scholarly journals Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error Bounds and Algorithms

2015 ◽  
Vol 13 (4) ◽  
pp. 1390-1419 ◽  
Author(s):  
Arnab Ganguly ◽  
Derya Altintan ◽  
Heinz Koeppl
Keyword(s):  
Error Bounds ◽  
Diffusion Approximation ◽  
Reaction Dynamics ◽  
Jump Diffusion ◽  
Stochastic Reaction

Noise and delay can shape distribution functions in stochastic reaction dynamics

2021 ◽  
Author(s):  
Jyoti Bhadana ◽  
Athokpam Langlen Chanu ◽  
Md. Zubbair Malik ◽  
R. K. Brojen Singh
Keyword(s):  
Reaction Dynamics ◽  
Distribution Functions ◽  
Shape Distribution ◽  
Stochastic Reaction

scholarly journals A Continuous-Time Ehrenfest Model with Catastrophes and Its Jump-Diffusion Approximation

2015 ◽  
Vol 161 (2) ◽  
pp. 326-345 ◽  
Author(s):  
Selvamuthu Dharmaraja ◽  
Antonio Di Crescenzo ◽  
Virginia Giorno ◽  
Amelia G. Nobile
Keyword(s):  
Diffusion Approximation ◽  
Continuous Time ◽  
Jump Diffusion

scholarly journals Stochastic reaction networks in dynamic compartment populations

2020 ◽  
Vol 117 (37) ◽  
pp. 22674-22683
Author(s):  
Lorenzo Duso ◽  
Christoph Zechner
Keyword(s):  
Biological Systems ◽  
Reaction Dynamics ◽  
Theoretical Models ◽  
Counting Processes ◽  
Mathematical Framework ◽  
Biological Processes ◽  
Biochemical Processes ◽  
Subcellular Compartmentalization ◽  
Stochastic Reaction ◽  
Stochastic Reaction Networks

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

scholarly journals Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks

2019 ◽  
Vol 60 (2) ◽  
pp. 261-294
Author(s):  
Derya Altıntan ◽  
Heinz Koeppl
Keyword(s):  
Master Equation ◽  
Probability Density ◽  
Diffusion Approximation ◽  
Joint Probability ◽  
Planck Equation ◽  
Jump Diffusion ◽  
Reaction Rates ◽  
Conditional Probability Density ◽  
Multi Scale ◽  
Joint Probability Density

AbstractCellular reactions have a multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary across orders of magnitude. This diversity naturally leads to hybrid models that combine continuous and discrete modeling regimes. In order to capture this multi-scale nature, we proposed jump-diffusion approximations in a previous study. The key idea was to partition reactions into fast and slow groups, and then to combine a Markov jump updating scheme for the slow group with a diffusion (Langevin) updating scheme for the fast group. In this study we show that the joint probability density function of the jump-diffusion approximation over the reaction counting process satisfies a hybrid master equation that combines terms from the chemical master equation and from the Fokker–Planck equation. Inspired by the method of conditional moments, we propose a efficient method to solve this master equation using the moments of reaction counters of the fast reactions given the reaction counters of the slow reactions. For each time point of interest, we then solve a set of maximum entropy problems in order to recover the conditional probability density from its moments. This finally allows us to reconstruct the complete joint probability density over all reaction counters and hence obtain an approximate solution of the hybrid master equation. Finally, we show the accuracy of the method applied to a simple multi-scale conversion process.

scholarly journals A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation

2011 ◽  
Vol 14 (4) ◽  
pp. 937-954 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Virginia Giorno ◽  
Balasubramanian Krishna Kumar ◽  
Amelia G. Nobile
Keyword(s):  
Diffusion Approximation ◽  
Jump Diffusion
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