Biomedical subjects

E Klipp

Publications and source records attributed to E Klipp.

5 recordsLinked to original sources

PubMed2005

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.

Animals↗

PubMed1999

Competition for enzymes in metabolic pathways: implications for optimal distributions of enzyme concentrations and for the distribution of flux control.

The structures of biochemical pathways are assumed to be determined by evolutionary optimization processes. In the framework of mathematical models, these structures should be explained by the formulation of optimization principles. In the present work, the principle of minimal total enzyme concentration at fixed steady state fluxes is applied to metabolic networks. According to this principle there exists a competition of the reactions for the available amount of enzymes such that all biological functions are maintained. In states which fulfil these optimization criteria the enzyme concentrations are distributed in a non-uniform manner among the reactions. This result has consequences for the distribution of flux control. It is shown that the flux control matrix c, the elasticity matrix epsilon, and the vector e of enzyme concentrations fulfil in optimal states the relations c(T)e = e and epsilon(T)e = 0. Starting from a well-balanced distribution of enzymes the minimization of total enzyme concentration leads to a lowering of the SD of the flux control coefficients.

Biological Evolution↗

PubMed1997

Theoretical approaches to the evolutionary optimization of glycolysis: thermodynamic and kinetic constraints.

It is analyzed whether the structural design of contemporary glycolysis can be explained theoretically on the basis of optimization principles originating from natural selection during evolution. Particular attention is paid to the problem of how the kinetic and thermodynamic properties of the glycolytic pathway are related to its stoichiometry with respect to the number and location of ATP-coupling sites. The mathematical analysis of a minimal model of unbranched energy-converting pathways shows that the requirement of high ATP-production rate favours a structural design that includes not only ATP-producing reactions (P-sites) but also ATP-consuming reactions (C-sites). It is demonstrated that, at fixed overall thermodynamic properties of a chain, the ATP-production rate may be enhanced by kinetic optimization. The ATP-production rate is increased if the C-sites are concentrated at the beginning and all the P-sites at the end of the pathway. An optimum is attained, which is characterized by numbers of coupling sites corresponding to those found in glycolysis. Various extensions of the minimal model are considered, which allow the effects of internal feedback-regulations, variable enzyme concentrations, and the symmetric branching of glycolysis at the aldolase step to be considered.

Adenosine Triphosphate↗

PubMed1996

Control analysis of unbranched enzymatic chains in states of maximal activity.

It is shown that optimized states of metabolic systems are characterized by special distributions of control coefficients. Maximization of the steady-state flux through unbranched chains leads, under the constraint of fixed total amount of enzymes within the pathway, to a proportionality between control coefficients and enzyme concentrations. A detailed analysis is presented for two types of systems involving (a) reactions with linear kinetics and (b) reactions with Michaelis kinetics, respectively. In the first case one obtains for reactions with equilibrium constants larger than unity a monotonic decrease of enzyme concentrations and of control coefficients from the upper end to the lower end of the chain. In the second case optimization is performed by optimizing the intrinsic parameters (elementary rate constants) as well as the amounts of the enzymes. In contrast to systems with linear kinetics the results for reactions with Michaelis-Menten kinetics are dependent on the concentrations of the external reactants.

Animals↗

PubMed1994

Evolutionary optimization of enzyme kinetic parameters; effect of constraints.

The distribution of the kinetic parameters of enzymic reactions is theoretically studied, on the assumption that, during evolution, the increase of reaction rates was an important target of natural selection. In extension of previous work on the optimization of enzyme kinetic parameters, the influence of constraints concerning upper limits of the individual rate constants is analyzed. The concept of "evolutionary effort" is applied to derive an expression for the cost function, leading to an overall upper limit for the values of the rate constants. The resulting optimization problem is solved for ordered mechanisms involving different numbers of elementary steps. It is shown that the optimum for the enzyme kinetic parameters strongly depends on the concentrations of the reactants. Low reactant concentrations lead generally to a tight binding of the reactants, while high concentrations result in a weak binding, favouring the rate constants of the other steps. In particular, states of maximum activity are not always characterized by maximal values of second-order rate constants. The results support the hypothesis that there is a mutual adaptation of Michaelis constants and reactant concentrations in an evolutionary timescale. In the limit of infinite values of the exponent of the cost function the results of the present "overall limit model" turn into the results of a model which takes into account individual upper limits for rate constants ("separate limit model"). The distributions of optimal rate constants are discussed in terms of free-energy profiles. The model is applied to the interpretation of the kinetic data of triosephosphate isomerase and inorganic pyrophosphatase.

Animals↗