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.

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Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks

The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

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Modeling and simulation of genetic regulatory systems: a literature review.

Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods.

Results: Here, we present COPASI, a platform-independent and user-friendly biochemical simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic--stochastic methods, and the importance of random number generator numerical resolution in stochastic simulation.

Availability: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel) and Sun Solaris (SPARC), as well as the full source code under an open source license from http://www.copasi.org.

Contact: mendes@vbi.vt.edu

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COPASI---a COmplex PAthway SImulator

Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.

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Stochastic Simulation of Chemical Kinetics

The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.

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Approximate accelerated stochastic simulation of chemically reacting systems

There are two fundamental ways to view coupled systems of chemical equations:  as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more common, systems with very small numbers of molecules are important in some applications (e.g., in small biological cells or in surface processes). In both views, most complicated systems with multiple reaction channels and multiple chemical species cannot be solved analytically. There are exact numerical simulation methods to simulate trajectories of discrete, stochastic systems, (methods that are rigorously equivalent to the Master Equation approach) but these do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate coupled chemical reactions that is also efficient:  it (a) uses only a single random number per simulation event, and (b) ...

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

The central dogma of molecular biology states that information is stored in DNA, transcribed to messenger RNA (mRNA) and then translated into proteins. This picture is significantly augmentated when we consider the action of certain proteins in regulating transcription. These transcription factors provide a feedback pathway by which genes can regulate one another's expression as mRNA and then as protein. To review: DNA, RNA and proteins have different functions. DNA is the molecular storehouse of genetic information. When cells divide, the DNA is replicated, so that each daughter cell maintains the same genetic information as the mother cell. RNA acts as a go-between from DNA to proteins. Only a single copy of DNA is present, but multiple copies of the same piece of RNA may be present, allowing cells to make huge amounts of protein. In eukaryotes (organisms with a nucleus), DNA is found in the nucleus only. RNA is copied in the nucleus then translocates(moves) outside the nucleus, where it is transcribed into proteins. Along the way, the RNA may be spliced, i.e., may have pieces cut out. RNA then attaches to ribosomes and is translated to proteins. Proteins are the machinery of the cell other than DNA and RNA, all the complex molecules of the cell are proteins. Proteins are specialized machines, each of which fulfills its own task, which may be transporting oxygen, catalyzing reactions, or responding to extracellular signals, just to name a few. One of the more interesting functions a protein may have is binding directly or indirectly to DNA to perform transcriptional regulation, thus forming a closed feedback loop of gene regulation. The structure of DNA and the central dogma were understood in the 50s; in the early 80s it became possible to make arbitrary modifications to DNA and use cellular machinery to transcribe and translate the resulting genes; more recently, genomes (i.e., the complete DNA sequence) of many organisms have been sequenced. This large-scale sequencing began with simple organisms, viruses and bacteria, progressed to eukaryotes such as yeast, and more recently (1998) progressed to a multi-cellular animal, the nematode Caenorhabditis elegans. Sequencers have now moved on to the fruit fly Drosophila melanogaster, whose sequence is slated for completion by the end of 1999. The human genome project is expected to determine the complete sequence of all 3 billion bases of human DNA within the next five years. In the wake of genome-scale sequencing, further instrumentation is being developed to assay gene expression and function on a comparably large scale. Much of the work in computational biology focuses on computational tools used in sequencing, finding genes that are related to a particular gene, finding which parts of the DNA code for proteins and which do not, understanding what proteins will be formed from a given length of DNA, predicting how the proteins will fold from a one-dimensional structure into a three dimensional structure, and so on. Much less computational work has been done regarding the function of proteins. One reason for this is that different proteins function very differently, and so work on protein function is very specific to certain classes of proteins. There are, for example, proteins such enzymes that catalyze various intracellular reactions, receptors that respond to extracellular signals and ion channels that regulate the flow of charged particles into and out of the cell. In this chapter, we will consider a particular class of proteins called transcription factors(TFs), which are responsible for regulating when a certain gene is expressed in a certain cell, which cells it is express in, and how much is expressed. Understanding these processes will involve developing a deeper understanding of transcription, translation, and the cellular processes that control those processes. All of these elements fall under the aegis of gene regulation or more narrowly transcriptional regulation. Some of the key questions in gene regulation are: What genes are expressed in a certain cell at a certain time? How does gene expression differ from cell to cell in a multicellular organism? Which proteins act as transcription factors, i.e., are important in regulating gene expression? From questions like these, we hope to understand which genes are important for various macroscopic processes. Nearly all of the cells of a multicellular organism contain the same DNA. Yet this same genetic information yields a large number of different cell types. The fundamental difference between a neuron and a liver cell, for example, is which genes are expressed. Thus understanding gene regulation is an important step in understanding development. Furthermore, understanding the usual genes that are expressed in cells may give important clues about various diseases. Some diseases, such as sickle cell anemia and cystic fibrosis, are caused by defects in single, non-regulatory genes; others, such as certain cancers, are caused when the cellular control circuitry malfunctions - an understanding of these diseases will involve pathways of multiple interacting gene products. There are numerous challenges in the area of understanding and modeling gene regulation. First and foremost, biologists would like to develop a deeper understanding of the processes involved, including which genes and families of genes are important, how they interact, etc. From a computation point of view, there has been embarrassingly little work done. In this chapter there are many areas in which we can phrase meaningful, non-trivial computational questions, but questions that have not been addressed. Some of these are purely computational (what is a good algorithm for dealing with a model of type X) and others are more mathematical (given a system with certain characteristics, what sort of model can one use? How does one find biochemical parameters from system-level behavior using as few experiments as possible?). In addition to biological and algorithmic problems, there is also the ever-present issue of theoretical biology - what general principles can be derived from these systems, what can one do with models other than just simulate time-courses, what can be deduced about a class of systems without knowing all the details? The fundamental challenge to computationalists and theorists is to add value to the biology - to use models, modeling techniques and algorithms to understand the biology in new ways.

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Modeling the Activity of Single Genes

The virtual completion of the genome project and prodigious amounts of work by different biologists throughout the world have elucidated many of the components of biological systems. The genes (and hence proteins) are largely known, and the tools of molecular biology allows one to manufacture and express them, so as to understand their function. Given this increased understanding of components, the next step in understanding complex biology will be understanding systems, which will almost certainly involve formal, detailed, and quantitative models. 
One of the great challenges of modeling biological systems is that they tend to “break the math.” Biological systems have small numbers of molecules, operate far from equilibrium, change shape and size, etc. This thesis develops mathematical and computational tools for biological systems with few molecules. Such systems are particularly problematic because the usual macroscopic view of chemistry, in which concentrations of molecules vary continuously, continually, and deterministically, does not work. Rather, one needs to use the mesoscopic view of chemistry: molecules undergo discrete reaction events, and the timing of these events is probabilistic. There are many standard numerical computational techniques for the macroscopic view, but far fewer for the mesoscopic view. 
This thesis develops (1) an efficient, exact stochastic simulation algorithm, to generate trajectories of mesoscopic biological systems, (2) a sensitivity analysis algorithm, to quantify how a model's predictions depend on the exact values of parameters (e.g., rate constants) used, and (3) a parameter estimation algorithm, to estimate the values of model parameters from observed trajectories.

Computational methods for stochastic biological systems

The previous chapter described several different kinds of models that are used to model gene regulation This chapter focuses exclusively on stochastic models (Van Kampen, 1992),(McQuarrie, 1967) As mentioned in the previous chapter, the stochastic framework is important when the number of molecules involved is small, the time scale is short, or both This chapter will not rehash the theoretical underpinnings of the previous chapter, but rather, will provide an extensive example, which illustrates many of the biological processes involved in (prokaryotic) gene regulation and also many of the stochastic processes used to model these biological processes The system to be modeled is part of the regulatory circuitry of lambda phage, and is a small subset of the complete model in (Arkin et al, 1998)

A probabilistic model of a prokaryotic gene and its regulation

Systems of weakly coupled chemical equations occur in gene regulation and other biological
systems. For small numbers of molecules (as in a small cell), the usual differential equations
approach to chemical kinetics must be replaced with a stochastic approach. To deal with this
kind of system, one generates trajectories through stochastic phase space. By generating a large
enough number of trajectories, one can understand the statistics of the behavior of the complex,
non-linear system.
The algorithms for dealing with sparsely connected stochastic processes are not as advanced
as those for sparse deterministic processes. In particular. the existing algorithm of choice for
generating trajectories, which is not optimized in any way for sparseness, is O(rE), where r is
the number of reactions and E is the number of reaction events in the trajectory. \Ye present
two algorithms of O(r + Elogr), one of which is a simple extension of the existing algorithm,
and the other of which is more subtle. The latter is more easily extended to include stochastic
processes of different types.
We apply our faster algorithm to a model of bacteriophage lambda and are able to run the
same calculations on a cluster of desktop workstations that previously required a supercomputer.
This allows us to run more complicated calculations than could be done previously. As an
example of this, we analyse the sensitivity of the lambda model to the values of several of
its parameters. We find that the model is relatively insensitive to changes in the translation
rate, protein dimerization rates and protein degradation rates; is somewhat sensitive to the
transcription rate. and is extremely sensitive to the average number of proteins per mRNA
transcript.

Michael A. Gibson

Papers

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

Modeling the Activity of Single Genes

Computational methods for stochastic biological systems

A probabilistic model of a prokaryotic gene and its regulation

An Efficient Algorithm for Generating Trajectories of Stochastic Gene Regulation Reactions