Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results

A new twist for the simulation of hybrid systems using the true jump method

The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the simulation of these models in evolving environments, are limited by the need to find the next jumping time at each recursion of the algorithm. Here, we report on a new general method to find this jumping time for the True Jump Method. It is based on an expression in terms of ordinary differential equations for which efficient numerical methods are available. As such, our new result makes it possible to study numerically stochastic models for which analytical formulas are not available thereby providing a way to approximate the state distribution for example. We conclude that the wide use of event detection schemes for the simulation of PDMPs should be strongly reconsidered. The only relevant remaining question being the efficiency of our method compared to the Fictitious Jump Method, question which is strongly case dependent

Improving Diffusion-Based Molecular Communication with Unanchored Enzymes

In this paper, we propose adding enzymes to the propagation environment of a diffusive molecular communication system as a strategy for mitigating intersymbol interference. The enzymes form reaction intermediates with information molecules and then degrade them so that they have a smaller chance of interfering with future transmissions. We present the reaction-diffusion dynamics of this proposed system and derive a lower bound expression for the expected number of molecules observed at the receiver. We justify a particle-based simulation framework, and present simulation results that show both the accuracy of our expression and the potential for enzymes to improve communication performance.Comment: 15 pages, 4 figures, presented at the 7th International Conference on Bio-Inspired Models of Network, Information, and Computing Systems (BIONETICS 2012) in Lugano, Switzerlan

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 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

Perfect Sampling of the Master Equation for Gene Regulatory Networks

We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and combines it with the Dominated Coupling From The Past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for GRNs have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system, and the repressilator, a six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa

Simulator adaptation at runtime for component-based simulation software

Component-based simulation software can provide many opportunities to compose and configure simulators, resulting in an algorithm selection problem for the user of this software. This thesis aims to automate the selection and adaptation of simulators at runtime in an application-independent manner. Further, it explores the potential of tailored and approximate simulators - in this thesis concretely developed for the modeling language ML-Rules - supporting the effectiveness of the adaptation scheme.Komponenten-basierte Simulationssoftware kann viele Möglichkeiten zur Komposition und Konfiguration von Simulatoren bieten und damit zu einem Konfigurationsproblem für Nutzer dieser Software führen. Das Ziel dieser Arbeit ist die Entwicklung einer generischen und automatisierten Auswahl- und Adaptionsmethode für Simulatoren. Darüber hinaus wird das Potential von spezifischen und approximativen Simulatoren anhand der Modellierungssprache ML-Rules untersucht, welche die Effektivität des entwickelten Adaptionsmechanismus erhöhen können

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior