Hybrid CME–ODE method for efficient simulation of the galactose switch in yeast

Abstract

It is well known that stochasticity in gene expression is an important source of noise that can have profound effects on the fate of a living cell. In the galactose genetic switch in yeast, the unbinding of a transcription repressor is induced by high concentrations of sugar particles activating gene expression of sugar transporters. This response results in high propensity for all reactions involving interactions with the metabolite. The reactions for gene expression, feedback loops and transport are typically described by chemical master equations (CME). Sampling the CME using the stochastic simulation algorithm (SSA) results in large computational costs as each reaction event is evaluated explicitly. To improve the computational efficiency of cell simulations involving high particle number systems, the authors have implemented a hybrid stochastic–deterministic (CME–ODE) method into the publically available, GPU‐based lattice microbes (LM) software suite and its python interface pyLM. LM and pyLM provide a convenient way to simulate complex cellular systems and interface with high‐performance RDME/CME/ODE solvers. As a test of the implementation, the authors apply the hybrid CME‐ODE method to the galactose switch in Saccharomyces cerevisiae, gaining a 10–50× speedup while yielding protein distributions and species traces similar to the pure SSA CME.

Generating Chromosome Geometries in a Minimal Cell From Cryo-Electron Tomograms and Chromosome Conformation Capture Maps

“…Computational modeling of spatially-resolved kinetics in Syn3A is done by simulating the reaction-diffusion master equation (RDME) in Lattice Microbes (LM) (Roberts et al, 2013;Hallock et al, 2014;Earnest et al, 2017Earnest et al, , 2018Bianchi et al, 2018) using a stochastic simulation algorithm. When using the RDME, physical space is discretized into a cubic lattice representation.…”

The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

“…The model is not molecularly detailed, i.e., it does not model individual proteins and their interactions. The model also does not consider the stochastic nature of individual gene expression and protein synthesis [10][11][12][13]. Rather, we model the overall population of proteins and ribosomes, and therefore is a coarsegrained cell scale model.…”

Fundamental behaviors emerge from simulations of a living minimal cell

“…The first term is the chemical master equation (CME) probabilistic description of the subvolume-localized reactions for every subvolume in the system and the second term is the diffusion operator D for each particle type a in the x, y, and z directions specified by i, j, and k. For clarity, within the context of the spatially-resolved simulations, we will use the term local CME to describe the modeling of subvolume-localized stochastic reactions and the term global CME to describe the modeling of cell-wide stochastic reactions between species assumed to be well-stirred in the full cellular volume. In the whole-cell simulations presented in this study, we combine the above simulation methods with ordinary differential equation (ODE) solvers in hybrid methods that use the results of each method to update the particle counts of the subsequent method in a backward-updating fashion (Bianchi et al, 2018), which we present schematically in Figure S3. LM allows for periodic communication between its stochastic CME and RDME solvers and other simulation methods, such as an ordinary differential equations solver for metabolic reactions.…”