On the Properties of the Reaction Counts Chemical&#x0D;
Master Equation

Sunkara, Vikram

doi:10.3390/e21060607

Cited by 3 publications

(7 citation statements)

References 18 publications

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“…The [20] and its variants [19,23,25,26] are based on r-step reachability [25], whereas, [17] is also a based method but employ stochastic simulation algorithm ( ) for finding the domain which proves better than and suitable for stiff problems. Add-on weighting functions like [27] and likelihoods [23] methods are used to improve the expansion. It is reported that [27] removes the states with small probabilities before the calculation of Eq.…”

Section: Initial Value Problemmentioning

confidence: 99%

“…Add-on weighting functions like [27] and likelihoods [23] methods are used to improve the expansion. It is reported that [27] removes the states with small probabilities before the calculation of Eq. (5) which saves the computational time and performs faster than conventional r-step reachability.…”

Section: Initial Value Problemmentioning

confidence: 99%

“…where, = (1, … 1) is of an appropriate length. Declaring some states as non-probable and removing them before calculation of the probabilities as seen in [27] will decrease the accuracy of Ӕ with the cumulative step errors. This can be validated from the state probabilities that have been ignored in the domain:…”

Section: (B) Expansion Criterion For State Spacementioning

confidence: 99%

“…which improves the solution. Removing without calculating the probabilities of some states is one of the lag, the current methods [17,19,20,23,[25][26][27] are facing over the cost of achieving the truncated domain and saving computation time. To address this, we set a ( ) ( ′ ) leakage point based on:…”

Section: (B) Expansion Criterion For State Spacementioning

confidence: 99%

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Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Kosarwal¹,

Kulasiri²,

Samarasinghe³

2020

Preprint

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Background: Numerical solutions of the chemical master equation (CME) are important to understand the stochasticity of biochemical systems. However, solving CMEs is a formidable task due to the nonlinear nature of the reactions and size of the networks that result in different realisations and, most importantly, the exponential growth of the size of the state-space with respect to the number of different species in the system. When the size of the biochemical system is very large in terms of the number of variables, the solution to the CME becomes intractable. Therefore, we introduce the intelligent state projection (𝐼𝑆𝑃) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment to describe the dynamic behaviour of the system. 𝐼𝑆𝑃 is based on a state-space search and the data structure standards of artificial intelligence (𝐴𝐼) to explore and update the states of a biochemical system. To support the expansion in 𝐼𝑆𝑃, we also develop a Bayesian likelihood node projection (𝐵𝐿𝑁𝑃) function to predict the likelihood of the states. Results: To show the acceptability and effectiveness of our method, we apply the 𝐼𝑆𝑃 to several biological models previously discussed in the literature. According to the results of our computational experiments, we show that 𝐼𝑆𝑃 is effective in terms of speed and accuracy of the expansion, accuracy of the solution, and provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions: The 𝐼𝑆𝑃 is the de-novo method to address the accuracy as well as the performance problems for the solution of the CME. It systematically expands the projection space based on predefined inputs, which are useful in providing accuracy in the approximation and an exact analytical solution at the time of interest. The 𝐼𝑆𝑃 was more effective in terms of predicting the behaviour of the state-space of the system and in performance management, which is a vital step towards modelling large biochemical systems.

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Section: Initial Value Problemmentioning

confidence: 99%

Section: Initial Value Problemmentioning

confidence: 99%

Section: (B) Expansion Criterion For State Spacementioning

confidence: 99%

Section: (B) Expansion Criterion For State Spacementioning

confidence: 99%

See 2 more Smart Citations

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Kosarwal¹,

Kulasiri²,

Samarasinghe³

2020

Preprint

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show abstract

“…This is more effective than FSP and suitable for stiff problems. Add-on weighting functions like GORDE [ 28 ] and likelihoods [ 24 ] methods are used to improve the expansion. FSP GORDE [ 28 ] removes the states with small probabilities before the calculation of Eq.…”

Section: Introductionmentioning

confidence: 99%

Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

2020

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Background Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.

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Modeling bursty transcription and splicing with the chemical master equation

Gorin¹,

Pachter²

2022

Biophysical Journal

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On the Properties of the Reaction Counts Chemical Master Equation

Cited by 3 publications

References 18 publications

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

Modeling bursty transcription and splicing with the chemical master equation

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