scholarly journals Finite state projection based bounds to compare chemical master equation models using single-cell data

2016 ◽  
Vol 145 (7) ◽  
pp. 074101 ◽  
Author(s):  
Zachary Fox ◽  
Gregor Neuert ◽  
Brian Munsky
Keyword(s):  
Master Equation ◽  
Single Cell ◽  
Chemical Master Equation ◽  
Finite State ◽  
Cell Data

Modeling Stochastic Gene Regulatory Networks Using Direct Solutions of Chemical Master Equation and Rare Event Sampling

2016 ◽  
pp. 80-122
Author(s):  
Youfang Cao ◽  
Anna Terebus ◽  
Jie Liang
Keyword(s):  
Master Equation ◽  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Rare Event ◽  
Planck Equation ◽  
Chemical Master Equation ◽  
Copy Numbers ◽  
Finite State ◽  
Gene Regulatory

Stochasticity plays important roles in many biological networks. A fundamental framework for studying the full stochasticity is the Discrete Chemical Master Equation (dCME). Under this framework, the combination of copy numbers of molecular species defines the microstate of the molecular interactions in the network. The probability distribution over these microstates provide a full description of the properties of a stochastic molecular network. However, it is challenging to solve a dCME. In this chapter, we will first discuss how to derive approximation methods including Fokker-Planck equation and the chemical Langevin equation from the dCME. We also discuss the widely used stochastic simulation method. After that, we focus on the direct solutions to the dCME. We first discuss the Finite State Projection (FSP) method, and then introduce the recently developed finite buffer method (fb-dCME) for directly solving both steady state and time-evolving probability landscape of dCME. We show the advantages of the fb-dCME method using two realistic gene regulatory networks.

scholarly journals Identification of Gene Regulation Models from Single-Cell Data

2017 ◽  
Author(s):  
Lisa Weber ◽  
William Raymond ◽  
Brian Munsky
Keyword(s):  
Gene Regulation ◽  
Single Cell ◽  
Nuclear Translocation ◽  
Model Fitting ◽  
Simulated Data ◽  
Stochastic Simulations ◽  
Heterogeneous Processes ◽  
Finite State ◽  
Regulation Model ◽  
Cell Data

AbstractIn quantitative analyses of biological processes, one may use many different scales of models (e.g., spatial or non-spatial, deterministic or stochastic, time-varying or at steady-state) or many different approaches to match models to experimental data (e.g., model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ Matlab and Python software to consider a time-dependent input signal (e.g., a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g., deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast [1] and human cells [2]‡.PACS numbers: 87.10.+e, 87.15.Aa, 05.10.Gg, 05.40.Ca,02.50.-rSubmitted to: Phys. Biol.

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