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 interactions (for example, reactions). Mesoscopic (lattice-based) stochastic reaction-diffusion approaches divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment, while macroscopic models are often written in terms of mean-field reaction-diffusion partial differential equations for spatially varying concentrations.
I will discuss the development, analysis and applications of multiscale methods for spatio-temporal modelling of intracellular processes, which use (detailed) BD or MD simulations in localized regions of particular interest (in which accuracy and microscopic details are important) and a (less-detailed) coarser model in other regions in which accuracy may be traded for simulation efficiency [1,2,3]. I will discuss error analysis and convergence properties of the developed multiscale methods, their software implementation  and applications of these multiscale methodologies to modelling of intracellular calcium dynamics , actin dynamics [6,7] and DNA dynamics . I will also discuss the development of multiscale methods which couple MD and coarser stochastic models in the same dynamic simulation [3,9].
 M. Flegg, S.J. Chapman and R. Erban (2012). Two Regime Method for optimizing stochastic reaction-diffusion simulations. Journal of the Royal Society Interface 9: 859-868.
 B. Franz, M. Flegg, S.J. Chapman and R. Erban (2013). Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics. SIAM Journal on Applied Mathematics 73: 1224-1247.
 R. Erban (2014). From molecular dynamics to Brownian dynamics. Proceedings of the Royal Society A 470: 20140036.
 M. Robinson, S. Andrews and R. Erban (2015). Multiscale reaction-diffusion simulations with Smoldyn. Bioinformatics 31: 2406-2408.
 U. Dobramysl, S. Rudiger and R. Erban (2016). Particle-based multiscale modeling of calcium puff dynamics. Multiscale Modelling and Simulation 14: 997-1016.
 R. Erban, M. Flegg and G. Papoian (2014). Multiscale stochastic reaction-diffusion modelling: application to actin dynamics in filopodia. Bulletin of Mathematical Biology 76: 799-818.
 U. Dobramysl, G. Papoian and R. Erban (2016). Steric effects induce geometric remodeling of actin bundles in filopodia. Biophysical Journal 110: 2066-2075.
 E. Rolls, Y. Togashi and R. Erban (2017). Varying the resolution of the Rouse model on temporal and spatial scales: application to multiscale modelling of DNA dynamics. Multiscale Modelling and Simulation 15(4): 1672-1693.
 R. Erban (2016). Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics. Proceedings of the Royal Society A 472: 20150556.