E-CELL: software environment for whole-cell simulation

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.

An evaluation of a system that recommends microarray experiments to perform to discover gene-regulation pathways

The main topic of this paper is modeling the expected value of experimentation (EVE) for discovering causal pathways in gene expression data. By experimentation we mean both interventions (e.g., a gene knockout experiment) and observations (e.g., passively observing the expression level of a "wild-type" gene). We introduce a system called GEEVE (causal discovery in Gene Expression data using Expected Value of Experimentation), which implements expected value of experimentation in discovering causal pathways using gene expression data. GEEVE provides the following assistance, which is intended to help biologists in their quest to discover gene-regulation pathways: Recommending which experiments to perform (with a focus on "knockout" experiments) using an expected value of experimentation method. Recommending the number of measurements (observational and experimental) to include in the experimental design, again using an EVE method. Providing a Bayesian analysis that combines prior knowledge with the results of recent microarray experimental results to derive posterior probabilities of gene regulation relationships. In recommending which experiments to perform (and how many times to repeat them) the EVE approach considers the biologist's preferences for which genes to focus the discovery process. Also, since exact EVE calculations are exponential in time, GEEVE incorporates approximation methods. GEEVE is able to combine data from knockout experiments with data from wild-type experiments to suggest additional experiments to perform and then to analyze the results of those microarray experimental results. It models the possibility that unmeasured (latent) variables may be responsible for some of the statistical associations among the expression levels of the genes under study. To evaluate the GEEVE system, we used a gene expression simulator to generate data from specified models of gene regulation. The results show that the GEEVE system gives better results than two recently published approaches (1) in learning the generating models of gene regulation and (2) in recommending experiments to perform.

Simulating complex intracellular processes using object-oriented computational modelling

The aim of this paper is to give an overview of computer modelling and simulation in cellular biology, in particular as applied to complex biochemical processes within the cell. This is illustrated by the use of the techniques of object-oriented modelling, where the computer is used to construct abstractions of objects in the domain being modelled, and these objects then interact within the computer to simulate the system and allow emergent properties to be observed. The paper also discusses the role of computer simulation in understanding complexity in biological systems, and the kinds of information which can be obtained about biology via simulation.

An enzyme mechanism language for the mathematical modeling of metabolic pathways

MOTIVATION

As a first step toward the elucidation of the systems biology of complex biological systems, it was our goal to mathematically model common enzyme catalytic and regulatory mechanisms that repeatedly appear in biological processes such as signal transduction and metabolic pathways.

RESULTS

We describe kMech, a Cellerator language extension that describes a suite of enzyme mechanisms. Each enzyme mechanism is parsed by kMech into a set of fundamental association-dissociation reactions that are translated by Cellerator into ordinary differential equations that are numerically solved by Mathematica. In addition, we present methods that use commonly available kinetic measurements to estimate rate constants required to solve these differential equations.

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.

Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks

The biochemical reaction networks include elementary reactions differing by many orders of magnitude in the numbers of molecules involved. The kinetics of reactions involving small numbers of molecules can be studied by exact stochastic simulation. This approach is not practical for the simulation of metabolic processes because of the computational cost of accounting for individual molecular collisions. We present the "maximal time step method," a novel approach combining the Gibson and Bruck algorithm with the Gillespie tau-leap method. This algorithm allows stochastic simulation of systems composed of both intensive metabolic reactions and regulatory processes involving small numbers of molecules. The method is applied to the simulation of glucose, lactose, and glycerol metabolism in Escherichia coli. The gene expression, signal transduction, transport, and enzymatic activities are modeled simultaneously. We show that random fluctuations in gene expression can propagate to the level of metabolic processes. In the cells switching from glucose to a mixture of lactose and glycerol, random delays in transcription initiation determine whether lactose or glycerol operon is induced. In a small fraction of cells severe decrease in metabolic activity may also occur. Both effects are epigenetically inherited by the progeny of the cell in which the random delay in transcription initiation occurred.

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.

Simulation tools for biochemical networks: evaluation of performance and usability

MOTIVATION

Simulation of dynamic biochemical systems is receiving considerable attention due to increasing availability of experimental data of complex cellular functions. Numerous simulation tools have been developed for numerical simulation of the behavior of a system described in mathematical form. However, there exist only a few evaluation studies of these tools. Knowledge of the properties and capabilities of the simulation tools would help bioscientists in building models based on experimental data.

RESULTS

We examine selected simulation tools that are intended for the simulation of biochemical systems. We choose four of them for more detailed study and perform time series simulations using a specific pathway describing the concentration of the active form of protein kinase C. We conclude that the simulation results are convergent between the chosen simulation tools. However, the tools differ in their usability, support for data transfer to other programs and support for automatic parameter estimation. From the experimentalists' point of view, all these are properties that need to be emphasized in the future.

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.

Determination of the core of a minimal bacterial gene set

The availability of a large number of complete genome sequences raises the question of how many genes are essential for cellular life. Trying to reconstruct the core of the protein-coding gene set for a hypothetical minimal bacterial cell, we have performed a computational comparative analysis of eight bacterial genomes. Six of the analyzed genomes are very small due to a dramatic genome size reduction process, while the other two, corresponding to free-living relatives, are larger. The available data from several systematic experimental approaches to define all the essential genes in some completely sequenced bacterial genomes were also considered, and a reconstruction of a minimal metabolic machinery necessary to sustain life was carried out. The proposed minimal genome contains 206 protein-coding genes with all the genetic information necessary for self-maintenance and reproduction in the presence of a full complement of essential nutrients and in the absence of environmental stress. The main features of such a minimal gene set, as well as the metabolic functions that must be present in the hypothetical minimal cell, are discussed.

From the sequence to cell modeling: comprehensive functional genomics in Escherichia coli

As a result of the enormous amount of information that has been collected with E. coli over the past half century (e.g. genome sequence, mutant phenotypes, metabolic and regulatory networks, etc.), we now have detailed knowledge about gene regulation, protein activity, several hundred enzyme reactions, metabolic pathways, macromolecular machines, and regulatory interactions for this model organism. However, understanding how all these processes interact to form a living cell will require further characterization, quantification, data integration, and mathematical modeling, systems biology. No organism can rival E. coli with respect to the amount of available basic information and experimental tractability for the technologies needed for this undertaking. A focused, systematic effort to understand the E. coli cell will accelerate the development of new post-genomic technologies, including both experimental and computational tools. It will also lead to new technologies that will be applicable to other organisms, from microbes to plants, animals, and humans. E. coli is not only the best studied free-living model organism, but is also an extensively used microbe for industrial applications, especially for the production of small molecules of interest. It is an excellent representative of Gram-negative commensal bacteria. E. coli may represent a perfect model organism for systems biology that is aimed at elucidating both its free-living and commensal life-styles, which should open the door to whole-cell modeling and simulation.

New strategy for the representation and the integration of biomolecular knowledge at a cellular scale

The combination of sequencing and post-sequencing experimental approaches produces huge collections of data that are highly heterogeneous both in structure and in semantics. We propose a new strategy for the integration of such data. This strategy uses structured sets of sequences as a unified representation of biological information and defines a probabilistic measure of similarity between the sets. Sets can be composed of sequences that are known to have a biological relationship (e.g. proteins involved in a complex or a pathway) or that share similar values for a particular attribute (e.g. expression profile). We have developed a software, BlastSets, which implements this strategy. It exploits a database where the sets derived from diverse biological information can be deposited using a standard XML format. For a given query set, BlastSets returns target sets found in the database whose similarity to the query is statistically significant. The tool allowed us to automatically identify verified relationships between correlated expression profiles and biological pathways using publicly available data for Saccharomyces cerevisiae. It was also used to retrieve the members of a complex (ribosome) based on the mining of expression profiles. These first results validate the relevance of the strategy and demonstrate the promising potential of BlastSets.

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.

A modular minimal cell model: purine and pyrimidine transport and metabolism

A more complete understanding of the relationship of cell physiology to genomic structure is desirable. Because of the intrinsic complexity of biological organisms, only the simplest cells will allow complete definition of all components and their interactions. The theoretical and experimental construction of a minimal cell has been suggested as a tool to develop such an understanding. Our ultimate goal is to convert a "coarse-grain" lumped parameter computer model of Escherichia coli into a genetically and chemically detailed model of a "minimal cell." The base E. coli model has been converted into a generalized model of a heterotrophic bacterium. This coarse-grain minimal cell model is functionally complete, with growth rate, composition, division, and changes in cell morphology as natural outputs from dynamic simulations where only the initial composition of the cell and of the medium are specified. A coarse-grain model uses pseudochemical species (or modules) that are aggregates of distinct chemical species that share similar chemistry and metabolic dynamics. This model provides a framework in which these modules can be "delumped" into chemical and genetic descriptions while maintaining connectivity to all other functional elements. Here we demonstrate that a detailed description of nucleotide precursors transport and metabolism is successfully integrated into the whole-cell model. This nucleotide submodel requires fewer (12) genes than other theoretical predictions in minimal cells. The demonstration of modularity suggests the possibility of developing modules in parallel and recombining them into a fully functional chemically and genetically detailed model of a prokaryote cell.

Network-based analysis of metabolic regulation in the human red blood cell

Reconstruction of cell-scale metabolic networks is now possible. A description of allowable metabolic network functions can be obtained using extreme pathways, which are the convex basis vectors of the solution space containing all steady state flux distributions. However, only a portion of these allowable network functions are physiologically possible due to kinetic and regulatory constraints. Methods are now needed that enable us to take a defined metabolic network and deduce candidate regulatory structures that control the selection of these physiologically relevant states. One such approach is the singular value decomposition (SVD) of extreme pathway matrices (P), which allows for the characterization of steady state solution spaces. Eigenpathways, which are the left singular vectors from the SVD of P, can be described and categorized by their biochemical function. SVD of P for the human red blood cell showed that the first five eigenpathways, out of a total of 23, effectively characterize all the relevant physiological states of red blood cell metabolism calculated with a detailed kinetic model. Thus, with five degrees of freedom the magnitude and nature of the regulatory needs are defined. Additionally, the dominant features of these first five eigenpathways described key metabolic splits that are indeed regulated in the human red blood cell. The extreme pathway matrix is derived directly from network topology and only knowledge of Vmax values is needed to reach these conclusions. Thus, we have implemented a network-based analysis of regulation that complements the study of individual regulatory events. This topological approach may provide candidate regulatory structures for metabolic networks with known stoichiometry but poorly characterized regulation.

Large-scale evaluation of in silico gene deletions in Saccharomyces cerevisiae

A large-scale in silico evaluation of gene deletions in Saccharomyces cerevisiae was conducted using a genome-scale reconstructed metabolic model. The effect of 599 single gene deletions on cell viability was simulated in silico and compared to published experimental results. In 526 cases (87.8%), the in silico results were in agreement with experimental observations when growth on synthetic complete medium was simulated. Viable phenotypes were correctly predicted in 89.4% (496 out of 555) and lethal phenotypes were correctly predicted in 68.2% (30 out of 44) of the cases considered. The in silico evaluation was solely based on the topological properties of the metabolic network which is based on well-established reaction stoichiometry. No interaction or regulatory information was accounted for in the in silico model. False predictions were analyzed on a case-by-case basis for four possible inadequacies of the in silico model: (1) incomplete media composition, (2) substitutable biomass components, (3) incomplete biochemical information, and (4) missing regulation. This analysis eliminated a number of false predictions and suggested a number of experimentally testable hypotheses. A genome-scale in silico model can thus be used to systematically reconcile existing data and fill in our knowledge gaps about an organism.

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.

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.

Modelling of Mammalian cells and cell culture processes

Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction - the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model.

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.

Description and interpretation of adaptive evolution of Escherichia coli K-12 MG1655 by using a genome-scale in silico metabolic model

Genome-scale in silico metabolic networks of Escherichia coli have been reconstructed. By using a constraint-based in silico model of a reconstructed network, the range of phenotypes exhibited by E. coli under different growth conditions can be computed, and optimal growth phenotypes can be predicted. We hypothesized that the end point of adaptive evolution of E. coli could be accurately described a priori by our in silico model since adaptive evolution should lead to an optimal phenotype. Adaptive evolution of E. coli during prolonged exponential growth was performed with M9 minimal medium supplemented with 2 g of alpha-ketoglutarate per liter, 2 g of lactate per liter, or 2 g of pyruvate per liter at both 30 and 37 degrees C, which produced seven distinct strains. The growth rates, substrate uptake rates, oxygen uptake rates, by-product secretion patterns, and growth rates on alternative substrates were measured for each strain as a function of evolutionary time. Three major conclusions were drawn from the experimental results. First, adaptive evolution leads to a phenotype characterized by maximized growth rates that may not correspond to the highest biomass yield. Second, metabolic phenotypes resulting from adaptive evolution can be described and predicted computationally. Third, adaptive evolution on a single substrate leads to changes in growth characteristics on other substrates that could signify parallel or opposing growth objectives. Together, the results show that genome-scale in silico metabolic models can describe the end point of adaptive evolution a priori and can be used to gain insight into the adaptive evolutionary process for E. coli.

Kinetic simulation of signal transduction system in hippocampal long-term potentiation with dynamic modeling of protein phosphatase 2A

We modeled and analyzed a signal transduction system of long-term potentiation (LTP) in hippocampal post-synapse. Bhalla and Iyengar [Science 283(1999) 381] have developed a hippocampal LTP model. In the conventional model, the concentration of protein phosphatase 2A (PP2A) was fixed. However, it was reported that dynamic inactivation of PP2A was essential for LTP [J. Neurochem. 74 (2000) 807]. We introduced a dynamic modeling of PP2A; inactivation (phosphorylation) of PP2A by calcium/calmodulin-dependent protein kinase II (CaMKII) in the presence of calcium/calmodulin, self-activation (autodephosphorylation) of PP2A, and inactivation (dephosphorylation) of CaMKII by PP2A. This model includes complex feedback loops; both CaMKII and PP2A are autoactivated, while they inactivate each other. Moreover, we proposed an analysis strategy for model validation by applying the results of sensitivity analysis. In our system, calcineurin (CaN) played an essential role, rather than the activation of protein kinase C (PKC) as documented in the conventional model. From results of the analysis of our model, we found the following robustness as characteristics of bistability in our model: (1). PP2A reactions against calcium ion (Ca(2+)) perturbation; (2). PP2A inactivation against PP2A increase; (3). protein phosphatase 1 (PP1) activation against PF2A increase; and (4). PP2A reactions against PP2A initial concentration. These properties facilitated LTP induction in our system. We showed that another mechanism could introduce bistable behavior by adding dynamic reactions of PP2A.

DiMSim: a discrete-event simulator of metabolic networks

A novel, scalable, quantitative, discrete-event simulator of metabolic and more general reaction pathways-DiMSim-has been developed. Rather than being modeled by systems of differential equations, metabolic pathways are viewed as bipartite graphs consisting of metabolites and reactions, linked by unidirectional or bidirectional arcs, and fluxes of metabolites emerge as the product of flows of the metabolites through the individual reactions. If required, DiMSim is able to model reactions involving single molecules up to molar concentrations so it is able to cope with the special characteristics of biochemical systems, including reversible reactions and discontinuous behavior, e.g. due to competition between reactions for limited quantities of reactants, product or allosteric inhibition and highly nonlinear behavior, e.g. due to cascades. It is also able to model membrane-bound compartments and the channels used to transport metabolites between them (both passive diffusion and active transport). While Michaelis-Menten kinetics is supported, DiMSim makes almost no assumptions other than each reaction having a fixed stoichiometry and that each reaction takes a stated amount of time.

Constraints-based models: regulation of gene expression reduces the steady-state solution space

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.

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.

Fluctuations and slow variables in genetic networks

Computer simulations of large genetic networks are often extremely time consuming because, in addition to the biologically interesting translation and transcription reactions, many less interesting reactions like DNA binding and dimerizations have to be simulated. It is desirable to use the fact that the latter occur on much faster timescales than the former to eliminate the fast and uninteresting reactions and to obtain effective models of the slow reactions only. We use three examples of self-regulatory networks to show that the usual reduction methods where one obtains a system of equations of the Hill type fail to capture the fluctuations that these networks exhibit due to the small number of molecules; moreover, they may even miss describing the behavior of the average number of proteins. We identify the inclusion of fast-varying variables in the effective description as the cause for the failure of the traditional schemes. We suggest a different effective description, which entails the introduction of an additional species, not present in the original networks, that is slowly varying. We show that this description allows for a very efficient simulation of the reduced system while retaining the correct fluctuations and behavior of the full system. This approach ought to be applicable to a wide range of genetic networks.

Sequence-based analysis of metabolic demands for protein synthesis in prokaryotes

Constraints-based models for microbial metabolism can currently be constructed on a genome-scale. These models do not account for RNA and protein synthesis. A scalable formalism to describe translation and transcription that can be integrated with the existing metabolic models is thus needed. Here, we developed such a formalism. The fundamental protein synthesis network described by this formalism was analysed via extreme pathway and flux balance analyses. The protein synthesis network exhibited one extreme pathway per messenger RNA synthesized and one extreme pathway per protein synthesized. The key parameters in this network included promoter strengths, messenger RNA half-lives, and the availability of nucleotide triphosphates, amino acids, RNA polymerase, and active ribosomes. Given these parameters, we were able to calculate a cell's material and energy expenditures for protein synthesis using a flux balance approach. The framework provided herein can subsequently be integrated with genome-scale metabolic models, providing a sequence-based accounting of the metabolic demands resulting from RNA and protein polymerization.

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.

Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth

Annotated genome sequences can be used to reconstruct whole-cell metabolic networks. These metabolic networks can be modelled and analysed (computed) to study complex biological functions. In particular, constraints-based in silico models have been used to calculate optimal growth rates on common carbon substrates, and the results were found to be consistent with experimental data under many but not all conditions. Optimal biological functions are acquired through an evolutionary process. Thus, incorrect predictions of in silico models based on optimal performance criteria may be due to incomplete adaptive evolution under the conditions examined. Escherichia coli K-12 MG1655 grows sub-optimally on glycerol as the sole carbon source. Here we show that when placed under growth selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700 generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico model. These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis.

Genotype-phenotype mapping: genes as computer programs

The effects of genes on phenotype are mediated by processes that are typically unknown but whose determination is desirable. The conversion from gene to phenotype is not a simple function of individual genes, but involves the complex interactions of many genes; it is what is known as a nonlinear mapping problem. A computational method called genetic programming allows the representation of candidate nonlinear mappings in several possible trees. To find the best model, the trees are 'evolved' by processes akin to mutation and recombination, and the trees that more closely represent the actual data are preferentially selected. The result is an improved tree of rules that represent the nonlinear mapping directly. In this way, the encoding of cellular and higher-order activities by genes is seen as directly analogous to computer programs. This analogy is of utility in biological genetics and in problems of genotype-phenotype mapping.

Cell Simulation for Circadian Rhythm Based on Michaelis-MentenModel

We report here the development of a cell biological simulation systembased on ordinary differential equations and the results on the simulationof the heat pulses' effects on the circadian rhythm in Drosophila.The simulator implements intra-cellular processes: transcription,translation, transport, modification (association, disassociation),degradation. It simulates the temporal behavior of concentrations ofproteins and mRNA involved in various biological phenomena. Moreover, thesystem is able to determine the exact type of reaction for a givenregulatory pathway. In order to prove the usefulness of the simulator weconstruct a model of the circadian rhythm in Drosophilaand wesimulate the effect of the heat pulses applied in early afternoon on thecircadian clock proteins PER and TIM. Our simulation results show therobustness of the genetic network as well as the important role playedby dClk mRNA in the mechanism of phase-shift responses.

Computational cell biology: spatiotemporal simulation of cellular events

The field of computational cell biology has emerged within the past 5 years because of the need to apply disciplined computational approaches to build and test complex hypotheses on the interacting structural, physical, and chemical features that underlie intracellular processes. To meet this need, newly developed software tools allow cell biologists and biophysicists to build models and generate simulations from them. The construction of general-purpose computational approaches is especially challenging if the spatial complexity of cellular systems is to be explicitly treated. This review surveys some of the existing efforts in this field with special emphasis on a system being developed in the authors' laboratory, Virtual Cell. The theories behind both stochastic and deterministic simulations are discussed. Examples of respective applications to cell biological problems in RNA trafficking and neuronal calcium dynamics are provided to illustrate these ideas.

Modeling and simulation of genetic regulatory systems: a literature review

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.

Exploring the formation of Alzheimer's disease senile plaques in silico

An experimental simulation environment suitable for exploring the neuroinflammatory hypothesis of Alzheimer's disease (AD) has been developed. Using scientific literature, we have calculated parameters and rates and constructed an interactive model system. The simulation can be manipulated to explore competing hypotheses about AD pathology, i.e. can be used as an experimental "in silico" system. In this paper, we outline the assumptions and aspects of the model, and illustrate qualitative and quantitative findings. The interactions of amyloid beta deposits, glial cell dynamics, inflammation and secreted cytokines, and the stress, recovery, and death of neuronal tissue are investigated. The model leads to qualitative insights about relative roles of the cells and chemicals in the disease pathology.

Metabolomics: quantification of intracellular metabolite dynamics

The rational improvement of microbial strains for the production of primary and secondary metabolites ('metabolic engineering') requires a quantitative understanding of microbial metabolism. A process by which this information can be derived from dynamic fermentation experiments is presented. By applying a substrate pulse to a substrate-limited, steady state culture, cellular metabolism is shifted away from its metabolic steady state. With the aid of a rapid sampling and quenching routine it is possible to take 4-5 samples per second during this process, thus capturing the metabolic response to this stimulus. Over 30 metabolites, nucleotides and cofactors from Escherichia coli metabolism can be extracted and analysed using a range of different techniques, for example enzymatic assays, HPLC and LC-MS methods. Using different substrates as limiting and pulse-substrates (glucose, glycerol), different metabolic pathways and substrate uptake systems are investigated. The resulting plots of intracellular metabolite concentrations against time serve as a data basis for modelling microbial metabolic networks.

Physiologically-based pharmacokinetic simulation modelling

Drug selection is now widely viewed as an important and relatively new, yet largely unsolved, bottleneck in the drug discovery and development process. In order to achieve an efficient selection process, high quality, rapid, predictive and correlative ADME models are required in order for them to be confidently used to support critical financial decisions. Systems that can be relied upon to accurately predict performance in humans have not existed, and decisions have been made using tools whose capabilities could not be verified until candidates went to clinical trial, leading to the high failure rates historically observed. However, with the sequencing of the human genome, advances in proteomics, the anticipation of the identification of a vastly greater number of potential targets for drug discovery, and the potential of pharmacogenomics to require individualized evaluation of drug kinetics as well as drug effects, there is an urgent need for rapid and accurately computed pharmacokinetic properties.

Modeling and simulation: tools for metabolic engineering

Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments are discussed.