Statistical Abstraction for Multi-scale Spatio-Temporal Systems

Michaelides, Michalis P.; Hillston, Jane; Sanguinetti, Guido

doi:10.1007/978-3-319-66335-7_15

Cited by 6 publications

(2 citation statements)

References 17 publications

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“…The dynamics of these processes is therefore well described by stochastic Markov processes in continuous time with discrete state space [15,22,42]. While few-component or linear-kinetics systems [16] allow for exact analysis, in more complex system one often uses approximative methods [12], such as moment closure [4], linear-noise approximation [3,9], hybrid formulations [25,26,33], and multi-scale techniques [38,39].…”

Section: Introductionmentioning

confidence: 99%

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Çelik

Bokes

Singh

2020

Preprint

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Regulatory molecules such as transcription factors are often present at relatively small copy numbers in living cells. The copy number of a particular molecule fluctuates in time due to the random occurrence of production and degradation reactions. Here we consider a stochastic model for a self-regulating transcription factor whose lifespan (or time till degradation) follows a general distribution modelled as per a multidimensional phase-type process. We show that at steady state the protein copy-number distribution is the same as in a one-dimensional model with exponentially distributed lifetimes. This invariance result holds only if molecules are produced one at a time: we provide explicit counterexamples in the bursty production regime. Additionally, we consider the case of a bistable genetic switch constituted by a positively autoregulating transcription factor. The switch alternately resides in states of up-and downregulation and generates bimodal protein distributions. In the context of our invariance result, we investigate how the choice of lifetime distribution affects the rates of metastable transitions between the two modes of the distribution. The phase-type model, being non-linear and multi-dimensional whilst possessing an explicit stationary distribution, provides a valuable test example for exploring dynamics in complex biological systems.

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Section: Introductionmentioning

confidence: 99%

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Çelik

Bokes

Singh

2020

Preprint

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“…This paper is an extension of our previous conference paper [Michaelides et al 2017]. The major extension compared to the conference version consists in adapting the statistical framework to also handle agent-environment interactions, thereby closing the information loop and allowing for environment-mediated agent-agent interactions.…”

Section: Introductionmentioning

confidence: 99%

Statistical Abstraction for Multi-scale Spatio-temporal Systems

Michaelides

Hillston

Sanguinetti

2019

ACM Trans. Model. Comput. Simul.

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Modelling spatio-temporal systems exhibiting multi-scale behaviour is a powerful tool in many branches of science, yet it still presents significant challenges. Here, we consider a general two-layer (agent-environment) modelling framework, where spatially distributed agents behave according to external inputs and internal computation; this behaviour may include influencing their immediate environment, creating a medium over which agent-agent interaction signals can be transmitted. We propose a novel simulation strategy based on a statistical abstraction of the agent layer, which is typically the most detailed component of the model and can incur significant computational cost in simulation. The abstraction makes use of Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning, to estimate the agent’s behaviour given the environmental input. We show on two biological case studies how this technique can be used to speed up simulations and provide further insights into model behaviour.

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Bayesian Abstraction of Markov Population Models

Bortolussi

Cairoli

2019

Quantitative Evaluation of Systems

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Markov Population Models are a widespread formalism, with applications in Systems Biology, Performance Evaluation, Ecology, and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when simulations have to be performed in a multi-scale model (e.g. simulating individual cells in a tissue). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous work [3] and constructing an approximate kernel for a Markov process in continuous space and discrete time, capturing the evolution at fixed ∆t time steps. This kernel is learned automatically from simulations of the original model. Differently form [3], which relies on deep neural networks, we explore here a Bayesian density regression approach based on Dirichlet processes, which provides a principled way to estimate uncertainty.

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Statistical Abstraction for Multi-scale Spatio-Temporal Systems

Cited by 6 publications

References 17 publications

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Statistical Abstraction for Multi-scale Spatio-temporal Systems

Bayesian Abstraction of Markov Population Models

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