Incorporating postleap checks in tau-leaping

Anderson, David F.

doi:10.1063/1.2819665

Cited by 101 publications

(108 citation statements)

References 18 publications

(18 reference statements)

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“…To further study the new strategy, we adopt a Poisson process formulation of the SSA proposed by Anderson. 34 Let k j (t) denote the total number of firings for reaction R j from initial time 0 to t. Then,…”

Section: Analysis Of the Partitioning Strategymentioning

confidence: 99%

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

Liu

Yang

et al. 2012

The Journal of Chemical Physics

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The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.

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Section: Analysis Of the Partitioning Strategymentioning

confidence: 99%

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

Liu

Yang

et al. 2012

The Journal of Chemical Physics

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“…As a result, much effort has been invested in the speed-up of exact or approximate SSAs, 18,[23][24][25][26][27][28][29][30][31][32][33][34][35][36] producing different algorithms that require different tradeoffs. 18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] Tau-Leaping has emerged as an important approximate SSA. 21,24,37,[41][42][43] Below we present an algorithm that trades a very small amount of accuracy for a substantial reduction in computing time by skipping some updates in a special category of parts, which we call "hubs."…”

Section: Introductionmentioning

confidence: 99%

“…18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] Tau-Leaping has emerged as an important approximate SSA. 21,24,37,[41][42][43] Below we present an algorithm that trades a very small amount of accuracy for a substantial reduction in computing time by skipping some updates in a special category of parts, which we call "hubs." The usefulness of such an approximation depends on the biological importance of hubs.…”

Section: Introductionmentioning

confidence: 99%

Lazy Updating of hubs can enable more realistic models by speeding up stochastic simulations

Ehlert

Loewe

2014

The Journal of Chemical Physics

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To respect the nature of discrete parts in a system, stochastic simulation algorithms (SSAs) must update for each action (i) all part counts and (ii) each action's probability of occurring next and its timing. This makes it expensive to simulate biological networks with well-connected "hubs" such as ATP that affect many actions. Temperature and volume also affect many actions and may be changed significantly in small steps by the network itself during fever and cell growth, respectively. Such trends matter for evolutionary questions, as cell volume determines doubling times and fever may affect survival, both key traits for biological evolution. Yet simulations often ignore such trends and assume constant environments to avoid many costly probability updates. Such computational convenience precludes analyses of important aspects of evolution. Here we present "Lazy Updating," an add-on for SSAs designed to reduce the cost of simulating hubs. When a hub changes, Lazy Updating postpones all probability updates for reactions depending on this hub, until a threshold is crossed. Speedup is substantial if most computing time is spent on such updates. We implemented Lazy Updating for the Sorting Direct Method and it is easily integrated into other SSAs such as Gillespie's Direct Method or the Next Reaction Method. Testing on several toy models and a cellular metabolism model showed >10× faster simulations for its use-cases-with a small loss of accuracy. Thus we see Lazy Updating as a valuable tool for some special but important simulation problems that are difficult to address efficiently otherwise. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

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“…Various refinements of the tau-leaping method have been proposed in the literature. [17][18][19][20][21][22][23][24] Another approach for gaining computational efficiency is to consider hybrid methods. [25][26][27][28][29][30] However, in many applications the cell cannot be assumed to be well-stirred and the spatial distribution of some molecular species may be important for studying key cellular processes.…”

Section: Introductionmentioning

confidence: 99%

“…Simply discarding the rejected time-step will skew the statistics of the solution. To guarantee that the sample paths' statistics are unbiased we employ the conditioning technique developed by Anderson 20 for the tau-leaping method when steps are rejected.…”

Section: Introductionmentioning

confidence: 99%

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Padgett

Ilie

2016

AIP Advances

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Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.

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Incorporating postleap checks in tau-leaping

Cited by 101 publications

References 18 publications

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

Lazy Updating of hubs can enable more realistic models by speeding up stochastic simulations

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

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