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Stochastic Hybrid Systems in Cellular Neuroscience.

ABSTRACT: We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators.

SUBMITTER: Bressloff PC

PROVIDER: S-EPMC6104574 | biostudies-other | 2018 Aug

REPOSITORIES: biostudies-other

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Stochastic Hybrid Systems in Cellular Neuroscience.

Bressloff Paul C PC Maclaurin James N JN

Journal of mathematical neuroscience 20180822 1

We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast ...[more]

PMID: 30136005

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Project description:BackgroundThe wet-lab synthesis of the simplest forms of life (minimal cells) is a challenging aspect in modern synthetic biology. Quasi-cellular systems able to produce proteins directly from DNA can be obtained by encapsulating the cell-free transcription/translation system PURESYSTEM(PS) in liposomes. It is possible to detect the intra-vesicle protein production using DNA encoding for GFP and monitoring the fluorescence emission over time. The entrapment of solutes in small-volume liposomes is a fundamental open problem. Stochastic simulation is a valuable tool in the study of biochemical reaction at nanoscale range. QDC (Quick Direct-Method Controlled), a stochastic simulation software based on the well-known Gillespie's SSA algorithm, was used. A suitable model formally describing the PS reactions network was developed, to predict, from inner species concentrations (very difficult to measure in small-volumes), the resulting fluorescence signal (experimentally observable).ResultsThanks to suitable features specific of QDC, we successfully formalized the dynamical coupling between the transcription and translation processes that occurs in the real PS, thus bypassing the concurrent-only environment of Gillespie's algorithm. Simulations were firstly performed for large liposomes (2.67µm of diameter) entrapping the PS to synthetize GFP. By varying the initial concentrations of the three main classes of molecules involved in the PS (DNA, enzymes, consumables), we were able to stochastically simulate the time-course of GFP-production. The sigmoid fit of the GFP-production curves allowed us to extract three quantitative parameters which are significantly dependent on the various initial states. Then we extended this study for small-volume liposomes (575 nm of diameter), where it is more complex to infer the intra-vesicle composition, due to the expected anomalous entrapment phenomena. We identified almost two extreme states that are forecasted to give rise to significantly different experimental observables.ConclusionsThe present work is the first one describing in the detail the stochastic behavior of the PS. Thanks to our results, an experimental approach is now possible, aimed at recording the GFP production kinetics in very small micro-emulsion droplets or liposomes, and inferring, by using the simulation as a reverse-engineering procedure, the internal solutes distribution, and shed light on the still unknown forces driving the entrapment phenomenon.

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Stochastic Hybrid Systems in Cellular Neuroscience.

Publications

Stochastic Hybrid Systems in Cellular Neuroscience.

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