Conservation analysis in biochemical networks: computational issues for software writers

First-order ultrasensitivity in phosphorylation cycles

Cellular signal transduction takes place through a network of phosphorylation cycles. These pathways take the form of a multi-layered cascade of cycles. This work focuses on the sensitivity of single, double and n length cycles. Cycles that operate in the zero-order regime can become sensitive to changes in signal, resulting in zero-order ultrasensitivity (ZOU). Using frequency analysis, we confirm previous efforts that cascades can act as noise filters by computing the bandwidth. We show that n length cycles display what we term first-order ultrasensitivity which occurs even when the cycles are not operating in the zero-order regime. The magnitude of the sensitivity, however, has an upper bound equal to the number of cycles. It is known that ZOU can be significantly reduced in the presence of retroactivity. We show that the first-order ultrasensitivity is immune to retroactivity and that the ZOU and first-order ultrasensitivity can be blended to create systems with constant sensitivity over a wider range of signal. We show that the ZOU in a double cycle is only modestly higher compared with a single cycle. We therefore speculate that the double cycle has evolved to enable amplification even in the face of retroactivity.

Sensitivity and Frequency Response of Biochemical Cascades

Signal transduction from a cell's surface to cytoplasmic and nuclear targets takes place through a complex network of interconnected pathways. Phosphorylation cycles are common components of many pathways and may take the form of a multi-layered cascade of cycles or incorporate species with multiple phosphorylation sites that effectively create a sequence of cycles with increasing states of phosphorylation. This work focuses on the frequency response and sensitivity of such systems, two properties that have not been thoroughly examined. Starting with a singularly phosphorylated single-cycle system, we compare the sensitivity to perturbation at steady-state across a range of input signal strengths. This is followed by a frequency response analysis focusing on the gain and associated bandwidth. Next, we consider a two-layer cascade of single phosphorylation cycles and focus on how the two cycles interact to produce various effects on the bandwidth and damping properties. Then we consider the (ultra)sensitivity of a doubly phosphorylated system, where we describe in detail first-order ultrasensitivity, a unique property of these systems, which can be blended with zero-order ultrasensitivity to create systems with relatively constant gain over a range of signal input. Finally, we give an in-depth analysis of the sensitivity of an n-phosphorylated system.

BioUML: an integrated environment for systems biology and collaborative analysis of biomedical data

BioUML (homepage: http://www.biouml.org, main public server: https://ict.biouml.org) is a web-based integrated environment (platform) for systems biology and the analysis of biomedical data generated by omics technologies. The BioUML vision is to provide a computational platform to build virtual cell, virtual physiological human and virtual patient. BioUML spans a comprehensive range of capabilities, including access to biological databases, powerful tools for systems biology (visual modelling, simulation, parameters fitting and analyses), a genome browser, scripting (R, JavaScript) and a workflow engine. Due to integration with the Galaxy platform and R/Bioconductor, BioUML provides powerful possibilities for the analyses of omics data. The plug-in-based architecture allows the user to add new functionalities using plug-ins. To facilitate a user focus on a particular task or database, we have developed several predefined perspectives that display only those web interface elements that are needed for a specific task. To support collaborative work on scientific projects, there is a central authentication and authorization system (https://bio-store.org). The diagram editor enables several remote users to simultaneously edit diagrams.

Application of Parameter Optimization to Search for Oscillatory Mass-Action Networks Using Python

Biological systems can be described mathematically to model the dynamics of metabolic, protein, or gene-regulatory networks, but locating parameter regimes that induce a particular dynamic behavior can be challenging due to the vast parameter landscape, particularly in large models. In the current work, a Pythonic implementation of existing bifurcation objective functions, which reward systems that achieve a desired bifurcation behavior, is implemented to search for parameter regimes that permit oscillations or bistability. A differential evolution algorithm progressively approximates the specified bifurcation type while performing a global search of parameter space for a candidate with the best fitness. The user-friendly format facilitates integration with systems biology tools, as Python is a ubiquitous programming language. The bifurcation–evolution software is validated on published models from the BioModels Database and used to search populations of randomly-generated mass-action networks for oscillatory dynamics. Results of this search demonstrate the importance of reaction enrichment to provide flexibility and enable complex dynamic behaviors, and illustrate the role of negative feedback and time delays in generating oscillatory dynamics.

Tellurium: An extensible python-based modeling environment for systems and synthetic biology

Here we present Tellurium, a Python-based environment for model building, simulation, and analysis that facilitates reproducibility of models in systems and synthetic biology. Tellurium is a modular, cross-platform, and open-source simulation environment composed of multiple libraries, plugins, and specialized modules and methods. Tellurium is a self-contained modeling platform which comes with a fully configured Python distribution. Two interfaces are provided, one based on the Spyder IDE which has an accessible user interface akin to MATLAB and a second based on the Jupyter Notebook, which is a format that contains live code, equations, visualizations, and narrative text. Tellurium uses libRoadRunner as the default SBML simulation engine which supports deterministic simulations, stochastic simulations, and steady-state analyses. Tellurium also includes Antimony, a human-readable model definition language which can be converted to and from SBML. Other standard Python scientific libraries such as NumPy, SciPy, and matplotlib are included by default. Additionally, we include several user-friendly plugins and advanced modules for a wide-variety of applications, ranging from complex algorithms for bifurcation analysis to multidimensional parameter scanning. By combining multiple libraries, plugins, and modules into a single package, Tellurium provides a unified but extensible solution for biological modeling and analysis for both novices and experts.

AVAILABILITY

tellurium.analogmachine.org.

A portable structural analysis library for reaction networks

The topology of a reaction network can have a significant influence on the network's dynamical properties. Such influences can include constraints on network flows and concentration changes or more insidiously result in the emergence of feedback loops. These effects are due entirely to mass constraints imposed by the network configuration and are important considerations before any dynamical analysis is made. Most established simulation software tools usually carry out some kind of structural analysis of a network before any attempt is made at dynamic simulation. In this paper, we describe a portable software library, libStructural, that can carry out a variety of popular structural analyses that includes conservation analysis, flux dependency analysis and enumerating elementary modes. The library employs robust algorithms that allow it to be used on large networks with more than a two thousand nodes. The library accepts either a raw or fully labeled stoichiometry matrix or models written in SBML format. The software is written in standard C/C++ and comes with extensive on-line documentation and a test suite. The software is available for Windows, Mac OS X, and can be compiled easily on any Linux operating system. A language binding for Python is also available through the pip package manager making it simple to install on any standard Python distribution. The bulk of the source code is licensed under the open source BSD license with other parts using as either the MIT license or more simply public domain. All source is available on GitHub (https://github.com/sys-bio/Libstructural).

Acceleration Strategies to Enhance Metabolic Ensemble Modeling Performance

Developing reliable, predictive kinetic models of metabolism is a difficult, yet necessary, priority toward understanding and deliberately altering cellular behavior. Constraint-based modeling has enabled the fields of metabolic engineering and systems biology to make great strides in interrogating cellular metabolism but does not provide sufficient insight into regulation or kinetic limitations of metabolic pathways. Moreover, the growth-optimized assumptions that constraint-based models often rely on do not hold when studying stationary or persistor cell populations. However, developing kinetic models provides many unique challenges, as many of the kinetic parameters and rate laws governing individual enzymes are unknown. Ensemble modeling (EM) was developed to circumnavigate this challenge and effectively sample the large kinetic parameter solution space using consistent experimental datasets. Unfortunately, EM, in its base form, requires long solve times to complete and often leads to unstable kinetic model predictions. Furthermore, these limitations scale prohibitively with increasing model size. As larger metabolic models are developed with increasing genetic information and experimental validation, the demand to incorporate kinetic information increases. Therefore, in this work, we have begun to tackle the challenges of EM by introducing additional steps to the existing method framework specifically through reducing computation time and optimizing parameter sampling. We first reduce the structural complexity of the network by removing dependent species, and second, we sample locally stable parameter sets to reflect realistic biological states of cells. Lastly, we presort the screening data to eliminate the most incorrect predictions in the earliest screening stages, saving further calculations in later stages. Our complementary improvements to this EM framework are easily incorporated into concurrent EM efforts and broaden the application opportunities and accessibility of kinetic modeling across the field.

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.

A combined model reduction algorithm for controlled biochemical systems

BACKGROUND

Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest.

METHODS

In this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an 'averaged' lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of 'controlled' biochemical networks.

RESULTS

The algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system's input-output response even for highly complex networks.

CONCLUSIONS

Through application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation.

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

Conserved moieties are transferred between metabolites in internal reactions of a metabolic network but are not synthesised, degraded or exchanged with the environment. The total amount of a conserved moiety in the metabolic network is therefore constant over time. Metabolites that share a conserved moiety have interdependent concentrations because their total amount is constant. Identification of conserved moieties results in a concise description of all concentration dependencies in a metabolic network. The problem of identifying conserved moieties has previously been formulated in terms of the stoichiometry of metabolic reactions. Methods based on this formulation are computationally intractable for large networks. We show that reaction stoichiometry alone gives insufficient information to identify conserved moieties. By first incorporating additional data on the fate of atoms in metabolic reactions, we developed and implemented a computationally tractable algorithm to identify conserved moieties and their atomic structure.

Cell scale host-pathogen modeling: another branch in the evolution of constraint-based methods

Constraint-based models have become popular methods for systems biology as they enable the integration of complex, disparate datasets in a biologically cohesive framework that also supports the description of biological processes in terms of basic physicochemical constraints and relationships. The scope, scale, and application of genome scale models have grown from single cell bacteria to multi-cellular interaction modeling; host-pathogen modeling represents one of these examples at the current horizon of constraint-based methods. There are now a small number of examples of host-pathogen constraint-based models in the literature, however there has not yet been a definitive description of the methodology required for the functional integration of genome scale models in order to generate simulation capable host-pathogen models. Herein we outline a systematic procedure to produce functional host-pathogen models, highlighting steps which require debugging and iterative revisions in order to successfully build a functional model. The construction of such models will enable the exploration of host-pathogen interactions by leveraging the growing wealth of omic data in order to better understand mechanism of infection and identify novel therapeutic strategies.

Systems Biology Markup Language (SBML) Level 2 Version 5: Structures and Facilities for Model Definitions

Computational models can help researchers to interpret data, understand biological function, and make quantitative predictions. The Systems Biology Markup Language (SBML) is a file format for representing computational models in a declarative form that can be exchanged between different software systems. SBML is oriented towards describing biological processes of the sort common in research on a number of topics, including metabolic pathways, cell signaling pathways, and many others. By supporting SBML as an input/output format, different tools can all operate on an identical representation of a model, removing opportunities for translation errors and assuring a common starting point for analyses and simulations. This document provides the specification for Version 5 of SBML Level 2. The specification defines the data structures prescribed by SBML as well as their encoding in XML, the eXtensible Markup Language. This specification also defines validation rules that determine the validity of an SBML document, and provides many examples of models in SBML form. Other materials and software are available from the SBML project web site, http://sbml.org.

The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 1 Core

Computational models can help researchers to interpret data, understand biological function, and make quantitative predictions. The Systems Biology Markup Language (SBML) is a file format for representing computational models in a declarative form that can be exchanged between different software systems. SBML is oriented towards describing biological processes of the sort common in research on a number of topics, including metabolic pathways, cell signaling pathways, and many others. By supporting SBML as an input/output format, different tools can all operate on an identical representation of a model, removing opportunities for translation errors and assuring a common starting point for analyses and simulations. This document provides the specification for Version 1 of SBML Level 3 Core. The specification defines the data structures prescribed by SBML as well as their encoding in XML, the eXtensible Markup Language. This specification also defines validation rules that determine the validity of an SBML document, and provides many examples of models in SBML form. Other materials and software are available from the SBML project web site, http://sbml.org/.

Exploiting stoichiometric redundancies for computational efficiency and network reduction

Analysis of metabolic networks typically begins with construction of the stoichiometry matrix, which characterizes the network topology. This matrix provides, via the balance equation, a description of the potential steady-state flow distribution. This paper begins with the observation that the balance equation depends only on the structure of linear redundancies in the network, and so can be stated in a succinct manner, leading to computational efficiencies in steady-state analysis. This alternative description of steady-state behaviour is then used to provide a novel method for network reduction, which complements existing algorithms for describing intracellular networks in terms of input-output macro-reactions (to facilitate bioprocess optimization and control). Finally, it is demonstrated that this novel reduction method can be used to address elementary mode analysis of large networks: the modes supported by a reduced network can capture the input-output modes of a metabolic module with significantly reduced computational effort.

Identifying all moiety conservation laws in genome-scale metabolic networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Nonlinear biochemical signal processing via noise propagation

Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance, fluctuations in biochemical activities become significant and such "noise" can propagate through regulatory cascades in terms of biochemical reaction networks. Here we develop an intuitive, yet fully quantitative method for analyzing how noise affects cellular phenotypes based on identifying a system's nonlinearities and noise propagations. We observe that such noise can simultaneously enhance sensitivities in one behavioral region while reducing sensitivities in another. Employing this novel phenomenon we designed three biochemical signal processing modules: (a) A gene regulatory network that acts as a concentration detector with both enhanced amplitude and sensitivity. (b) A non-cooperative positive feedback system, with a graded dose-response in the deterministic case, that serves as a bistable switch due to noise-induced ultra-sensitivity. (c) A noise-induced linear amplifier for gene regulation that requires no feedback. The methods developed in the present work allow one to understand and engineer nonlinear biochemical signal processors based on fluctuation-induced phenotypes.

Network reconstruction of platelet metabolism identifies metabolic signature for aspirin resistance

Recently there has not been a systematic, objective assessment of the metabolic capabilities of the human platelet. A manually curated, functionally tested, and validated biochemical reaction network of platelet metabolism, iAT-PLT-636, was reconstructed using 33 proteomic datasets and 354 literature references. The network contains enzymes mapping to 403 diseases and 231 FDA approved drugs, alluding to an expansive scope of biochemical transformations that may affect or be affected by disease processes in multiple organ systems. The effect of aspirin (ASA) resistance on platelet metabolism was evaluated using constraint-based modeling, which revealed a redirection of glycolytic, fatty acid, and nucleotide metabolism reaction fluxes in order to accommodate eicosanoid synthesis and reactive oxygen species stress. These results were confirmed with independent proteomic data. The construction and availability of iAT-PLT-636 should stimulate further data-driven, systems analysis of platelet metabolism towards the understanding of pathophysiological conditions including, but not strictly limited to, coagulopathies.

Basic concepts and principles of stoichiometric modeling of metabolic networks

Metabolic networks supply the energy and building blocks for cell growth and maintenance. Cells continuously rewire their metabolic networks in response to changes in environmental conditions to sustain fitness. Studies of the systemic properties of metabolic networks give insight into metabolic plasticity and robustness, and the ability of organisms to cope with different environments. Constraint-based stoichiometric modeling of metabolic networks has become an indispensable tool for such studies. Herein, we review the basic theoretical underpinnings of constraint-based stoichiometric modeling of metabolic networks. Basic concepts, such as stoichiometry, chemical moiety conservation, flux modes, flux balance analysis, and flux solution spaces, are explained with simple, illustrative examples. We emphasize the mathematical definitions and their network topological interpretations.

Symbolic flux analysis for genome-scale metabolic networks

Background

With the advent of genomic technology, the size of metabolic networks that are subject to analysis is growing. A common task when analyzing metabolic networks is to find all possible steady state regimes. There are several technical issues that have to be addressed when analyzing large metabolic networks including accumulation of numerical errors and presentation of the solution to the researcher. One way to resolve those technical issues is to analyze the network using symbolic methods. The aim of this paper is to develop a routine that symbolically finds the steady state solutions of large metabolic networks.

Results

A symbolic Gauss-Jordan elimination routine was developed for analyzing large metabolic networks. This routine was tested by finding the steady state solutions for a number of curated stoichiometric matrices with the largest having about 4000 reactions. The routine was able to find the solution with a computational time similar to the time used by a numerical singular value decomposition routine. As an advantage of symbolic solution, a set of independent fluxes can be suggested by the researcher leading to the formation of a desired flux basis describing the steady state solution of the network. These independent fluxes can be constrained using experimental data. We demonstrate the application of constraints by calculating a flux distribution for the central metabolic and amino acid biosynthesis pathways of yeast.

Conclusions

We were able to find symbolic solutions for the steady state flux distribution of large metabolic networks. The ability to choose a flux basis was found to be useful in the constraint process and provides a strong argument for using symbolic Gauss-Jordan elimination in place of singular value decomposition.

Genome-scale metabolic networks

During the last decade, models have been developed to characterize cellular metabolism at the level of an entire metabolic network. The main concept that underlies whole-network metabolic modeling is the identification and mathematical definition of constraints. Here, we review large-scale metabolic network modeling, in particular, stoichiometric- and constraint-based approaches. Although many such models have been reconstructed, few networks have been extensively validated and tested experimentally, and we focus on these. We describe how metabolic networks can be represented using stoichiometric matrices and well-defined constraints on metabolic fluxes. We then discuss relatively successful approaches, including flux balance analysis (FBA), pathway analysis, and common extensions or modifications to these approaches. Finally, we describe techniques for integrating these approaches with models of other biological processes.

Towards a genome-scale kinetic model of cellular metabolism

Background

Advances in bioinformatic techniques and analyses have led to the availability of genome-scale metabolic reconstructions. The size and complexity of such networks often means that their potential behaviour can only be analysed with constraint-based methods. Whilst requiring minimal experimental data, such methods are unable to give insight into cellular substrate concentrations. Instead, the long-term goal of systems biology is to use kinetic modelling to characterize fully the mechanics of each enzymatic reaction, and to combine such knowledge to predict system behaviour.

Results

We describe a method for building a parameterized genome-scale kinetic model of a metabolic network. Simplified linlog kinetics are used and the parameters are extracted from a kinetic model repository. We demonstrate our methodology by applying it to yeast metabolism. The resultant model has 956 metabolic reactions involving 820 metabolites, and, whilst approximative, has considerably broader remit than any existing models of its type. Control analysis is used to identify key steps within the system.

Conclusions

Our modelling framework may be considered a stepping-stone toward the long-term goal of a fully-parameterized model of yeast metabolism. The model is available in SBML format from the BioModels database (BioModels ID: MODEL1001200000) and at http://www.mcisb.org/resources/genomescale/.

Computational modeling in systems biology

Interactions among cellular constituents play a crucial role in overall cellular function and organization. These interactions can be viewed as being complementary to the usual "parts list" of genes and proteins and, in conjunction with the expression states of these parts, are key to a systems level understanding of the cell. Here, we review computational approaches to the understanding of the functional roles of cellular networks, ranging from "static" models of network topology to dynamical and stochastic simulations.

Modeling molecular regulatory networks with JigCell and PET

We demonstrate how to model macromolecular regulatory networks with JigCell and the Parameter Estimation Toolkit (PET). These software tools are designed specifically to support the process typically used by systems biologists to model complex regulatory circuits. A detailed example illustrates how a model of the cell cycle in frog eggs is created and then refined through comparison of simulation output with experimental data. We show how parameter estimation tools automatically generate rate constants that fit a model to experimental data.

Network dynamics

Probably one of the most characteristic features of a living system is its continual propensity to change as it juggles the demands of survival with the need to replicate. Internally these adjustments are manifest as changes in metabolite, protein, and gene activities. Such changes have become increasingly obvious to experimentalists, with the advent of high-throughput technologies. In this chapter we highlight some of the quantitative approaches used to rationalize the study of cellular dynamics. The chapter focuses attention on the analysis of quantitative models based on differential equations using biochemical control theory. Basic pathway motifs are discussed, including straight chain, branched, and cyclic systems. In addition, some of the properties conferred by positive and negative feedback loops are discussed, particularly in relation to bistability and oscillatory dynamics.

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.

How does a cell know what type of cell it is supposed to become? How do external chemical signals change the underlying “state” of the cell? How are response pathways triggered on the application of a stress? Such questions of differentiation, signal transduction, and stress response, while seemingly diverse, all pertain to the storage of state information, or “memory,” by biochemical switches. Just as a computer memory unit can store a bit of 0 or 1 through electrical signals, a biochemical switch can be in one of two states, where chemical signals are on or off. This lets the cell record the presence/absence of an environmental stimulus, the level of a signaling molecule, or the result of a cell fate decision. There are a small number of published ways by which a group of chemical reactions come together to realize a switch. We undertook an exhaustive computational exploration to see if chemical switches are indeed rare and found, surprisingly, that they are actually abundant, highly diverse, but related to one another. Our catalog of switches opens up new bioinformatics approaches to understanding cellular decision making and cellular memory.

Facile: a command-line network compiler for systems biology

BACKGROUND

A goal of systems biology is the quantitative modelling of biochemical networks. Yet for many biochemical systems, parameter values and even the existence of interactions between some chemical species are unknown. It is therefore important to be able to easily investigate the effects of adding or removing reactions and to easily perform a bifurcation analysis, which shows the qualitative dynamics of a model for a range of parameter values.

RESULTS

We present Facile, a Perl command-line tool for analysing the dynamics of a systems biology model. Facile implements the law of mass action to automatically compile a biochemical network (written as, for example, E + S <-> C) into scripts for analytical analysis (Mathematica and Maple), for simulation (XPP and Matlab), and for bifurcation analysis (AUTO). Facile automatically identifies mass conservations and generates the reduced form of a model with the minimum number of independent variables. This form is essential for bifurcation analysis, and Facile produces a C version of the reduced model for AUTO.

CONCLUSION

Facile is a simple, yet powerful, tool that greatly accelerates analysis of the dynamics of a biochemical network. By acting at the command-line and because of its intuitive, text-based input, Facile is quick to learn and can be incorporated into larger programs or into automated tasks.

Systems biology--an engineering perspective

The interdisciplinary field of systems biology has evolved rapidly over the last years. Different disciplines have aided the development of both its experimental and theoretical branches. One field, which has played a significant role is engineering science and, in particular chemical engineering. Here, we review and illustrate some of these contributions, ranging from modeling approaches to model analysis with a special focus on technique which have not yet been substantially exploited but can be potentially useful in the analysis of biochemical systems.

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.

Conservation analysis of large biochemical networks

MOTIVATION

Large biochemical networks pose a unique challenge from the point of view of evaluating conservation laws. The computational problem in most cases exceeds the capability of available software tools, often resulting in inaccurate computation of the number and form of conserved cycles. Such errors have profound effects on subsequent calculations, particularly in the evaluation of the Jacobian which is a critical quantity in many other calculations. The goal of this paper is to outline a new algorithm that is computationally efficient and robust at extracting the correct conservation laws for very large biochemical networks.

RESULTS

We show that our algorithm can perform the conservation analysis of large biochemical networks, and can evaluate the correct conserved cycles when compared with other similar software tools. Biochemical simulators such as Jarnac and COPASI are successful at extracting only a subset of the conservation laws that our algorithm can. This is illustrated with examples for some large networks which show the advantages of our method.

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.