K-leap method for stochastic simulation of gene expression

2006 ◽  
Author(s):  
Xiaodong Cai ◽  
Zhouyi Xu
Keyword(s):  
Gene Expression ◽  
Stochastic Simulation

scholarly journals An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics

2011 ◽  
Vol 9 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Daniel A. Charlebois ◽  
Jukka Intosalmi ◽  
Dawn Fraser ◽  
Mads Kærn
Keyword(s):  
Gene Expression ◽  
Population Dynamics ◽  
Steady State ◽  
Stochastic Simulation ◽  
Molecular Level ◽  
Single Cells ◽  
Heterogeneous Population ◽  
Population Heterogeneity ◽  
Time Dependent ◽  
Cell Populations

AbstractWe present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steady-state and time-dependent analytical solutions for several scenarios, including steady-state and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within “bet-hedging” cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details and phenotypic variability.

scholarly journals Inferring single-cell gene expression mechanisms using stochastic simulation

2015 ◽  
Vol 31 (9) ◽  
pp. 1428-1435 ◽  
Author(s):  
Bernie J. Daigle ◽  
Mohammad Soltani ◽  
Linda R. Petzold ◽  
Abhyudai Singh
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Stochastic Simulation ◽  
Cell Gene Expression ◽  
Cell Gene

scholarly journals Stochastic Simulation to Visualize Gene Expression and Error Correction in Living Cells

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Kevin Y. Chen ◽  
Daniel M. Zuckerman ◽  
Philip C. Nelson
Keyword(s):  
Gene Expression ◽  
Experimental Data ◽  
Error Correction ◽  
Stochastic Simulation ◽  
Single Molecule ◽  
Stochastic Simulation Algorithm ◽  
Stochastic Error ◽  
Statistical Measures ◽  
Mean And Variance ◽  
Cellular Control

ABSTRACT Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential equation approach by generating typical system histories, instead of just statistical measures such as the mean and variance of a population. Simple simulations are now easy for students to construct from scratch—that is, without recourse to black-box packages. In some cases, their results can also be compared directly with single-molecule experimental data. After introducing the stochastic simulation algorithm, this article gives two case studies involving gene expression and error correction, respectively. For gene expression, stochastic simulation results are compared with experimental data, an important research exercise for biophysics students. For error correction, several proofreading models are compared to find the minimal components necessary for sufficient accuracy in translation. Animations of the stochastic error correction models provide insight into the proofreading mechanisms. Code samples and resulting animations showing results are given in the online Supplemental Material.

scholarly journals Inferring extrinsic noise from single-cell gene expression data using Approximate Bayesian Computation.

2015 ◽  
Author(s):  
Oleg Lenive ◽  
Paul DW Kirk ◽  
Michael PH Stumpf
Keyword(s):  
Gene Expression ◽  
Stochastic Simulation ◽  
Approximate Bayesian Computation ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Expression Data ◽  
Extrinsic Noise ◽  
Protein Molecules ◽  
Approximate Bayesian ◽  
Time Point

Background: Gene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed “intrinsic noise”, does not account for all the variability between genetically identical cells growing in a homogeneous environment. Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly. In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point. Results: To make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules. We employ this algorithm, approximate Bayesian computation, and published gene expression data for Escherichia coli to simultaneously infer the model's rate parameters and parameters describing extrinsic noise for 86 genes.

Modeling Gene Regulatory Networks with Delayed Stochastic Dynamics

2010 ◽  
pp. 198-218
Author(s):  
Andre S. Ribeiro ◽  
John J. Grefenstette ◽  
Stuart A. Kauffman
Keyword(s):  
Gene Expression ◽  
Stochastic Simulation ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Stochastic Dynamics ◽  
Single Gene ◽  
Stochastic Simulation Algorithm ◽  
Simulation Algorithm ◽  
Gene Regulatory ◽  
Modeling Strategy

We present a recently developed modeling strategy of gene regulatory networks (GRN) that uses the delayed stochastic simulation algorithm to drive its dynamics. First, we present experimental evidence that led us to use this strategy. Next, we describe the stochastic simulation algorithm (SSA), and the delayed SSA, able to simulate time-delayed events. We then present a model of single gene expression. From this, we present the general modeling strategy of GRN. Specific applications of the approach are presented, beginning with the model of single gene expression which mimics a recent experimental measurement of gene expression at single-protein level, to validate our modeling strategy. We also model a toggle switch with realistic noise and delays, used in cells as differentiation pathway switches. We show that its dynamics differs from previous modeling strategies predictions. As a final example, we model the P53-Mdm2 feedback loop, whose malfunction is associated to 50% of cancers, and can induce cells apoptosis. In the end, we briefly discuss some issues in modeling the evolution of GRNs, and outline some directions for further research.

scholarly journals Stochastic Simulation to Visualize Gene Expression and Error Correction in Living Cells

2018 ◽  
Author(s):  
Kevin Y. Chen ◽  
Daniel M. Zuckerman ◽  
Philip C. Nelson
Keyword(s):  
Gene Expression ◽  
Error Correction ◽  
Stochastic Simulation ◽  
Single Molecule ◽  
Stochastic Simulation Algorithm ◽  
Molecular Processes ◽  
Statistical Measures ◽  
Mean And Variance ◽  
The Mean ◽  
Cellular Control

AbstractStochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and variance of a population. Simple simulations are now easy for students to construct from scratch, that is, without recourse to black-box packages. In some cases, their results can also be compared directly to single-molecule experimental data. After introducing the stochastic simulation algorithm, this article gives two case studies, involving gene expression and error correction, respectively. Code samples and resulting animations showing results are given in the online supplement.

Sign in / Sign up

Export Citation Format

Share Document