Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions

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 reserved 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 computing 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.Comment: 29 pages with 6 figures, 2 table

On Quantitative Comparison of Chemical Reaction Network Models

Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations. Their dynamic behaviours are then analysed, often by using deterministic methods based on differential equations with a focus on the steady states. Here, we propose a method for comparing CRNs with respect to their behaviour in stochastic simulations. Our method is based on using the flux graphs that are delivered by stochastic simulations as abstract representations of their dynamic behaviour. This allows us to compare the behaviour of any two CRNs for any time interval, and define a notion of equivalence on them that overlaps with graph isomorphism at the lowest level of representation. The similarity between the compared CRNs can be quantified in terms of their distance. The results can then be used to refine the models or to replace a larger model with a smaller one that produces the same behaviour or vice versa.Comment: In Proceedings HCVS/PERR 2019, arXiv:1907.0352

Optimization Algorithms for Computational Systems Biology

Computational systems biology aims at integrating biology and computational methods to gain a better understating of biological phenomena. It often requires the assistance of global optimization to adequately tune its tools. This review presents three powerful methodologies for global optimization that fit the requirements of most of the computational systems biology applications, such as model tuning and biomarker identification. We include the multi-start approach for least squares methods, mostly applied for fitting experimental data. We illustrate Markov Chain Monte Carlo methods, which are stochastic techniques here applied for fitting experimental data when a model involves stochastic equations or simulations. Finally, we present Genetic Algorithms, heuristic nature-inspired methods that are applied in a broad range of optimization applications, including the ones in systems biology