Sensitivity Analysis for Multiscale Stochastic Reaction Networks Using Hybrid Approximations

Gupta, Ankit; Khammash, Mustafa

doi:10.1007/s11538-018-0521-4

Cited by 9 publications

(16 citation statements)

References 39 publications

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“…all model parameters without any extra effort. Such parametric sensitivities are important for many applications, such as evaluating a network’s robustness properties [40] or identifying its critical components [41], but they are even more difficult to estimate than solutions to the CME [23, 24, 25, 26, 27, 28, 29, 30, 31].…”

Section: Discussionmentioning

confidence: 99%

“…Denoting the θ -dependent CTMC as ( X θ ( t )) t ≥0 , it is often of interest to compute the parametric sensitivity of the observed output at time T . Such sensitivity values are important for many applications and their direct calculation is generally impossible but a number of simulation-based approaches have recently been developed to provide efficient numerical estimation of these sensitivity values; we mention only [23, 24, 25, 26, 27, 28, 29, 30, 31].…”

Section: Preliminariesmentioning

confidence: 99%

“…all model parameters. Estimating these parametric sensitivities is important for many applications, but it is considered a difficult problem towards which a lot of research effort has recently been directed [23,24,25,26,27,28,29,30,31]. This paper is organised as follows.…”

Section: Introductionmentioning

confidence: 99%

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DeepCME: A deep learning framework for solving the Chemical Master Equation

Gupta

Schwab

Khammash

2021

Preprint

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Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov's forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for solving high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov's backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) and is algorithmically based on reinforcement learning. It only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the "policy function". This allows not just the numerical approximation of the CME solution but also of its sensitivities to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

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Section: Discussionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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DeepCME: A deep learning framework for solving the Chemical Master Equation

Gupta

Schwab

Khammash

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

2021

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Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov’s forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov’s backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the “policy function”. This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

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“…To highlight Dan Gillespie's impact on related fields, this special issue also features contributions that are related to his work from other areas, such as the network-free simulation method (Suderman et al 2018), rare event analysis (Roh 2018), sensitivity analysis for multiscale stochastic systems (Gupta and Khammash 2018), and an application of stochastic dynamics to simulation of eukaryotic flagellar growth (Rathinam and Sverchkov 2018).…”

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Stochastic Simulation of Biochemical Systems: In Memory of Dan T. Gillespie’s contributions

2019

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sad news hit all of us in the research communities of computational biology, stochastic simulation and applied physics. Our beloved friend, Dan T. Gillespie, a research physicist best known for the stochastic simulation algorithm (SSA, also known as the Gillespie Algorithm), passed away at his home in Castaic California at the age of 78.The impact of Dan Gillespie's work on the field of stochastic physics, computational biology and other related areas has been huge. When he first presented his original work in Gillespie (1976), it was called "completely wrong" by some prominent researchers in the field of chemistry. Certainly, it was far ahead of its time. In the late 1990s, it came to light that intrinsic stochasticity, arising from extremely small populations of key molecular species, was playing an important role in cell biology. The Gillespie algorithm was perfectly suited for simulating these systems. Since that time, it has been widely used in cell biology. Dan Gillespie's foundational publications would eventually receive over ten thousand citations, and he was well recognized as one of the founders of the field of stochastic physics in biology. His research contributions spanned a wide range of fields, including cloud physics, random variable theory, Brownian motion, Markov process theory, electrical noise, light scattering in aerosols, and quantum mechanics.The contributions in this special issue come from researchers working in many different disciplines that have benefitted from Dan Gillespie's pioneering work. The Gillespie algorithm (Gillespie 1976(Gillespie , 1977 is an important modeling and simulation method, but it also suffers from inefficiency when applied to large scale systems. He and his collaborators developed different methods to improve the algorithm, such as the tau-leaping method (Gillespie 2001;Rathinam et al. 2003;Cao et al. 2005b), and the

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Sensitivity Analysis for Multiscale Stochastic Reaction Networks Using Hybrid Approximations

Cited by 9 publications

References 39 publications

DeepCME: A deep learning framework for solving the Chemical Master Equation

DeepCME: A deep learning framework for solving the Chemical Master Equation

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

Stochastic Simulation of Biochemical Systems: In Memory of Dan T. Gillespie’s contributions

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