Complex networks theory for analyzing metabolic networks

One of the main tasks of post-genomic informatics is to systematically investigate all molecules and their interactions within a living cell so as to understand how these molecules and the interactions between them relate to the function of the organism, while networks are appropriate abstract description of all kinds of interactions. In the past few years, great achievement has been made in developing theory of complex networks for revealing the organizing principles that govern the formation and evolution of various complex biological, technological and social networks. This paper reviews the accomplishments in constructing genome-based metabolic networks and describes how the theory of complex networks is applied to analyze metabolic networks.Comment: 13 pages, 2 figure

The economic basis of periodic enzyme dynamics

Periodic enzyme activities can improve the metabolic performance of cells. As an adaptation to periodic environments or by driving metabolic cycles that can shift fluxes and rearrange metabolic processes in time to increase their efficiency. To study what benefits can ensue from rhythmic gene expression or posttranslational modification of enzymes, I propose a theory of optimal enzyme rhythms in periodic or static environments. The theory is based on kinetic metabolic models with predefined metabolic objectives, scores the effects of harmonic enzyme oscillations, and determines amplitudes and phase shifts that maximise cell fitness. In an expansion around optimal steady states, the optimal enzyme profiles can be computed by solving a quadratic optimality problem. The formulae show how enzymes can increase their efficiency by oscillating in phase with their substrates and how cells can benefit from adapting to external rhythms and from spontaneous, intrinsic enzyme rhythms. Both types of behaviour may occur different parameter regions of the same model. Optimal enzyme profiles are not passively adapted to existing substrate rhythms, but shape them actively to create opportunities for further fitness advantage: in doing so, they reflect the dynamic effects that enzymes can exert in the network. The proposed theory combines the dynamics and economics of metabolic systems and shows how optimal enzyme profiles are shaped by network structure, dynamics, external rhythms, and metabolic objectives. It covers static enzyme adaptation as a special case, reveals the conditions for beneficial metabolic cycles, and predicts optimally combinations of gene expression and posttranslational modification for creating enzyme rhythms

Analysis of the impact degree distribution in metabolic networks using branching process approximation

Theoretical frameworks to estimate the tolerance of metabolic networks to various failures are important to evaluate the robustness of biological complex systems in systems biology. In this paper, we focus on a measure for robustness in metabolic networks, namely, the impact degree, and propose an approximation method to predict the probability distribution of impact degrees from metabolic network structures using the theory of branching process. We demonstrate the relevance of this method by testing it on real-world metabolic networks. Although the approximation method possesses a few limitations, it may be a powerful tool for evaluating metabolic robustness.Comment: 17 pages, 4 figures, 4 table

Metabolic Heat in Microbial Conflict and Cooperation

Many microbes live in habitats below their optimum temperature. Retention of metabolic heat by aggregation or insulation would boost growth. Generation of excess metabolic heat may also provide benefit. A cell that makes excess metabolic heat pays the cost of production, whereas the benefit may be shared by neighbors within a zone of local heat capture. Metabolic heat as a shareable public good raises interesting questions about conflict and cooperation of heat production and capture. Metabolic heat may also be deployed as a weapon. Species with greater thermotolerance gain by raising local temperature to outcompete less thermotolerant taxa. Metabolic heat may provide defense against bacteriophage attack, by analogy with fever in vertebrates. This article outlines the theory of metabolic heat in microbial conflict and cooperation, presenting several predictions for future study

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

A physical model of cell metabolism

Cell metabolism is characterized by three fundamental energy demands: to sustain cell maintenance, to trigger aerobic fermentation and to achieve maximum metabolic rate. The transition to aerobic fermentation and the maximum metabolic rate are currently understood based on enzymatic cost constraints. Yet, we are lacking a theory explaining the maintenance energy demand. Here we report a physical model of cell metabolism that explains the origin of these three energy scales. Our key hypothesis is that the maintenance energy demand is rooted on the energy expended by molecular motors to fluidize the cytoplasm and counteract molecular crowding. Using this model and independent parameter estimates we make predictions for the three energy scales that are in quantitative agreement with experimental values. The model also recapitulates the dependencies of cell growth with extracellular osmolarity and temperature. This theory brings together biophysics and cell biology in a tractable model that can be applied to understand key principles of cell metabolism