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

Fox, Zachary; Neuert, Gregor; Munsky, Brian

doi:10.1063/1.4960505

Cited by 38 publications

(56 citation statements)

References 23 publications

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“…78 For example, the reduced models considered here achieved levels of accuracy (i.e., relative errors of 10 −5 or less) that are much higher than one would expect to be necessary to compare models in light of far less accurate data. In light of this finding and the fact that parameter discrimination can be achieved at different levels of accuracy for different combinations of models and data, 79 we suspect that it could be advantageous to build less accurate models that can be evaluated in less time.…”

Section: Discussionmentioning

confidence: 99%

Bayesian estimation for stochastic gene expression using multifidelity models

Fox

Baetica

et al. 2018

Preprint

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The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

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Section: Discussionmentioning

confidence: 99%

Bayesian estimation for stochastic gene expression using multifidelity models

Fox

Baetica

et al. 2018

Preprint

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“…The methodology requires solving only a sparse system of ODEs, which can be considerably more efficient than performing large numbers of coupled simulations. Moreover, the method directly provides the precise probability distributions of cell responses, which can be used directly to compute the likelihood that observed experimental heterogeneity data is from a proposed combination of model and parameters [25, 28, 29]. For these reasons, it is expected that the pFSP will become a valuable tool to fit and predict experimentally measured single-cell heterogeneity in fluctuating population sizes.…”

Section: Discussionmentioning

confidence: 99%

“…The particular advantage of the FSP approach is that it can directly and systematically compare stochastic biochemical models to the type of single-cell data that is readily measured using flow cytometry or fluorescence microscopy [25], and as a result the FSP has seen substantial success in the fitting and predicting of single-cell molecular distributions in bacterial [26, 27], yeast [28], and human [29] cells. However, in each of these cases, the population size has been assumed to be constant, and little attention has been given to adapt the FSP approach to explore the coupling of population growth and discrete stochastic molecular dynamics.…”

Section: Methodsmentioning

confidence: 99%

The finite state projection approach to analyze dynamics of heterogeneous populations

Johnson

Munsky

2017

Phys. Biol.

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Population modeling aims to capture and predict the dynamics of cell populations in constant or fluctuating environments. At the elementary level, population growth proceeds through sequential divisions of individual cells. Due to stochastic effects, populations of cells are inherently heterogeneous in phenotype, and some phenotypic variables have an effect on division or survival rates, as can be seen in partial drug resistance. Therefore, when modeling population dynamics where the control of growth and division is phenotype dependent, the corresponding model must take account of the underlying cellular heterogeneity. The finite state projection (FSP) approach has often been used to analyze the statistics of independent cells. Here, we extend the FSP analysis to explore the coupling of cell dynamics and biomolecule dynamics within a population. This extension allows a general framework with which to model the state occupations of a heterogeneous, isogenic population of dividing and expiring cells. The method is demonstrated with a simple model of cell-cycle progression, which we use to explore possible dynamics of drug resistance phenotypes in dividing cells. We use this method to show how stochastic single-cell behaviors affect population level efficacy of drug treatments, and we illustrate how slight modifications to treatment regimens may have dramatic effects on drug efficacy.

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“…Because the CME has no exact solution for most models, we employ the finite state projection (FSP) method to approximate the CME solution and to estimate the full joint probability distributions for gene switching behavior and transcript accumulation [20]. Several recent reviews of the FSP approach and its applications can be found at [14,21,22,23]. A key advantage of the CME and FSP formulation is that they provide systematic approaches to compute and compare the likelihood of data arising from multiple models [1,10,21].…”

Section: A Standard Computational Toolbox For Quantitative Biologymentioning

confidence: 99%

“…Several recent reviews of the FSP approach and its applications can be found at [14,21,22,23]. A key advantage of the CME and FSP formulation is that they provide systematic approaches to compute and compare the likelihood of data arising from multiple models [1,10,21]. With this in mind, we use the Metropolis-Hastings algorithm in conjunction with the FSP analysis to attain more precise constraints on the parameters when fit to simulated data [11].…”

Section: A Standard Computational Toolbox For Quantitative Biologymentioning

confidence: 99%

Identification of Gene Regulation Models from Single-Cell Data

Weber

Raymond

Munsky

2017

Preprint

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Abstract. In 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] ‡.

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

Cited by 38 publications

References 23 publications

Bayesian estimation for stochastic gene expression using multifidelity models

Bayesian estimation for stochastic gene expression using multifidelity models

The finite state projection approach to analyze dynamics of heterogeneous populations

Identification of Gene Regulation Models from Single-Cell Data

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