Integrating BioPAX pathway knowledge with SBML models.

Online databases store thousands of molecular interactions and pathways, and numerous modelling software tools provide users with an interface to create and simulate mathematical models of such interactions. However, the two most widespread used standards for storing pathway data (biological pathway exchange; BioPAX) and for exchanging mathematical models of pathways (systems biology markup language; SBML) are structurally and semantically different. Conversion between formats (making data present in one format available in another format) based on simple one-to-one mappings may lead to loss or distortion of data, is difficult to automate, and often impractical and/or erroneous. This seriously limits the integration of knowledge data and models. In this paper we introduce an approach for such integration based on a bridging format that we named systems biology pathway exchange (SBPAX) alluding to SBML and BioPAX. It facilitates conversion between data in different formats by a combination of one-to-one mappings to and from SBPAX and operations within the SBPAX data. The concept of SBPAX is to provide a flexible description expanding around essential pathway data - basically the common subset of all formats describing processes, the substances participating in these processes and their locations. SBPAX can act as a repository for molecular interaction data from a variety of sources in different formats, and the information about their relative relationships, thus providing a platform for converting between formats and documenting assumptions used during conversion, gluing (identifying related elements across different formats) and merging (creating a coherent set of data from multiple sources) data.

Virtual Cell modelling and simulation software environment.

The Virtual Cell (VCell; http://vcell.org/) is a problem solving environment, built on a central database, for analysis, modelling and simulation of cell biological processes. VCell integrates a growing range of molecular mechanisms, including reaction kinetics, diffusion, flow, membrane transport, lateral membrane diffusion and electrophysiology, and can associate these with geometries derived from experimental microscope images. It has been developed and deployed as a web-based, distributed, client-server system, with more than a thousand world-wide users. VCell provides a separation of layers (core technologies and abstractions) representing biological models, physical mechanisms, geometry, mathematical models and numerical methods. This separation clarifies the impact of modelling decisions, assumptions and approximations. The result is a physically consistent, mathematically rigorous, spatial modelling and simulation framework. Users create biological models and VCell will automatically (i) generate the appropriate mathematical encoding for running a simulation and (ii) generate and compile the appropriate computer code. Both deterministic and stochastic algorithms are supported for describing and running non-spatial simulations; a full partial differential equation solver using the finite volume numerical algorithm is available for reaction-diffusion-advection simulations in complex cell geometries including 3D geometries derived from microscope images. Using the VCell database, models and model components can be reused and updated, as well as privately shared among collaborating groups, or published. Exchange of models with other tools is possible via import/export of SBML, CellML and MatLab formats. Furthermore, curation of models is facilitated by external database binding mechanisms for unique identification of components and by standardised annotations compliant with the MIRIAM standard. VCell is now open source, with its native model encoding language (VCML) being a public specification, which stands as the basis for a new generation of more customised, experiment-centric modelling tools using a new plug-in based platform.

Complexity and modularity of intracellular networks: a systematic approach for modelling and simulation.

Assembly of quantitative models of large complex networks brings about several challenges. One of them is the combinatorial complexity, where relatively few signalling molecules can combine to form thousands or millions of distinct chemical species. A receptor that has several separate phosphorylation sites can exist in hundreds of different states, many of which must be accounted for individually when simulating the time course of signalling. When assembly of protein complexes is being included, the number of distinct molecular species can easily increase by a few orders of magnitude. Validation, visualisation and understanding the network can become intractable. Another challenge appears when the modeller needs to recast or grow a model. Keeping track of changes and adding new elements present a significant difficulty. An approach to solve these challenges within the virtual cell (VCell) is described. Using (i) automatic extraction from pathway databases of model components (http://vcell.org/biopax) and (ii) rules of interactions that serve as reaction network generators (http://vcell.org/bionetgen), a way is provided for semi-automatic generation of quantitative mathematical models that also facilitates the reuse of model elements. In this approach, kinetic models of large, complex networks can be assembled from separately constructed modules, either directly or via rules. To implement this approach, the strength of several related technologies is combined: the BioPAX ontology, the BioNetGen rule-based description of molecular interactions and the VCell modelling and simulation framework.

Combinatorial complexity and dynamical restriction of network flows in signal transduction.

The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular species implied by specified interactions of four proteins involved in signalling by the immunoreceptor FcepsilonRI, we determine the relative importance of molecular species that can be generated during signalling, chemical transitions among these species, and reaction paths that lead to activation of the protein tyrosine kinase (PTK) Syk. By all of these measures and over two- and ten-fold ranges of model parameters--rate constants and initial concentrations--only a small portion of the biochemical network is active. The spectrum of active complexes, however, can be shifted dramatically, even by a change in the concentration of a single protein, which suggests that the network can produce qualitatively different responses under different cellular conditions and in response to different inputs. Reduced models that reproduce predictions of the full model for a particular set of parameters lose their predictive capacity when parameters are varied over two-fold ranges.