Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

Formulating genome-scale kinetic models in the post-genome era.

The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues

A biophysical approach to large-scale protein-DNA binding data

About this book * Cutting-edge genome analysis methods from leading bioinformaticians An accurate description of current scientific developments in the field of bioinformatics and computational implementation is presented by research of the BioSapiens Network of Excellence. Bioinformatics is essential for annotating the structure and function of genes, proteins and the analysis of complete genomes and to molecular biology and biochemistry. Included is an overview of bioinformatics, the full spectrum of genome annotation approaches including; genome analysis and gene prediction, gene regulation analysis and expression, genome variation and QTL analysis, large scale protein annotation of function and structure, annotation and prediction of protein interactions, and the organization and annotation of molecular networks and biochemical pathways. Also covered is a technical framework to organize and represent genome data using the DAS technology and work in the annotation of two large genomic sets: HIV/HCV viral genomes and splicing alternatives potentially encoded in 1% of the human genome

Improved Network Performance via Antagonism: From Synthetic Rescues to Multi-drug Combinations

Recent research shows that a faulty or sub-optimally operating metabolic network can often be rescued by the targeted removal of enzyme-coding genes--the exact opposite of what traditional gene therapy would suggest. Predictions go as far as to assert that certain gene knockouts can restore the growth of otherwise nonviable gene-deficient cells. Many questions follow from this discovery: What are the underlying mechanisms? How generalizable is this effect? What are the potential applications? Here, I will approach these questions from the perspective of compensatory perturbations on networks. Relations will be drawn between such synthetic rescues and naturally occurring cascades of reaction inactivation, as well as their analogues in physical and other biological networks. I will specially discuss how rescue interactions can lead to the rational design of antagonistic drug combinations that select against resistance and how they can illuminate medical research on cancer, antibiotics, and metabolic diseases.Comment: Online Open "Problems and Paradigms" articl

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure -- network modularity (the propensity for edges to be cluster into dense groups that are sparsely connected between each other). To reach this goal, we design a model of reaction-systems where network modularity can be controlled and measure how well the reduction to simple graphs capture the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate-product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction-systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreate correlations between degree and mass of the molecules.Comment: to appear in J. Roy. Soc. Intefac