Simulation Of Biochemical Networks Research Articles

Selected-node stochastic simulation algorithm.

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.

Petri Net-Based Collaborative Simulation and Steering of Biochemical Reaction Networks

Computational steering is an interactive remote control of a long running application. The user can adopt it, e.g., to adjust simulation parameters on the fly. Simulation of large-scale biochemical networks is often computationally expensive, particularly stochastic and hybrid simulation. Such extremely time-consuming computations necessitate an interactive mechanism to permit users to try different paths and ask “what-if-questions” while the simulation is in progress. Furthermore, with the progress of computational modelling and the simulation of biochemical networks, there is a need to manage multi-scale models, which may contain species or reactions at different scales. In this context, Petri nets are of special importance, since they provide an intuitive visual representation of reaction networks. In this paper, we introduce a framework and its implementation for combining Petri nets and computational steering for the representation and interactive simulation of biochemical networks. The main merits of the developed framework are: intuitive representation of biochemical networks by means of Petri nets, distributed collaborative and interactive simulation, and tight coupling of simulation and visualisation.

Hybrid representation and simulation of stiff biochemical networks

With the progress of computational modelling and simulation of biochemical networks, there is a need to manage multi-scale models, which may contain species or reactions at different scales. A visual language such as Petri nets can provide a valuable tool for representing and simulating such stiff biochemical networks. In this paper, we introduce a new Petri nets class, generalised hybrid Petri nets (GHPNbio), tailored to the specific needs for modelling and simulation of biochemical networks. It provides rich modelling and simulation functionalities by combining all features of continuous Petri nets and generalised stochastic Petri nets, extended by three types of deterministic transition. Herein, we focus on modelling and simulation of stiff biochemical networks, in which some reactions are represented and simulated stochastically, while others are carried out deterministically. Additionally, two related simulation algorithms are presented, supporting static (off-line) partitioning and dynamic (on-line) partitioning. This paper comes with a fully fledged implementation, supporting the introduced net class as well as the discussed simulation algorithms. We discuss three case studies, demonstrating the use of GHPNbio and the efficiency of the developed simulation algorithms.

A Continuous-Time, Discrete-State Method for Simulating the Dynamics of Biochemical Systems

Computational systems biology is largely driven by mathematical modeling and simulation of biochemical networks, via continuous deterministic methods or discrete event stochastic methods. Although the deterministic methods are efficient in predicting the macroscopic behavior of a biochemical system, they are severely limited by their inability to represent the stochastic effects of random molecular fluctuations at lower concentration. In this work, we have presented a novel method for simulating biochemical networks based on a deterministic solution with a modification that permits the incorporation of stochastic effects. To demonstrate the feasibility of our approach, we have tested our method on three previously reported biochemical networks. The results, while staying true to their deterministic form, also reflect the stochastic effects of random fluctuations that are dominant as the system transitions into a lower concentration. This ability to adapt to a concentration gradient makes this method particularly attractive for systems biology-based applications.

Discrete-time stochastic modeling and simulation of biochemical networks

Since inherent randomness in chemically reacting systems is evident, stochastic modeling and simulation are exceedingly important for investigating complex biological networks. Within the most common stochastic approach a network is modeled by a continuous-time Markov chain governed by the chemical master equation. We show how the continuous-time Markov chain can be converted to a stochastically identical discrete-time Markov chain and obtain a discrete-time version of the chemical master equation. Simulating the discrete-time Markov chain is equivalent to the Gillespie algorithm but requires less effort in that it eliminates the generation of exponential random variables. Thus, exactness as possessed by the Gillespie algorithm is preserved while the simulation can be performed more efficiently.

Eliminating fast reactions in stochastic simulations of biochemical networks: A bistable genetic switch

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.

Stochastic simulation GUI for biochemical networks

This article describes the development of a useful graphical user interface for stochastic simulation of biochemical networks which allows model builders to run stochastic simulations of their models and perform statistical analysis on the results. These include the construction of correlations, power-spectral densities and transfer functions between selected inputs and outputs. The software is licensed under the BSD open source license and is available at http://sourceforge.net/projects/jdesigner. In addition, a more detailed account of the algorithms employed in the tool can be found at the Wiki at http://www.sys-bio.org/sbwWiki. Supplementary data are available at Bioinformatics online.

Parameter Reconstruction for Biochemical Networks Using Interval Analysis

In recent years, the modeling and simulation of biochemical networks has attracted increasing attention. Such networks are commonly modeled by systems of ordinary differential equations, a special class of which are known as S-systems. These systems are specifically designed to mimic kinetic reactions, and are sufficiently general to model genetic networks, metabolic networks, and signal transduction cascades. The parameters of an S-system correspond to various kinetic rates of the underlying reactions, and one of the main challenges is to determine approximate values of these parameters, given measured (or simulated) time traces of the involved reactants. Due to the high dimensionality of the problem, a straight-forward optimization strategy will rarely produce correct parameter values. Instead, almost all methods available utilize genetic/evolutionary algorithms to perform the non-linear parameter fitting. We propose a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. The proposed method can in principle be applied to any system of finitely parameterized differential equations, and, as we demonstrate, yields encouraging results for low dimensional S-systems.

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

The origin of correlations in metabolomics data

A phenomenon observed earlier in the development of metabolomics as a systems biology methodology, consists of a small but significant number of metabolites whose levels are highly correlated between biological replicates. Contrary to initial interpretations, these correlations are not necessarily only between neighboring metabolites in the metabolic network. Most metabolites that participate in common reactions are not correlated in this way, while some non-neighboring metabolites are highly correlated. Here we investigate the origin of such correlations using metabolic control analysis and computer simulation of biochemical networks. A series of cases is identified which lead to high correlation between metabolite pairs in replicate measurement. These are (1) chemical equilibrium, (2) mass conservation, (3) asymmetric control distribution, and (4) unusually high variance in the expression of a single gene. The importance of identifying metabolite correlations within a physiological state and changes of correlation between different states is discussed in the context of systems biology.

Automatic generation of cellular reaction networks with Moleculizer 1.0

Accurate simulation of intracellular biochemical networks is essential to furthering our understanding of biological system behavior. The number of protein complexes and of chemical interactions among them has traditionally posed significant problems for simulation algorithms. Here we describe an approach to the exact stochastic simulation of biochemical networks that emphasizes the contribution of protein complexes to these systems. This simulation approach starts from a description of monomeric proteins and specifications for binding, unbinding and other reactions. This manageable specification is reasonably intuitive for biologists. Rather than requiring the inclusion of all possible complexes and reactions from the outset, our approach incorporates new complexes and reactions only when needed as the simulation proceeds. As a result, the simulation generates much smaller reaction networks, which can be exported to other simulators for further analysis. We apply this approach to the automatic generation of reaction systems for the study of signal transduction networks.

Interactive modelling and simulation of biochemical networks

The analysis of biochemical processes can be supported using methods of modelling and simulation. New methods of computer science are discussed in this field of research. This paper presents a new method which allows the modelling and analysis of complex metabolic networks. Moreover, our simulation shell is based on this formalization and represents the first tool for the interactive simulation of metabolic processes.