Conditions for duality between fluxes and concentrations in biochemical networks

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. That is, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes

METANNOGEN: compiling features of biochemical reactions needed for the reconstruction of metabolic networks

BACKGROUND: One central goal of computational systems biology is the mathematical modelling of complex metabolic reaction networks. The first and most time-consuming step in the development of such models consists in the stoichiometric reconstruction of the network, i. e. compilation of all metabolites, reactions and transport processes relevant to the considered network and their assignment to the various cellular compartments. Therefore an information system is required to collect and manage data from different databases and scientific literature in order to generate a metabolic network of biochemical reactions that can be subjected to further computational analyses. RESULTS: The computer program METANNOGEN facilitates the reconstruction of metabolic networks. It uses the well-known database of biochemical reactions KEGG of biochemical reactions as primary information source from which biochemical reactions relevant to the considered network can be selected, edited and stored in a separate, user-defined database. Reactions not contained in KEGG can be entered manually into the system. To aid the decision whether or not a reaction selected from KEGG belongs to the considered network METANNOGEN contains information of SWISSPROT and ENSEMBL and provides Web links to a number of important information sources like METACYC, BRENDA, NIST, and REACTOME. If a reaction is reported to occur in more than one cellular compartment, a corresponding number of reactions is generated each referring to one specific compartment. Transport processes of metabolites are entered like chemical reactions where reactants and products have different compartment attributes. The list of compartmentalized biochemical reactions and membrane transport processes compiled by means of METANNOGEN can be exported as an SBML file for further computational analysis. METANNOGEN is highly customizable with respect to the content of the SBML output file, additional data-fields, the graphical input form, highlighting of project specific search terms and dynamically generated Web-links. CONCLUSION: METANNOGEN is a flexible tool to manage information for the design of metabolic networks. The program requires Java Runtime Environment 1.4 or higher and about 100 MB of free RAM and about 200 MB of free HD space. It does not require installation and can be directly Java-webstarted from

Reverse-engineering of polynomial dynamical systems

Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such systems from a partial specification of dynamic properties, e.g., from a collection of state transition measurements. Here, we consider static models, which are directed graphs that represent the causal relationships between system variables, so-called wiring diagrams. This paper contains an algorithm which computes all possible minimal wiring diagrams for a given set of state transition measurements. The paper also contains several statistical measures for model selection. The algorithm uses primary decomposition of monomial ideals as the principal tool. An application to the reverse-engineering of a gene regulatory network is included. The algorithm and the statistical measures are implemented in Macaulay2 and are available from the authors

Cyclin-dependent kinases as drug targets for cell growth and proliferation disorders. A role for systems biology approach in drug development. Part II - CDKs as drug targets in hypertrophic cell growth. Modelling of drugs targeting CDKs

Cyclin-dependent kinases (CDKs) are key regulators of cell growth and proliferation. Impaired regulation of their activity leads to various diseases such as cancer and heart hypertrophy. Consequently, a number of CDKs are considered as targets for drug discovery. We review the development of inhibitors of CDK2 as anti-cancer drugs in the first part of the paper and in the second part, respectively, the development of inhibitors of CDK9 as potential therapeutics for heart hypertrophy. We argue that the above diseases are systems biology, or network diseases. In order to fully understand the complexity of the cell growth and proliferation disorders, in addition to experimental sciences, a systems biology approach, involving mathematical and computational modelling ought to be employed

Application of new probabilistic graphical models in the genetic regulatory networks studies

This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an Independence Graph (IG) model with either a forward or a backward search algorithm and the other one is a Gaussian Network (GN) model with a novel greedy search method. The performances of both models were evaluated on four MAPK pathways in yeast and three simulated data sets. Generally, an IG model provides a sparse graph but a GN model produces a dense graph where more information about gene-gene interactions is preserved. Additionally, we found two key limitations in the prediction of genetic regulatory networks using DNA microarray data, the first is the sufficiency of sample size and the second is the complexity of network structures may not be captured without additional data at the protein level. Those limitations are present in all prediction methods which used only DNA microarray data.Comment: 38 pages, 3 figure

A Fast Reconstruction Algorithm for Gene Networks

This paper deals with gene networks whose dynamics is assumed to be generated by a continuous-time, linear, time invariant, finite dimensional system (LTI) at steady state. In particular, we deal with the problem of network reconstruction in the typical practical situation in which the number of available data is largely insufficient to uniquely determine the network. In order to try to remove this ambiguity, we will exploit the biologically a priori assumption of network sparseness, and propose a new algorithm for network reconstruction having a very low computational complexity (linear in the number of genes) so to be able to deal also with very large networks (say, thousands of genes). Its performances are also tested both on artificial data (generated with linear models) and on real data obtained by Gardner et al. from the SOS pathway in Escherichia coli.Comment: 12 pages, 3 figure