Prediction of enzyme kinetic parameters based on statistical learning

Values of enzyme kinetic parameters are a key requisite for the kinetic modelling of biochemical systems. For most kinetic parameters, however, not even an order of magnitude is known, so the estimation of model parameters from experimental data remains a major task in systems biology. We propose a statistical approach to infer values for kinetic parameters across species and enzymes making use of parameter values that have been measured under various conditions and that are nowadays stored in databases. We fit the data by a statistical regression model in which the substrate, the combination enzyme-substrate and the combination organism-substrate have a linear effect on the logarithmic parameter value. As a result, we obtain predictions and error ranges for unknown enzyme parameters. We apply our method to decadic logarithmic Michaelis-Menten constants from the BRENDA database and confirm the results with leave-one-out crossvalidation, in which we mask one value at a time and predict it from the remaining data. For a set of 8 metabolites we obtain a standard prediction error of 1.01 for the deviation of the predicted values from the true values, while the standard deviation of the experimental values is 1.16. The method is applicable to other types of kinetic parameters for which many experimental data are available

Biochemical networks with uncertain parameters

The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the `dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients

Modelling of signal transduction in yeast – sensitivity and model analysis

Experimental research has revealed components and mechanisms of cellular stress sensing and adaptation. In addition, mathematical modelling has proven to foster the understanding of some basic principles of signal transduction and signal processing as well as of sensitivity and robustness of information perception and cellular response. Here we review some modelling principles, results and open questions exemplified for a model organism, the yeast Saccharomyces cerevisiae

J Theor Biol

One of the most important antioxidant enzymes is superoxide dismutase (SOD), which catalyses the dismutation of superoxide radicals to hydrogen peroxide. The enzyme plays an important role in diseases like trisomy 21 and also in theories of the mechanisms of aging. But instead of being beneficial, intensified oxidative stress is associated with the increased expression of SOD and also studies on bacteria and transgenic animals show that high levels of SOD actually lead to increased lipid peroxidation and hypersensitivity to oxidative stress. Using mathematical models we investigate the question how overexpression of SOD can lead to increased oxidative stress, although it is an antioxidant enzyme. We consider the following possibilities that have been proposed in the literature: (i) Reaction of H2O2 with CuZnSOD leading to hydroxyl radical formation. (ii) Superoxide radicals might reduce membrane damage by acting as radical chain breaker. (iii) While detoxifying superoxide radicals SOD cycles between a reduced and oxidized state. At low superoxide levels the intermediates might interact with other redox partners and increase the superoxide reductase (SOR) activity of SOD. This short-circuiting of the SOD cycle could lead to an increased hydrogen peroxide production. We find that only one of the proposed mechanisms is under certain circumstances able to explain the increased oxidative stress caused by SOD. But furthermore we identified an additional mechanism that is of more general nature and might be a common basis for the experimental findings. We call it the alternative pathway mechanism

The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

A model for the spatiotemporal organization of DNA replication in Saccharomyces cerevisiae

DNA replication in eukaryotes is considered to proceed according to a precise program in which each chromosomal region is duplicated in a defined temporal order. However, recent studies reveal an intrinsic temporal disorder in the replication of yeast chromosome VI. Here we provide a model of the chromosomal duplication to study the temporal sequence of origin activation in budding yeast. The model comprises four parameters that influence the DNA replication system: the lengths of the chromosomes, the explicit chromosomal positions for all replication origins as well as their distinct initiation times and the replication fork migration rate. The designed model is able to reproduce the available experimental data in form of replication profiles. The dynamics of DNA replication was monitored during simulations of wild type and randomly perturbed replication conditions. Severe loss of origin function showed only little influence on the replication dynamics, so systematic deletions of origins (or loss of efficiency) were simulated to provide predictions to be tested experimentally. The simulations provide new insights into the complex system of DNA replication, showing that the system is robust to perturbation, and giving hints about the influence of a possible disordered firing

A modelling approach to quantify dynamic crosstalk between the pheromone and the starvation pathway in baker's yeast

Cells must be able to process multiple information in parallel and, moreover, they must also be able to combine this information in order to trigger the appropriate response. This is achieved by wiring signalling pathways such that they can interact with each other, a phenomenon often called crosstalk. In this study, we employ mathematical modelling techniques to analyse dynamic mechanisms and measures of crosstalk. We present a dynamic mathematical model that compiles current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We consider the main dynamic features and the interconnections between the two pathways in order to study dynamic crosstalk between these two pathways in haploid cells. We introduce two new measures of dynamic crosstalk, the intrinsic specificity and the extrinsic specificity. These two measures incorporate the combined signal of several stimuli being present simultaneously and seem to be more stable than previous measures. When both pathways are responsive and stimulated, the model predicts that (a) the filamentous growth pathway amplifies the response of the pheromone pathway, and (b) the pheromone pathway inhibits the response of filamentous growth pathway in terms of mitogen activated protein kinase activity and transcriptional activity, respectively. Among several mechanisms we identified leakage of activated Ste11 as the most influential source of crosstalk. Moreover, we propose new experiments and predict their outcomes in order to test hypotheses about the mechanisms of crosstalk between the two pathways. Studying signals that are transmitted in parallel gives us new insights about how pathways and signals interact in a dynamical way, e.g., whether they amplify, inhibit, delay or accelerate each other

SBMLmerge, a System for Combining Biochemical Network Models

The Systems Biology Markup Language (SBML) is an XML-based format for representing mathematical models of biochemical reaction networks, and it is likely to become a main standard in the systems biology community. As published mathematical models in cell biology are growing in number and size, modular modelling approaches will gain additional importance. The main issue to be addressed in computer-assisted model combination is the specification and handling of model semantics. The software SBMLmerge assists the user in combining models of biological subsystems to larger biochemical networks. First, the program helps the user in annotating all model elements with unique identifiers pointing to databases such as KEGG or Gene Ontology. Second, during merging, SBMLmerge detects and resolves various syntactic and semantic problems. Typical problems are conflicting variable names, elements which appear in more than one input model, and mathematical problems arising from the combination of equations. If the input models make contradicting statements about a biochemical quantity, the user is asked to choose between them. In the end the merging process results in a new, valid SBML model

SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool

<p>Abstract</p> <p>Background</p> <p>It has long been recognized that sensitivity analysis plays a key role in modeling and analyzing cellular and biochemical processes. Systems biology markup language (SBML) has become a well-known platform for coding and sharing mathematical models of such processes. However, current SBML compatible software tools are limited in their ability to perform global sensitivity analyses of these models.</p> <p>Results</p> <p>This work introduces a freely downloadable, software package, SBML-SAT, which implements algorithms for simulation, steady state analysis, robustness analysis and local and global sensitivity analysis for SBML models. This software tool extends current capabilities through its execution of global sensitivity analyses using multi-parametric sensitivity analysis, partial rank correlation coefficient, SOBOL's method, and weighted average of local sensitivity analyses in addition to its ability to handle systems with discontinuous events and intuitive graphical user interface.</p> <p>Conclusion</p> <p>SBML-SAT provides the community of systems biologists a new tool for the analysis of their SBML models of biochemical and cellular processes.</p

Fkh1 and Fkh2 associate with Sir2 to control CLB2 transcription under normal and oxidative stress conditions

The Forkhead (Fkh) box family of transcription factors is evolutionary conserved from yeast to higher eukaryotes and its members are involved in many physiological processes including metabolism, DNA repair, cell cycle, stress resistance, apoptosis, and aging. In budding yeast, four Fkh transcription factors were identified, namely Fkh1, Fkh2, Fhl1, and Hcm1, which are implicated in chromatin silencing, cell cycle regulation, and stress response. These factors impinge transcriptional regulation during cell cycle progression, and histone deacetylases (HDACs) play an essential role in this process, e.g., the nuclear localization of Hcm1 depends on Sir2 activity, whereas Sin3/Rpd3 silence cell cycle specific gene transcription in G2/M phase. However, a direct involvement of Sir2 in Fkh1/Fkh2-dependent regulation of target genes is at present unknown. Here, we show that Fkh1 and Fkh2 associate with Sir2 in G1 and M phase, and that Fkh1/Fkh2-mediated activation of reporter genes is antagonized by Sir2. We further report that Sir2 overexpression strongly affects cell growth in an Fkh1/Fkh2-dependent manner. In addition, Sir2 regulates the expression of the mitotic cyclin Clb2 through Fkh1/Fkh2-mediated binding to the CLB2 promoter in G1 and M phase. We finally demonstrate that Sir2 is also enriched at the CLB2 promoter under stress conditions, and that the nuclear localization of Sir2 is dependent on Fkh1 and Fkh2. Taken together, our results show a functional interplay between Fkh1/Fkh2 and Sir2 suggesting a novel mechanism of cell cycle repression. Thus, in budding yeast, not only the regulation of G2/M gene expression but also the protective response against stress could be directly coordinated by Fkh1 and Fkh2. © 2013 Linke, Klipp, Lehrach, Barberis and Krobitsch