Section: Research Program

Introduction

At small spatial scales, or at spatial scales of individual matter components, where heterogeneities in the medium occur, agent-based models are developed ( (Drasdo, Hoehme, Block, J. Stat. Phys., 2007), [75] , Dirk Drasdo's former associate team QUANTISS). Another approach, that is considered in the project-team MAMBA consists in considering gene expression at the individual level by stochastic processes (as in M. Sturrock et al., Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation, Journal of The Royal Society Interface, 2013) or by ordinary differential equations (as in A. Friedman et al, Asymptotic limit in a cell differentiation model with consideration of transcription, J. Diff. Eq., 2012), or by a mixed representation of Markov processes and ordinary differential equations (as in R. Yvinec et al., Adiabatic reduction of stochastic gene expression with jump Markov processes, J. Math. Biol., 2013.), the outputs of which quantify focused aspects of biological variability in a population of individuals (cells) under study.

Both these approaches complement the partial differential equation models considered on scales at which averages over the individual components behave sufficiently smoothly. Investigating the links between these models through scales is also part of our research (H. Byrne and D. Drasdo, Individual-based and continuum models of growing cell populations: a comparison, J. Math. Biol, 2009). Moreover, in order to quantitatively assess the adequacy between the biological phenomena we study and the mathematical models we use, we also develop inverse problem methods.