Parameter Balancing in Kinetic Models of Cell Metabolism

Lubitz, Timo; Schulz, Marvin; Klipp, Edda; Liebermeister, Wolfram

doi:10.1021/jp108764b

Cited by 46 publications

(76 citation statements)

References 36 publications

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“…So far, the majority of mathematical models of biochemical pathways have been developed based on data collected from different sources [6]. The enzyme kinetic data used in such models have usually been measured at each enzyme's optimal pH; however the optimal pH of each enzyme in a pathway is normally different and the physiological pH and other conditions would not match the optimal conditions for each enzyme [7].…”

Section: Introductionmentioning

confidence: 99%

“…5 The control properties of the system are evaluated computationally and the reaction step exerting the major control over the system fluxes is identified. 6 The kinetic properties of the most controlling reaction step are experimentally measured. More particularly, the turnover number (k cat ), concentration and affinity constants of each of the corresponding isoenzymes are measured and their value is used to refine the model.…”

Section: Introductionmentioning

confidence: 99%

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A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

et al. 2013

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We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

et al. 2013

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“…Several studies grapple with missing k cat values by sampling from the distribution of k cat values measured in vitro or by using measurements of the same enzyme from related species (13)(14)(15)(16). These approximations systematically ignore any errors resulting from the differences between in vitro and in vivo environments.…”

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confidence: 99%

Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro k _cat measurements

Davidi

Noor

Liebermeister

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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242

382

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Turnover numbers, also known as k cat values, are fundamental properties of enzymes. However, k cat 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 k cat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate k vivo max , the observed maximal catalytic rate of an enzyme inside cells. Comparison with k cat values from Escherichia coli, yields a correlation of r 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 k vivo max and k cat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a highthroughput method for extracting enzyme kinetic constants from omics data. (1-6). Many models of cellular metabolism include k cat values, the maximal turnover rates of enzymes, as key inputs to predict the behavior of metabolic pathways and networks (7-9). However, most values have never been measured experimentally. Escherichia coli is the most intensely biochemically characterized organism, but k cat values are available for only about 10% of its ≈ 2, 000 enzyme-reaction pairs (Dataset S1). Indeed, k cat values are missing for several central metabolic enzymes. The scarcity of kinetic data limits the scope of models and necessitates generic parameter assignments that significantly reduce the predictive power of cellular models.Even if a larger collection of k cat values was made available, their current use poses a major difficulty: k cat values are measured through in vitro enzyme assays, representing the initial rate of the reaction, i.e., full substrates saturation and negligible levels of products. Such assays may underrepresent factors like cellular metabolite concentrations, thermodynamic constraints, posttranslational modifications, chaperones, cellular crowding, and activating and inhibiting molecules, which can substantially alter enzyme kinetics in vivo. These omissions call into question the relevance of k cat measurements in vivo (10-12). Furthermore, an effort to measure a large number of k cat values under in vivo-like conditions presents a daunting challenge, given how many unknown biochemical factors might be involved.Several studies grapple with missing k cat values by sampling from the distribution of k cat values measured in vitro or by using measurements of the same enzyme from related species (13-16). These approximations systematically ignore any errors resulting from the differences between in vitro and in vivo environments. Approximations of this sort may also introduce significant errors, as k cat values can deviate by orders of magnitude between isozymes in the same organism as well a...

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“…This is by now a commonality in flux balance analysis 4,17,18 . A series of attempts have been made to estimate thermodynamically consistent parameters in enzyme kinetic models such as parameter balancing 19 or the assignment of G r ∆ to enzyme kinetics [20][21][22] . However, there have also been some misconceptions about how to apply thermodynamics to metabolic networks.…”

Section: Beyond Culture Conditionsmentioning

confidence: 99%

Entropic regulation of dynamical metabolic processes

Adler

Klipp

2019

Preprint

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Life depends on the input of energy, either directly provided by sunlight or in form of highenergy matter. The rules and conditions for the conversion of chemical or electromagnetic energy into living structure and all the processes related with life are governed by the laws of thermodynamics. Hence, to understand the potential and the limitations of cell growth and metabolism, it is unavoidable to take these laws into account. During the last years, systems biology has developed many mathematical models aiming to describe steady states and dynamic behavior of cellular processes in qualitative and quantitative terms. The validity of the model predictions depends strongly on whether the model formulation is in agreement with the laws of physics, chemistry, and, specifically, thermodynamics.Here, we review basic principles of thermodynamics for equilibrium and non-equilibrium processes as well as for closed and open systems as far as they concern metabolic processes, especially in their dynamics. We illustrate the application of thermodynamic laws for some practical cases that are currently intensively studied in systems and computational biology. Specifically, we will discuss the concept of entropy production and energy dissipation for isolated and open systems and its interpretation for the feasibility of biological processes, especially metabolism. We demonstrate that steady states of metabolic systems cannot show energy dissipation, while in dynamical modes entropy of the system can be both increased or decreased, depending on the type of perturbation and the kinetics of the reaction system. These findings are very important for biotechnological processes where energy dissipation should be limited, but also for analysis of healthy and diseased cellular metabolism.

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Parameter Balancing in Kinetic Models of Cell Metabolism

Cited by 46 publications

References 36 publications

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro k _cat measurements

Entropic regulation of dynamical metabolic processes

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Parameter Balancing in Kinetic Models of Cell Metabolism

Cited by 46 publications

References 36 publications

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro k cat measurements

Entropic regulation of dynamical metabolic processes

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Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro k _cat measurements