Motif frequency and evolutionary search times in RNA populations

RNA molecules, through their dual identity as sequence and structure, are an appropriate experimental and theoretical model to study the genotype-phenotype map and evolutionary processes taking place in simple replicator populations. In this computational study, we relate properties of the sequence-structure map, in particular the abundance of a given secondary structure in a random pool, with the number of replicative events that an initially random population of sequences needs to find that structure through mutation and selection. For common structures, this search process turns out to be much faster than for rare structures. Furthermore, search and fixation processes are more efficient in a wider range of mutation rates for common structures, thus indicating that evolvability of RNA populations is not simply determined by abundance. We also find significant differences in the search and fixation processes for structures of same abundance, and relate them with the number of base pairs forming the structure. Moreover, the influence of the nucleotide content of the RNA sequences on the search process is studied. Our results advance in the understanding of the distribution and attainability of RNA secondary structures. They hint at the fact that, beyond sequence length and sequence-to-function redundancy, the mutation rate that permits localization and fixation of a given phenotype strongly depends on its relative abundance and global, in general non-uniform, distribution in sequence space.     

Reducing complexity in metabolic networks: making metabolic meshes manageable

The dynamics of complex systems can be effectively analyzed by judicious use of intrinsic time constants. Order of magnitude estimation based on time constants has been used successfully to examine the dynamic behavior of complicated processes. The main goal of this paper is to introduce this approach to the analysis of complex metabolic systems. Time constants and dynamic modes of motion are defined within the context of well-established linear algebra. The order of magnitude estimation is then introduced into the systemic framework. The main goals of the analysis are: to provide improved understanding of biochemical dynamics and their physiological significance, and to yield reduced dynamic models that are physiologically realistic but tractable for practical use.     

RELATCH: relative optimality in metabolic networks explains robust metabolic and regulatory responses to perturbations

Predicting cellular responses to perturbations is an important task in systems biology. We report a new approach, RELATCH, which uses flux and gene expression data from a reference state to predict metabolic responses in a genetically or environmentally perturbed state. Using the concept of relative optimality, which considers relative flux changes from a reference state, we hypothesize a relative metabolic flux pattern is maintained from one state to another, and that cells adapt to perturbations using metabolic and regulatory reprogramming to preserve this relative flux pattern. This constraint-based approach will have broad utility where predictions of metabolic responses are needed.     

The generalized flux-minimization method and its application to metabolic networks affected by enzyme deficiencies

The flux-minimization method [Holzhütter, H.G., 2004. The principle of flux-minimization and its application to calculate stationary fluxes in metabolic networks. Eur. J. Biochem. 271, 2905-2922] has been proposed as an alternative to kinetic modeling to calculate stationary fluxes in metabolic networks. Here a generalization of this method is proposed that takes into account possible limitations of internal fluxes, e.g. due to enzyme defects or partial inhibition of enzyme activities by drugs. The generalized method consists in the minimization of an objective function which expresses the compromise that has to be made between minimization of internal fluxes on one hand and maintenance of the metabolic output required for various cellular functions on the other. Fulfillment of the latter condition is measured through a fitness function, which evaluates the relative deviation of the output fluxes from demanded target values. The method is applied to assess the metabolic consequences caused by a deficiency of enzymes involved in the metabolism of erythrocytes. The obtained results are in good agreement with those obtained on the basis of a comprehensive kinetic model.     

METATOOL: for studying metabolic networks

MOTIVATION: To reconstruct metabolic pathways from biochemical and/or genome sequence data, the stoichiometric and thermodynamic feasibility of the pathways has to be tested. This is achieved by characterizing the admissible region of flux distributions in steady state. This region is spanned by what can be called a convex basis. The concept of 'elementary flux modes' provides a mathematical tool to define all metabolic routes that are feasible in a given metabolic network. In addition, we define 'enzyme subsets' to be groups of enzymes that operate together in fixed flux proportions in all steady states of the system. RESULTS: Algorithms for computing the convex basis and elementary modes developed earlier are briefly reviewed. A newly developed algorithm for detecting all enzyme subsets in a given network is presented. All of these algorithms have been implemented in a novel computer program named METATOOL, whose features are outlined here. The algorithms are illustrated by an example taken from sugar metabolism. AVAILABILITY: METATOOL is available from ftp://bmsdarwin.brookes.ac. uk/pub/software/ibmpc/metatool. SUPPLEMENTARY INFORMATION: http://www. biologie.hu-berlin.de/biophysics/Theory/tpfeiffer/metatoo l.html     

The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks.

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.     

Systemic properties of ensembles of metabolic networks: application of graphical and statistical methods to simple unbranched pathways

MOTIVATION: Mathematical models are the only realistic method for representing the integrated dynamic behavior of complex biochemical networks. However, it is difficult to obtain a consistent set of values for the parameters that characterize such a model. Even when a set of parameter values exists, the accuracy of the individual values is questionable. Therefore, we were motivated to explore statistical techniques for analyzing the properties of a given model when knowledge of the actual parameter values is lacking. RESULTS: The graphical and statistical methods presented in the previous paper are applied here to simple unbranched biosynthetic pathways subject to control by feedback inhibition. We represent these pathways within a canonical nonlinear formalism that provides a regular structure that is convenient for randomly sampling the parameter space. After constructing a large ensemble of randomly generated sets of parameter values, the structural and behavioral properties of the model with these parameter sets are examined statistically and classified. The results of our analysis demonstrate that certain properties of these systems are strongly correlated, thereby revealing aspects of organization that are highly probable independent of selection. Finally, we show how specification of a given behavior affects the distribution of acceptable parameter values.     

PathMiner: predicting metabolic pathways by heuristic search

MOTIVATION: Automated methods for biochemical pathway inference are becoming increasingly important for understanding biological processes in living and synthetic systems. With the availability of data on complete genomes and increasing information about enzyme-catalyzed biochemistry it is becoming feasible to approach this problem computationally. In this paper we present PathMiner, a system for automatic metabolic pathway inference. PathMiner predicts metabolic routes by reasoning over transformations using chemical and biological information. RESULTS: We build a biochemical state-space using data from known enzyme-catalyzed transformations in Ligand, including, 2917 unique transformations between 3890 different compounds. To predict metabolic pathways we explore this state-space by developing an informed search algorithm. For this purpose we develop a chemically motivated heuristic to guide the search. Since the algorithm does not depend on predefined pathways, it can efficiently identify plausible routes using known biochemical transformations.     

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data

Background

Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.

Results

We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.

Conclusion

We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.     

Flux modules in metabolic networks

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.     

基于约束的建模方法在代谢网络中的应用研究

代谢网络在各种细胞功能和生命过程中发挥着至关重要的作用。随着细胞网络重建工程的迅速发展,可用的基因组水平代谢网络越来越多,因而计算方法在这些网络的结构功能分析中越来越重要。基于约束的建模方法不像图论方法那样仅考虑代谢模型的纯拓扑结构,也不像各种动力学建模方法那样需求详尽的热力学参数,因而极具优势。采用基于约束的建模方法对一个含619个基因,655个代谢物和743个代谢反应的金黄色葡萄球菌(Staphylococcusaureus)代谢网络进行了分析,主要研究了该模型的网络结构特征,以及其最优生长率、动态生长情况和基因删除学习等。本研究提供了一个对金黄色葡萄球菌代谢网络进行约束建模分析的初步框架。     

A new method for assembling metabolic networks, with application to the Krebs citric acid cycle

To understand why a molecular network has a particular connectivity one can generate an ensemble of alternative networks, all of which meet the same performance criteria as the real network. We have generated alternatives to the Krebs cycle, allowing group transfers and B(12)-mediated shifts that were excluded in previous work. Our algorithm does not use a reaction list, but determines the reactants and products in generic reactions. It generates networks in order of increasing number of reaction steps. We find that alternatives to the Krebs cycle are very likely to be cycles. Many of the alternatives produce toxic or unstable compounds and use group transfer reactions, which have unfavorable consequences. Although alternatives are better than the Krebs cycle in some respects, the Krebs cycle has the most favorable combination of traits.     

Bioinformatic-driven search for metabolic biomarkers in disease

The search and validation of novel disease biomarkers requires the complementary power of professional study planning and execution, modern profiling technologies and related bioinformatics tools for data analysis and interpretation. Biomarkers have considerable impact on the care of patients and are urgently needed for advancing diagnostics, prognostics and treatment of disease. This survey article highlights emerging bioinformatics methods for biomarker discovery in clinical metabolomics, focusing on the problem of data preprocessing and consolidation, the data-driven search, verification, prioritization and biological interpretation of putative metabolic candidate biomarkers in disease. In particular, data mining tools suitable for the application to omic data gathered from most frequently-used type of experimental designs, such as case-control or longitudinal biomarker cohort studies, are reviewed and case examples of selected discovery steps are delineated in more detail. This review demonstrates that clinical bioinformatics has evolved into an essential element of biomarker discovery, translating new innovations and successes in profiling technologies and bioinformatics to clinical application.     

Metabolite coupling in genome-scale metabolic networks

Background  

Biochemically detailed stoichiometric matrices have now been reconstructed for various bacteria, yeast, and for the human cardiac mitochondrion based on genomic and proteomic data. These networks have been manually curated based on legacy data and elementally and charge balanced. Comparative analysis of these well curated networks is now possible. Pairs of metabolites often appear together in several network reactions, linking them topologically. This co-occurrence of pairs of metabolites in metabolic reactions is termed herein "metabolite coupling." These metabolite pairs can be directly computed from the stoichiometric matrix, S. Metabolite coupling is derived from the matrix ŜŜ ^T, whose off-diagonal elements indicate the number of reactions in which any two metabolites participate together, where Ŝ is the binary form of S.     

Genotype networks in metabolic reaction spaces

Background  

A metabolic genotype comprises all chemical reactions an organism can catalyze via enzymes encoded in its genome. A genotype is viable in a given environment if it is capable of producing all biomass components the organism needs to survive and reproduce. Previous work has focused on the properties of individual genotypes while little is known about how genome-scale metabolic networks with a given function can vary in their reaction content.     

Essentiality and damage in metabolic networks

Understanding the architecture of physiological functions from annotated genome sequences is a major task for postgenomic biology. From the annotated genome sequence of the microbe Escherichia coli, we propose a general quantitative definition of enzyme importance in a metabolic network. Using a graph analysis of its metabolism, we relate the extent of the topological damage generated in the metabolic network by the deletion of an enzyme to the experimentally determined viability of the organism in the absence of that enzyme. We show that the network is robust and that the extent of the damage relates to enzyme importance. We predict that a large fraction (91%) of enzymes causes little damage when removed, while a small group (9%) can cause serious damage. Experimental results confirm that this group contains the majority of essential enzymes. The results may reveal a universal property of metabolic networks.