# Efficient finite-difference method for computing sensitivities of biochemical reactions

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**Efficient finite-difference method for computing sensitivities of biochemical reactions.** / Thanh, Vo Hong; Zunino, Roberto; Priami, Corrado.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 474, no. 2218, pp. 1-20. https://doi.org/10.1098/rspa.2018.0303

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*474*(2218), 1-20. https://doi.org/10.1098/rspa.2018.0303

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TY - JOUR

T1 - Efficient finite-difference method for computing sensitivities of biochemical reactions

AU - Thanh, Vo Hong

AU - Zunino, Roberto

AU - Priami, Corrado

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite-difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is preserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to compute sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.

AB - Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite-difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is preserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to compute sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.

KW - Finite-difference sensitivity analysis

KW - Rejection-based simulation

KW - Stochastic simulation

UR - http://www.scopus.com/inward/record.url?scp=85056507598&partnerID=8YFLogxK

U2 - 10.1098/rspa.2018.0303

DO - 10.1098/rspa.2018.0303

M3 - Article

VL - 474

SP - 1

EP - 20

JO - PROCEEDINGS OF THE ROYAL SOCIETY A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

JF - PROCEEDINGS OF THE ROYAL SOCIETY A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

SN - 1364-5021

IS - 2218

ER -

ID: 30099127