A conceptual and computational framework for modelling and understanding the non-equilibrium gene regulatory networks of mouse embryonic stem cells

Abstract

The capacity of pluripotent embryonic stem cells to differentiate into any cell type in the body makes them invaluable in the field of regenerative medicine. However, because of the complexity of both the core pluripotency network and the process of cell fate computation it is not yet possible to control the fate of stem cells. We present a theoretical model of stem cell fate computation that is based on Halley and Winkler’s Branching Process Theory (BPT) and on Greaves et al.’s agent-based computer simulation derived from that theoretical model. BPT abstracts the complex production and action of a Transcription Factor (TF) into a single critical branching process that may dissipate, maintain, or become supercritical. Here we take the single TF model and extend it to multiple interacting TFs, and build an agent-based simulation of multiple TFs to investigate the dynamics of such coupled systems. We have developed the simulation and the theoretical model together, in an iterative manner, with the aim of obtaining a deeper understanding of stem cell fate computation, in order to influence experimental efforts, which may in turn influence the outcome of cellular differentiation. The model used is an example of self-organization and could be more widely applicable to the modelling of other complex systems. The simulation based on this model, though currently limited in scope in terms of the biology it represents, supports the utility of the Halley and Winkler branching process model in describing the behaviour of stem cell gene regulatory networks. Our simulation demonstrates three key features: (i) the existence of a critical value of the branching process parameter, dependent on the details of the cistrome in question; (ii) the ability of an active cistrome to “ignite” an otherwise fully dissipated cistrome, and drive it to criticality; (iii) how coupling cistromes together can reduce their critical branching parameter values needed to drive them to criticality.

The recent advances in the mathematical modelling of human pluripotent stem cells

“…However, the parameters of such a model are difficult to estimate accurately [ 108 ]. More recently, PTFs have been modelled through branching processes [ 109 ]. A thorough review of the models of pluripotency is available [ 18 ], along with a review of computational modelling of the fate control of mouse embryonic stem cells, with many models transferable to hPSCs [ 105 ].…”

Report on Workshop: Planning the Future of Agent Simulation

“…On the first day of the workshop, participants presented their perspectives on the state of the art in simulation and simulation tools, introducing their existing work. On the application side, this included work using simulation in immunology (e.g., [1,7,11,13,15,17]), vascular biology (e.g., [4,5]), and synthetic biology [12], as well as in the social sciences [8] and, more generally, the evaluation of simulation results (e.g., [9,10]). Equally, Cosmo Tech, Slingshot Simulations, and the FLAME GPU Team presented on different approaches to high-performance simulation platforms that allow for domain specialization.…”

“…The CoSMoS process has been used in cell-level and immune systems research simulation: See, for instance, [1,7,11,13,15,17]. It proposes a principled approach that supports a close collaboration between domain experts and software engineers.…”

“…1. Re-engineering existing agent-based biological system applications, notably the CoSMoS simulations (above) and the work of Bentleyʼs Cellular Adaptive Behavior Lab at the Francis Crick Institute, 7 to support extension, further analysis, improved documentation, and so on.…”

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

“…In these models, the extracellular signals may vary according to the position of a cell within a spatial domain. It is possible that these complex mechanisms could also participate in defining the fate of SCs' progeny 5,[17][18][19][20][21][22][23][24][25] , where some of the spatial signals could be emanating from the organizer or other niche cells 1,2,[26][27][28][29][30][31][32][33][34][35] . Dynamical models of gene regulatory networks define an attractor landscape: a multidimensional and non-linear potential that restricts the possible transitions among the network attractors (cell types) 16,[36][37][38] .…”