Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional “backward” bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or “forward” bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research.
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14 March 2013
Research Article|
March 13 2013
Reduction of chemical reaction networks through delay distributions
Manuel Barrio;
Manuel Barrio
1Departamento de Informática,
Universidad de Valladolid
, Valladolid, Spain
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André Leier;
André Leier
2
Okinawa Institute of Science and Technology
, Okinawa, Japan
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Tatiana T. Marquez-Lago
Tatiana T. Marquez-Lago
b)
3Integrative Systems Biology Unit,
Okinawa Institute of Science and Technology
, Okinawa, Japan
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Manuel Barrio
1
André Leier
2
Tatiana T. Marquez-Lago
3,b)
1Departamento de Informática,
Universidad de Valladolid
, Valladolid, Spain
2
Okinawa Institute of Science and Technology
, Okinawa, Japan
3Integrative Systems Biology Unit,
Okinawa Institute of Science and Technology
, Okinawa, Japan
a)
Authors to whom correspondence should be addressed. Electronic addresses: [email protected] and [email protected].
b)
M. Barrio, A. Leier, and T. T. Marquez-Lago contributed equally to this work.
J. Chem. Phys. 138, 104114 (2013)
Article history
Received:
October 29 2012
Accepted:
February 17 2013
Citation
Manuel Barrio, André Leier, Tatiana T. Marquez-Lago; Reduction of chemical reaction networks through delay distributions. J. Chem. Phys. 14 March 2013; 138 (10): 104114. https://doi.org/10.1063/1.4793982
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