Distributions for negative-feedback-regulated stochastic gene expression: Dimension reduction and numerical solution of the chemical master equation

2010 ◽  
Vol 264 (2) ◽  
pp. 377-385 ◽  
Author(s):  
Eduardo S. Zeron ◽  
Moisés Santillán
Keyword(s):  
Gene Expression ◽  
Dimension Reduction ◽  
Numerical Solution ◽  
Master Equation ◽  
Negative Feedback ◽  
Chemical Master Equation ◽  
Stochastic Gene Expression

scholarly journals Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

2021 ◽  
Vol 18 (178) ◽  
pp. 20210274
Author(s):  
Philipp Thomas ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Master Equation ◽  
Cell Size ◽  
Chemical Master Equation ◽  
Gillespie Algorithm ◽  
Agent Based Models ◽  
Extrinsic Noise ◽  
Gene Expression Noise ◽  
Agent Based ◽  
Expression Noise

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis , a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

scholarly journals Coordination of gene expression noise with cell size: extrinsic noise versus agent-based models of growing cell populations

2020 ◽  
Author(s):  
Philipp Thomas ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Master Equation ◽  
Cell Size ◽  
Chemical Master Equation ◽  
Simulation Algorithm ◽  
Agent Based Models ◽  
Extrinsic Noise ◽  
Gene Expression Noise ◽  
Agent Based ◽  
Expression Noise

The chemical master equation and the stochastic simulation algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled for through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise in a growing population. We find that the solution of the chemical master equation – including static extrinsic noise – exactly agrees with the one of the agent-based formulation when a simple condition on the network’s topology is met. We illustrate this result for a range of common gene expression networks. When these conditions are not met, we demonstrate using analytical solutions of the agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the effective master equation. Surprisingly, the latter distorts total noise in gene regulatory networks by at most 8% independently of network parameters. Our results highlight the accuracy of extrinsic noise modelling within the chemical master equation framework.

scholarly journals Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Rahul Kosarwal ◽  
Don Kulasiri ◽  
Sandhya Samarasinghe
Keyword(s):  
Master Equation ◽  
State Space ◽  
Performance Management ◽  
Numerical Solutions ◽  
De Novo ◽  
Exact Analytical Solution ◽  
Chemical Master Equation ◽  
The State ◽  
Biochemical System ◽  
Biochemical Systems

Abstract Background Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.

Delay model of circadian gene expression with two negative feedback loops

2006 ◽  
Vol 37 (5) ◽  
pp. 405-417
Author(s):  
Andreas Bohn ◽  
José R. Lopes ◽  
Luís A. Diambra ◽  
Luiz S. Menna-Barreto
Keyword(s):  
Gene Expression ◽  
Negative Feedback ◽  
Feedback Loops ◽  
Delay Model ◽  
Circadian Gene ◽  
Negative Feedback Loops
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