The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

McCollum, James M.; Peterson, Gregory D.; Cox, Chris D.; Simpson, Michael L.; Samatova, Nagiza F.

doi:10.1016/j.compbiolchem.2005.10.007

Cited by 154 publications

(113 citation statements)

References 31 publications

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“…This algorithm performs n wSSA simulation runs to estimate the probability that the system moves to a state in E-which we presume to be a rare event-within the time limit t max . Note that, while Algorithm 1 is presented in a similar fashion as the counterpart direct method of the SSA, various optimization techniques of the direct method, such as [1,18], can also be applied to an implementation of the wSSA to further reduce the simulation cost.…”

Section: Algorithmmentioning

confidence: 99%

An efficient and exact stochastic simulation method to analyze rare events in biochemical systems

Kuwahara

Mura

2008

The Journal of Chemical Physics

117

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In robust biological systems, wide deviations from highly controlled normal behavior may be rare, yet they may result in catastrophic complications. While in silico analysis has gained an appreciation as a tool to offer insights into systems-level properties of biological systems, analysis of such rare events provides a particularly challenging computational problem. This paper proposes an efficient stochastic simulation method to analyze rare events in biochemical systems. Our new approach can substantially increase the frequency of the rare events of interest by appropriately manipulating the underlying probability measure of the system, allowing high-precision results to be obtained with substantially fewer simulation runs than the conventional direct Monte Carlo simulation. Here, we show the algorithm of our new approach, and we apply it to the analysis of rare deviant transitions of two systems, resulting in several orders of magnitude speedup in generating high-precision estimates compared with the conventional Monte Carlo simulation.

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Section: Algorithmmentioning

confidence: 99%

An efficient and exact stochastic simulation method to analyze rare events in biochemical systems

Kuwahara

Mura

2008

The Journal of Chemical Physics

117

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“…It can therefore work with a broad range of relevant algorithms, including Gillespie's Direct Method, 11 the Next Reaction Method, 18,23 and others. We implemented Lazy Updating within the Sorting Direct Method, 27 which is a variant of Gillespie's Direct Method. 11…”

Section: B the Lazy Update Algorithmmentioning

confidence: 99%

“…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%

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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“…The position of each reaction in the list is thereby determined after some pre-simulations. McCollum et al [7] maintain a loosely sorted order of the reactions as the simulation proceeds. Instead of arranging the reactions in a linear list, Gibson & Bruck [5] propose to use advanced data structures (trees) to speed up the search for the next reaction that will occur.…”

Section: Stochastic Simulationmentioning

confidence: 99%

Simulative Model Checking of Steady State and Time-Unbounded Temporal Operators

Röhr

2013

Transactions on Petri Nets and Other Models of Concurrency VIII

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Abstract. When working with large stochastic models simulation remains the only possible analysis technique. Therefore, simulative model checking is the way to go. While finite time horizon algorithms are well known for probabilistic linear-time temporal logic, we provide an infinite time horizon procedure as well as steady state computation, based on exact stochastic simulation algorithms. We demonstrate the approach on models of the RKIP inhibited ERK pathway and angiogenetic process.

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The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

Cited by 154 publications

References 31 publications

An efficient and exact stochastic simulation method to analyze rare events in biochemical systems

An efficient and exact stochastic simulation method to analyze rare events in biochemical systems

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

Simulative Model Checking of Steady State and Time-Unbounded Temporal Operators

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