Parameter sensitivity analysis for biochemical reaction networks

Giorgos Minas; David A Rand; Giorgos Minas; David A Rand

doi:10.3934/mbe.2019196

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3965-3987. doi: 10.3934/mbe.2019196

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Parameter sensitivity analysis for biochemical reaction networks

Giorgos Minas ^{1
,
,},
David A Rand ²

1.
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
2.
Mathematics Institute & Zeeman Institute for Systems Biology and Infectious Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK

Received: 31 December 2018 Accepted: 01 April 2019 Published: 06 May 2019

Biochemical reaction networks describe the chemical interactions occurring between molecular populations inside the living cell. These networks can be very noisy and complex and they often involve many variables and even more parameters. Parameter sensitivity analysis that studies the effects of parameter changes to the behaviour of biochemical networks can be a powerful tool in unravelling their key parameters and interactions. It can also be very useful in designing experiments that study these networks and in addressing parameter identifiability issues. This article develops a general methodology for analysing the sensitivity of probability distributions of stochastic processes describing the time-evolution of biochemical reaction networks to changes in their parameter values. We derive the coefficients that efficiently summarise the sensitivity of the probability distribution of the network to each parameter and discuss their properties. The methodology is scalable to large and complex stochastic reaction networks involving many parameters and can be applied to oscillatory networks. We use the two-dimensional Brusselator system as an illustrative example and apply our approach to the analysis of the Drosophila circadian clock. We investigate the impact of using stochastic over deterministic models and provide an analysis that can support key decisions for experimental design, such as the choice of variables and time-points to be observed.
- parameter sensitivity analysis,
- reaction networks,
- oscillation,
- molecular biology
Citation: Giorgos Minas, David A Rand. Parameter sensitivity analysis for biochemical reaction networks[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3965-3987. doi: 10.3934/mbe.2019196

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Abstract

Biochemical reaction networks describe the chemical interactions occurring between molecular populations inside the living cell. These networks can be very noisy and complex and they often involve many variables and even more parameters. Parameter sensitivity analysis that studies the effects of parameter changes to the behaviour of biochemical networks can be a powerful tool in unravelling their key parameters and interactions. It can also be very useful in designing experiments that study these networks and in addressing parameter identifiability issues. This article develops a general methodology for analysing the sensitivity of probability distributions of stochastic processes describing the time-evolution of biochemical reaction networks to changes in their parameter values. We derive the coefficients that efficiently summarise the sensitivity of the probability distribution of the network to each parameter and discuss their properties. The methodology is scalable to large and complex stochastic reaction networks involving many parameters and can be applied to oscillatory networks. We use the two-dimensional Brusselator system as an illustrative example and apply our approach to the analysis of the Drosophila circadian clock. We investigate the impact of using stochastic over deterministic models and provide an analysis that can support key decisions for experimental design, such as the choice of variables and time-points to be observed.

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