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How individual enzymes evolved is relatively well understood. However, individual enzymes rarely confer a physiological advantage on their own. Judging by its current state, the emergence of metabolism seemingly demanded the simultaneous emergence of many enzymes. Indeed, how multicomponent interlocked systems, like metabolic pathways, evolved is largely an open question. This complexity can be unlocked if we assume that survival of the fittest applies not only to genes and enzymes but also to the metabolites they produce. This review develops our current knowledge of enzyme evolution into a wider hypothesis of pathway and network evolution. We describe the current models for pathway evolution and offer an integrative metabolite-enzyme coevolution hypothesis. Our hypothesis addresses the origins of new metabolites and of new enzymes and the order of their recruitment. We aim to not only survey established knowledge but also present open questions and potential ways of addressing them.

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified., Competing Interests: The authors have declared that no competing interests exist.

Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kmax(vivo), the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation ofr(2)= 0.62 in log scale (p < 10(-10)), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between kmax(vivo) and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions.

Michaelis and Menten's mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis-Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis., (Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.)

The kinetic parameters of enzymes are key to understanding the rate and specificity of most biological processes. Although specific trends are frequently studied for individual enzymes, global trends are rarely addressed. We performed an analysis of k(cat) and K(M) values of several thousand enzymes collected from the literature. We found that the "average enzyme" exhibits a k(cat) of ~0 s(-1) and a k(cat)/K(M) of ~10(5) s(-1) M(-1), much below the diffusion limit and the characteristic textbook portrayal of kinetically superior enzymes. Why do most enzymes exhibit moderate catalytic efficiencies? Maximal rates may not evolve in cases where weaker selection pressures are expected. We find, for example, that enzymes operating in secondary metabolism are, on average, ~30-fold slower than those of central metabolism. We also find indications that the physicochemical properties of substrates affect the kinetic parameters. Specifically, low molecular mass and hydrophobicity appear to limit K(M) optimization. In accordance, substitution with phosphate, CoA, or other large modifiers considerably lowers the K(M) values of enzymes utilizing the substituted substrates. It therefore appears that both evolutionary selection pressures and physicochemical constraints shape the kinetic parameters of enzymes. It also seems likely that the catalytic efficiency of some enzymes toward their natural substrates could be increased in many cases by natural or laboratory evolution.

Motivation: Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations., Results: We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass-action, Michaelis-Menten and uni-uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic-kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language., Availability: An online tool for inserting the rate laws into SBML models is freely available at www.semanticsbml.org., Supplementary Information: Supplementary data are available at Bioinformatics online.

We describe a workflow to translate a given metabolic network into a kinetic model; the model summarises kinetic information collected from different data sources. All reactions are modelled by convenience kinetics; where detailed kinetic laws are known, they can also be incorporated. Confidence intervals and correlations of the resulting model parameters are obtained from Bayesian parameter estimation; they can be used to sample parameter sets for Monte-Carlo simulations. The integration method ensures that the resulting parameter distributions are thermodynamically feasible. Here we summarise different previous works on this topic: we give an overview over the convenience kinetics, thermodynamic criteria for parameter sets, Bayesian parameter estimation, the collection of kinetic data, and different machine learning techniques that can be used to obtain prior distributions for kinetic parameters. All methods have been assembled into a workflow that facilitates the integration of biochemical data and the modelling of metabolic networks from scratch.

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.