STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

Hepburn, Iain; Chen, Weiliang; Wils, Stefan; Schutter, Erik De

doi:10.1186/1752-0509-6-36

Cited by 141 publications

(144 citation statements)

References 63 publications

(88 reference statements)

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“…In principle, the SSA can be applied to arbitrarily complex systems with multiple types of particles and possibly spatial degrees of freedom. Consequently, the algorithm is commonly used in biological studies [138,139,142] and extensions of it have been implemented in various simulation packages [250][251][252][253][254][255][256][257]. A fast but only approximate alternative to the SSA for the simulation of processes evolving on multiple time scales is τ -leaping [78,249,[258][259][260][261][262][263][264][265][266][267].…”

Section: Discussionmentioning

confidence: 99%

“…Efficient variations of the above "direct" version of the SSA are, for example, described in [78,[247][248][249]. Algorithms for the fast simulation of biochemical networks or processes with spatial degrees of freedom are implemented in the simulation packages [250][251][252][253][254][255][256][257]. The evaluation of the average A = n A(n)p(t, n|·) of an observable A typically requires the computation of a larger number of sample paths.…”

Section: Analytical and Numerical Methods For The Solution Of Master mentioning

confidence: 99%

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Master equations and the theory of stochastic path integrals

2017

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Abstract. This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of masters equations most often rely on lownoise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a "generating functional", which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a "forward" and a "backward" path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit. arXiv:1609.02849v2 [cond-mat...

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Section: Discussionmentioning

confidence: 99%

Section: Analytical and Numerical Methods For The Solution Of Master mentioning

confidence: 99%

Master equations and the theory of stochastic path integrals

2017

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“…Cerebellar long-term potentiation (LTP) was not considered. The model was solved stochastically and deterministically using STEPS (http://steps.sourceforge.net/), a well validated simulator (Hepburn et al, 2012) that implements the Stochastic Simulation Algorithm (SSA) (Gillespie, 1977). The model script and a table listing all reactions and all model parameters with full reference to the relevant data are available at ModelDB (http://senselab.med.…”

Section: Methodsmentioning

confidence: 99%

A Stochastic Signaling Network Mediates the Probabilistic Induction of Cerebellar Long-Term Depression

Antunes

Schutter²

2012

Journal of Neuroscience

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Many cellular processes involve a small number of molecules and undergo stochastic fluctuations in their levels of activity. Cerebellar long-term depression (LTD) is a form of synaptic plasticity expressed as a reduction in the number of synaptic AMPA receptors (AMPARs) in Purkinje cells. We developed a stochastic model of the LTD signaling network, including a PKC-ERK-cPLA 2 positive feedback loop and mechanisms of AMPAR trafficking, and tuned the model to replicate calcium uncaging experiments. The signaling network activity in single synapses switches between two discrete stable states (LTD and non-LTD) in a probabilistic manner. The stochasticity of the signaling network causes threshold dithering and allows at the macroscopic level for many different and stable mean magnitudes of depression. The probability of LTD occurrence in a single spine is only modulated by the concentration and duration of the signal used to trigger it, and inputs with the same magnitude can give rise to two different responses; there is no threshold for the input signal. The stochasticity is intrinsic to the signaling network and not mostly dependent on noise in the calcium input signal, as has been suggested previously. The activities of the ultrasensitive ERK and of cPLA 2 undergo strong stochastic fluctuations. Conversely, PKC, which acts as a noise filter, is more constantly activated. Systematic variation of the biochemical population size demonstrates that threshold dithering and the absence of spontaneous LTD depend critically on the number of molecules in a spine, indicating constraints on spine size in Purkinje cells.

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“…As a result stochastic discrete-event simulation has emerged as a method to complement differential equations in biochemical simulations [6] [7].…”

Section: Introductionmentioning

confidence: 99%

Parallel Stochastic Discrete Event Simulation of Calcium Dynamics in Neuron

Patoary

Tropper

McDougal

et al. 2019

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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the correctness and performance of NTW by comparing it to a sequential deterministic simulation in NEURON. The derivation of a discrete event calcium wave model using the stochastic IP 3 R structure is one of my main scientific contributions of this thesis. This newly derived stochastic discrete event calcium wave model is described in chapter-5. In high performance issue, a dynamic load balancing algorithm and a dynamic window control algorithm for NTW was also developed for the stochastic calcium wave model. We use Q-learning to determine the basic control parameters of the algorithm. Prof. Tropper motivated me to employ Q-learning to optimize the performance of NTW in calcium wave simulation. Developing such an intelligent dynamic load balancing algorithm with dynamic window control is another research contribution of this thesis. All algorithms are described in chapter 6. vi ABSTRACTThe intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and the calcium concentrations are so low that one molecule diffusing into the compartment can make a nontrivial difference in calcium concentration. Such events can affect dynamics discretely in such a way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. My research focuses on the development of a high performance parallel discrete event simulation environment, NTW , which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-cellular calcium signaling. We make use of two models, a calcium buffer model and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a sequential deterministic simulation in NEURON. NEURON is a framework for simulating neurons which is used by neuroscientists world-wide. Our work is part of the NEURON project and has the long term goal of developing a multiscale simulation for large scale neuronal networks. We derived a discrete event calcium wave model from a deterministic model using the stochastic inositol 1,4,5-trisphosphate receptors, IP 3 R, structure. A dynamic load balancing algorithm and a dynamic window control algorithm for NTW was also developed for the stochastic calcium wave model.We make use of Q-learning to determine the basic control parameters of the algorithm.

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STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

Cited by 141 publications

References 63 publications

Master equations and the theory of stochastic path integrals

Master equations and the theory of stochastic path integrals

A Stochastic Signaling Network Mediates the Probabilistic Induction of Cerebellar Long-Term Depression

Parallel Stochastic Discrete Event Simulation of Calcium Dynamics in Neuron

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