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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 ).

Synthetic gene regulatory networks show significant stochastic fluctuations in expression levels due to the low copy number of transcription factors. When a synthetic gene network is allowed to regulate a downstream network, the response time of the regulating transcription factors increases. This effect has been termed “retroactivity”. In this article, we describe a method for estimating the retroactivity of a given system by measuring the stochastic noise in the transcription factor expression. We show that the noise in the output signal of the network can be affected significantly when the output is connected to a downstream module. More specifically, the output signal noise can show significantly longer correlations. We define retroactivity by the change in the correlation time. This measure of retroactivity corresponds well to the deterministic retroactivity described in another study. We provide an estimation method for measuring retroactivity from the gene expression noise by investigating its autocorrelation function. When retroactivity is defined using the decay (correlation) times from the gene expression autocorrelation functions, it is found not to depend on whether the module output is defined as either the free transcription factor or the total of the bound and free transcription factor. The frequency domain response, however, depends strongly on which output variable is considered. The proposed estimation method for measuring retroactivity, based on the gene expression noise, can serve as a practical method for characterizing interface conditions between two synthetic modules and eventually provide a step toward large-scale circuit design for synthetic biology.

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window (ϵ) within which reaction events are counted for measuring a single flux. It is found that the degree of the ϵ-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This ϵ-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.

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.

Metabolic control analysis is a framework for characterizing the parametric sensitivity of metabolic pathways and genetic networks. We establish a connection between metabolic control analysis and control theory. The main result is that we can use classical control theory and the associated signal-flow (block) diagrams to analyze biochemical reaction networks and that many results in metabolic control analysis have direct counterparts in control In the process, we illustrate how some problems in biochemical network analysis can be reformulated in a control-theoretic framework.

Large scale genomic studies are generating significant amounts of data on the structure of cellular networks. This is in contrast to kinetic data, which is frequently absent, unreliable or fragmentary. There is, therefore, a desire by many in the community to investigate the potential rewards of analyzing the more readily available topological data. This brief review is concerned with a particular property of biological networks, namely structural conservations (e.g. moiety conserved cycles). There has been much discussion in the literature on these cycles but a review on the computational issues related to conserved cycles has been missing 1 . This review is concerned with the detection and characterization of conservation relations in arbitrary networks and related issues, which impinge on simulation simulation software writers. This review will not address flux balance constraints or small-world type analyses in any significant detail.

A sensitivity analysis of general stoichiometric networks is considered. The results are presented as a generalization of Metabolic Control Analysis, which has been concerned primarily with system sensitivities at steady state. An expression for time-varying sensitivity coefficients is given and the Summation and Connectivity Theorems are generalized. The results are compared to previous treatments. The analysis is accompanied by a discussion of the computation of the sensitivity coefficients and an application to a model of phototransduction.

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 ( R T V ), and the response coefficient with respect to perturbations to the internal state of a pathway ( R T V ). 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.

Previously developed metabolic simulation programs have concentrated on providing the facility to make time-dependent simulations of metabolic networks; few have been concerned with the steady state and even fewer with any steady state analysis, in particular metabolic control analysis. Here we describe a new simulation program SCAMP, which includes the facility to make time-dependent simulations, but in addition incorporates many of the concepts of metabolic control analysis. SCAMP makes available all the coefficients defined in the control analysis of Kacser and Burns [1] and Heinrich and Rapoport [2]. Thus control coefficients, response coefficients (including the conserved cycle coefficients defined by Hofmeyr et al. [3]) and elasticities (including kappa and pi elasticities [4]) can all be calculated easily. Two other special facilities have also been incorporated; conserved cycle identification and the inclusion of a simple data base of enzyme rate laws. SCAMP will accept models in terms of mass action reactions, user-defined (or data base-defined) rate law reactions or differential equations. SCAMP was primarily implemented for the Atari ST microcomputer since the ST supports a large continuous memory map. However, it is possible to run SCAMP on an MS-DOS type microcomputer provided there is at least 640K of memory. We also supply a simple command shell which integrates the various parts for both the Atari and MS-DOS version. The Atari version also includes a useful graphics plotting package.

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.