scholarly journals Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

2021 ◽  
Author(s):  
Farida Ansari
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Growth Factor Receptor ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Biochemical Networks ◽  
Random Time Change ◽  
Simulation Strategy ◽  
Epidermal Growth ◽  
Exact Stochastic Simulation

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

scholarly journals Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

2021 ◽  
Author(s):  
Farida Ansari
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Growth Factor Receptor ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Biochemical Networks ◽  
Random Time Change ◽  
Simulation Strategy ◽  
Epidermal Growth ◽  
Exact Stochastic Simulation

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

scholarly journals APPROXIMATE EXPONENTIAL ALGORITHMS TO SOLVE THE CHEMICAL MASTER EQUATION

2015 ◽  
Vol 20 (3) ◽  
pp. 382-395
Author(s):  
Azam Mooasvi ◽  
Adrian Sandu
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Stochastic Simulation Algorithm ◽  
Approximate Solutions ◽  
Chemical Master Equation ◽  
Matrix Exponential ◽  
Stochastic Chemical Kinetics ◽  
Stochastic Simulation Algorithms ◽  
The Matrix ◽  
Simulation Algorithms

This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.

scholarly journals Delay chemical master equation: direct and closed-form solutions

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150049 ◽  
Author(s):  
Andre Leier ◽  
Tatiana T. Marquez-Lago
Keyword(s):  
Master Equation ◽  
Closed Form ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Kolmogorov Equation ◽  
Closed Form Solutions ◽  
Mrna Maturation ◽  
First Time ◽  
Nonlinear Markov Process ◽  
Reaction Schemes

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

scholarly journals Dynamical reorganization of transcriptional events governs robust Nanog heterogeneity

2019 ◽  
Author(s):  
Tagari Samanta ◽  
Sandip Kar
Keyword(s):  
Cell Fate ◽  
Stochastic Simulation ◽  
Transcriptional Regulatory Network ◽  
Mrna Level ◽  
Embryonic Stem ◽  
Stochastic Simulation Algorithm ◽  
Culture Conditions ◽  
Transcriptional Regulatory ◽  
Simulation Strategy ◽  
Fate Decision

Nanog maintains pluripotency of embryonic stem cells (ESC's), while demonstrating high expression heterogeneity within an ESC population. Intriguingly, in ESC's, the overall heterogeneity at the Nanog mRNA level under various culture conditions gets precisely partitioned into intrinsic (~45%) and extrinsic (~55%) fluctuations. However, the dynamical origin of such a robust transcriptional noise regulation, still remains illusive. Herein, we conceived a new stochastic simulation strategy centered around Gillespie's stochastic simulation algorithm to efficiently capture fluctuations of different origins that are operative within a simple Nanog transcriptional regulatory network. Our model simulations reconcile the strict apportioning of Nanog transcriptional fluctuation, while predicting possible experimental scenarios to avoid such an exact noise segregation. Importantly, model analyses reveal that different culture conditions essentially preserve the Nanog expression heterogeneity by altering the dynamics of transcriptional events. These insights will be essential to systematically maneuver cell-fate decision making events of ESC's for therapeutic applications.

scholarly journals On evolution of solution times for the chemical master equation of the enzymatic futile cycle

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Sergey V. Dolgov ◽  
Eugene E. Tyrtyshnikov
Keyword(s):  
Systems Biology ◽  
Computational Complexity ◽  
Tensor Product ◽  
Data Compression ◽  
Master Equation ◽  
Numerical Data ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Simulation Algorithm ◽  
Futile Cycle

AbstractWe investigate three tensor product numerical data compression techniques in solution of the chemical master equation for the enzymatic futile cycle and compare them with the previously reported results, obtained by the stochastic simulation algorithm. On this particular example from systems biology, we show the history how the newly proposed tensor product methods reduced the computational complexity of the futile cycle modelling from days on a HPC cluster to hours and even minutes on a workstation.

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