Robust Stochastic Chemical Reaction Networks and Bounded Tau-Leaping

The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection between robustness and efficiency of simulation. Without robustness guarantees, stochastic simulation seems to require computational time proportional to the total number of reaction events. Even if the concentration (molecular count per volume) stays bounded, the number of reaction events can be linear in the duration of simulated time and total molecular count. We show that the behavior of robust systems can be predicted such that the computational work scales linearly with the duration of simulated time and concentration, and only polylogarithmically in the total molecular count. Thus our asymptotic analysis captures the dramatic speedup when molecular counts are large, and shows that for bounded concentrations the computation time is essentially invariant with molecular count. Finally, by noticing that even robust stochastic chemical reaction networks are capable of embedding complex computational problems, we argue that the linear dependence on simulated time and concentration is likely optimal

A gillespie algorithm for non-markovian stochastic processes

The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modeled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, the inter-event times of various phenomena obey long-tailed distributions. The Gillespie algorithm and its variants either assume Poisson processes (i.e., exponentially distributed inter-event times), use particular functions for time courses of the event rate, or work for non-Poissonian renewal processes, including the case of long-tailed distributions of inter-event times, but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. The algorithm makes use of the fact that a class of point processes is represented as a mixture of Poisson processes with different event rates. The method is applicable to multivariate renewal processes whose survival function of inter-event times is completely monotone. It is an exact algorithm and works faster than a recently proposed Gillespie algorithm for general renewal processes, which is exact only in the limit of infinitely many processes. We also propose a method to generate sequences of event times with a tunable amount of positive correlation between inter-event times. We demonstrate our algorithm with exact simulations of epidemic processes on networks, finding that a realistic amount of positive correlation in inter-event times only slightly affects the epidemic dynamics

Extending the multi-level method for the simulation of stochastic biological systems

The multi-level method for discrete state systems, first introduced by Anderson and Higham [Multiscale Model. Simul. 10:146--179, 2012], is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum, and, as such, the method has the potential to revolutionise the field of stochastic simulation. The first term in the sum is calculated using an approximate simulation algorithm, and can be calculated quickly but is of significant bias. Subsequent terms successively correct this bias by combining estimators from approximate stochastic simulations algorithms of increasing accuracy, until a desired level of accuracy is reached. In this paper we present several refinements of the multi-level method which render it easier to understand and implement, and also more efficient. Given the substantial and complex nature of the multi-level method, the first part of this work (Sections 2 - 5) is written as a tutorial, with the aim of providing a practical guide to its use. The second part (Sections 6 - 8) takes on a form akin to a research article, thereby providing the means for a deft implementation of the technique, and concludes with a discussion of a number of open problems.Comment: 38 page

Efficient simulation techniques for biochemical reaction networks

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered analytically intractable. As such, a variety of Monte Carlo simulation algorithms have been developed to explore model dynamics empirically. Whilst well-known methods, such as the Gillespie Algorithm, can be implemented to investigate a given model, the computational demands of traditional simulation techniques remain a significant barrier to modern research. In order to further develop and explore biologically relevant stochastic models, new and efficient computational methods are required. In this thesis, high-performance simulation algorithms are developed to estimate summary statistics that characterise a chosen reaction network. The algorithms make use of variance reduction techniques, which exploit statistical properties of the model dynamics, to improve performance. The multi-level method is an example of a variance reduction technique. The method estimates summary statistics of well-mixed, spatially homogeneous models by using estimates from multiple ensembles of sample paths of different accuracies. In this thesis, the multi-level method is developed in three directions: firstly, a nuanced implementation framework is described; secondly, a reformulated method is applied to stiff reaction systems; and, finally, different approaches to variance reduction are implemented and compared. The variance reduction methods that underpin the multi-level method are then re-purposed to understand how the dynamics of a spatially-extended Markov model are affected by changes in its input parameters. By exploiting the inherent dynamics of spatially-extended models, an efficient finite difference scheme is used to estimate parametric sensitivities robustly.Comment: Doctor of Philosophy thesis submitted at the University of Oxford. This research was supervised by Prof Ruth E. Baker and Dr Christian A. Yate

Computational Methods in Systems Biology. 17th International Conference, CMSB 2019, Trieste, Italy, September 18\u201320, 2019, Proceedings

This volume contains the papers presented at CMSB 2019, the 17th Conference on Computational Methods in Systems Biology, held during September 18\u201320, 2019, at the University of Trieste, Italy. The CMSB annual conference series, initiated in 2003, provides a unique discussion forum for computer scientists, biologists, mathematicians, engineers, and physicists interested in a system-level understanding of biological processes. Topics covered by the CMSB proceedings include: formalisms for modeling biological processes; models and their biological applications; frameworks for model verification, validation, anal- ysis, and simulation of biological systems; high-performance computational systems biology and parallel implementations; model inference from experimental data; model integration from biological databases; multi-scale modeling and analysis methods; computational approaches for synthetic biology; and case studies in systems and synthetic biology. This year there were 53 submissions in total for the 4 conference tracks. Each regular submission and tool paper submission were reviewed by at least three Program Committee members. Additionally, tools were subjected to an additional review by members of the Tool Evaluation Committee, testing the usability of the software and the reproducibility of the results. For the proceedings, the Program Committee decided to accept 14 regular papers, 7 tool papers, and 11 short papers. This rich program of talks was complemented by a poster session, providing an opportunity for informal discussion of preliminary results and results in related fields. In view of the broad scope of the CMSB conference series, we selected the fol- lowing five high-profile invited speakers: Kobi Benenson (ETH Zurich, Switzerland), Trevor Graham (Barts Cancer Hospital, London, UK), Gaspar Tkacik (IST, Austria), Adelinde Uhrmacher (Rostock University, Germany), and Manuel Zimmer (University of Vienna, Austria). Their invited talks covered a broad area within the technical and applicative domains of the conference, and stimulated fruitful discussions among the conference attendees. Further details on CMSB 2019 are available on the following website: https://cmsb2019.units.it. Finally, as the program co-chairs, we are extremely grateful to the members of the Program Committee and the external reviewers for their peer reviews and the valuable feedback they provided to the authors. Our special thanks go to Laura Nenzi as local organization co-chair, Dimitrios Milios as chair of the Tool Evaluation Committee, and to Fran\ue7ois Fages and all the members of the CMSB Steering Committee, for their advice on organizing and running the conference. We acknowledge the support of the EasyChair conference system during the reviewing process and the production of these proceedings. We also thank Springer for publishing the CMSB proceedings in its Lecture Notes in Computer Science series. Additionally, we would like to thank the Department of Mathematics and Geo- sciences of the University of Trieste, for sponsoring and hosting this event, and Confindustria Venezia Giulia, for supporting this event and providing administrative help. Finally, we would like to thank all the participants of the conference. It was the quality of their presentations and their contribution to the discussions that made the meeting a scientific success