HIV models. We assumed that the parameters are random variables with intra-level noise and inter-level noise. Individual-level parameters of HIV model are estimated by generalized least squares method based on the...
Tick-borne pathogens are transmitted when ticks take blood meals from vertebrate hosts. Ticks need to take blood meals to progress through immature life-stages and reach adulthood. For the most important zoonotic pathogens, including Borrelia burgdorferi (the causative agent of Lyme disease), two immature life-stages of the tick vector, termed larvae and nymphs, maintain the pathogens. Key...
Predicting the carbon balance of terrestrial plants, and its vulnerability to environmental change, is a fundamental problem common to agriculture, ecology and ecosystem science. Plant productivity is fuelled by the carbon taken up during photosynthesis, but other limitations to growth may restrict the ability of plants to utilise this carbon in production, a phenomenon known as sink...
The Proliferation-Invasion (PI) mathematical model of patient specific glioblastoma (GBM) growth utilizes T1 and T2-weighted/fluid attenuated inversion recovery (FLAIR) magnetic resonance (MR) images to estimate net proliferation (ρ) and net invasion (D) rates. We have previously developed methods to parametrize this model from these routine MRIs such that higher D/ρ tumours are considered...
Infectious diseases affect individuals (immunology) and populations (epidemiology). While these two scales of infection are intimately linked, the vast majority of studies of infectious diseases ignore or greatly simplify the effects of the other scale. As a result, public health programs can be ill-informed. Mathematical models that link the in-host and population scales of infection can...
Spatial structure owing to localized dispersal in hosts can have dramatic impacts upon the coevolutionary dynamics of hosts and parasites. The basic idea is that localized dispersal in hosts can lead to localized transmission, thereby selecting for costly resistance in hosts and lower virulence in parasites. Both of these evolutionary forces are grounded on the altruism (i.e., costly to the...
Evolutionary game theory has been used to model cancer for more than a decade. Efforts to date have focused on understanding the effect of interactions between cancer cells of different types, and between aspects of the tumour microenvironment and cancer cells. To realise the full potential of these modelling efforts however, we submit that a method for direct parameterisation is required. In...
All social insects live in elaborately organised societies. Their social structures enable them to continuously manage a large set of simultaneous tasks; from scouting and foraging to colony defence, nest building, thermoregulation, and brood care. To ensure colony survival and reproduction it is vital that the colony workforce is adequately allocated to these different tasks. Social insect...
Influenza A viruses have caused a number of global pandemics, the most recent being the H1N1 pandemic in 2009, resulting in considerable human mortality. Despite influenza pandemics being rare events, with it currently being nearly impossible to predict the next influenza emergence event, it may be the case that the virus itself provides us with outbreak signals that should prompt us to be...
Gene drives are a powerful technique to reduce the size of a population or to transform it to become less troublesome. Major concerns include accidental escape of a gene drive, which might lead to widespread elimination of a species, or unintended consequences of released individuals, which might include evolution of resistance to an effector gene. Both spatial localization of a gene drive and...
Viral interference, whereby infection with one type of virus may temporarily “protect” the host from subsequent infection with another virus has been described for a number of influenza strains and in a number of different host species. In particular, experiments performed in ferrets with influenza A(H1N1)pdm09, A(H3N2) and B have demonstrated strong levels of interference dependent upon the...
Memory translates into time delays naturally in a number of regulatory processes at all levels of organisation in the life sciences: transcription and translation times in molecular biology, finite axonal conduction velocities between neurons, maturation times of precursor cells in hematopoiesis and infection and temporary immune periods in infectious disease propagation are but a few...
It is difficult to mix and pump fluid in microfluidics devices because the traditional methods of mixing and pumping at large length scales don’t work at small length scales. Experimental work has suggested that rotating helical flagella may be used to effectively mix and pump fluid in microfluidics devices. To further explore this idea and to characterize the flow features around rotating...
The first mathematical models for an argasid tick are developed to explore the dynamics and identify knowledge gaps of these poorly studied ticks. These models focus on Ornithodoros moubata, an important tick species throughout Africa and Europe. Ornithodoros moubata is a known vector for African swine fever (ASF), a catastrophically fatal disease for domesticated pigs in Africa and...
Anterior-posterior (AP) polarity formation of cell membrane proteins plays a crucial role in determining cell asymmetry, which depends not only on the several genetic process but also biochemical and biophysical interactions. In Caenorhabditis elegans, a single fertilized egg cell (P0), its daughter cell (P1), and the germline precursors (P2 and P3 cells) form two exclusive domains of PAR...
In volume transmission, neurons in one brain nucleus send their axons to a second nucleus where neurotransmitter is released into the extracellular space. In [1] we showed how to calculate the average amount of neurotransmitter at different parts of the extracellular space, depending on neural properties and the geometry of the projections and extracellular space. We showed how to formulate...
In social insect colonies we often observe substantial levels of laziness, i.e., workers that do not engage or appear not to engage in any tasks. This is puzzling, because colonies with lazy individuals seem to be wasteful and may not be using their resources optimally. A common hypothesis is that lazy workers are a reserve workforce that can be quickly activated when rapid changes in the...
Modelling the spread of influenza across Australia is of substantial public health concern. However, there are many challenges in creating accurate models, including how best to capture the spatial and temporal characteristics of the disease spreading process, and aligning with the actual contact process and mobility of individuals in the population. How influenza spreads spatially, whether by...
Many cells within epithelial tissues display polarity along a particular axis. This axis is perpendicular to the tissue plane and apico-basal axis (from top to bottom of tissues) of the cell. This phenomenon is called “planar cell polarity, PCP”, and is a common phenomenon found in many multicellular organisms. For example, hair cells in the inner ear of humans have many hairs on each...
Microscale filtering and protective layers appear in a variety of places throughout the biological world, with examples including both internal physiological examples (extracellular proteins, microvilli, cilia) and external biological structures (trichomes, swimming legs, bristled wings). In this talk, I describe an agent-based framework built for exploring the biological environment created...
In this talk presented at the Mathematical Neuroscience Subgroup Minisymposium I will discuss a numerical analysis of the steady-state solutions of a neural field model of the corticothalamic system. The independent synaptic connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical,...
Most of the viral gene products are shared among a viral population in a host cell, which accumulates up to $10^6$ to $10^7$ genomes. High mutation rates in viral genome replication bring genetic variety to the intracellular population, and this makes the situation social: mutant genomes that do not code intact gene products can survive as free riders, by using the gene products from the other...
Synthetically-constructed gene drives, that use CRISPR-Cas9 technology to bias inheritance of a particular gene, have been proposed for exotic pest eradication. This is a controversial idea, as there is an apparent potential risk in the use of such technologies, for example to non-target populations of the species. Further, the basic question — Is the technology actually able to achieve its...
Although antiretroviral therapy (ART) suppresses viral replication, patients still suffer from both low CD4 T-cell counts and HIV persistence, requiring them to remain on complex ART regimens for life. A naturally occurring 32-base pair deletion in the CCR5 gene, the major co-receptor for HIV entry, is associated with infection resistance.
In the study initiated by Sangamo Therapeutics,...
Hepatitis B Virus (HBV) is widespread infectious disease and more than 240 million people are chronic infected so far. Although some patients can suppress the viral load under detection limits by current drug treatments, these are not effective for over 60% of patients. The obstacles for developing effective drugs are the existence of a reservoir in infected cells, which is known as covalently...
The importance of host transmissibility in disease emergence has been demonstrated in historical and recent pandemics that involve infectious individuals, known as superspreaders, that are capable of transmitting the infection to a large number of susceptible individuals. To investigate the impact of superspreaders on epidemic dynamics, we formulate deterministic and stochastic models that...
Several types of cancer initiate or metastasize to the bone. These include the most prevalent and lethal cancers: lung, breast and prostate. Thus understanding the bone ecosystem is key if we want to predict what phenotypes will successfully metastasize to the bone and the subsequent evolutionary dynamics that will ensue as the invading tumour cells learn how to co-opt the bone resident cells....
While there exist a number of mathematical approaches to modelling the spread of disease on a network, analyzing such systems in the presence of uncertainty introduces significant complexity. In scenarios where system parameters must be inferred from limited observations, general approaches to uncertainty quantification can generate approximate distributions of the unknown parameters, but...
Viruses have two modes spread in a host body, one is to release infectious particles from infected cells (cell-free) and the other is to infect directly from an infected cell to an adjacent cell (cell-to-cell). Since the mode of spread affects the evolution of life history traits, such as virulence, it is important to reveal which mode is selected. Here we show the evolutionarily stable...
The host range of human immunodeficiency virus (HIV) is quite narrow. Therefore, analyzing HIV-1 pathogenesis in vivo has been limited owing to lack of appropriate animal model systems. To overcome this, chimeric simian and human immunodeficiency viruses (SHIVs) that encode HIV-1 Env and are infectious to macaques have been developed and used to investigate the pathogenicity of HIV-1 *in...
Cell division requires the precise placement of the division ring at mid-cell to ensure both daughter cells are viable. However, the mechanisms behind this localization remain poorly characterized. There are a limited number of known ways to identify the centre of the cell. One such mechanism is a Turing pattern. One intracellular Turing pattern has been identified, that produced by the Min...
A nematocyst is a specialized organelle within cells of jellyfish and other Cnidarians that sting. Nematocysts are also present in some single celled protists. They contain a barbed, venomous thread that accelerates faster than almost anything else in the animal kingdom. Here we simulate the fluid-structure interaction of the barbed thread accelerating through water to puncture its prey using...
Glioblastoma is the most aggressive primary brain cancer, with poor survival that can be largely attributed to intra-tumoural heterogeneity. While these tumours are primarily monitored via contrast-enhanced (CE) T1-weighted and T2-weighted magnetic resonance (MR) images, these standard clinical images are known to be non-specific in their correlation with tumour cell density. This lack of...
The liver is a spatially complex and heterogeneous network of blood and bile flows coupled with metabolic processing and a favoured target for infection by hepatic viruses. We present here a mathematical model aimed at investigating these intrinsic heterogeneities and their impact on the dynamic of the Hepatitis-B variant (HBV). Dramatic spatio-temporal scaling from individual hepatocytes to...
The field of neuromechanics, which attempts to integrate neural control with muscle activation and the resulting movement of an organism, is an emerging field of organismal biology. Approaches from experimental biology, robotics, and mathematics have now reached the point where their knowledge about the different facets of (animal) locomotion can be combined and integrated into...
Thermoregulatory responses are partially controlled by the preoptic area and anterior hypothalamus (PO/AH), which contains a mixed population of temperature-sensitive and insensitive neurons. In [1] based on physiological data, a Hodgkin-Huxley-like conductance based model was constructed. This model suggests that most PO/AH neurons have the same types of ionic channels, but different levels...
In recent years honey bee colonies have been experiencing increased loss of hives. One cause of hive loss is colony collapse disorder (CCD). Colony collapse disorder is characterised by a previously healthy hive having few or no adult bees but with food and brood still present. This occurs over several weeks. It is not known if there is an exact cause of CCD but rather it is thought to be the...
Novel strategies for controlling mosquito vectors of human diseases involve introductions of selfish genetic elements (SGEs), or elements that spread through the mosquito population by means of non-Mendelian inheritance. The releases of the endosymbiotic bacteria Wolbachia into Aedes aegypti populations in order to reduce their capacity for arbovirus transmission are the first application...
Influenza in humans exhibits a strong seasonal cycle in temperate climates, with a peak of varying intensity appearing each winter. However, the exact cause of this seasonal cycle remains poorly understood. We develop a climate-based SIR modelling framework to understand influenza seasonality, with the transmission rate as a function of climate data. By using a variety of climate-based...
A conceptual model was constructed to define the network of potential routes of exposure of pollinators to pesticides in greater detail than has previously been done. This model provides a basis for biologically and ecologically realistic basis for mathematical estimation of exposure versus time both individually and at the colony level. It also shows the distinction between primary exposure...
Reinfection is known to induce complex epidemiological dynamics (e.g. sustained oscillation) due to the time-series change in susceptibility. The simplest model describing reinfection shows three epidemiological dynamics; disease-free, epidemic and endemic. These three dynamics can be classified by two reproduction numbers, basic reproduction number and reproduction number by only reinfection....
In recent years, new technology has allowed us to achieve measurements of hundreds of metabolites and the expression of thousands of genes. With this large scale, all-encompassing, ‘omics’ data comes a critical need to reduce these datasets to the most functional elements so that we can discover key components driving disease pathogenesis. Current techniques to analyze omics data are not...
Tumours consist of a hierarchical population of cells that differ in their phenotype and genotype. This hierarchical organization of cells means that a few clones (i.e., cells and several generations of offspring) are abundant while most are rare, which is called clonal dominance. Such dominance also occurred in published in vitro iterated growth and passage experiments with tumour cells in...
The impact of spatial structure on evolutionary outcomes can be profound due to both ecological and genetic correlations. One of the best developed areas of spatial evolutionary theory has focused on the coevolution of hosts and parasites. There are profound impacts of local as opposed to global infection on both parasite and host evolutionary outcomes. Using a combination of pair...
During development of multicellular organisms, multiple signalling systems play important roles. However, it is very hard to understand the interplays between many signalling pathways using conventional methods of molecular biology, biochemistry and genetics. Mathematical modelling should be combined with these biological methods to solve biological problem.
The waves of differentiation in...
The advent of CRISPR/Cas9-based gene editing and its demonstrated ability to streamline the development of gene drive systems has reignited interest in its application to the control of mosquitoes and the diseases they transmit. The versatility of this technology has also enabled a wide range of gene drive architectures to be realized, creating a need for their population-level and spatial...
Thrombopoiesis is the process for producing platelets, which uses a negative feedback to maintain homeostasis in normal individuals. However, pathological states exist where platelet concentrations in the body oscillate. An age-structured model for thrombopoiesis was developed and fitted to clinical data for subjects with normal and pathological platelet production. Variations on this model...
It has been known for some decades that fertilisation of some amphibian and fish eggs is followed by a wave of calcium ions over the surface of the egg, which is associated with a physical change to the surface. Similar waves are seen at other stages of embryonic development. An unfertilized mammalian egg is surrounded by cumulus cells to form a cumulus-oocyte complex (COC). Just a few years...
One of the main focuses of HIV research today concerns allowing people living with HIV to experience prolonged periods where they do not need to remain on treatment. Current therapies are able to suppress HIV to undetectable levels, however as soon as therapy is interrupted the virus “rebounds” to pre-treatment levels and this leads to increased morbidity from HIV. This rebound likely occurs...
Neural spiking and bursting rhythms in space-clamped (i.e., ODE) models are typically driven by either canard dynamics or slow passage through Hopf bifurcations. In both cases, solutions which are attracted to quasi-stationary states (QSS) sufficiently before a fold or Hopf bifurcation remain near the QSS for long times after the states have become repelling, resulting in a significant delay...
Infections with Group A Streptoccocus (GAS) are highly prevalent in remote communities in
the Northern Territory, Australia. One of the primary drivers of GAS infection is scabies, a small mite which causes a break in the skin layer, potentially allowing GAS to take hold. This biological connection is reaffirmed by the observation that mass treatment for scabies in these remote communities...
For successful ecosystem management and biodiversity conservation, in addition to ecological and evolutionary processes, we need to consider social and economic influences on the management target. Here, we introduce four models that address economic and social aspects of human society in the context of ecosystem management.
- Lake water pollution. Players choose between cooperative (but...
Characterizing enzyme kinetics is critical to understand cellular systems and to utilize enzymes in industry. To estimate enzyme kinetics from reaction progress curves of substrates, the Michaelis-Menten equation has been widely used for a century. However, this canonical approach works in a limited condition such as a large excess of substrate over enzyme. Even when such condition is...
Motivated by the formation of fingerprint patterns we consider a class of interaction models with anisotropic interaction forces whose orientations depend on an underlying tensor field. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a long-range attraction structure. In contrast to isotropic...
The basic reproduction number, $R_0$, derived from ordinary differential equation models is a powerful predictor of the severity of an infection and can help inform prevention and mitigation strategies. Many of the parameters used in ODE models are mean values of time-dependent distributions. Here, we show how we can incorporate properties of these distributions to refine estimates of $R_0$...
The elderly population is particularly susceptible to infectious diseases, such as influenza, as evidenced by increased occurrence and severity of infection, and reduced vaccine efficacy. Studies suggest an association between persistent cytomegalovirus (CMV) infection and deficiencies of the aged immune system. CMV is a common herpes virus that infects up to 85% of the population aged 40...
Immune system dynamics in the context of a number of diseases, including certain cancers and type I diabetes, continues to play an increasingly central role in the development of new treatment strategies. The critical importance of the immune system in fighting such diseases has been verified clinically, as well as through mathematical models.
Many open questions remain, however, including...
Adipose tissue and adipocytes play a central role in the pathogenesis of metabolic diseases related to obesity. Size of fat cells depends on the balance of synthesis and mobilization of lipids and can undergo important variations throughout the life of the organism. These variations usually occur when storing and releasing lipids according to energy demand. This energy is stored as lipid...
Multidrug resistance consists of a series of genetic and epigenetic alternations that involve multifactorial and complex processes, which are a challenge to successful cancer treatments. Accompanied by advances in biotechnology and high dimensional data analysis techniques that are bringing in new opportunities in modelling biological systems with continuous phenotypic structured models, we...
Populations are formed of their constituent interacting individuals, each with their own respective within-host biological processes. Infection not only spreads within the host organism but also spreads between individuals. We propose and study a nested multilevel model which links the within-host statuses of immunity and parasite density to population epidemiology under sub-lethal and lethal...
Impaired oxygen delivery and blood flow have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. It is unknown, however, whether changes in blood flow to the retina are the cause or effect of retinal ganglion cell death, and a combined experimental and theoretical approach is needed to analyze the relationship between blood flow...
Walking through any forest, one is struck by the variety of plant forms coexisting. To explain vegetation structure and diversity, models must allow for multiple species to coexist, and ultimately, predict the outcome of community assembly in different environments. In this talk, I describe how adaptive dynamics theory provides a new framework for predicting the mixtures of species traits that...
Many PDE-based models of collective cell behaviour implicitly assume that the population of cells is ‘well mixed’. This is called a spatial mean-field assumption. In reality, populations often have a more complex spatial structure, such as clusters and/or spatial segregation of cells. This spatial structure is both a cause and an effect of non-local interactions among cells and can make a...
A gene is imprinted when its level of expression is dependent on the sex of the parent it was inherited from. An unusual consequence of imprinting is that male and female additive genetic variances differ, and so ignoring imprinting can lead to misspecification of a number of evolutionary parameters, including the predicted response to selection. QST - the differentiation of quantitative...
The deliberate release of Cyprinid herpes virus 3 (CyHV-3) to control invasive common carp (Cyprinus carpio) in the Murray-Darling Basin of south-eastern Australia has been dubbed `Carpageddon' and is highly controversial. Common carp now represent up to 90% of the biomass in invaded waterways and mortality rates of 70-80% have been observed during outbreaks of CyHV-3 in the northern...
In this presentation we consider a recent experimental dataset describing heat conduction in living porcine tissues. This novel dataset is important because porcine skin is similar to human skin, and improving our understanding of heat conduction in human skin is directly relevant to understanding burn injuries, which are common, painful and can require expensive treatments. A key feature of...
Recent studies show that human immune system interacts with intestinal microbiome. A certain group of intestinal bacteria is known to be possible suppressor of undesirable immune response [1]. They produce short chain fatty acid such as butyrate and induce regulatory T cells [1]. Regulatory T cells are suppressor of exaggerated immune responses [2]. Therefore, collapse of the ecological...
Cancer cell invasion, recognised as one of the hallmarks of cancer, is a complex process involving the secretion of matrix-degrading enzymes that have the ability to degrade the surrounding extracellular matrix (ECM). Combined with cell proliferation, migration, and changes in cell-cell and cell-matrix adhesion, a tumour is able to spread into the surrounding tissue. We highlight the...
Drug resistance is a major cause of the failure of chemotherapy. Resistance manifests through a diverse set of molecular mechanisms, such as the upregulation of efflux transporters on the cell membrane, enhanced DNA damage repair mechanisms, and/or the presence of cancer stem cells. Classically, these mechanisms are understood as conferred to the cell by random genetic mutations, from which...
We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph nodes into two compartments, namely, S and I, denoting susceptible and infected nodes, respectively. In addition to the sizes of these two compartments, we study counts of SI-edges...
Diversification and extinction are ubiquitously repeated in the evolutionary histories of biological communities. A minimal mechanism for driving the repeated diversification and extinction is a combination of resource competition in one trait and a weak directional selection in another trait; resource competition induces diversification in the first trait, but inevitably nonuniform...
Background: Measles and rubella are rash illnesses that typically afflicted young children in the pre-vaccination era, but rubella usually is mild while measles may be severe. Because child deaths to which measles contributes often have other proximate causes, measles mortality is under-ascertained. Rubella during the first trimester invariably causes miscarriages, stillbirths and, among...
Arguments about the evolutionary modification of genetic dominance have a long history in genetics, dating back over 100 years. Mathematical investigations have shown that modifiers of the level of dominance at the locus of interest can only spread at a reasonable rate if heterozygotes at that locus are common. One hitherto neglected scenario is that of sexually antagonistic selection, which...
In this talk we present a mesoscopic model for natural network formation processes, acting as a bridge between a discrete and continuous network approach proposed by Hu and Cai. All models describe the pressure field and the dynamics of the conductance network under pressure force effects.
We start by presenting the different approaches and analyze their corresponding properties. We will...
Recently, nonlocal interactions (spatial long range interactions) have attracted attention in many fields. Mathematical treatment of nonlocal interaction is mainly based on convolution with kernels. If the profile of a nonlocal interaction is detected by experiments, we can easily investigate how patterns are generated by numerical simulations. However, nonlocal interactions are often...
The kidney plays an essential role in regulating the blood pressure and a number of its func- tions operate at the functional unit of the kidney, the nephron. To understand the impacts of internephron coupling on the overall nephrons’ dynamics, we develop a mathematical model of a tubuloglomerular feedback (TGF) system, a negative feedback mechanism for nephron’s fluid capacity. Specifically,...
A vaccine is a biological preparation, providing long-term protection of the host to a disease by miming the interactions between the pathogen and the immune response. For decades vaccines have been the most effective means to fight and eradicate infectious diseases, from human diseases to animals diseases, including poultry and porcine viruses. One of the most significant endemic swine...
Circadian analysis is becoming increasingly important as a diagnostic tool to quantify deviations from regularity in circadian cycles. Circadian rhythms become less dominant and less regular with ageing and disease. It has been hypothesized that insomnia might be related to alterations, albeit small, in circadian and ultradian rhythms, but this topic remains an open problem. In this work, we...
Tuberculosis (TB), a deadly infectious disease caused by the bacterium Mycobacterium tuberculosis (Mtb). The disease is characterized by the development of granulomas consisting of immune cells that form a cluster around the bacteria to limit bacterial growth and disease outcomes. Control of the TB epidemic is limited by a complicated drug regimen, development of antibiotic resistance, and the...
Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical microcircuits. To integrate these properties from anatomy and physiology, and to elucidate the mechanistic links between them, we develop a cortical microcircuit model that captures a range of realistic features of synaptic connectivity. We show...
Mutualism based on reciprocal exchange of costly services must avoid exploitation by “free-rides”. Accordingly, hosts discriminate against free-riding symbionts in many mutualistic relationships. However, as the selective advantage of discriminators comes from the presence of variability in symbiont quality that they eliminate, discrimination and thus mutualism have been considered to be...
Background and Purpose: Renal hypoxia is postulated to be a leading cause of acute kidney injury, and the renal medulla is known to be most susceptible to hypoxia. The ability to accurately predict normal and abnormal oxygen states in terms of tissue oxygen tension (PO2) within the renal medulla is highly desirable, as among other uses predicted medullary PO2 can be correlated with local...
In the study of the Human Immunodeficiency Virus (HIV) infection dynamics, the reproductive ratio is a well known tool which provides a steady-state condition to determine the outcome of the infection. This paper assesses the control of HIV by the immune response. Dynamical conditions for the containment of HIV infection by the HIV-specific CD8+ T cell response are evaluated using a model of...
Organisms often modify their environments to their advantage through a process of niche construction. Environments that are improved through positive niche construction can be viewed as a public good. If free riders appear that do not contribute to the shared resource and therefore do not incur any associated costs, the constructed niche may become degraded resulting in a tragedy of the...
After reviewing the basics about the relation between some motion flow models (pedestrians, animals, vehicles) and a class of Hamilton-Jacobi-Bellmann equations on Networks we introduce and discuss some numerical methods for the approximation of the solution. Several tests are performed to illustrate the properties previously theoretically presented.
The spectacular patterns of collective animal movement have been, and remain, a long standing and major interest in many branches of science, including biology, mathematics, physics and computational science. It is thought that the emergent patterns of coordinated motion are the consequence of individuals applying simple rules to adjust their velocity based on the relative locations and...
Cytotoxic T-lymphocytes, commonly called killer T cells, are among our immune system’s most potent and well-understood weapons against cancer. However, checkpoint receptors such as CTLA-4 and PD-1 on the surfaces of T cells inhibit their activation and proliferation. These receptors can be blocked by antibody drugs, which pave the way for an anti-tumour immune response. We will present...
Understanding the mechanisms of HIV latency is important in the development of strategies for managing infection. Time from infection until production of virus has been shown to vary among infected cells, hence challenging the dichotomous assumption that cells are either latent or productively infected at time of infection. In this paper, we will explore the implications of an alternative...
Middle East Respiratory Syndrome Coronavirus (MERS-CoV) has been persistent in the Middle East region since 2012. Abundant scientific evidence showed that dromedary camels are the primary host of the virus. Majority of human cases (i.e. 75% or 88%) are due to human-to-human transmission, while the others are due to camel-to-human transmission. Mathematical modelling of MERS-CoV camel-to-camel...
In this talk I will introduce several quasi steady-state approximations (QSSAs) applied to the stochastic enzyme kinetics models. Different assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in the literature in deterministic ordinary...
Experiments in rhesus macaques have shown that for simian immunodeficiency virus the size of the viral inoculum and the infection stage of the donor animal alter the likelihood of establishment of infection. In this study, we postulate a role for the host and donor antibodies in explaining the dependence of infectiousness on donor infection stage. The resulting mathematical model exhibits...
Variability in electrophysiological properties, between different cells in a given heart and between the hearts of different members in a population, has a profound impact on deciding both the susceptibility to dangerous arrhythmias and the success or failure of anti-arrhythmic treatments. This variability also complicates the interpretation of both experimental and clinical data, and the...
Transitive inference (TI) that uses known relationships to deduce unknown ones (using A > B and B > C to infer A > C given no direct interactions between A and C) to assess the opponent’s strength, or resource-holding potential (RHP), is widely reported in animals living in a group. This sounds counter-intuitive because the mechanism of TI seems to require social cognition and large memory...
Growing tumours are infiltrated by a variety of immune cells, including macrophages, a type of immune cell which can adopt a range of pro- or anti-tumour phenotypes depending on microenvironmental cues. The spatial distribution of macrophages within a tumour varies from patient to patient and between different tumour types, and is related to patient outcome. There is considerable interest in...
We consider a network of coupled excitatory and inhibitory theta neurons which is capable of supporting stable spatially-localised “bump” solutions. We randomly add long-range and simultaneously remove short-range connections within the network to form a small-world network and investigate the effects of this rewiring on the existence and stability of the bump solution. We consider two limits...
Strict maternal inheritance renders the mitochondrial genome susceptible to accumulating mutations that harm males, but are otherwise benign or beneficial for females. This ‘mother's curse’ effect can degrade male survival and fertility if unopposed by counteracting evolutionary processes. Coadaptation between nuclear and mitochondrial genomes—with nuclear genes evolving to compensate for...
Starting from a detailed physical model for the interplay of actin filaments, myosin motor proteins and cross-linker proteins in a contracting cell division ring, we derive a continuum model as a short filament limit of the agent based model. The model features highly nontrivial pattern formation and traveling wave solutions and explains the aggregation of actin and myosin predicted by the...
Infections with the malaria parasite can lead to severe illness and mortality, with nearly half a million deaths attributed to malaria globally each year. Adults from malaria endemic regions often have immunity to malaria and are much less susceptible to disease, compared with children. Understanding how a host can control malaria infections is critical in guiding the development of a much...
Analyzing humankind’s interactions with our collective environment typically requires understanding eco-evolutionary dynamics in complex adaptive systems. This is especially important for mitigating anthropogenic impacts on the biosphere, managing the multifaceted services provided by ecosystems, and shaping social interactions among agents utilizing these systems. Understanding complex...
The inference for the reaction rates in chemical networks is often challenging due to intrinsic and extrinsic biological noise, missing data and lack of experimental reproducibility. The talk will provide an overview of some recent work on new efficient methods of rates estimation in stochastic biochemical networks both at molecular and population scales. Stochastic SIR and Michaelis...
Transient activation of a region of the brain cortex results in an increase in the local rate of oxygen consumption, and stimulates an increase in blood flow to the stimulated region, a phenomenon known as neurovascular coupling. Under normal conditions, the relative increase in blood flow during activation is observed to exceed the relative increase in oxygen consumption, by a factor $n>1$....
Chlamydia trachomatis is the most common cause of bacterial sexually transmitted infection. It can also infect the eyes and is a major cause of blindness in many developing countries. During the infection of a mammalian host, Chlamydia must decide when to proliferate and when to convert into a differentiated form, since the differentiated form is the only form to survive outside the host...
Multiple selective pressures drive evolution of malaria parasite, and determine its phenotypic traits, like virulence, transmissibility, drug resistance, as well as its population structure in host communities. Immune regulation plays an important part in this process, both within-host and on population level. The key to parasite survival within host is its antigenic variation, whereby...
Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle (ASM) wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction which occurs...
There are now over 50 conservation science journals and the field is booming. The world’s top journals, Science and Nature, routinely cover conservation science issues, but the field has been dominated by ecologists. Solving conservation problems is as much about maths and economics, as it is about ecology. Our group at the University of Queensland, and our national ARC Centre of Excellence...
Identifying the epidemiological key-stone communities in a metapopulation network is primarily important in designing efficient control against an infectious disease. Various network centrality measures commonly utilized for this purpose haven’t directly focused on the most important measure in epidemiology: the basic reproductive number, $R_0$, of epidemiological dynamics on the network,...
In this paper, we study power law kinetics on chemical reaction networks with Independent decompositions, i.e. the network is the union of subnetworks whose reaction sets form a partition of the network's reaction set and the network's stoichiometric subspace is the direct sum of the stoichiometric subspaces of the subnetworks. Our main result is a Deficiency Zero Theorem when the subnetworks...
Photoreceptors are cells in the retina that convert light to chemical signals. To offset the extreme optical and metabolic demands, and thereby prevent the toxic effects of accumulated photo-oxidative products, photoreceptors undergo renewal and periodic shedding of their outer segment (OS) discs. The OS are a substructure that carries the light sensitive molecule, opsin. People afflicted with...
The development of ecotoxicological models over the last couple decades has significantly contributed to interpreting how contaminants impact organisms and cycle through food webs. However, there is increasing evidence that organisms experience interactive effects of contaminant stressors and food conditions, such as resource stoichiometry and nutrient availability. *Stoichiometric...
Environmental fluctuations, such as those caused by seasonality, are common, and climate change is expected to increase the amplitude of environmental oscillations. Therefore it is important to understand how increasing the amplitude of environmental oscillations will affect evolutionary processes, and in particular host-parasite evolution, where the extent of evolution is likely to be...
It is becoming increasingly clear that tumour cells recruit cells in their surrounding microenvironment to aid in their proliferation. Tumour-associated macrophages and stromal cells are now believed to play a prominent role in tumour growth. Some evidence points to the fact that iron is a key player in the complex interactions between cancer cells and the microenvironment. This talk will...
The placenta is critical for our first nine months of life, as it provides nutrients from mother’s blood and clears waste from the fetal circulation. The main structures that make up the placenta are villus trees, so called because they form a complex branching structure, like the branching of a tree, to provide a large surface area for exchange. Many pregnancy complications are associated...
In this seminar, I will present the results obtained from investigating the optimal control strategies for malaria in the presence of temperature variation using a temperature dependent malaria model. A 2015 study by Agusto et al. identified the suitable temperature ranges for mosquitoes in four different geographical regions of Sub-Saharan Africa as [22.61$\rm^o$C - 28.58$\rm^o$C] in West...
Acute graft-versus-host disease (aGVHD) is the major complication of Allogeneic Hematopoietic Stem Cell Transplantation (allo-HSCT). A lot of previous studies showed that the importance of DNAM-1(CD226) which is expressed on CD4+ T cells, CD8+ T cells, natural killer (NK) cells, and monocytes Therefore, DNAM-1 has been considered as essential molecule of developing aGVHD in vitro and vivo...
Quantitative Undergraduate Biology Education and Synthesis (QUBES) is an NSF funded project with the mission to improve learning opportunities for all students enrolled in undergraduate biology courses by reflecting the centrality of quantitative approaches in modern biology. We will provide an overview of the QUBES project, then discuss the Quantitative Modelling assessment QM BUGS. The...
In order for an organism to have an robust mode of locomotion, the underlying neuromuscular organization must be maneuverable in a changing environment. In jellyfish, the activation and release of muscular tension is governed by the interaction of pacemakers with the underlying motor nerve net that communicates with the musculature. This set of equally-spaced pacemakers located at bell rim...
The idea of cancer as an evolutionary disease is well established. Cancer development is driven by mutation and selective forces, including the action of the immune system, interspecific competition and therapies. Different tumour types exhibit resistance to the immune system suggesting the investigation of different aspects of the tumoural microenvironment to better understand cancer.
The...
During differentiation process, cell type specific gene expression pattern is established by orchestrate regulatory network of transcription factors (TFs). Resolving the structure of the transcriptional regulatory network (TRN) is promising way to understand the detailed mechanism of cell differentiation.
Here I estimate a transcriptional regulatory network determining the cell type specific...
As dengue is one of the human diseases with global concern, the host-vector shuttle and the bottleneck of dengue transmission is a significant aspect to study. For the four serotypes of dengue virus within host and their transmission to the vectors, we try to capture the variability in blood viremia and antibody levels of patients and their infectiousness to mosquitoes. The present model...
Heterogeneity in cancer is increasingly being recognized as a key determinant of tumour progression and response to therapy. However, much of our current understanding of this heterogeneity has been driven by our ability to measure it, and therefore has largely focused on the genomic scale. Ultimately such heterogeneity is realized through the generation of distinct phenotypes. In recent years...
The gut microbiome is implicated in a growing array of diseases, spanning asthma, allergies, obesity and autoimmunity. The need for interventions that return aberrant dysbiotic communities to symbiotic partners is clear. Yet, despite known sensitivities to diet, a conceptual framework through which to design rational interventions remains elusive.
We adopted an ecological perspective in...
While there are many opinions on what mathematical modelling in biology is, in essence, modelling is a mathematical tool which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modelling can be less useful or even...
Human Immunodeficiency Virus typeⅠ (HIV-1) mutations are rapidly accumulated through recombination events which are largely caused by HIV-1 coinfection [1]. Therefore, HIV-1 coinfection has the potential to produce the drug-resistant viruses, which leads to the high pathologies and disease progression. Recently, it has been reported that coinfection occurs more frequently than at random both...
The lamprey is an eel-like organism used as a model for both neurophysiology and locomotion studies. Like other animals, the lamprey moves through the use of a neural network called a central pattern generator to generate a rhythmic signals down the body, inducing muscle contractions. This signal is adjusted through information using mechanosensors (edge cells) which detect changes to the body...
The abundance of a pollinator species can be affected by other pollinators sharing the nutrients from the same plants. Such an exploitative competition between the animal species may affect the species abundance the network structure of plant-pollinator mutualistic communities, which remains to be understood. Here we study a model of the mutualistic network evolution towards increasing the...
Falciparum malaria is a major parasitic disease causing widespread morbidity and mortality globally. Artemisinin derivatives – the most effective and widely-used antimalarials that have helped reduce the burden of malaria by 60% in some areas over the past decade – have recently been found to induce growth retardation of blood-stage Plasmodium falciparum when applied at clinically relevant...
Advanced prostate cancer is often treated by androgen suppression therapy, since prostate cells depend on androgens for proliferation and survival. To improve the patients' quality of life and possibly delay the development of resistance, intermittent androgen suppression (IAS) therapy can be given rather than continuous therapy. We consider a mathematical model of IAS therapy involving tumour...
In this talk, we present our results on power law kinetic systems whose kinetic order vectors (which we call “interactions”) are reactant-determined (i.e. reactions with the same reactant complex have identical kinetic order vectors) and are linear independent per linkage class. In particular, we focus on its subset called PL-TLK systems. Our main result states that any weakly reversible...
Mitochondria are specialised organelles that produce adenosine triphosphate (ATP), a molecule used by cells as an energy source. Mitochondria form dynamic networks that constantly undergo fission and fusion in response to increased ATP demand. There is a lack of high-resolution data tracking the reorganisation mitochondrial networks in a beating heart cell. We use an agent-based model to...
Mutualisms are reciprocally beneficial interactions between heterospecific organisms. Theoretical studies have predicted that genetic diversity in mutualistic systems should decrease over time because of innate positive feedback structure of the interaction. Negative feedback due to asymmetry in the exchange of benefits can maintain the diversity and stabilize multi-strain mutualistic systems,...
Accurate clinical assessment of a patient's response to treatment is a critical task in the era of precision medicine. Glioblastoma (GBM), a primary brain tumour with dismal median survival times of 12-16 months, has a highly heterogeneous, invasive profile, causing tumour dynamics and therapeutic response to vary widely from patient to patient. Currently, two sets of standard assessment...
The growing threat of antimicrobial drug resistance presents a significant challenge not only to the medical community, but the wider general population. Alarmingly, resistant strains of infectious diseases are already endemic in many communities – particularly in developing countries and lower socio-economic settings – with new strains, which enjoy even more extensive resistance, continually...
Binary genetic switches are widely used in synthetic biology for switching between two expression states, ON and OFF. In particular, single input switches, which alternate between ON and OFF in response to the same input signals, are the key elements of counting devices which count the occurrence of a repeated intracellular or extracellular signal. Most existing DNA switches require two...
Infectious diseases undergo evolutionary changes as they spread and persist in populations. Different diseases present substantially different evolutionary dynamics, with both large-scale changes that create different strains, or more incremental shifts within a strain. In this talk, we demonstrate how a general stochastic epidemic model can be used to explain different types of evolutionary...
The relationship between gut microbiota and health has been of keen interest for the past several years. The physical inaccessibility of the colon makes alternative research approaches a valuable addition to the clinical research done in this area. In this seminar, we discuss the compuGUT - a numerical simulation tool for studying anaerobic digestion and physiology in the colon. The underlying...
High-frequency physiological data poses unique challenges for signal processing and computational analysis. This dataset was obtained from a cohort of Macaca mulatta and Macaca fascicularis infected with Plasmodium knowlesi using a customized telemetry system. The data set is comprised of electrocardiogram signals collected at a sampling rate of 1 kHz, temperature measures collected at 1...
Fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualisation of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to...
The basic reproduction number, $R_0$, is a key quantity allowing public health officials to track how quickly an outbreak spreads through a population. In this talk, we compare several different estimators of $R_0$ assuming that only weekly data is available, with a focus on the early stages of an outbreak. We compare four estimators: a variant on maximum likelihood, incidence decay,...
Residual premalignant lesions after the first treatment such as surgery and chemotherapy are considered to be a cause of cancer recurrence. A previous study showed that the presence of premalignant lesions surrounding the primary tumour drives the high rate of local cancer recurrence. If cancerization requires m specific mutations in one cell, cells which have less than m mutations are still...
From heart tubes to respiratory breathing, many organisms use valveless pumping mechanisms for internal flow transport. These pumping mechanisms were first seen in basal chordates, e.g., tunicates, where the drove through through their open circulatory systems. As evolution took its course these pumping techniques begun to be found in insect hearts and during first stage of vertebrate heart...
Pharmacokinetics (PK) describes a drug's affect on a medium (such as bacteria or tumours) while pharmacodynamics (PD) describes how a drug moves throughout and is processed by the body (along with changes in drug concentration). Taken together, these models are known as PK/PD models and ordinary differential equations (ODE) are used to describe the system. We consider an existing model in the...
Classical results give structural conditions under which the steady state set of a (bio)chemical reaction system has a monomial parametrization. This property has been studied extensively in the context of characterizing a mechanism's capacity for mono- and multi-stationarity. In this talk, we generalize the existing structural framework and derive sufficient conditions for guaranteeing that...
In recent times, unprecedented rates of biodiversity loss have resulted in a pressing need for greater understanding of key processes maintaining biodiversity. These processes are often studied in island communities because they exhibit low complexity relative to their mainland counterparts, which helps to simplify experiments, data analyses and mathematical models. Much previous work on...
In recent years, advances in cancer research have shown that the body’s immune response to tumour cells plays a significant role in fighting cancer growth. Although the immune system is intrinsically capable of destroying tumour cells, tumours and their microenvironment have an ability to suppress the immune response. Whereas the roles of some immune cells have been greatly studied, the role...
Over the last years, a number of stochastic models have been proposed for analysing the spread of nosocomial infections in hospital settings. These models often account for a number of factors governing the spread dynamics: spontaneous patient colonization, patient-staff contamination/colonization, environmental contamination, patient cohorting, or health-care workers (HCWs) hand-washing...
Introduction. Radiation therapy is a critical portion of the standard-of-care for patients with brain tumours, as it targets residual disease and non-operable tumours. However, one of the shortcomings of radiation therapy is the heterogeneity of response observed in the patient population which may be due to fundamental limitations in the way radiation therapy plans are currently selected....
Typically, discrete stochastic models of cell proliferation use a rate to determine whether or not a cell proliferates at a particular time, producing an exponential distribution for the time between proliferation events. Actual experiments, however, suggest that cells actually have a Gaussian distribution in their time to proliferate, with a relatively small standard deviation. This talk will...
Male juveniles of several species of salmonids spawning in fresh water streams migrate to the ocean and return to their natal stream when they mature (migratory tactic); others stay and mature in the stream (resident tactic). Large individuals become residents and small ones become migrants. This is an evolutionary outcome according to the status-dependent strategy model, which assumes that...
The structure of an ecosystem and the interaction of the species within it can determine whether a pathogen can persist. We have described a model for interacting species that are hosts and non-hosts of a pathogen. The population densities of the ecosystem species can determine the value of the basic reproduction number, $\mathcal{R}_0$. We have defined concepts of ecological and...
Over the last decade, control measures have significantly reduced malaria morbidity and mortality. However, the burden of malaria remains high, with more than 70% of malaria deaths occurring in children under the age of five. The spread of antimalarial resistant parasites challenges the efficacy of current interventions, such as Intermittent Preventive Treatment (IPT), whose aim it is to...
Multistationarity is defined as the existence of several positive equilibria of an ordinary differential equations model. Multistationarity is a required property of biological switches- reaction networks that govern important cellular functions, such as cell differentiation and cell death. This is the case, because biological switches are modelled by differential equations systems whose...
Protein misfolding is one of the major causes of apoptosis in Retinitis Pigmentosa, where apoptosis is programmed cell death. Mesencephalic-Astrocyte-derived-Neurotrophic Factor (MANF) is a protein that has been shown to correct protein misfolding, thus reducing the death of cells due to “cell suicide”. In this talk, we formulate an optimal control problem that incorporates MANF treatment to...
Very small insects that are 1 mm in length or less, such as thrips and fairyflies, often clap their wings together at the end of each upstroke and fling them apart at the beginning of each downstroke. This 'clap and fling' motion augments the lift forces generated during flight, but very large forces are required to clap the wings together and to fling the wings apart. As the opposing forces...
Tailoring therapies to individuals for personalized care can be safer and yield superior outcomes with lower doses for conditions such as diabetes, Alzheimers disease, or even certain cancers. However, widespread use of personalized care is currently limited by our inability to routinely measure pathology and detect biomarkers. Moreover, existing strategies require specialized facilities, can...
Modern anti-retroviral therapy can effectively control HIV. However, the virus cannot be eradicated due to the presence of latently infected CD4+ cells that cause the reactivation of virus when a patient stops anti-retroviral treatment.
There is a lack of knowledge about the basic dynamics of reactivation of latently infected cells and the interaction of virus with immunity. We combined...
Rapidly dividing tissues, like intestinal crypts, are frequently chosen to investigate the process of tumour initiation, because of their high rate of mutations. To study the interplay between normal and mutant as well as immortal cells in the human colon or intestinal crypt, we developed a 4-compartmental stochastic model for cell dynamics based on current discoveries. Recent studies of the...
Antibiotic resistance has become one of the major health issues in the world. It kills around 700,000 people each year worldwide, and will become even worse if no new antibiotics are developed (Nature, 2017). Therefore, serious efforts are required to prevent more severe conditions in the future. One important effort in this case is understanding the dynamics of the problem so that effective...
Batesian mimicry is a common phenomenon in nature, and it has been reported in various taxa. In Batesian mimicry, there are two species that have a similar colouration. One species is toxic or unpalatable, we call it “model-species”. The other is nontoxic or palatable, we call it “mimic”.
While many mathematical models focused on the evolution of mimicry, only a few mathematical models...
Through combination of novel microscopy protocols for imaging live cells and tissues as well as experimental mechanics methods, we have begun to elucidate mechanisms underpinning emergent properties of hierarchical materials such as tissues [1,2]. We refer to the process as Microscopy Aided Design And Manufacture (MADAMe). We apply this paired imaging and computational technology approach to...
A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density $x$, $x\ge0$. The individuals with density $x=0$ are not infected, but rather susceptible or...
The arterial wall is composed of three distinct layers: the innermost intima, the media, and the adventitia. Atherosclerosis is an inflammatory disease of the artery characterized mainly by an expansion of the intima. In 1987, Seymour Glagov quantified arterial remodelling as atherosclerosis progressed. He found that the remodelling occurred in two stages: first a compensatory phase in which...
We have developed several models of the physical control of branching morphogenesis in the lung, considering a variety of factors, including transport and mechanics. Simple models can explain complex phenomena, though how reasonable a model initially seems is not necessarily correlated with its ultimate explanatory power. In this talk, we will present a variety of models of branching...
Student progress in “interdisciplinary (ID) thinking” is remarkably resistant to many established means of evaluation. A sophisticated skill, such thinking does not fit well into old instruments, like timed exams. In contrast to discipline-specific skill sets, a student’s ability to view problems from multiple-disciplinary perspectives cannot be evaluated in terms of an objective standard,...
Influenza A virus (IAV) infections are often complicated by bacterial pathogens like Streptococcus pneumoniae (SP, pneumococcus), which have accounted for 40-95% of IAV-associated mortality. IAV-SP coinfection is characterized by rapid, uncontrolled bacterial growth, a rebound in viral titers, and a robust inflammatory response. Several factors contribute to influenza-pneumococcal...
Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the...
A central debate when studying ecological communities concerns the relative importance of selective processes relative to stochastic ones. This has significance for understanding the dynamic behaviour of these systems, for assessing features such as fragility and resilience, and ultimately, for determining how to correctly approach them. At the core of dealing with this challenge is the need...
Mast seeding is the intermittent synchronous production of large seed crops by a population of perennial plants. This process is noteworthy in various ways. To the lay public, masting is noteworthy because it is very obvious when an occasional huge seed crop covers large areas.
In evolutionary terms it is noteworthy because delayed reproduction imposes inescapable costs on the plants, so it...
Background: Japan experienced a nationwide rubella epidemic from 2012 to 2013, mostly in urban prefectures with large population sizes. The present study aimed to capture the spatiotemporal patterns of rubella using a parsimonious metapopulation epidemic model and examine the potential usefulness of spatial vaccination.
Methodology/Principal Findings: A metapopulation epidemic model in...
The artemisinins are our most effective class of antimalarials, and are the internationally recommended drugs for treating malaria. This class of antimalarials has been an important factor in reducing mortality due to malaria globally. However, the emergence of resistance to this most effective and widely used class of antimalarials threatens this progress. Despite their high efficacy the...
Circadian rhythms originate at the cellular level from feedback processes in genetic regulatory networks. Based on experimental observations, computational models of have been proposed for the molecular mechanism of circadian rhythms, which occur spontaneously with a period of the order of 24 h in all eukaryotic organisms, as well as in cyanobacteria. Mathematical models were initially...
Traditionally the study of host response to an infection has focussed on the effect of the pathogen on host health and the ability of the host immune system to clear the pathogen. In this paradigm the host experiences an initial reduction in health (assessed by suitable metrics e.g. temperature rise, weight loss, subjective feelings of ill health) as the pathogen load in the body increases....
Waning immunity is known to occur for some infectious diseases after natural infection and vaccination. We present a susceptible-infectious-recovered-susceptible (SIRS)-type transmission model that includes the waning and boosting of immunity. We study how the infection prevalence changes with differences in (i) the durations of infection- and vaccine-acquired immunity and (ii) the assumed...
Unobserved heterogeneity was introduced in 1920 as a modifier of individual hazards. The concept was termed frailty in demography to describe variation in individual longevity [1], and has been incorporated in methods for survival analysis. As the frailest individuals are removed earlier from a heterogeneous group, mean hazards appear to decrease over time – cohort selection – leading to some...
Atherosclerosis is among the leading causes of death worldwide due to its implication in heart attacks and strokes. The disease is characterised by the localised thickening of artery walls due to the buildup of fatty cholesterol-filled streaks. A key factor in determining whether an atherosclerotic plaque becomes problematic is the interplay between low density lipoprotein (LDL) and high low...
There are many benefits to incorporating coding into mathematics classrooms: students begin to think algorithmically about mathematics, students learn a transferable skill, and the courses can include more real-world, data-driven problems. However, bringing programming into the math curriculum presents challenges. Success and difficulties of integrating programming into the liberal arts...
Oncolytic viruses such as herpes simplex virus-1 (oHSV) are genetically modified to target and kill cancer cells while not harming healthy normal cells and are currently under multiple clinical trials for safety and efficacy [1]. Bortezomib is a peptide-based proteasome inhibitor and is an FDA-approved drug for myeloma and mantle cell lymphoma. Yoo et al. [2] have previously demonstrated...
Circadian clocks of many organisms consist of cell autonomous rhythms of gene expression in a pacemaker tissue. Negative feedback loops in clock gene regulation are responsible for the generation of the expression rhythms. One of the characteristics of the circadian clock is its phase responses to light input signals. A light signal changes the rates of biochemical reactions in the negative...
The parotid salivary gland consists of groups of acinar cells all transporting water into a lumen with a complex branched structure. In addition, each acinar cell itself has a complex spatial structure, with heterogenous spatial distributions of the channels that control water transport. The goal of our model is to determine the relationships between structure and function, both at the level...
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium...
Complex protein interaction networks complicate the understanding of what most promotes the rate of cancer progression. High dimensional data provides new insights into possible mechanisms for the proliferative nature of aggressive cancers, but these datasets often require fresh techniques and ideas for exploration and analysis. In this talk, we consider expression levels of tens of proteins...
The highly variable and synchronized production of large seed crops by plant populations, called masting or mast seeding, has been reported across a broad group of plant species. While there is consensus on the evolutionary drivers of masting, the proximate mechanisms are more controversial. Several hypotheses make predictions about the possible drivers of synchrony in masting species,...
Malaria is an infectious disease caused by parasites from genus Plasmodium that kills an average of a half a million people around the world annually. Plasmodium sporozoites are injected to humans by mosquitoes during their probing for blood. Injected sporozoites migrate to liver and invade hepatocytes. The liver stage that lasts 7 to 10 days is a target for vaccine development for...
Rotavirus is a viral disease - mainly transmitted by the fecal-oral mode - that is the leading cause of severe acute gastroenteritis among infants and children less than 5 years of age. The symptoms vary from mild to severe diarrhea with fever and vomiting that may produce rapid dehydration. In most of the cases, severe symptoms require hospitalization and eventually can lead to death.
There...
The Human African Trypanosomiasis (HAT) parasite, which causes African Sleeping Sickness, is transmitted by the tsetse fly as a vector. It has several possible hosts, including wild and domestic animals, who are not as negatively impacted by the disease as the human host. It has long been assumed that because domestic animals can be hosts for the parasite, that keeping domestic animals near...
Tuberculosis (TB) is the number one cause of death world-wide due to infection. 2 billion are infected and 10 million die each year. Understanding the immune response to TB is crucial to developing vaccines and improving treatment strategies. The immune response to infection with Mycobacterium tuberculosis (Mtb), the bacteria that causes TB, results in the formation of granulomas, spherical...
An ecological community is called structurally unstable if it is feasible (a positive equilibrium exists) but feasibility is sensitive to changes in parameters, external pressures, or species composition. Absent such sensitivities, a feasible community is called structurally stable.
Mathematically one can show that, due to amplification of perturbations through indirect interactions,...
Understanding lymphatic development is clinically relevant in applications from the viability of embryos, to chronic inflammation, to cancer metastasis. I specifically quantify the branching structure of developing lymphatic vessels and numerically solve for the flow through these vessels. Branching in arterial development is understood to consistently follow Murray’s Law, which states that...
Eating behaviour is known to influence our sleep-wake cycle, and the mechanism remains elusive. We have focused on RNA methylation that possibly connect metabolic and circadian systems. Recently, RNA methylation inhibition was found to elongate circadian period by as-yet-unknown mechanism. Since the regulatory network for circadian rhythm has been studied well, modelling can be a powerful tool...
Cancer presents one of the largest problems in our modern society. Understanding even the smallest aspect of this disease is immensely challenging due to its heterogeneous nature, a characteristic we term the 'same-same but different' nature of cancer. Heterogeneity can exist across tumour types depending on what stage the tumour is at or what organ the tumour exists in. There are many...
Although many of the most important academic problems lie at the interface of traditional disciplines, undergraduate students are rarely exposed to true interdisciplinary learning in their courses. Indeed, despite the necessity for mathematical and computational skills in modern biological and environmental research, most life science students lack any experience with higher-level mathematics...
The mathematical modelling of metastasis is a challenge. The occurrence of metastasis is basically random, hence the use of stochastic modelling seems appropriate. We introduce a stochastic process called branched random walk with settlement to derive equations for the expected number of particles, the variance, the furthest particle and the extinction probability. We are able to identify a...
The intermittent and synchronized production of a large amount of flowers and seeds is called masting or mast seeding. A family of resource budget models have been effective to evaluate proximate causes of masting. Applying recent advances in molecular and genetic studies about flowering time control to masting species is increasingly useful to unravel the underlying mechanism of masting. To...
Group A Streptococcus (GAS) is a ubiquitous human pathogen composed of over 230 different molecular sequence types. GAS is responsible for a broad spectrum of diseases - from superficial infections of the skin and throat to life-threatening invasive infections and post-infection sequelae. Even though most GAS infections are mild and easily treated, GAS-related disease remains a major cause...
In this talk, we will present several mathematical models of tuberculosis (TB) based on the reported data in the Republic of Korea and Philippines, and also propose the optimal treatment strategies depending on the various scenarios in each country. Korea has ranked the highest TB incidence among members of the Organization for Economic Cooperation and Development (OECD). TB is the sixth...
Inflamed tissues are densely populated with macrophages that influence the balance between inflammation amplification and resolution. Macrophages that accumulate immunogenic substances such as cholesterol (in atherosclerosis) and uric acid (in gout) become pro-inflammatory and drive inflammatory responses that never resolve.
I use in vitro experiments to show that substances dynamically...
Immune responses to cancer-including innate responses and immunotherapy-involve complex biochemical and biomechanical interactions between tumour cells and many types of immune cells. To date, most modelling has not focused on the spatial and mechanical effects of these interactions. In this talk, we will adapt PhysiCell (an open source platform for 3-D multicellular systems biology [1]) to...
Circadian (~ 24 h) rhythms can be synchronized to the earth’s 24 h periodic environment through external cues such as light - dark (LD) cycle. The misalignment of circadian timings with the external environment can lead to crucial physiological problems, such as jet lag, bipolar disorders and cancer. To treat the misalignment problem, we investigate the pharmacological manipulation of...
In this talk I will describe a series of population modelling computer labs used in an applied calculus class. The labs showcase different types of population growth, including Fibonacci, exponential, and logistic. Exponential growth is revisited as a differential equation, which is approximated by discrete growth, that is, approximation via tangent lines, using different time intervals. In...
Biologists are interested in functional performance based on complicated mechanical systems to understand how structures may have evolved. Since direct manipulation of these systems in an organism are not always possible, many functional systems are modelled using computational methods, such computational fluid dynamics. These functional systems and their simplified models involve many...
We propose and analyze a mathematical model of a vector-borne disease that includes vector feeding preference for carrier hosts and intrinsic incubation in hosts. Analysis of the model reveals the following novel results. We show theoretically and numerically that vector feeding preference for carrier hosts plays an important role for the existence of both the endemic equilibria and backward...
Some northern communities in Canada see inordinately high tuberculosis incidence compared to the rest of the country. Most of the affected locations are isolated First Nations communities and while this means that the usual argument of tuberculosis as an indicator disease of poverty is applicable, it does not explain the specifics of the situation. To try to understand the role of the various...
Carrie Diaz Eaton, Moderator and Education Subgroup Chair, Bates College, USA
As higher education moves towards evidence-based curriculum reform, assessing interdisciplinary thinking becomes a challenge for those in multidisciplinary frontiers. We will discuss how to best support SMB Education subgroup members. We will also introduce some resources for assessing interdisciplinary...
The process by which a skin wound heals is complicated and requires the concerted action of a large number of cell types, chemicals and fibres. There have been many attempts to mathematically describe the wound healing process using a variety of different mathematical approaches. In this talk, I will review some of the earlier mathematical models developed for wound healing and the biological...
There exists a growing body of empirical evidence that suggests biodiversity regulation – the emergence of dynamic equilibrium diversity – may be a common or even general feature of ecosystems. However a mechanistic understanding of what tends to constrain diversity in nature remains elusive. Here we introduce a metacommunity assembly model in which regional diversity converges on dynamic...
Monitoring the fluid status of end-stage renal disease (ESRD) patients remains an important aspect in hemodialysis. Recently, de los Reyes et al. developed a two-compartment model describing vascular refilling with ultrafiltration during short-term hemodialysis in ESRD patients. Ultrafiltration is taking out fluid from the vascular space; and vascular refilling occurs through the...
A common modelling technique to include stochastic effects in biochemical reaction networks is the use of discrete-state continuous time Markov chains. Analytic results for the resulting systems are rare and one often has to rely on stochastic simulation approaches to quantitatively probe their dynamics. Many conventional simulation methods, however, become prohibitively slow if the system is...
To date we have no understanding of why two patients with similar clinical stage and molecular profile would have different radiotherapy outcomes. Reliable biomarkers are direly needed to predict which patients will be cured, with the hope to de-escalate dose when possible or increase where necessary. It is increasingly appreciated that radiation can induce a robust antitumour immune response...
Modelling with real data in the classroom not only gives students a sense of why the mathematics matters, but it also gives them perspective on how messy the real world is and how we adapt our models to suit non-perfect data. We present a class activity and project for an introductory numerical methods course in which Calculus 1 and 2 are prerequisites. In the classroom we introduce curvature...
Maintaining regular and sufficient sleep is important to many aspects of human health. Mathematical models of human sleep/wake patterns have typically been trained against highly regular, prescribed schedules in healthy individuals under laboratory conditions or idealized versions of real-world work schedules. Consequently, most models are deterministic and do not capture measured...
Birth-death-movement processes, modulated by interactions between individuals, are fundamental to many biological processes such as development, repair and disease. Similar interactions are also relevant in ecology. A key feature of the movement of cells within in vivo environments are the interactions between motile cells and stationary obstacles, such as the extracellular matrix and...
HIV progression studies have asserted three stages: acute infection, chronic infection, and AIDS. We develop a model with three stages and include an infection class with non-uniform Highly Active Anti-Retroviral Treatment leading to viral suppression. Capturing the incidence rate of HIV in minority U.S. women requires a model stratified by race/ethnicity and sexual behaviour in addition to...
Bamboos are clonal plants that undergo mass flowering followed by simultaneous death after a long-term period of rhizomatous vegetative growth. The time to flowering after germination depends on species and shows a geographic cline in which it is short in tropical region and becomes longer as we move to northward into temperate region. As another geographic tendency in bamboo, rhizome systems...
Budding yeasts, such as Saccharomyces cerevisiae (baker's yeast), that are grown on a solid substrate are able to alter their growth pattern to suit the surrounding nutrient level. When nutrient is readily available, buds separate from the mother cell to produce colonies that appear close to circular when viewed from above. When nutrient is limited, the cells reproduce via the pseudohyphal...
Blood clots are physiologically degraded via a biochemical cascade initiated by tissue plasminogen activator (tPA). tPA, which is also used clinically to treat stroke, creates plasmin, the main protein involved in degradation. We explore the effects of tPA unbinding and diffusion on clot degradation. We propose that plasmin can “force” tPA to unbind from the clot, which has significant...
Making effective management decisions is challenging in multi-species, multi-threat systems because of uncertainty about the effects of different threats on different species. To inform management decisions, we often monitor species to detect spatial or temporal trends that can help us learn about threatening processes. However, which species to monitor and how to monitor to inform the...