Evaluation of rate law approximations in bottom-up kinetic models of metabolism

Du, Bin; Zielinski, Daniel C.; Kavvas, Erol; Dräger, Andreas; Tan, Jiaying; Zhang, Zhen; Ruggiero, Kayla E.; Arzumanyan, Garri A.; Palsson, Bernhard Ø.

doi:10.1186/s12918-016-0283-2

Cited by 30 publications

(53 citation statements)

References 46 publications

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“…5 If desired, prior and likelihood terms for thermodynamic forces may be included. 6 In the matlab implementation, in contrast, this prefactor is used. 7 Since P and L are convex in the vectors x and e, and since e is convex in x, the loss terms P and L are convex in x.…”

Section: By Adding Eqsmentioning

confidence: 99%

Model balancing: in search of consistent metabolic states and in-vivo kinetic constants

Liebermeister

Noor

2019

Preprint

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Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. In theory, kinetic constants can be fitted to measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, but these estimation problems are typically non-convex. This makes them hard to solve, especially if models are large. Here I assume that the metabolic fluxes are given and show that consistent kinetic constants, metabolite levels, and enzyme levels can then be found by solving a convex optimality problem. If logarithmic kinetic constants and metabolite concentrations are used as free variables and if Gaussian priors are employed, the posterior density is strictly convex. The resulting estimation method, called model balancing, can employ a wide range of rate laws, accounts for thermodynamic constraints on parameters, and considers the dependences between flux directions and metabolite concentrations through thermodynamic forces. It can be used to complete and adjust available data, to estimate in-vivo kinetic constants from omics data, or to construct plausible metabolic states with a predefined flux distribution. To demonstrate model balancing and to assess its practical use, I balance a model of E. coli central metabolism with artificial or experimental data. The tests show what information about kinetic constants can be extracted from omics data and reveal practical limits of estimating kinetic constants in vivo.Large models have been parameterised [21,22], and pipelines for model parameterization have been developed [23,24]. Finally, even if parameters are unknown, methods for parameter sampling and ensemble modelling allow to find plausible parameter sets [25] and to draw conclusions about possible dynamic behaviour [26].The key problem here is to obtain realistic, consistent values of kinetic constants. In-vivo values are hard to measure, and in-vitro values as proxies may be unreliable -or at least, this is hard to assess unless in-vivo values are known. So how can we infer model parameters from omics data? To obtain realistic model parameters and metabolic states, various types of measurement data must be combined. In an ideal case, in which kinetic constants and enzyme concentrations are precisely known, metabolite levels and fluxes could be computed by simulating the model. In another ideal case, in which enzyme levels, metabolite levels and fluxes are precisely known for a number of states, we can solve for the kinetic constants. In reality, we are in between these two cases: data of different types are available, but these data are incomplete and too noisy to be used directly in models. In practice, in model construction we may have different aims, for example (i) finding consistent kinetic constants in plausible ranges; (ii) adjusting and completing a data set of measured kinetic constants to obtain consistent model parameters; (iii) estimating in-vivo kinetic constants from omics data (measured enzyme levels, metabolite levels, and fluxes); (iv) completing and adju...

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Section: By Adding Eqsmentioning

confidence: 99%

Model balancing: in search of consistent metabolic states and in-vivo kinetic constants

Liebermeister

Noor

2019

Preprint

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“…Reaction rates were defined using mass action kinetics, representing enzyme catalysis as a single step. These simplified reactions were systematically replaced with enzyme modules following the procedure outlined by Du et al [16]. Additionally, a phosphate exchange reaction was incorporated into the glycolytic network utilizing parameters obtained from Prankerd et al [33].…”

Section: Glycolysis and The Rapoport-luebering Shuntmentioning

confidence: 99%

“…Hexokinase (HEX): HEX (EC 2.7.1.1) was modeled as a monomer to account for the fact that it contains only one active catalytic site. The previously specified mechanism was chosen to match that used by [16] because all kinetic parameters were obtained from this source. A hemoglobin module is necessary to include when the HEX module is included because it affects the level of 2,3 DPG, which serves as a regulatory molecule for HEX.…”

Section: Enzyme Module Constructionmentioning

confidence: 99%

“…Phosphofructokinase (PFK): PFK (EC 2.7.1.11) was modeled as a homotetramer to account for its four catalytic and allosteric binding sites [37]. The previously specified mechanism was chosen to match that used by [16] because all kinetic parameters were obtained from this source. The PFK module consisted of the following chemical reactions: where the bold text represents the enzyme and dashes show bound species.…”

Section: Enzyme Module Constructionmentioning

confidence: 99%

“…The first whole-cell kinetic model of RBC metabolism was published in the late 1980s [10]- [13], with other such models produced since then [14], [15]. More recently, enzyme modules have been introduced and used to explicitly model detailed binding events of ligands involved in allosteric regulation as an alternative to the traditional use of allosteric rate laws [16]. Such a fine-grained view of the activity and state of a regulated enzyme opens up many new possibilities in understanding the metabolic regulation that results from complex interactions of regulatory signals, as well as a way to explicitly represent biological data types.…”

Section: Introductionmentioning

confidence: 99%

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Catalytic potential and disturbance rejection of glycolytic kinases in the human red blood cell

Yurkovich

Alcantar

Haiman

et al. 2017

Preprint

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Abstract-The allosteric regulation of metabolic enzymes plays a key role in controlling the flux through metabolic pathways. The activity of such enzymes is traditionally described by allosteric rate laws in complex kinetic models of metabolic network function. As an alternative, we describe the fraction of the regulated enzyme that is in an active form by developing a detailed reaction network of all known ligand binding events to the enzyme. This fraction is the fundamental result of metabolic regulation as it represents the "tug of war" among the various regulators and substrates that determine the utilization of the enzyme. The active fraction corresponds to the utilization of the catalytic potential of the enzyme. Using well developed kinetic models of human red blood cell (RBC) glycolysis, we characterize the catalytic potential of its three key kinases: hexokinase (HEX), phosphofructokinase (PFK), and pyruvate kinase (PYK). We then compute their time-dependent interacting catalytic potentials. We show how detailed kinetic models of the management of the catalytic potential of the three kinases elucidates disturbance rejection capabilities of glycolysis. Further, we examine the sensitivity of the catalytic potential through an examination of existing personalized RBC models, providing a physiologically-meaningful sampling of the feasible parameter space. The graphical representation of the dynamic interactions of the individual kinase catalytic potential adjustment provides an easy way to understand how a robust homeostatic state is maintained through interacting allosteric regulatory mechanisms.

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