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

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

Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators

The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a reduced version of the LNA under conditions of timescale separation. In this paper, we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC Systems Biology 6, 39 (2012

Controlling complex networks: How much energy is needed?

The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems.Comment: 4 pages paper + 5 pages supplement. accepted for publication in Physical Review Letters; http://link.aps.org/doi/10.1103/PhysRevLett.108.21870

Measurement in biological systems from the self-organisation point of view

Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological systems as dynamical systems far from not only their chemical equilibrium, but, in most cases, also of their Lyapunov stable states. Thus, in biological experiments, we do not observe states, but distinct trajectories followed by the examined organism. If one of the possible sequences is selected, a minute sub-section of the whole problem is obtained, sometimes in a seemingly highly reproducible manner. But the state of the organism is known only if a complete set of possible trajectories is known. And this is often practically impossible. Therefore, we propose a different framework for reporting and analysis of biological experiments, respecting the view of non-linear mathematics. This view should be used to avoid overoptimistic results, which have to be consequently retracted or largely complemented. An increase of specification of experimental procedures is the way for better understanding of the scope of paths, which the biological system may be evolving. And it is hidden in the evolution of experimental protocols.Comment: 13 pages, 5 figure

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto

Dispensability of Escherichia coli's latent pathways

Gene-knockout experiments on single-cell organisms have established that expression of a substantial fraction of genes is not needed for optimal growth. This problem acquired a new dimension with the recent discovery that environmental and genetic perturbations of the bacterium Escherichia coli are followed by the temporary activation of a large number of latent metabolic pathways, which suggests the hypothesis that temporarily activated reactions impact growth and hence facilitate adaptation in the presence of perturbations. Here we test this hypothesis computationally and find, surprisingly, that the availability of latent pathways consistently offers no growth advantage, and tends in fact to inhibit growth after genetic perturbations. This is shown to be true even for latent pathways with a known function in alternate conditions, thus extending the significance of this adverse effect beyond apparently nonessential genes. These findings raise the possibility that latent pathway activation is in fact derivative of another, potentially suboptimal, adaptive response

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