Simplification of a complex signal transduction model using invariants and flow equivalent servers

Cordero, Francesca; Horváth, András; Manini, Daniele; Napione, Lucia; Pierro, Massimiliano De; Pavan, Simona; Picco, Andrea; Veglio, Andrea; Sereno, Matteo; Bussolino, Federico; Balbo, Gianfranco

doi:10.1016/j.tcs.2011.06.013

Cited by 14 publications

(11 citation statements)

References 34 publications

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“…The PDE in (14) together with the boundary and initial conditions can be solved numerically by discretizing the involved variables (u and x) and by applying a finite volume scheme. In Fig.…”

Section: H E R W I S Ementioning

confidence: 99%

“…The figures show three probability mass functions (pmf). The first one was obtained by solving the original CTMC, the second was calculated by the finite volume scheme applied to the PDE given in (14) and the third was obtained by simulating the HSJD given in (13). We created 10 6 simulation traces, which took about two hours to complete, and still insufficient to produce a smooth pmf.…”

Section: H E R W I S Ementioning

confidence: 99%

“…Since the number of states can be huge even if not all states are considered, in [10,11] approximate randomization methods have been proposed. Another natural approach is aggregation of states which can be done either by aggregating nearby states [12,13] or by exploiting the idea of flow equivalence [14]. Techniques that are based on imposing a special dependency structure on the probabilities of the states were proposed in [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Approximate analysis of biological systems by hybrid switching jump diffusion

Angius

Balbo

Beccuti

et al. 2015

Theoretical Computer Science

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In this paper we consider large state space continuous time Markov chains arising in the field of systems biology. For a class of such models, namely, for density dependent families of Markov chains that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations and provides a deterministic approximation, while the other uses a diffusion process with which the resulting approximation is stochastic. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior that cannot be captured by a single deterministic quantity. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation in order to cover the case when the process reaches the boundary with non-negligible probability. In this paper we generalize the method so that it can be applied to any density dependent Markov chains. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion, i.e., a diffusion with hybrid state space and jumps where the discrete state changes can be seen as switches that take the diffusion from one condition to another. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so-called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation.

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Section: H E R W I S Ementioning

confidence: 99%

Section: H E R W I S Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate analysis of biological systems by hybrid switching jump diffusion

Angius

Balbo

Beccuti

et al. 2015

Theoretical Computer Science

Self Cite

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“…As a result, dividing large systems into small subgroups to decrease the computational cost of analyzing the dynamics of original system is very popular among researchers. For example, in [7], authors used invariants and flow equivalent servers to transform complex biological models into simplified models which preserve the dynamics of the original model. In [8], two different approaches based on conservation relations and differences in the speed of reactions are proposed to simplify complex systems.…”

Section: Introductionmentioning

confidence: 99%

Using Conserved Cycles in Exact Stochastic Simulation Algorithms

Altintan¹

2016

SAUFenBilDer

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Biochemical reaction systems involve many different species interacting via many different reaction channels. When the number of species and the abundance of species are so high, pure modeling approaches based on differential equations suffer from curse of dimensionality. If a system involves conserved cycles, abundances of some species can be obtained via algebraic relations which in turn will reduce the dimension of differential equations representing the dynamics of the system. In the present paper, we propose a numerical algorithm that uses Gauss-Jordan method to obtain conserved cycles in biochemical systems. We give this algorithm in Direct Method (DM), First Reaction Method (FRM) and Next Reaction Method (NRM) which obtain exact realizations of the state vector in stochastic modeling approach. We apply these three algorithms with/without using conservation relations to biochemical systems in different sizes and compare the computational costs of two different versions of each exact algorithm.

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“…Since the calculations can be slow even on the reduced state space, recently, faster approximate uniformisation methods have been proposed [17,28]. Another possibility is to apply aggregation: nearby states are aggregated in [27,4] and a more intricate aggregation can be obtained by applying flow equivalence [3,5]. An important body of works uses simulation to the analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis of stochastic reaction networks with Markov reward models

Angius

Horváth

2011

Proceedings of the 9th International Conference on Computational Methods in Systems Biology

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This paper considers Markov chains describing stochastic reaction networks. These Markov chains often have a huge state space which make their analysis unfeasible. We show that there exist cases when the original Markov chain can be transformed into a Markov reward model with a smaller state space and whose analysis gives information on the moments of the quantity of the involved species. We derive the necessary mathematics and provide numerical examples to illustrate the approach.

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Simplification of a complex signal transduction model using invariants and flow equivalent servers

Cited by 14 publications

References 34 publications

Approximate analysis of biological systems by hybrid switching jump diffusion

Approximate analysis of biological systems by hybrid switching jump diffusion

Using Conserved Cycles in Exact Stochastic Simulation Algorithms

Analysis of stochastic reaction networks with Markov reward models

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