Dynamic Partitioning of Large Discrete Event Biological Systems for Hybrid Simulation and Analysis

Neogi, Natasha A.

doi:10.1007/978-3-540-24743-2_31

Cited by 22 publications

(32 citation statements)

References 14 publications

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“…In this paper, we construct a stochastic hybrid model for the lactose regulation system using the work of Yildirim and Mackey as a starting point. Stochasticity in the system naturally arises due to the low copy numbers of molecules involved in the reaction within the cell [10], [37]. In this situation, a model where the reactions are viewed as discrete Poisson random processes is more accurate than a deterministic one [27].…”

Section: B Lactose Metabolism Control Networkmentioning

confidence: 99%

“…The model is based on the idea that the messenger RNA and the -galactosidase are expressed as molecule counts that evolve following some Poisson processes, while the other substances, internal TMG and permease , are expressed as chemical concentrations that evolve following deterministic ODE. A similar approach, i.e., part stochastic and part deterministic simulation for chemical processes, is reported in [37]. The reason behind this idea is that a fully stochastic model is computationally expensive, while a hybrid model already demonstrates the stochastic noise that is lacking in the deterministic model.…”

Section: B Stochastic Modelmentioning

confidence: 99%

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Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System ofEscherichia Coli

Julius

Halász

Sakar

et al. 2008

IEEE Trans. Automat. Contr.

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Abstract-In this paper, we present a comprehensive framework for stochastic modeling, model abstraction, and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models. We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous-time Markov chain. The second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result.

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Section: B Lactose Metabolism Control Networkmentioning

confidence: 99%

Section: B Stochastic Modelmentioning

confidence: 99%

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System ofEscherichia Coli

Julius

Halász

Sakar

et al. 2008

IEEE Trans. Automat. Contr.

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“…This idea has been exploited in various hybrid schemes [22][23][24][25][26][27][28][29][30][31][32][33] , which mostly differ in the way that the partitioning is performed and the way in which the hybrid system is simulated. The partitioning of the species and/or reactions is either done manually or certain threshold-values are chosen for different properties of the system, e.g.…”

Section: Introductionmentioning

confidence: 99%

Adaptive hybrid simulations for multiscale stochastic reaction networks

Hepp

Gupta

Khammash

2015

The Journal of Chemical Physics

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The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases these simulations can take an impractical amount of computational time. Therefore many methods have been developed that approximate the Stochastic Process underlying the Chemical Master Equation. Prominent strategies are Hybrid Models that regard the firing of some reaction channels as being continuous and applying the quasi-stationary assumption to approximate the dynamics of fast subnetworks. However as the dynamics of a Stochastic Reaction Network changes with time these approximations might have to be adapted during the simulation. We develop a method that approximates the solution of a CME by automatically partitioning the reaction dynamics into discrete/continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks.Our method does not require user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from Systems Biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time.Keywords: adaptive hybrid models, stochastic reaction networks, quasi-stationary, adaptive piecewise deterministic markov processes 1

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“…As an example, consider a partition strategy based only on the size of populations, like the one adopted in [34]. In this case, the function f c e for transition e can be the following: 14…”

mentioning

confidence: 99%

(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

Bortolussi¹,

Policriti²

2011

Journal of Logic and Computation

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We define a semantics for stochastic Concurrent Constraint Programming (sCCP), a stochastic process algebra, in terms of stochastic hybrid automata with piecewise deterministic continuous dynamics. To each program we associate a lattice of hybrid models, parameterized with respect to the degree of discreteness left. We study some properties of this lattice, presenting also an alternative semantics in which the degree of discreteness can be dynamically changed.

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Dynamic Partitioning of Large Discrete Event Biological Systems for Hybrid Simulation and Analysis

Cited by 22 publications

References 14 publications

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System ofEscherichia Coli

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System ofEscherichia Coli

Adaptive hybrid simulations for multiscale stochastic reaction networks

(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

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