A C library for retrieving specific reactions from the BioModels database.

SUMMARY: We describe libSBMLReactionFinder, a C library for retrieving specific biochemical reactions from the curated systems biology markup language models contained in the BioModels database. The library leverages semantic annotations in the database to associate reactions with human-readable descriptions, making the reactions retrievable through simple string searches. Our goal is to provide a useful tool for quantitative modelers who seek to accelerate modeling efforts through the reuse of previously published representations of specific chemical reactions. AVAILABILITY AND IMPLEMENTATION: The library is open-source and dual licensed under the Mozilla Public License Version 2.0 and GNU General Public License Version 2.0. Project source code, downloads and documentation are available at http://code.google.com/p/lib-sbml-reaction-finder.

Mathematical modeling and synthetic biology.

Synthetic biology is an engineering discipline that builds on our mechanistic understanding of molecular biology to program microbes to carry out new functions. Such predictable manipulation of a cell requires modeling and experimental techniques to work together. The modeling component of synthetic biology allows one to design biological circuits and analyze its expected behavior. The experimental component merges models with real systems by providing quantitative data and sets of available biological 'parts' that can be used to construct circuits. Sufficient progress has been made in the combined use of modeling and experimental methods, which reinforces the idea of being able to use engineered microbes as a technological platform.

In silico evolution of functional modules in biochemical networks.

Understanding the large reaction networks found in biological systems is a daunting task. One approach is to divide a network into more manageable smaller modules, thus simplifying the problem. This is a common strategy used in engineering. However, the process of identifying biological modules is still in its infancy and very little is understood about the range and capabilities of motif structures found in biological modules. In order to delineate these modules, a library of functional motifs has been generated via in silico evolution techniques. On the basis of their functional forms, networks were evolved from four broad areas: oscillators, bistable switches, homeostatic systems and frequency filters. Some of these motifs were constructed from simple mass action kinetics, others were based on Michaelis-Menten kinetics as found in protein/protein networks and the remainder were based on Hill equations as found in gene/protein interaction networks. The purpose of the study is to explore the capabilities of different network architectures and the rich variety of functional forms that can be generated. Ultimately, the library may be used to delineate functional motifs in real biological networks.

The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

The ERATO Systems Biology Workbench: enabling interaction and exchange between software tools for computational biology.

Researchers in computational biology today make use of a large number of different software packages for modeling, analysis, and data manipulation and visualization. In this paper, we describe the ERATO Systems Biology Workbench (SBW), a software framework that allows these heterogeneous application components--written in diverse programming languages and running on different platforms--to communicate and use each others' data and algorithmic capabilities. Our goal is to create a simple, open-source software infrastructure which is effective, easy to implement and easy to understand. SBW uses a broker-based architecture and enables applications (potentially running on separate, distributed computers) to communicate via a simple network protocol. The interfaces to the system are encapsulated in client-side libraries that we provide for different programming languages. We describe the SBW architecture and the current set of modules, as well as alternative implementation technologies.

Elasticities in Metabolic Control Analysis: algebraic derivation of simplified expressions.

MOTIVATION: Metabolic Control Analysis is one of many disciplines that make use of scaled derivatives. In particular, 'elasticities' are used to quantify the effect of an effector or substrate concentration on an enzyme rate under locally specified conditions. Normally an algebraic expression for the elasticity of an enzyme is obtained by differentiating its rate law, multiplying by the effector concentration and dividing by the rate law itself: this results in considerable expression expansion, and when the results are subsequently simplified it is often at the expense of biological comprehensibility. RESULTS: We present a novel algorithm which not only circumvents the expression expansion, but preserves an elegant separation of the components in enzyme behaviour. Easily implemented, and producing gains in both performance and numerical precision, the algorithm is potentially applicable to a number of existing packages. It also greatly assists the manual derivation and evaluation of elasticities, allowing the elasticity of even quite complex enzyme systems to be written by inspection.

In vitro control analysis of an enzyme system: experimental and analytical developments.

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, CLDH and Cpump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.

Coenzyme cycles and metabolic control analysis: the determination of the elasticity coefficients from the generalised connectivity theorem.

Metabolic control analysis allows one to express the elasticity coefficients (which describe the "local" kinetic features of enzymes) in terms of the control coefficients (quantitative indicators of the "global" control properties). However, when coenzymes (or metabolites linked by conservation constraints) are present in the pathway this procedure yields the "apparent" values of elasticity coefficients that correspond to the kinetic responses of the enzymes to such a simultaneous change of the coenzyme forms which leaves the total concentration of these forms unchanged (e.g., NAD+ + NADH in the glycolysis). We show that a generalised connectivity theorem (Kholodenko et al, Eur. J. Biochem. (1994) 225, 179-186) makes it possible to express the elasticity coefficients with respect to every coenzyme form separately. Such expressions include (i) the control coefficients and (ii) the responses to changes in the total concentrations of the coenzymes.

Control by enzymes, coenzymes and conserved moieties. A generalisation of the connectivity theorem of metabolic control analysis.

The control and regulation of metabolic systems are determined by their responses to changes in the internal metabolites (the internal state) and parameters of the system. In many cases, the concentrations of the intermediates are constrained by moiety conservations, for example those requiring that all intermediate forms of any enzyme sum to the conserved total concentration of that enzyme. In this study, we show how responses to changes in the internal state are related to responses to changes in the total amounts of conserved moieties. The relationship between these two different measures of control leads to a generalisation of the connectivity theorems. The results have important implications for the study of a variety of phenomena such as metabolite (coenzyme) sequestration, group-transfer and channelling. The relationships we derive make it possible to determine the control features of these pathways. As an illustration, two examples are chosen. The first shows the effect of sequestration of substrate moiety while the second deals with the sequestration of the enzyme moieties and enzyme/enzyme interactions.

Moiety-conserved cycles and metabolic control analysis: problems in sequestration and metabolic channelling.

This paper considers certain aspects of the analysis of moiety-conserved cycles in terms of metabolic control analysis. Two response coefficients are discussed: the response coefficient with respect to the total number of moles in a cycle (RVT), and the response coefficient with respect to perturbations to the internal state of a pathway (RVS). The relationship between these two different measures is derived and two examples are given to illustrate how the results may be used to simplify the analysis of particular complex pathways. One example considers how metabolite sequestration affects the flux summation theorem for which the analysis confirms the known result that sequestration can depress the value of the summation to below unity. The second example investigates the effect of metabolic channelling on the summation theorems. The analysis indicates that in contrast to metabolite sequestration, metabolic channelling can cause the flux summation theorem to exceed the value of unity. In addition, the maximum value that the summation theorem can reach under these conditions is shown to be equal to 2. Finally, this analysis indicates how one might use control analysis through the use of enzyme titration to determine whether metabolic channelling occurs in real systems or not.

SCAMP: a general-purpose simulator and metabolic control analysis program.

SCAMP is a general-purpose simulator of metabolic and chemical networks. The program is written in C and is portable to all computer systems that support an ANSI C compiler. SCAMP accepts metabolic models described in a biochemical language, and this enables novice as well as experienced users rapidly to build and simulate metabolic systems. The language is sufficiently flexible to enable other types of model to be built, e.g. chemostat or ecological models. The language offers many facilities, including: the ability to describe metabolic pathways of any structure and possessing any kinetics using normal chemical notation; optionally build models directly from the differential equations; differing compartment volumes; access to flux, concentration and rate of change information; detection of conserved cycles; access to all coefficients and elasticities of metabolic control analysis; user-defined forcing functions at the model boundaries; user-defined monitoring functions; user-configurable output of any quantity. From the model description SCAMP can either generate C code for later compilation to produce fast executable stand-alone models or run-time code for input to a run-time interpreter for immediate execution. The simulator also incorporates an inbuilt symbolic differentiator for evaluating the Jacobian and elasticity matrices.

Metabolic control analysis. The effects of high enzyme concentrations.

Differing views have been given in the literature as to whether the presence in a pathway of an enzyme at a concentration comparable to that of its substrate affects the values of control coefficients and the theorems of metabolic control analysis. Here we argue in favour of one of those views: that there is no effect unless the enzyme sequesters a substrate that contains a conserved moiety. In this particular case, we derive both a general criterion for estimating whether such an effect will be of a significant magnitude, and equations for determining the changes in the flux control coefficients. The nature of the phenomenom and the application of the equations are illustrated with a numerical simulation.

Enzyme-enzyme interactions and control analysis. 1. The case of non-additivity: monomer-oligomer associations.

Two usual assumptions of the treatment of metabolism are: (a) the rates of isolated enzyme reactions are additive, i.e., that rate is proportional to enzyme concentration; (b) in a system, the rates of individual enzyme reactions are not influenced by interactions with other enzymes, i.e. that they are acting independently, except by being coupled through shared metabolites. On this basis, control analysis has established theorems and experimental methods for studying the distribution of control. These assumptions are not universally true and it is shown that the theorems can be modified to take account of such deviations. This is achieved by defining additional elasticity coefficients, designated by the symbol pi, which quantify the effects of homologous and heterologous enzyme interactions. Here we show that for the case of non-proportionality of rate with enzyme concentration, (pi ii not equal to 1), the summation theorems are given by (Formula: see text). The example of monomer-oligomer equilibria is used to illustrate non-additive behaviour and experimental methods for their study are suggested.

Enzyme-enzyme interactions and control analysis. 2. The case of non-independence: heterologous associations.

The association of different enzymes into a complex may induce changes in the kinetic parameters of its component enzymes. This implies that they cannot be treated as independent catalysts. It will affect the formulations and theorems of control analysis and necessitates the introduction of additional elasticities reflecting the effect of one enzyme on the rate of another. We show how this is achieved as an extension of the classical treatment. We present modified summation and connectivity theorems incorporating both homologous and heterologous interactions. The case of channelling of metabolites in such complexes is considered and an experimental method for its detection is suggested.

Metabolic control analysis by computer: progress and prospects.

In metabolic control analysis, the set of rules called the matrix method simplifies writing the matrix equation that relates the control coefficients to elasticities of enzymes, and a subset of the velocities and substrate concentrations in a metabolic system. However, since the process of writing and solving these equations can be clearly defined, a computer program is being produced that will write the equations for the control coefficients given only the reactions of the metabolic system. In this way, the results of metabolic control analysis can be made available to all those who can use them, even if they do not know the theory in detail. The computational strategies underlying such a program, and the similarities to a biochemical simulation program developed previously are described.

Control analysis of time-dependent metabolic systems.

Metabolic Control Analysis is extended to time dependent systems. It is assumed that the time derivative of the metabolite concentrations can be written as a linear combination of rate laws, each one of first order with respect to the corresponding enzyme concentration. The definitions of the control and elasticity coefficients are extended, and a new type of coefficient ("time coefficient", "T") is defined. First, we prove that simultaneous changes in all enzyme concentrations by the same arbitrary factor, is equivalent to a change in the time scale. When infinitesimal changes are considered, these arguments lead to the derivation of general summation theorems that link control and time coefficients. The comparison of two systems with identical rates, that only differ in one metabolite concentration, leads to a method for the construction of general connectivity theorems, that relate control and elasticity coefficients. A mathematical proof in matrix form, of the summation and connectivity relationships, for time dependent systems is given. Those relationships allow one to express the control coefficients in terms of the elasticity and time coefficients for the case of unbranched pathway.

Metabolic control and its analysis. Extensions to the theory and matrix method.

The matrix algebra procedure for determining the flux control coefficients of enzymes in metabolic pathways has been extended to allow determination of the concentration control coefficients. Although it is shown that the procedure is essentially unchanged in most cases, the presence of moiety-conserved cycles in a pathway places additional limitations on the form of the equations that can be used in the matrix formulation for concentration control coefficients. In the case of branched pathways, a new coefficient has been defined, the branch distribution control coefficient, which can be obtained via the matrix procedure. Thus a single matrix equation permits calculation or algebraic evaluation of the control coefficients for flux, concentration and distribution of flux at branches, so that the complete response of a pathway to alteration of enzyme content, or to modulation by an effector, can be determined. The relationships have been determined between flux control coefficients in isolated sections of metabolic pathways and the coefficients for the same enzymes when part of a larger metabolic system. It is shown that the control analysis of the isolated system provides useful information towards determining the control properties of the extended system.

Metabolic control and its analysis. Additional relationships between elasticities and control coefficients.

Existing theorems from the analysis of metabolic control have been taken and embedded in a simple matrix algebra procedure for calculating the flux control coefficients of enzymes (formerly known as sensitivities) in a metabolic pathway from their kinetic properties (their elasticities). New theorems governing the flux control coefficients of branched pathways and substrate cycles have been derived to allow the procedure to be applied to complex pathway configurations. Modifications to the elasticity terms used in the equations have been theoretically justified so that the method remains valid for pathways with conserved metabolites (for example, the adenine nucleotide pool or the intermediates of a catalytic cycle such as the tricarboxylic acid cycle) or with pools of metabolites kept very near to equilibrium by very rapid reactions. The matrix equations generated using these theorems and relationships may be solved algebraically or numerically. Algebraic solutions have been used to determine the factors responsible for the degree of amplification of flux control coefficients by substrate cycles and to show that it is possible to derive expressions for the elasticities of a group of enzymes.