Generating rate equations for complex enzyme systems by a computer-assisted systematic method

Qi, Feng; Dash, Ranjan K.; Yu, Han; Beard, Daniel A.

doi:10.1186/1471-2105-10-238

Cited by 37 publications

(40 citation statements)

References 31 publications

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“…The mechanism in Fig. 3a was solved using steady-state treatment and software for the King Altman procedure [62]. The resulting complex equation was analyzed numerically.…”

Section: Resultsmentioning

confidence: 99%

When substrate inhibits and inhibitor activates: implications of β-glucosidases

Kuusk

Väljamaë

2017

Biotechnol Biofuels

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Backgroundβ-glucosidases (BGs) catalyze the hydrolysis of β-glycosidic bonds in glucose derivatives. They constitute an important group of enzymes with biotechnological interest like supporting cellulases in degradation of lignocellulose to fermentable sugars. In the latter context, the glucose tolerant BGs are of particular interest. These BGs often show peculiar kinetics, including inhibitory effects of substrates and activating effects of inhibitors, such as glucose or xylose. The mechanisms behind the activating/inhibiting effects are poorly understood. The nonproductive binding of substrate is expected in cases where enzymes with multiple consecutive binding subsites are studied on substrates with a low degree of polymerization. The effects of inhibitors to BGs exerting nonproductive binding of substrate have not been discussed in the literature before.ResultsHere, we performed analyses of different reaction schemes using the catalysis by retaining BGs as a model. We found that simple competition of inhibitor with nonproductive binding of substrate can account for the activation of enzyme by inhibitor without involving any allosteric effects. The transglycosylation to inhibitor was also able to explain the activating effect of inhibitor. For both mechanisms, the activation was caused by the increase of k cat with increasing inhibitor concentration, while k cat/K m always decreased. Therefore, the activation by inhibitor was more pronounced at high substrate concentrations. The possible contribution of the two mechanisms in the activation by inhibitor was dependent on the rate-limiting step of glycosidic bond hydrolysis as well as on whether and which glucose-unit-binding subsites are interacting.ConclusionKnowledge on the mechanisms of the activating/inhibiting effects of inhibitors helps the rational engineering and selection of BGs for biotechnological applications. Provided that the catalysis is consistent with the reaction schemes addressed here and underlying assumptions, the mechanism of activation by inhibitor reported here is applicable for all enzymes exerting nonproductive binding of substrate.Electronic supplementary materialThe online version of this article (doi:10.1186/s13068-016-0690-z) contains supplementary material, which is available to authorized users.

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“…The mechanism in Fig. 3a was solved using steady-state treatment and software for the King Altman procedure [62]. The resulting complex equation was analyzed numerically.…”

Section: Resultsmentioning

confidence: 99%

When substrate inhibits and inhibitor activates: implications of β-glucosidases

Kuusk

Väljamaë

2017

Biotechnol Biofuels

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“…Steady-state treatment of the mechanisms in Fig. 6 using software for the King Altman procedure (69) resulted in complex equations containing squared terms for the inhibitor and substrate concentrations (supplemental Equations S1 and S2). Therefore, the influence of product inhibition on enzyme kinetics was analyzed numerically.…”

Section: C-cnw Hydrolysis (Equation 1)mentioning

confidence: 99%

The Predominant Molecular State of Bound Enzyme Determines the Strength and Type of Product Inhibition in the Hydrolysis of Recalcitrant Polysaccharides by Processive Enzymes

Kuusk

Sørlie

Väljamaë

2015

Journal of Biological Chemistry

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Background: Rate-limiting steps in the hydrolysis of recalcitrant polysaccharides by processive enzymes are not known. Results:The predominant molecular state of bound enzyme was revealed by the type and strength of product inhibition. Conclusion: Complexation with the polymer chain is rate-limiting for ChiA, whereas Cel7A is limited by dissociation. Significance: Knowledge of rate-limiting steps aids the engineering of better catalysts.

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“…The net reaction velocity equation is derived for GPx based on steady-state assumption for the unified catalytic scheme shown in Figure 1B using our freely available KAPattern Matlab tool for generating rate equations [44]. Assuming A, B, and P are concentrations of H 2 O 2 (or hydroperoxides), GSH and GSSG, respectively, the net reaction velocity equation is given by:

ν = \frac{E_{0} (k_{1 f} k_{2 f} f_{2} k_{3 f} f_{3} k_{4 f} A B^{2} - k_{1 r} f_{1 r} k_{2 r} f_{2 r} k_{3 r} k_{4 r} P)}{(\begin{matrix} k_{1 r} f_{1 r} k_{2 r} f_{2 r} (k_{4 f} + k_{3 r}) + k_{1 f} k_{2 r} f_{2 r} (k_{4 f} + k_{3 r}) A + k_{3 f} f_{3} k_{4 f} k_{1} f_{1 r} B + k_{2 f} f_{2} k_{3 f} f_{3} k_{4 f} B^{2} \\ + k_{1 f} (k_{2 f} f_{2} k_{4 f} + k_{3 f} f_{3} k_{4 f} + k_{2 f} f_{2} k_{3 r}) A B + k_{1 f} k_{2 f} f_{2} k_{3 f} f_{3} A B^{2} + k_{2 f} f_{2} k_{3 f} f_{3} k_{4 r} B^{2} P \\ + k_{4 r} (k_{1 r} f_{1 r} k_{3 <...>} \end{matrix}}

…”

Section: Methodsmentioning

confidence: 99%

A mechanistic mathematical model for the catalytic action ofglutathione peroxidase

Pannala¹,

Bazil²,

Camara³

et al. 2014

Free Radical Research

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Glutathione peroxidase (GPx) is a well-known seleno-enzyme that protects cells from oxidative stress (e.g., lipid peroxidation and oxidation of other cellular proteins and macromolecules), by catalyzing the reduction of harmful peroxides (e.g., hydrogen peroxide: H2O2) with reduced glutathione (GSH). However, the catalytic mechanism of GPx kinetics is not well characterized in terms of a mathematical model. We developed here a mechanistic mathematical model of GPx kinetics by considering a unified catalytic scheme and estimated the unknown model parameters based on different experimental data from the literature on the kinetics of the enzyme. The model predictions are consistent with the consensus that GPx operates via a ping-pong mechanism. The unified catalytic scheme proposed here for GPx kinetics clarifies various anomalies, such as what are the individual steps in the catalytic scheme by estimating their associated rate constant values and a plausible rationale for the contradicting experimental results. The developed model presents a unique opportunity to understand the effects of pH and product GSSG on the GPx activity under both physiological and pathophysiological conditions. Although model parameters related to the product GSSG were not identifiable due to lack of product-inhibition data, the preliminary model simulations with the assumed range of parameters show that the inhibition by the product GSSG is negligible, consistent with what is known in the literature. In addition, the model is able to simulate the bi-modal behavior of the GPx activity with respect to pH with the pH-range for maximal GPx activity decreasing significantly as the GSH levels decrease and H2O2 provides a key component for an integrated model of H2O2 levels increase (characteristics of oxidative stress). The model balance under normal and oxidative stress conditions.

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Generating rate equations for complex enzyme systems by a computer-assisted systematic method

Cited by 37 publications

References 31 publications

When substrate inhibits and inhibitor activates: implications of β-glucosidases

When substrate inhibits and inhibitor activates: implications of β-glucosidases

The Predominant Molecular State of Bound Enzyme Determines the Strength and Type of Product Inhibition in the Hydrolysis of Recalcitrant Polysaccharides by Processive Enzymes

A mechanistic mathematical model for the catalytic action ofglutathione peroxidase

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