Bridging from molecular simulation to biochemical networks

How can we make the connection between the three-dimensional structures of individual proteins and understanding how complex biological systems involving many proteins work? The modelling and simulation of protein structures can help to answer this question for systems ranging from multimacromolecular complexes to organelles and cells. On one hand, multiscale modelling and simulation techniques are advancing to permit the spatial and temporal properties of large systems to be simulated using atomic-detail structures. On the other hand, the estimation of kinetic parameters for the mathematical modelling of biochemical pathways using protein structure information provides a basis for iterative manipulation of biochemical pathways guided by protein structure. Recent advances include the structural modelling of protein complexes on the genomic level, novel coarse-graining strategies to increase the size of the system and the time span that can be simulated, and comparative molecular field analyses to estimate enzyme kinetic parameters.     

Stochastic P systems and the simulation of biochemical processes with dynamic compartments

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.     

Stochastic models for an open biochemical system

This paper uses the theory of Markov processes to derive stochastic models for a single open biochemical system at st?ady state under 3 sets of assumptions. The system is a one substrate, one product reaction. Each set of assumptions results in a separate solution for the probability functions. A system of linear equations in the probability function as well as an equivalent differential equation in its generating function are derived. The assumption of no flux leads to the first (exact) solution of the linear equations. The form agrees with that of the closed systems. Making assumptions that simplify the system to model active transport results in the second (exact) solution to the linear equations. Assuming the presence of a large number of molecules in the system facilitates obtaining the third (approximate) solution to the differential equations.     

A graphical notation for biochemical networks

A solid definition and comprehensive graphical representation of biological networks is essential for efficient and accurate dissemination of information on biological models. Several proposals have already been made toward this aim. The most well known representation of this kind is a molecular interaction map, or ‘Kohn Map’. However, although the molecular interaction map is a well-defined and compact notation, there are several drawbacks, such as difficulties in intuitive understanding of temporal changes of reactions and additional complexities arising from particular graphical representations. This article proposes several improvements to the molecular interaction map, as well as the use of the ‘process diagram’ to help understand temporal sequences of reactions.     

ChemChains: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists

Background  

New mathematical models of complex biological structures and computer simulation software allow modelers to simulate and analyze biochemical systems in silico and form mathematical predictions. Due to this potential predictive ability, the use of these models and software has the possibility to compliment laboratory investigations and help refine, or even develop, new hypotheses. However, the existing mathematical modeling techniques and simulation tools are often difficult to use by laboratory biologists without training in high-level mathematics, limiting their use to trained modelers.     

Stochastic approach in biochemical research

The logic foundations of the probabilistic style for thinking and its methodological significance in the modern science are given. Complex, joint, ambiguous systems are the object of biochemical investigations at all organization levels and therefore biochemists often cannot obtain unambiguous results. It is shown that such systems are subjects to the study with the use of propositions of the probability theory which considers "random" events as a result of many-channel determination and is aimed to transform knowledge of these events into events predicted with certain probability. This provides a more profound analysis of a sum of facts and specificity of their theoretical interpretation. It is proved expedient to apply the probabilistic approach to study intramolecular and intermolecular interaction of elements, to characterize enzymes and membranes, to investigate objects comparatively and chemotaxanomically. It is stated that comprehension of "random" as a manifestation of a part of a sum of the possible or one of its variants stimulates the theoretical generalization of facts, elucidation of regularities of functioning, adaptation, development and diversity of every living thing.     

Tools for kinetic modeling of biochemical networks

The number of software packages for kinetic modeling of biochemical networks continues to grow. Although most packages share a common core of functionality, the specific capabilities and user interfaces of different packages mean that choosing the best package for a given task is not trivial. We compare 12 software packages with respect to their functionality, reliability, efficiency, user-friendliness and compatibility. Although most programs performed reliably in all numerical tasks tested, SBML compatibility and the set-up of multicompartmentalization are problematic in many packages. For simple models, GEPASI seems the best choice for non-expert users. For large-scale models, environments such as Jarnac/JDesigner are preferable, because they allow modular implementation of models. Virtual Cell is the most versatile program and provides the simplest and clearest functionality for setting up multicompartmentalization.     

Condor-COPASI: high-throughput computing for biochemical networks

ABSTRACT: BACKGROUND: Mathematical modelling has become a standard technique to improve our understanding of complex biological systems. As models become larger and more complex, simulations and analyses require increasing amounts of computational power. Clusters of computers in a high-throughput computing environment can help to provide the resources required for computationally expensive model analysis. However, exploiting such a system can be difficult for users without the necessary expertise. RESULTS: We present Condor-COPASI, a server-based software tool that integrates COPASI, a biological pathway simulation tool, with Condor, a high-throughput computing environment. Condor-COPASI provides a web-based interface, which makes it extremely easy for a user to run a number of model simulation and analysis tasks in parallel. Tasks are transparently split into smaller parts, and and submitted for execution on a Condor pool. Result output is presented to the user in a number of formats, including tables and interactive graphical displays. CONCLUSIONS: Condor-COPASI can effectively use a Condor high-throughput computing environment to provide significant gains in performance for a number of model simulation and analysis tasks. Condor-COPASI is free, open source software, released under the Artistic License 2.0, and is suitable for use by any institution with access to a Condor pool. Source code is freely available for download at http://code.google.com/p/condor-copasi/, along with full instructions on deployment and usage.     

RMBNToolbox: random models for biochemical networks

Background  

There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models.     

Quantitative modeling of biochemical networks

Today different database systems for molecular structures (genes and proteins) and metabolic pathways are available. All these systems are characterized by the static data representation. For progress in biotechnology the dynamic representation of this data is important. The metabolism can be characterized as a complex biochemical network. Different models for the quantitative simulation of biochemical networks are discussed, but no useful formalization is available. This paper shows that the theory of Petrinets is useful for the quantitative modeling of biochemical networks.     

Associative learning in biochemical networks

It has been recently suggested that there are likely generic features characterizing the emergence of systems constructed from the self-organization of self-replicating agents acting under one or more selection pressures. Therefore, structures and behaviors at one length scale may be used to infer analogous structures and behaviors at other length scales. Motivated by this suggestion, we seek to characterize various "animate" behaviors in biochemical networks, and the influence that these behaviors have on genomic evolution. Specifically, in this paper, we develop a simple, chemostat-based model illustrating how a process analogous to associative learning can occur in a biochemical network. Associative learning is a form of learning whereby a system "learns" to associate two stimuli with one another. Associative learning, also known as conditioning, is believed to be a powerful learning process at work in the brain (associative learning is essentially "learning by analogy"). In our model, two types of replicating molecules, denoted as A and B, are present in some initial concentration in the chemostat. Molecules A and B are stimulated to replicate by some growth factors, denoted as G(A) and G(B), respectively. It is also assumed that A and B can covalently link, and that the conjugated molecule can be stimulated by either the G(A) or G(B) growth factors (and can be degraded). We show that, if the chemostat is stimulated by both growth factors for a certain time, followed by a time gap during which the chemostat is not stimulated at all, and if the chemostat is then stimulated again by only one of the growth factors, then there will be a transient increase in the number of molecules activated by the other growth factor. Therefore, the chemostat bears the imprint of earlier, simultaneous stimulation with both growth factors, which is indicative of associative learning. It is interesting to note that the dynamics of our model is consistent with certain aspects of Pavlov's original series of conditioning experiments in dogs. We discuss how associative learning can potentially be performed in vitro within RNA, DNA, or peptide networks. We also describe how such a mechanism could be involved in genomic evolution, and suggest relevant bioinformatics studies that could potentially resolve these issues.     

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion. Supported in part by NSF Grants DMS-0504557 and DMS-0614371.     

Stochastic reaction-diffusion simulation with MesoRD

SUMMARY: MesoRD is a tool for stochastic simulation of chemical reactions and diffusion. In particular, it is an implementation of the next subvolume method, which is an exact method to simulate the Markov process corresponding to the reaction-diffusion master equation. AVAILABILITY: MesoRD is free software, written in C++ and licensed under the GNU general public license (GPL). MesoRD runs on Linux, Mac OS X, NetBSD, Solaris and Windows XP. It can be downloaded from http://mesord.sourceforge.net. CONTACT: johan.elf@icm.uu.se; johan.hattne@embl-hamburg.de SUPPLEMENTARY INFORMATION: 'MesoRD User's Guide' and other documents are available at http://mesord.sourceforge.net.     

Stochastic synchronization of genetic oscillator networks

Background  

The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random intra- and inter-cellular fluctuations. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. From the synthetic biology viewpoint, it is also important to implement biological systems that minimizing the negative influence of the perturbations.     

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a "concentration-clamp" procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β(1)-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal "kinetic biomarkers" of the overall β(1)-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.     

Stochastic roadmap simulation for the study of ligand-protein interactions

Understanding the dynamics of ligand-protein interactions is indispensable in the design of novel therapeutic agents. In this paper, we establish the use of Stochastic Roadmap Simulation (SRS) for the study of ligand-protein interactions through two studies. In our first study, we measure the effects of mutations on the catalytic site of a protein, a process called computational mutagenesis. In our second study, we focus on distinguishing the catalytic site from other putative binding sites. SRS compactly represents many Monte Carlo (MC) simulation paths in a compact graph structure, or roadmap. Furthermore, SRS allows us to analyze all the paths in this roadmap simultaneously. In our application of SRS to the domain of ligand-protein interactions, we consider a new parameter called escape time, the expected number of MC simulation steps required for the ligand to escape from the 'funnel of attraction' of the binding site, as a metric for analyzing such interactions. Although computing escape times would probably be infeasible with MC simulation, these computations can be performed very efficiently with SRS. Our results for six mutant complexes for the first study and seven ligand-protein complexes for the second study, are very promising: In particular, the first results agree well with the biological interpretation of the mutations, while the second results show that escape time is a good metric to distinguish the catalytic site for five out of seven complexes.