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Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

ABSTRACT: Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems.

SUBMITTER: Eilertsen J

PROVIDER: S-EPMC6612542 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature

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Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

Eilertsen Justin J Stroberg Wylie W Schnell Santiago S

Journal of theoretical biology 20190105

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the cl ...[more]

PMID: 30615881

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Project description:In two-component regulatory systems, covalent phosphorylation typically activates the response regulator signaling protein, and hydrolysis of the phosphoryl group reestablishes the inactive state. Despite highly conserved three-dimensional structures and active-site features, the rates of catalytic autodephosphorylation for different response regulators vary by a factor of almost 10(6). Previous studies identified two variable active-site residues, corresponding to Escherichia coli CheY residues 59 and 89, that modulate response regulator autodephosphorylation rates about 100-fold. Here, a set of five CheY mutants, which match other "model" response regulators (ArcA, CusR, DctD, FixJ, PhoB, or Spo0F) at variable active-site positions corresponding to CheY residues 14, 59, and 89, were characterized functionally and structurally in an attempt to identify mechanisms that modulate autodephosphorylation rate. As expected, the autodephosphorylation rates of the CheY mutants were reduced 6- to 40-fold relative to wild-type CheY, but all still autodephosphorylated 12- to 80-fold faster than their respective model response regulators. Comparison of X-ray crystal structures of the five CheY mutants (complexed with the phosphoryl group analogue BeF(3)(-)) to wild-type CheY or corresponding model response regulator structures gave strong evidence for steric obstruction of the phosphoryl group from the attacking water molecule as one mechanism to enhance phosphoryl group stability. Structural data also suggested that impeding the change of a response regulator from the active to the inactive conformation might retard the autodephosphorylation reaction if the two processes are coupled, and that the residue at position '58' may contribute to rate modulation. A given combination of amino acids at positions '14', '59', and '89' adopted similar conformations regardless of protein context (CheY or model response regulator), suggesting that knowledge of residue identity may be sufficient to predict autodephosphorylation rate, and hence the kinetics of the signaling response, in the response regulator family of proteins.

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Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

Publications

Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

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