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SUMMARY:Statistical inference for parameters of biochemical networks
DTSTART;VALUE=DATE-TIME:20180711T020000Z
DTEND;VALUE=DATE-TIME:20180711T023000Z
DTSTAMP;VALUE=DATE-TIME:20220121T052825Z
UID:indico-contribution-16-38@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Grzegorz Rempała (The Ohio State University)\nThe i
nference for the reaction rates in chemical networks is often challenging
due to intrinsic and extrinsic biological noise\, missing data and lack o
f 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 S
IR and Michaelis Menten models will be used as examples to illustrate br
oader points.\n\nhttps://conferences.maths.unsw.edu.au/event/2/contributio
ns/38/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/38/
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SUMMARY:Function central limit theorem for Susceptible-Infected process on
configuration model graphs: Further insights into the accuracy of the cor
relation equations
DTSTART;VALUE=DATE-TIME:20180711T010000Z
DTEND;VALUE=DATE-TIME:20180711T013000Z
DTSTAMP;VALUE=DATE-TIME:20220121T052825Z
UID:indico-contribution-16-16@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Wasiur Rahman Khuda Bukhsh (Technische Universität
Darmstadt)\nWe 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 grap
h nodes into two compartments\, namely\, S and I\, denoting susceptible an
d infected nodes\, respectively. In addition to the sizes of these two com
partments\, we study counts of SI-edges (those connecting a susceptible an
d an infected node)\, and SS-edges (those connecting two susceptible nodes
). We describe the dynamical process in terms of these counts and present
a functional central limit theorem (FCLT) for them when the number of node
s in the random graph grows to infinity. To be precise\, we show that thes
e counts\, when appropriately scaled\, converge weakly to a continuous Gau
ssian vector semimartingale process in the space of vector-valued càdlàg
functions endowed with the Skorohod topology. Based on the results obtain
ed\, we further investigate the accuracy of the so-called correlation equa
tions from ecology literature. We show that for a certain class of degree
distributions\, called Poisson-type (PT) distributions\, the pair approxim
ation approach is exact in the sense that it correctly estimates the limit
ing first order moments of the various count variables.\n\nhttps://confere
nces.maths.unsw.edu.au/event/2/contributions/16/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/16/
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SUMMARY:An accurate and efficient estimation of enzyme kinetics using Baye
sian approach
DTSTART;VALUE=DATE-TIME:20180711T003000Z
DTEND;VALUE=DATE-TIME:20180711T010000Z
DTSTAMP;VALUE=DATE-TIME:20220121T052825Z
UID:indico-contribution-16-17@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Boseung Choi (Korea University Sejong Campus)\nChara
cterizing enzyme kinetics is critical to understand cellular systems and t
o utilize enzymes in industry. To estimate enzyme kinetics from reaction p
rogress curves of substrates\, the Michaelis-Menten equation has been wide
ly used for a century. However\, this canonical approach works in a limite
d condition such as a large excess of substrate over enzyme. Even when suc
h condition is satisfied\, identifiability of parameters is not guaranteed
\, and criteria for the identifiability is often not easy to be tested. T
o overcome these limits of the canonical approach\, here we propose a Baye
sian inference based on an equation derived with the total quasi-steady st
ate approximation. Estimates obtained with this approach have a little bia
s for any combination of enzyme and substrate concentrations in contrast t
o the canonical approach. Furthermore\, with our new approach\, an optimal
experiment leading to maximal increase of the identifiability can be easi
ly designed by simply analyzing scatter plots of estimates. Indeed\, with
this optimal protocol\, kinetics of diverse enzymes with disparate catalyt
ic efficiencies such as chymotrypsin\, fumarase and urease can be accurate
ly estimated from a minimal number of experimental data. A Bayesian infere
nce computational package that performs such accurate and efficient enzyme
kinetics is provided in this work.\n\nhttps://conferences.maths.unsw.edu.
au/event/2/contributions/17/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/17/
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SUMMARY:Quasi-steady-state approximations in the stochastic models of enzy
me kinetics
DTSTART;VALUE=DATE-TIME:20180711T013000Z
DTEND;VALUE=DATE-TIME:20180711T020000Z
DTSTAMP;VALUE=DATE-TIME:20220121T052825Z
UID:indico-contribution-16-18@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Hye-Won Kang (University of Maryland\, Baltimore Cou
nty)\nIn this talk I will introduce several quasi steady-state approximati
ons (QSSAs) applied to the stochastic enzyme kinetics models. Different as
sumptions about chemical species abundance and reaction rates lead to the
standard QSSA (sQSSA)\, the total QSSA (tQSSA)\, and the reverse QSSA (rQS
SA) approximations. These three QSSAs have been widely studied in the lite
rature in deterministic ordinary differential equation (ODE) settings and
several sets of conditions for their validity have been proposed. By using
multiscaling techniques for stochastic chemical reaction networks\, these
conditions for deterministic QSSAs largely agree with the ones for QSSAs
in the large volume limits of the underlying stochastic enzyme kinetic net
works. I will illustrate how our approach extends to more complex stochast
ic networks like\, for instance\, the enzyme-substrate-inhibitor system. T
his is joint work with Wasiur Khuda Bukhsh\, Heinz Koeppl\, and Grzegorz R
empała.\n\nhttps://conferences.maths.unsw.edu.au/event/2/contributions/18
/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/18/
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