The Virtual Cell: a software environment for computational cell biology

The evolution of CellML

CellML is an open XML-based markup language for describing and exchanging mathematical models of biological processes. While CellML was originally designed to describe and exchange models of cellular and subcellular processes, the design principles that were applied to the construction of a language with this relatively narrow focus are equally applicable to the specification of a language with a much wider scope. In this paper we describe the structure of CellML, how the language is evolving to broaden its scope, and what tools are being developed to facilitate its use.

Molecular stochastic simulations of chromatophore vesicles from Rhodobacter sphaeroides

A kinetic model is presented for photosynthetic processes under varying illumination based on the recently introduced steady state model of the photosynthetic chromatophore vesicles of the purple bacterium Rhodobacter sphaeroides. A stochastic simulation system is built up from independent copies of the different transmembrane proteins, each encapsulating its own set of binding sites and internal states. The proteins are then connected through pools for each of the metabolites. A number of steady state and time-dependent scenarios are presented showing that even under steady state conditions the stochastic model exhibits a different behavior than a continuous description. We find that the electronic coupling between the light harvesting complexes increases the efficiency of the core complexes which eventually allows the bacteria to bridge short illumination outages at already lower light intensities. Some new experiments are proposed by which the DeltapH dependent characteristic of the bc(1) complex or the proton buffering capacity of the vesicle could be determined.

Probability-based model of protein-protein interactions on biological timescales

BACKGROUND

Simulation methods can assist in describing and understanding complex networks of interacting proteins, providing fresh insights into the function and regulation of biological systems. Recent studies have investigated such processes by explicitly modelling the diffusion and interactions of individual molecules. In these approaches, two entities are considered to have interacted if they come within a set cutoff distance of each other.

RESULTS

In this study, a new model of bimolecular interactions is presented that uses a simple, probability-based description of the reaction process. This description is well-suited to simulations on timescales relevant to biological systems (from seconds to hours), and provides an alternative to the previous description given by Smoluchowski. In the present approach (TFB) the diffusion process is explicitly taken into account in generating the probability that two freely diffusing chemical entities will interact within a given time interval. It is compared to the Smoluchowski method, as modified by Andrews and Bray (AB).

CONCLUSION

When implemented, the AB & TFB methods give equivalent results in a variety of situations relevant to biology. Overall, the Smoluchowski method as modified by Andrews and Bray emerges as the most simple, robust and efficient method for simulating biological diffusion-reaction processes currently available.

The JigCell model builder: a spreadsheet interface for creating biochemical reaction network models

Converting a biochemical reaction network to a set of kinetic rate equations is tedious and error prone. We describe known interface paradigms for inputing models of intracellular regulatory networks: graphical layout (diagrams), wizards, scripting languages, and direct entry of chemical equations. We present the JigCell Model Builder, which allows users to define models as a set of reaction equations using a spreadsheet (an example of direct entry of equations) and outputs model definitions in the Systems Biology Markup Language, Level 2. We present the results of two usability studies. The spreadsheet paradigm demonstrated its effectiveness in reducing the number of errors made by modelers when compared to hand conversion of a wiring diagram to differential equations. A comparison of representatives of the four interface paradigms for a simple model of the cell cycle was conducted which measured time, mouse clicks, and keystrokes to enter the model, and the number of screens needed to view the contents of the model. All four paradigms had similar data entry times. The spreadsheet and scripting language approaches require significantly fewer screens to view the models than do the wizard or graphical layout approaches.

WebCell: a web-based environment for kinetic modeling and dynamic simulation of cellular networks

SUMMARY

WebCell is a web-based environment for managing quantitative and qualitative information on cellular networks and for interactively exploring their steady-state and dynamic behaviors in response to systemic perturbations. It is designed as a user-friendly web interface, allowing users to efficiently construct, visualize, analyze and store reaction network models, thereby facilitating kinetic modeling and in silico simulation of biological systems of interest. A collected model library is also available to provide comprehensive implications for cellular dynamics of the published models.

Hallucinogen actions on 5-HT receptors reveal distinct mechanisms of activation and signaling by G protein-coupled receptors

We review the effect of some key advances in the characterization of molecular mechanisms of signaling by G protein-coupled receptors (GPCRs) on our current understanding of mechanisms of drugs of abuse. These advances are illustrated by results from our ongoing work on the actions of hallucinogens on serotonin (5-HT) receptors. We show how a combined computational and experimental approach can reveal specific modes of receptor activation underlying the difference in properties of hallucinogens compared with nonhallucinogenic congeners. These modes of activation-that can produce distinct ligand-dependent receptor states-are identified in terms of structural motifs (SM) in molecular models of the receptors, which were shown to constitute conserved functional microdomains (FM). The role of several SM/FMs in the activation mechanism of the GPCRs is presented in detail to illustrate how this mechanism can lead to ligand-dependent modes of signaling by the receptors. Novel bioinformatics tools are described that were designed to support the quantitative mathematical modeling of ligand-specific signaling pathways activated by the 5-HT receptors targeted by hallucinogens. The approaches for mathematical modeling of signaling pathways activated by 5-HT receptors are described briefly in the context of ongoing work on detailed biochemical models of 5-HT2A, and combined 5-HT2A/5-HT1A, receptor-mediated activation of the MAPK 1,2 pathway. The continuing need for increasingly more realistic representation of signaling in dynamic compartments within the cell, endowed with spatio-temporal characteristics obtained from experiment, is emphasized. Such developments are essential for attaining a quantitative understanding of how the multiple functions of a cell are coordinated and regulated, and to evaluate the specifics of the perturbations caused by the drugs of abuse that target GPCRs.

Current challenges in quantitative modeling of epidermal growth factor signaling

Over the last decade, epidermal growth factor (EGF) signaling has been used repeatedly as a test-bed for pioneering computational systems biology. Recent breakthroughs in our molecular understanding of EGF signaling pose new challenges for mathematical modeling strategies. Three key areas emerge as particularly relevant: the pervasive importance of compartmentalization and endosomal trafficking; the complexity of signalosome complexes; and the regulatory influence of diffusion and spatiality. Each one of them demands a drastic change in current computational approaches. We discuss recent developments in the field that address these emerging aspects in a new generation of more realistic - and potential more useful - models of EGF signaling.

Modeling the emergence of multi-protein dynamic structures by principles of self-organization through the use of 3DSpi, a multi-agent-based software

Background

There is an increasing need for computer-generated models that can be used for explaining the emergence and predicting the behavior of multi-protein dynamic structures in cells. Multi-agent systems (MAS) have been proposed as good candidates to achieve this goal.

Results

We have created 3DSpi, a multi-agent based software that we used to explore the generation of multi-protein dynamic structures. Being based on a very restricted set of parameters, it is perfectly suited for exploring the minimal set of rules needed to generate large multi-protein structures. It can therefore be used to test the hypothesis that such structures are formed and maintained by principles of self-organization. We observed that multi-protein structures emerge and that the system behavior is very robust, in terms of the number and size of the structures generated. Furthermore, the generated structures very closely mimic spatial organization of real life multi-protein structures.

Conclusion

The behavior of 3DSpi confirms the considerable potential of MAS for modeling subcellular structures. It demonstrates that robust multi-protein structures can emerge using a restricted set of parameters and allows the exploration of the dynamics of such structures. A number of easy-to-implement modifications should make 3DSpi the virtual simulator of choice for scientists wishing to explore how topology interacts with time, to regulate the function of interacting proteins in living cells.

Dizzy: stochastic simulation of large-scale genetic regulatory networks

We describe Dizzy, a software tool for stochastically and deterministically modeling the spatially homogeneous kinetics of integrated large-scale genetic, metabolic, and signaling networks. Notable features include a modular simulation framework, reusable modeling elements, complex kinetic rate laws, multi-step reaction processes, steady-state noise estimation, and spatial compartmentalization.

Toward predictive models of mammalian cells

Progress in experimental and theoretical biology is likely to provide us with the opportunity to assemble detailed predictive models of mammalian cells. Using a functional format to describe the organization of mammalian cells, we describe current approaches for developing qualitative and quantitative models using data from a variety of experimental sources. Recent developments and applications of graph theory to biological networks are reviewed. The use of these qualitative models to identify the topology of regulatory motifs and functional modules is discussed. Cellular homeostasis and plasticity are interpreted within the framework of balance between regulatory motifs and interactions between modules. From this analysis we identify the need for detailed quantitative models on the basis of the representation of the chemistry underlying the cellular process. The use of deterministic, stochastic, and hybrid models to represent cellular processes is reviewed, and an initial integrated approach for the development of large-scale predictive models of a mammalian cell is presented.

simBio: a Java package for the development of detailed cell models

Quantitative dynamic computer models, which integrate a variety of molecular functions into a cell model, provide a powerful tool to create and test working hypotheses. We have developed a new modeling tool, the simBio package (freely available from ), which can be used for constructing cell models, such as cardiac cells (the Kyoto model from Matsuoka et al., 2003, 2004 a, b, the LRd model from Faber and Rudy, 2000, and the Noble 98 model from Noble et al., 1998), epithelial cells (Strieter et al., 1990) and pancreatic beta cells (Magnus and Keizer, 1998). The simBio package is written in Java, uses XML and can solve ordinary differential equations. In an attempt to mimic biological functional structures, a cell model is, in simBio, composed of independent functional modules called Reactors, such as ion channels and the sarcoplasmic reticulum, and dynamic variables called Nodes, such as ion concentrations. The interactions between Reactors and Nodes are described by the graph theory and the resulting graph represents a blueprint of an intricate cellular system. Reactors are prepared in a hierarchical order, in analogy to the biological classification. Each Reactor can be composed or improved independently, and can easily be reused for different models. This way of building models, through the combination of various modules, is enabled through the use of object-oriented programming concepts. Thus, simBio is a straightforward system for the creation of a variety of cell models on a common database of functional modules.

Intracellular Signaling: Spatial and Temporal Control

Cells integrate many inputs through complex networks of interacting signaling pathways. Systems approaches as well as computer-aided reductionist approaches attempt to “untangle the wires” and gain an intimate understanding of cells. But “understanding” any system is just the way that the human mind gains the ability to predict behavior. Computer simulations are an alternative way to achieve this goal—quite possibly the only way for complex systems. We have new tools to probe large sets of unknown interactions, and we have amassed enough detailed information to quantitatively describe many functional modules. Cell physiology has passed the threshold: the time to begin modeling is now.

Analyzing the biology on the system level

Although various genome projects have provided us enormous static sequence information, understanding of the sophisticated biology continues to require integrating the computational modeling, system analysis, technology development for experiments, and quantitative experiments all together to analyze the biology architecture on various levels, which is just the origin of systems biology subject. This review discusses the object, its characteristics, and research attentions in systems biology, and summarizes the analysis methods, experimental technologies, research developments, and so on in the four key fields of systems biology—systemic structures, dynamics, control methods, and design principles.

A systems analysis of importin-{alpha}-{beta} mediated nuclear protein import

Importin-beta (Impbeta) is a major transport receptor for Ran-dependent import of nuclear cargo. Impbeta can bind cargo directly or through an adaptor such as Importin-alpha (Impalpha). Factors involved in nuclear transport have been well studied, but systems analysis can offer further insight into regulatory mechanisms. We used computer simulation and real-time assays in intact cells to examine Impalpha-beta-mediated import. The model reflects experimentally determined rates for cargo import and correctly predicts that import is limited principally by Impalpha and Ran, but is also sensitive to NTF2. The model predicts that CAS is not limiting for the initial rate of cargo import and, surprisingly, that increased concentrations of Impbeta and the exchange factor, RCC1, actually inhibit rather than stimulate import. These unexpected predictions were all validated experimentally. The model revealed that inhibition by RCC1 is caused by sequestration of nuclear Ran. Inhibition by Impbeta results from depletion nuclear RanGTP, and, in support of this mechanism, expression of mRFP-Ran reversed the inhibition.

AgentCell: a digital single-cell assay for bacterial chemotaxis

MOTIVATION

In recent years, single-cell biology has focused on the relationship between the stochastic nature of molecular interactions and variability of cellular behavior. To describe this relationship, it is necessary to develop new computational approaches at the single-cell level.

RESULTS

We have developed AgentCell, a model using agent-based technology to study the relationship between stochastic intracellular processes and behavior of individual cells. As a test-bed for our approach we use bacterial chemotaxis, one of the best characterized biological systems. In this model, each bacterium is an agent equipped with its own chemotaxis network, motors and flagella. Swimming cells are free to move in a 3D environment. Digital chemotaxis assays reproduce experimental data obtained from both single cells and bacterial populations.

A signal transduction pathway model prototype II: Application to Ca2+-calmodulin signaling and myosin light chain phosphorylation

An agonist-initiated Ca(2+) signaling model for calmodulin (CaM) coupled to the phosphorylation of myosin light chains was created using a computer-assisted simulation environment. Calmodulin buffering was introduced as a module for directing sequestered CaM to myosin light chain kinase (MLCK) through Ca(2+)-dependent release from a buffering protein. Using differing simulation conditions, it was discovered that CaM buffering allowed transient production of more Ca(2+)-CaM-MLCK complex, resulting in elevated myosin light chain phosphorylation compared to nonbuffered control. Second messenger signaling also impacts myosin light chain phosphorylation through the regulation of myosin light chain phosphatase (MLCP). A model for MLCP regulation via its regulatory MYPT1 subunit and interaction of the CPI-17 inhibitor protein was assembled that incorporated several protein kinase subsystems including Rho-kinase, protein kinase C (PKC), and constitutive MYPT1 phosphorylation activities. The effects of the different routes of MLCP regulation depend upon the relative concentrations of MLCP compared to CPI-17, and the specific activities of protein kinases such as Rho and PKC. Phosphorylated CPI-17 (CPI-17P) was found to dynamically control activity during agonist stimulation, with the assumption that inhibition by CPI-17P (resulting from PKC activation) is faster than agonist-induced phosphorylation of MYPT1. Simulation results are in accord with literature measurements of MLCP and CPI-17 phosphorylation states during agonist stimulation, validating the predictive capabilities of the system.

STAT module can function as a biphasic amplitude filter

Signal transducer and actuator of transcription (STATs) are a family of transcription factors activated by various cytokines, growth factors and hormones. They are important mediators of immune responses and growth and differentiation of various cell types. The STAT signalling system represents a defined functional module with a pattern of signalling that is conserved from flies to mammals. In order to probe and gain insights into the signalling properties of the STAT module by computational means, we developed a simple non-linear ordinary differential equations model within the 'Virtual Cell' framework. Our results demonstrate that the STAT module can operate as a 'biphasic amplitude filter' with an ability to amplify input signals within a specific intermediate range. We show that dimerisation of phosphorylated STAT is crucial for signal amplification and the amplitude filtering function. We also demonstrate that maximal amplification at intermediate levels of STAT activation is a moderately robust property of STAT module. We propose that these observations can be extrapolated to the analogous SMAD signalling module.

UML as a cell and biochemistry modeling language

The systems biology community is building increasingly complex models and simulations of cells and other biological entities, and are beginning to look at alternatives to traditional representations such as those provided by ordinary differential equations (ODE). The lessons learned over the years by the software development community in designing and building increasingly complex telecommunication and other commercial real-time reactive systems, can be advantageously applied to the problems of modeling in the biology domain. Making use of the object-oriented (OO) paradigm, the unified modeling language (UML) and Real-Time Object-Oriented Modeling (ROOM) visual formalisms, and the Rational Rose RealTime (RRT) visual modeling tool, we describe a multi-step process we have used to construct top-down models of cells and cell aggregates. The simple example model described in this paper includes membranes with lipid bilayers, multiple compartments including a variable number of mitochondria, substrate molecules, enzymes with reaction rules, and metabolic pathways. We demonstrate the relevance of abstraction, reuse, objects, classes, component and inheritance hierarchies, multiplicity, visual modeling, and other current software development best practices. We show how it is possible to start with a direct diagrammatic representation of a biological structure such as a cell, using terminology familiar to biologists, and by following a process of gradually adding more and more detail, arrive at a system with structure and behavior of arbitrary complexity that can run and be observed on a computer. We discuss our CellAK (Cell Assembly Kit) approach in terms of features found in SBML, CellML, E-CELL, Gepasi, Jarnac, StochSim, Virtual Cell, and membrane computing systems.

Structure-based systems biology: a zoom lens for the cell

Systems biology seeks to explain complex biological systems, such as the cell, through the integration of many different types of information. Here, we discuss how the incorporation of high-resolution structural data can provide key molecular details often necessary to understand the complex connection between individual molecules and cell behavior. We suggest a process of zooming on the cell, from global networks through pathways to the precise atomic contacts at the interfaces of interacting proteins.

CESE

Cell electrophysiology simulation environment (CESE) is an integrated environment for performing simulations with a variety of electrophysiological models that have Hodgkin-Huxley and Markovian formulations of ionic currents. CESE is written in Java 2 and is readily portable to a number of operating systems. CESE allows execution of single-cell models and modification and clamping of model parameters, as well as data visualisation and analysis using a consistent interface. Model creation for CESE is facilitated by an object-oriented approach and use of an extensive modelling framework. The Web-based model repository is available.

AVAILABILITY

CESE and the Web-based model repository are available at http://cese.sourceforge.net/.

Modélisation numérique et simulation : nouvelles applications en pharmacologie

The complexity of pathophysiological mechanisms is beyond the capabilities of traditional approaches. Many of the decision-making problems in public health, such as initiating mass screening, are complex. Progress in genomics and proteomics, and the resulting extraordinary increase in knowledge with regard to interactions between gene expression, the environment and behaviour, the customisation of risk factors and the need to combine therapies that individually have minimal though well documented efficacy, has led doctors to raise new questions: how to optimise choice and the application of therapeutic strategies at the individual rather than the group level, while taking into account all the available evidence? This is essentially a problem of complexity with dimensions similar to the previous ones: multiple parameters with nonlinear relationships between them, varying time scales that cannot be ignored etc. Numerical modelling and simulation (in silico investigations) have the potential to meet these challenges. Such approaches are considered in drug innovation and development. They require a multidisciplinary approach, and this will involve modification of the way research in pharmacology is conducted.

Modeling of cell signaling pathways in macrophages by semantic networks

BACKGROUND

Substantial amounts of data on cell signaling, metabolic, gene regulatory and other biological pathways have been accumulated in literature and electronic databases. Conventionally, this information is stored in the form of pathway diagrams and can be characterized as highly "compartmental" (i.e. individual pathways are not connected into more general networks). Current approaches for representing pathways are limited in their capacity to model molecular interactions in their spatial and temporal context. Moreover, the critical knowledge of cause-effect relationships among signaling events is not reflected by most conventional approaches for manipulating pathways.

RESULTS

We have applied a semantic network (SN) approach to develop and implement a model for cell signaling pathways. The semantic model has mapped biological concepts to a set of semantic agents and relationships, and characterized cell signaling events and their participants in the hierarchical and spatial context. In particular, the available information on the behaviors and interactions of the PI3K enzyme family has been integrated into the SN environment and a cell signaling network in human macrophages has been constructed. A SN-application has been developed to manipulate the locations and the states of molecules and to observe their actions under different biological scenarios. The approach allowed qualitative simulation of cell signaling events involving PI3Ks and identified pathways of molecular interactions that led to known cellular responses as well as other potential responses during bacterial invasions in macrophages.

CONCLUSIONS

We concluded from our results that the semantic network is an effective method to model cell signaling pathways. The semantic model allows proper representation and integration of information on biological structures and their interactions at different levels. The reconstruction of the cell signaling network in the macrophage allowed detailed investigation of connections among various essential molecules and reflected the cause-effect relationships among signaling events. The simulation demonstrated the dynamics of the semantic network, where a change of states on a molecule can alter its function and potentially cause a chain-reaction effect in the system.

Analyzing cellular biochemistry in terms of molecular networks

One way to understand cells and circumscribe the function of proteins is through molecular networks. These networks take a variety of forms including webs of protein-protein interactions, regulatory circuits linking transcription factors and targets, and complex pathways of metabolic reactions. We first survey experimental techniques for mapping networks (e.g., the yeast two-hybrid screens). We then turn our attention to computational approaches for predicting networks from individual protein features, such as correlating gene expression levels or analyzing sequence coevolution. All the experimental techniques and individual predictions suffer from noise and systematic biases. These problems can be overcome to some degree through statistical integration of different experimental datasets and predictive features (e.g., within a Bayesian formalism). Next, we discuss approaches for characterizing the topology of networks, such as finding hubs and analyzing subnetworks in terms of common motifs. Finally, we close with perspectives on how network analysis represents a preliminary step toward a systems approach for modeling cells.

Two complementary, local excitation, global inhibition mechanisms acting in parallel can explain the chemoattractant-induced regulation of PI(3,4,5)P3 response in dictyostelium cells

Chemotaxing cells, such as Dictyostelium and mammalian neutrophils, sense shallow chemoattractant gradients and respond with highly polarized changes in cell morphology and motility. Uniform chemoattractant stimulation induces the transient translocations of several downstream signaling components, including phosphoinositide 3-kinase (PI3K), tensin homology protein (PTEN), and phosphatidylinositol 3,4,5-trisphosphate (PI(3,4,5)P3). In contrast, static spatial chemoattractant gradients elicit the persistent, amplified localization of these molecules. We have proposed a model in which the response to chemoattractant is regulated by a balance of a local excitation and a global inhibition, both of which are controlled by receptor occupancy. This model can account for both the transient and spatial responses to chemoattractants, but alone does not amplify the external gradient. In this article, we develop a model in which parallel local excitation, global inhibition mechanisms control the membrane binding of PI3K and PTEN. Together, the action of these enzymes induces an amplified PI(3,4,5)P3 response that agrees quantitatively with experimentally obtained plekstrin homology-green fluorescent protein distributions in latrunculin-treated cells. We compare the model's performance with that of several mutants in which one or both of the enzymes are disrupted. The model accounts for the observed response to multiple, simultaneous chemoattractant cues and can recreate the cellular response to combinations of temporal and spatial stimuli. Finally, we use the model to predict the response of a cell where only a fraction is stimulated by a saturating dose of chemoattractant.

Bioinformatics and cellular signaling

The understanding of cellular function requires an integrated analysis of context-specific, spatiotemporal data from diverse sources. Recent advances in describing the genomic and proteomic 'parts list' of the cell and deciphering the interrelationship of these parts are described, including genome-wide location analysis, standards for microarray data analysis, and two-hybrid and mass spectrometry approaches. This information is being collected and curated in databases such as the Alliance for Cellular Signaling (AfCS) Molecule Pages, which will serve as vital tools for the reconstruction and analysis of cellular signaling networks.

Quantitative analysis of signaling networks

The response of biological cells to environmental change is coordinated by protein-based signaling networks. These networks are to be found in both prokaryotes and eukaryotes. In eukaryotes, the signaling networks can be highly complex, some networks comprising of 60 or more proteins. The fundamental motif that has been found in all signaling networks is the protein phosphorylation/dephosphorylation cycle--the cascade cycle. At this time, the computational function of many of the signaling networks is poorly understood. However, it is clear that it is possible to construct a huge variety of control and computational circuits, both analog and digital from combinations of the cascade cycle. In this review, we will summarize the great versatility of the simple cascade cycle as a computational unit and towards the end give two examples, one prokaryotic chemotaxis circuit and the other, the eukaryotic MAPK cascade.

Toward large-scale modeling of the microbial cell for computer simulation

In the post-genomic era, the large-scale, systematic, and functional analysis of all cellular components using transcriptomics, proteomics, and metabolomics, together with bioinformatics for the analysis of the massive amount of data generated by these "omics" methods are the focus of intensive research activities. As a consequence of these developments, systems biology, whose goal is to comprehend the organism as a complex system arising from interactions between its multiple elements, becomes a more tangible objective. Mathematical modeling of microorganisms and subsequent computer simulations are effective tools for systems biology, which will lead to a better understanding of the microbial cell and will have immense ramifications for biological, medical, environmental sciences, and the pharmaceutical industry. In this review, we describe various types of mathematical models (structured, unstructured, static, dynamic, etc.), of microorganisms that have been in use for a while, and others that are emerging. Several biochemical/cellular simulation platforms to manipulate such models are summarized and the E-Cell system developed in our laboratory is introduced. Finally, our strategy for building a "whole cell metabolism model", including the experimental approach, is presented.

CellML: its future, present and past

Advances in biotechnology and experimental techniques have lead to the elucidation of vast amounts of biological data. Mathematical models provide a method of analysing this data; however, there are two issues that need to be addressed: (1) the need for standards for defining cell models so they can, for example, be exchanged across the World Wide Web, and also read into simulation software in a consistent format and (2) eliminating the errors which arise with the current method of model publication. CellML has evolved to meet these needs of the modelling community. CellML is a free, open-source, eXtensible markup language based standard for defining mathematical models of cellular function. In this paper we summarise the structure of CellML, its current applications (including biological pathway and electrophysiological models), and its future development--in particular, the development of toolsets and the integration of ontologies.

Integrating Gene Expression and Metabolic Profiles

Recent advances in high throughput technologies have generated an abundance of biological information, such as gene expression, protein-protein interaction, and metabolic data. These various types of data capture different aspects of the cellular response to environmental factors. Integrating data from different measurements enhances the ability of modeling frameworks to predict cellular function more accurately and can lead to a more coherent reconstruction of the underlying regulatory network structure. Different techniques, newly developed and borrowed, have been applied for the purpose of extracting this information from experimental data. In this study, we developed a framework to integrate metabolic and gene expression profiles for a hepatocellular system. Specifically, we applied genetic algorithm and partial least square analysis to identify important genes relevant to a specific cellular function. We identified genes 1) whose expression levels quantitatively predict a metabolic function and 2) that play a part in regulating a hepatocellular function and reconstructed their role in the metabolic network. The framework 1) preprocesses the gene expression data using statistical techniques, 2) selects genes using a genetic algorithm and couples them to a partial least squares analysis to predict cellular function, and 3) reconstructs, with the assistance of a literature search, the pathways that regulate cellular function, namely intracellular triglyceride and urea synthesis. This provides a framework for identifying cellular pathways that are active as a function of the environment and in turn helps to uncover the interplay between gene and metabolic networks.

Modeling regulatory networks at Virginia Tech

The life of a cell is governed by the physicochemical properties of a complex network of interacting macromolecules (primarily genes and proteins). Hence, a full scientific understanding of and rational engineering approach to cell physiology require accurate mathematical models of the spatial and temporal dynamics of these macromolecular assemblies, especially the networks involved in integrating signals and regulating cellular responses. The Virginia Tech Consortium is involved in three specific goals of DARPA's computational biology program (Bio-COMP): to create effective software tools for modeling gene-protein-metabolite networks, to employ these tools in creating a new generation of realistic models, and to test and refine these models by well-conceived experimental studies. The special emphasis of this group is to understand the mechanisms of cell cycle control in eukaryotes (yeast cells and frog eggs). The software tools developed at Virginia Tech are designed to meet general requirements of modeling regulatory networks and are collected in a problem-solving environment called JigCell.

The next step in systems biology: simulating the temporospatial dynamics of molecular network

As a result of the time- and context-dependency of gene expression, gene regulatory and signaling pathways undergo dynamic changes during development. Creating a model of the dynamics of molecular interaction networks offers enormous potential for understanding how a genome orchestrates the developmental processes of an organism. The dynamic nature of pathway topology calls for new modeling strategies that can capture transient molecular links at the runtime. The aim of this paper is to present a brief and informative, but not all-inclusive, viewpoint on the computational aspects of modeling and simulation of a non-static molecular network.

Simulating cellular dynamics through a coupled transcription, translation, metabolic model

In order to predict cell behavior in response to changes in its surroundings or to modifications of its genetic code, the dynamics of a cell are modeled using equations of metabolism, transport, transcription and translation implemented in the Karyote software. Our methodology accounts for the organelles of eukaryotes and the specialized zones in prokaryotes by dividing the volume of the cell into discrete compartments. Each compartment exchanges mass with others either through membrane transport or with a time delay effect associated with molecular migration. Metabolic and macromolecular reactions take place in user-specified compartments. Coupling among processes are accounted for and multiple scale techniques allow for the computation of processes that occur on a wide range of time scales. Our model is implemented to simulate the evolution of concentrations for a user-specifiable set of molecules and reactions that participate in cellular activity. The underlying equations integrate metabolic, transcription and translation reaction networks and provide a framework for simulating whole cells given a user-specified set of reactions. A rate equation formulation is used to simulate transcription from an input DNA sequence while the resulting mRNA is used via ribosome-mediated polymerization kinetics to accomplish translation. Feedback associated with the creation of species necessary for metabolism by the mRNA and protein synthesis modifies the rates of production of factors (e.g. nucleotides and amino acids) that affect the dynamics of transcription and translation. The concentrations of predicted proteins are compared with time series or steady state experiments. The expression and sequence of the predicted proteins are compared with experimental data via the construction of synthetic tryptic digests and associated mass spectra. We present the mathematical model showing the coupling of transcription, translation and metabolism in Karyote and illustrate some of its unique characteristics.

Local Excitation, Global Inhibition Mechanism for Gradient Sensing: An Interactive Applet

We have proposed a model in which cells detect gradients of chemoattractant by balancing a fast local excitation and a slower global inhibition. To illustrate this general mechanism, we have developed an interactive applet that mimics laboratory experiments in which either spatially homogeneous or heterogeneous stimuli of chemoattractant are applied.

Prospects of a computational origin of life endeavor

While the last century brought an exquisite understanding of the molecular basis of life, very little is known about the detailed chemical mechanisms that afforded the emergence of life on early earth. There is a broad agreement that the problem lies in the realm of chemistry, and likely resides in the formation and mutual interactions of carbon-based molecules in aqueous medium. Yet, present-day experimental approaches can only capture the synthesis and behavior of a few molecule types at a time. On the other hand, experimental simulations of prebiotic syntheses, as well as chemical analyses of carbonaceous meteorites, suggest that the early prebiotic hydrosphere contained many thousands of different compounds. The present paper explores the idea that given the limitations of test-tube approaches with regards to such a 'random chemistry' scenario, an alternative mode of analysis should be pursued. It is argued that as computational tools for the reconstruction of molecular interactions improve rapidly, it may soon become possible to perform adequate computer-based simulations of prebiotic evolution. We thus propose to launch a computational origin of life endeavor (http://ool.weizmann.ac.il/CORE), involving computer simulations of realistic complex prebiotic chemical networks. In the present paper we provide specific examples, based on a novel algorithmic approach, which constitutes a hybrid of molecular dynamics and stochastic chemistry. As one potential solution for the immense hardware requirements dictated by this approach, we have begun to implement an idle CPU harvesting scheme, under the title ool@home.

Protein-protein Interaction Networks: from Interactions to Networks

The goal of interaction proteomics that studies the protein-protein interactions of all expressed proteins is to understand biological processes that are strictly regulated by these interactions. The availability of entire genome sequences of many organisms and high-throughput analysis tools has led scientists to study the entire proteome (Pandey and Mann, 2000). There are various high-throughput methods for detecting protein interactions such as yeast two-hybrid approach and mass spectrometry to produce vast amounts of data that can be utilized to decipher protein functions in complicated biological networks. In this review, we discuss recent developments in analytical methods for large-scale protein interactions and the future direction of interaction proteomics.

Cytoscape: a software environment for integrated models of biomolecular interaction networks

Cytoscape is an open source software project for integrating biomolecular interaction networks with high-throughput expression data and other molecular states into a unified conceptual framework. Although applicable to any system of molecular components and interactions, Cytoscape is most powerful when used in conjunction with large databases of protein-protein, protein-DNA, and genetic interactions that are increasingly available for humans and model organisms. Cytoscape's software Core provides basic functionality to layout and query the network; to visually integrate the network with expression profiles, phenotypes, and other molecular states; and to link the network to databases of functional annotations. The Core is extensible through a straightforward plug-in architecture, allowing rapid development of additional computational analyses and features. Several case studies of Cytoscape plug-ins are surveyed, including a search for interaction pathways correlating with changes in gene expression, a study of protein complexes involved in cellular recovery to DNA damage, inference of a combined physical/functional interaction network for Halobacterium, and an interface to detailed stochastic/kinetic gene regulatory models.

Toward Automated Cell Model Development through Information Theory†

The objective of this paper is to present a methodology for developing and calibrating models of complex reaction/transport systems. In particular, the complex network of biochemical reaction/transport processes and their spatial organization make the development of a predictive model of a living cell a grand challenge for the 21st century. However, advances in reaction/transport modeling and the exponentially growing databases of genomic, proteomic, metabolic, and bioelectric data make cell modeling feasible, if these two elements can be automatically integrated in an unbiased fashion. In this paper, we present a procedure to integrate data with a new cell model, Karyote, that accounts for many of the physical processes needed to attain the goal of predictive modeling. Our integration methodology is based on the use of information theory. The model is integrated with a variety of types and qualities of experimental data using an objective error assessment approach. Data that can be used in this approach include NMR, spectroscopy, microscopy, and electric potentiometry. The approach is demonstrated on the well-studied Trypanosoma brucei system. A major obstacle for the development of a predictive cell model is that the complexity of these systems makes it unlikely that any model presently available will soon be complete in terms of the set of processes accounted for. Thus, one is faced with the challenge of calibrating and running an incomplete model. We present a probability functional method that allows the integration of experimental data and soft information such as choice of error measure, a priori information, and physically motivated regularization to address the incompleteness challenge.

In silico multicellular systems biology and minimal genomes

The in vivo and in silico understanding of genomes and networks in cellular and multicellular systems is essential for drug discovery for multicellular diseases. In silico methodologies, when integrated with in vivo engineering methods, lay the groundwork for understanding multicellular organisms and their genomes. The quest to construct a minimal cell can be followed by designed, minimal multicellular organisms. In silico multicellular systems biology will be essential in the design and construction of minimal genomes for minimal multicellular organisms. Advanced methodologies come to light that can aid drug discovery. These novel approaches include multicellular pharmacodynamics and networked multicellular pharmacodynamics.

Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores

We have developed a detailed mathematical model of ionic flux in beta-cells that includes the most essential channels and pumps in the plasma membrane. This model is coupled to equations describing Ca2+, inositol 1,4,5-trisphosphate (IP3), ATP, and Na+ homeostasis, including the uptake and release of Ca2+ by the endoplasmic reticulum (ER). In our model, metabolically derived ATP activates inward Ca2+ flux by regulation of ATP-sensitive K+ channels and depolarization of the plasma membrane. Results from the simulations support the hypothesis that intracellular Na+ and Ca2+ in the ER can be the main variables driving both fast (2-7 osc/min) and slow intracellular Ca2+ concentration oscillations (0.3-0.9 osc/min) and that the effect of IP3 on Ca2+ leak from the ER contributes to the pattern of slow calcium oscillations. Simulations also show that filling the ER Ca2+ stores leads to faster electrical bursting and Ca2+ oscillations. Specific Ca2+ oscillations in isolated beta-cell lines can also be simulated.

Kinetic analysis of receptor-activated phosphoinositide turnover

We studied the bradykinin-induced changes in phosphoinositide composition of N1E-115 neuroblastoma cells using a combination of biochemistry, microscope imaging, and mathematical modeling. Phosphatidylinositol-4,5-bisphosphate (PIP2) decreased over the first 30 s, and then recovered over the following 2-3 min. However, the rate and amount of inositol-1,4,5-trisphosphate (InsP3) production were much greater than the rate or amount of PIP2 decline. A mathematical model of phosphoinositide turnover based on this data predicted that PIP2 synthesis is also stimulated by bradykinin, causing an early transient increase in its concentration. This was subsequently confirmed experimentally. Then, we used single-cell microscopy to further examine phosphoinositide turnover by following the translocation of the pleckstrin homology domain of PLCdelta1 fused to green fluorescent protein (PH-GFP). The observed time course could be simulated by incorporating binding of PIP2 and InsP3 to PH-GFP into the model that had been used to analyze the biochemistry. Furthermore, this analysis could help to resolve a controversy over whether the translocation of PH-GFP from membrane to cytosol is due to a decrease in PIP2 on the membrane or an increase in InsP3 in cytosol; by computationally clamping the concentrations of each of these compounds, the model shows how both contribute to the dynamics of probe translocation.

Genome-scale microbial in silico models: the constraints-based approach

Genome sequencing and annotation has enabled the reconstruction of genome-scale metabolic networks. The phenotypic functions that these networks allow for can be defined and studied using constraints-based models and in silico simulation. Several useful predictions have been obtained from such in silico models, including substrate preference, consequences of gene deletions, optimal growth patterns, outcomes of adaptive evolution and shifts in expression profiles. The success rate of these predictions is typically in the order of 70-90% depending on the organism studied and the type of prediction being made. These results are useful as a basis for iterative model building and for several practical applications.

Understanding complex signaling networks through models and metaphors

Signaling networks are complex both in terms of the chemical and biophysical events that underlie them, and in the sheer number of interactions. Computer models are powerful tools to deal with both aspects of complexity, but their utility goes beyond simply replicating signaling events in silicon. Their great advantage is as a tool to understanding. The completeness of the description demanded by computer models highlights gaps in knowledge. The quantitative description in models facilitates a mapping between different kinds of analysis methods for complex systems. Systems analysis methods can highlight stable states of signaling networks and describe the transitions between them. Modeling also reveals functional similarities between signaling network properties and other well-understood systems such as electronic devices and neural networks. These suggest various metaphors as a tool to understanding. Based on such descriptions, it is possible to regard signaling networks as systems that decode complex inputs in time, space and chemistry into combinatorial output patterns of signaling activity. This would provide a natural interface to the combinatorial input patterns required by genetic circuits. Thus, a combination of computer modeling methods to capture the complexity and details, and useful abstractions revealed by these models, is necessary to achieve both rigorous description as well as human understanding.

Genetic "code": representations and dynamical models of genetic components and networks

Dynamical modeling of biological systems is becoming increasingly widespread as people attempt to grasp biological phenomena in their full complexity and make sense of an accelerating stream of experimental data. We review a number of recent modeling studies that focus on systems specifically involving gene expression and regulation. These systems include bacterial metabolic operons and phase-variable piliation, bacteriophages T7 and lambda, and interacting networks of eukaryotic developmental genes. A wide range of conceptual and mathematical representations of genetic components and phenomena appears in these works. We discuss these representations in depth and give an overview of the tools currently available for creating and exploring dynamical models. We argue that for modeling to realize its full potential as a mainstream biological research technique the tools must become more general and flexible, and formal, standardized representations of biological knowledge and data must be developed.

Modeling of signaling networks

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.