There is no doubt that nowadays, biology benefits greatly from mathematics. In particular, cellular biology is, besides population dynamics, a field where tech­ niques of mathematical modeling are widely used. This is reflected by the large number of journal articles and congress proceedings published every year on the dynamics of complex cellular processes. This applies, among others, to metabolic control analysis, where the number of articles on theoretical fundamentals and experimental applications has increased for about 15 years. Surprisingly, mono­ graphs and textbooks dealing with the modeling of metabolic systems are still exceptionally rare. We think that now time is ripe to fill this gap. This monograph covers various aspects of the mathematical description of enzymatic systems, such as stoichiometric analysis, enzyme kinetics, dynamical simulation, metabolic control analysis, and evolutionary optimization. We believe that, at present, these are the main approaches by which metabolic systems can be analyzed in mathematical terms. Although stoichiometric analysis and enzyme kinetics are classical fields tracing back to the beginning of our century, there are intriguing recent developments such as detection of elementary biochemical syn­ thesis routes and rate laws for the situation of metabolic channeling, which we have considered worth being included. Evolutionary optimization of metabolic systems is a rather new field with promising prospects. Its goal is to elucidate the structure and functions of these systems from an evolutionary viewpoint.

Introduction; Fundamentals of biochemical modeling; Balance equations; Rate laws; Generalized mass-action kinetics; Various enzyme kinetic rate laws; Thermodynamic flow-force relationships; Power-law approximation; Steady states of biochemical networks; General considerations; Stable and unstable steady states; Multiple steady states; Metabolic oscillations; Background; Mathematical conditions for oscillations; Glycolytic oscillations; Models of intracellular calcium oscillations; A simple three-variable model with only monomolecular and bimolecular reactions; Possible physiological significance of oscillations; Stoichiometric analysis; Conservation relations; Linear dependencies between the rows of the stoichiometry matrix; Non-negative flux vectors; Elementary flux modes; Thermodynamic aspects; A generalized Wegscheider condition; Strictly detailed balanced subnetworks; Onsager's reciprocity reactions for coupled enyme reactions; Time hierarchy in metabolism; Time constants; The quasi-steady-state approximation; The Rapid equilibrium approximation; Modal analysis; Metabolic control analysis;Basic definitions; A systematic approach; Theorems of metabolic control analysis; Summation theorems;Connectivity theorems; Calculation of control coefficients using the theorems; Geometrical interpretation; Control analysis of various systems; General remarks; Elasticity coefficients for specific rate laws; Control coefficients for simple hypothetical pathways; Unbranched chains; A branched system; Control of erythrocyte energy metabolism; The reaction system; Basic model; Interplay of ATP production and ATP consumption; Glycolytic energy metabolism and osmotic states; A simple model of oxidative phosphorylation; A three-step model of serine biosynthesis; Time-dependent control coefficients; Are control coefficients always parameter independent?; Posing the problem; A system without conserved moieties; A system with a conserved moiety; A system including dynamic channeling; Normalized versus non-normalized coefficients; Analysis in terms of variables other than steady-state concentrations and fluxes; General analysis; Concentration ratios and free-energy-differences as state variables; Entropy production as response variable; Control of transient times; Control of oscillations; A second-order approach; A quantitative approach to metabolic regulations; Co-response coefficients; Fluctuations of internal variables versus parameter perturbations; Internal response coefficients; Rephrasing the basic equations of metabolic control analysis in terms of co-response coefficients and internal response coefficients; Control within and between subsystems; Modular approach; Overall elasticities; Overall control coefficients; Flux control insusceptibility; Control exerted by elementary steps in enzyme catalysis; Control analysis of metabolic channeling; Comparison of metabolic control analysis and power-law formalism; Computational aspects; Application of optimization methods and the interrelation with evolution; Optimization of the catalytic properties of single enzymes; Basic assumptions; Optimal values of elementary rate constants; Optimal Michaelis constants; Optimization of multienzyme systems; Maximization of steady-state flux; Influence of osmotic constraints and minimization of intermediate concentrations; Minimization of transient times; Optimal stoichiometries.