Concentration effects on the rates of irreversible diffusion-influenced reactions

Kim, Minjung; Lee, Sangyoub; Kim, Jihyun

doi:10.1063/1.4893340

Cited by 9 publications

(6 citation statements)

References 51 publications

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“…, , and , are isomorphic to the corresponding equations for an irreversible A + B → C + B reaction with excess B. For the irreversible reaction, we have

\frac{d}{normald t} a ((), t) = prefix- λ_{f} true \int d boldr S_{0} ((), r) C_{AB} ((),, r, t)

\frac{\partial}{\partial t} C_{AB} ((),, r, t) = L_{2} ((), r) C_{AB} ((),, r, t) - λ_{f} S_{0} ((), r) C_{AB} ((),, r, t) - λ_{f} true \int d r^{'} S_{0} ((), r^{'}) C_{ABB} ((),,, r, {boldr}^{bold'}, t)

\frac{\partial}{\partial t} C_{ABB} ((),,, r, {boldr}^{bold'}, t) = L_{3} ((),, r, {boldr}^{bold'}) C_{ABB} ((),,, r, {boldr}^{bold'}, t) - λ_{f} ([], S_{0} ((), r) + S_{0} ((), r^{'})) C_{ABB} ((),,, r, {boldr}^{bold'}, t) - λ_{f} true \int d r^{″} S_{0} ((), r^{″}) C_{ABBB} ((),,,, r, {boldr}^{bold'}, {boldr}^{bold″}, t)

with a (0) = a 0 , a (∞) = 0, C AB ( r , 0) = a (0) C B ...…”

Section: Theorymentioning

confidence: 99%

“…does not rely on the assumption that the reactants are interaction‐free point particles. Therefore, the effects of interaction potential U BB ( r ) among the B molecules can be evaluated by utilizing the theory developed recently for an irreversible reaction . When the reaction sink function is given by

S_{f} ((), r) = κ_{f} δ ((), r - σ) false/ ((), 4 π σ^{2})

, we showed in Ref.…”

Section: Effects Of Excluded Volumesmentioning

confidence: 99%

“…When the reaction sink function is given by

S_{f} ((), r) = κ_{f} δ ((), r - σ) false/ ((), 4 π σ^{2})

, we showed in Ref. that

Y_{A}^{irrev} (();, t, κ_{normalf}) = Y_{A}^{0} (();, t, κ_{normalf}) normalexp ({}, prefix- L^{prefix- 1} ([], s^{prefix- 1} κ_{f} \overset{X}{true} ((),, σ, s)))

where L −1 denotes the inverse Laplace transformation operator, and s is the Laplace transform variable. The caret symbol denotes Laplace‐transformed quantities.…”

Section: Effects Of Excluded Volumesmentioning

confidence: 99%

“…Furthermore, our analysis does not require the assumption that the reactants are interaction‐free point particles. Therefore, the effect of excluded volumes among the B molecules that are present in much excess can also be evaluated by utilizing the theory developed for an irreversible reaction …”

Section: Introductionmentioning

confidence: 99%

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Excluded Volume Effects on the Kinetics of Diffusion‐influenced Reversible Bimolecular Reactions: A + B ⇄ C + B

Kim

Lee

2016

Bulletin Korean Chem Soc

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We propose a new approach to treat the kinetics of diffusion-influenced reversible bimolecular reactions and apply it first to the reactions of the type A + B ⇄ C + B. For this type of reactions with some provisions, Gopich et al. showed that the relaxation kinetics can be described exactly in the same way as the reactant decay in an "equivalent" irreversible A + B ! C + B reaction. In this article, we will show that the same relationship can be derived in a very elementary way by using a new approach based on the hierarchical kinetic equations governing the reduced distribution functions of reactant molecules. Because our analysis does not require the assumption that the reactants are interaction-free point particles, the effect of excluded volumes among the reactants can also be evaluated by utilizing the result derived for an irreversible reaction.

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“…, , and , are isomorphic to the corresponding equations for an irreversible A + B → C + B reaction with excess B. For the irreversible reaction, we have

\frac{d}{normald t} a ((), t) = prefix- λ_{f} true \int d boldr S_{0} ((), r) C_{AB} ((),, r, t)

\frac{\partial}{\partial t} C_{AB} ((),, r, t) = L_{2} ((), r) C_{AB} ((),, r, t) - λ_{f} S_{0} ((), r) C_{AB} ((),, r, t) - λ_{f} true \int d r^{'} S_{0} ((), r^{'}) C_{ABB} ((),,, r, {boldr}^{bold'}, t)

\frac{\partial}{\partial t} C_{ABB} ((),,, r, {boldr}^{bold'}, t) = L_{3} ((),, r, {boldr}^{bold'}) C_{ABB} ((),,, r, {boldr}^{bold'}, t) - λ_{f} ([], S_{0} ((), r) + S_{0} ((), r^{'})) C_{ABB} ((),,, r, {boldr}^{bold'}, t) - λ_{f} true \int d r^{″} S_{0} ((), r^{″}) C_{ABBB} ((),,,, r, {boldr}^{bold'}, {boldr}^{bold″}, t)

with a (0) = a 0 , a (∞) = 0, C AB ( r , 0) = a (0) C B ...…”

Section: Theorymentioning

confidence: 99%

S_{f} ((), r) = κ_{f} δ ((), r - σ) false/ ((), 4 π σ^{2})

, we showed in Ref.…”

Section: Effects Of Excluded Volumesmentioning

confidence: 99%

“…When the reaction sink function is given by

S_{f} ((), r) = κ_{f} δ ((), r - σ) false/ ((), 4 π σ^{2})

, we showed in Ref. that

Y_{A}^{irrev} (();, t, κ_{normalf}) = Y_{A}^{0} (();, t, κ_{normalf}) normalexp ({}, prefix- L^{prefix- 1} ([], s^{prefix- 1} κ_{f} \overset{X}{true} ((),, σ, s)))

where L −1 denotes the inverse Laplace transformation operator, and s is the Laplace transform variable. The caret symbol denotes Laplace‐transformed quantities.…”

Section: Effects Of Excluded Volumesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Excluded Volume Effects on the Kinetics of Diffusion‐influenced Reversible Bimolecular Reactions: A + B ⇄ C + B

Kim

Lee

2016

Bulletin Korean Chem Soc

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“…Possible alternatives are, for example, the Cichocki-Hinsen algorithm (30), the reaction Brownian dynamic algorithm (34), the Green's function reaction dynamics algorithm (35), smoldyn (36), or Readdy (37). In this work, we used an algorithm that combines hard-sphere Brownian dynamics (38) and Brownian reaction dynamics (39)(40)(41)(42).…”

Section: Introductionmentioning

confidence: 99%

Particle-Based Simulation Reveals Macromolecular Crowding Effects on the Michaelis-Menten Mechanism

Weilandt

Hatzimanikatis

2019

Biophysical Journal

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Many computational models for analyzing and predicting cell physiology rely on in vitro data collected in dilute and controlled buffer solutions. However, this can mislead models because up to 40% of the intracellular volume-depending on the organism, the physiology, and the cellular compartment-is occupied by a dense mixture of proteins, lipids, polysaccharides, RNA, and DNA. These intracellular macromolecules interfere with the interactions of enzymes and their reactants and thus affect the kinetics of biochemical reactions, making in vivo reactions considerably more complex than the in vitro data indicates. In this work, we present a new, to our knowledge, type of kinetics that captures and quantifies the effect of volume exclusion and other spatial phenomena on the kinetics of elementary reactions. We further developed a framework that allows for the efficient parameterization of these kinetics using particle simulations. Our formulation, entitled generalized elementary kinetics, can be used to analyze and predict the effect of intracellular crowding on enzymatic reactions and was herein applied to investigate the influence of crowding on phosphoglycerate mutase in Escherichia coli, which exhibits prototypical reversible Michaelis-Menten kinetics. Current research indicates that many enzymes are reaction limited and not diffusion limited, and our results suggest that the influence of fractal diffusion is minimal for these reaction-limited enzymes. Instead, increased association rates and decreased dissociation rates lead to a strong decrease in the effective maximal velocities V max and the effective Michaelis-Menten constants K M under physiologically relevant volume occupancies. Finally, the effects of crowding were explored in the context of a linear pathway, with the finding that crowding can have a redistributing effect on the effective flux responses in the case of twofold enzyme overexpression. We suggest that this framework, in combination with detailed kinetics models, will improve our understanding of enzyme reaction networks under nonideal conditions. SIGNIFICANCE Kinetic models are essential for understanding and designing biochemical and biophysical processes in living organisms. Currently, kinetic models rely on the in vitro characterization of biochemical reactions, although intracellular reactions are taking place in crowded, nonideal conditions. The interactions of the enzymes and their reactants with other macromolecules in a cell alter the enzyme kinetics significantly, but little has been done to model and quantify the impact of these interactions on the in vivo reaction rates. We present a computational framework that allows us for the first time, to our knowledge, to estimate the in vivo apparent kinetic parameters of an enzyme that follows Michaelis-Menten kinetics. Interestingly, crowding conditions similar to those in Escherichia coli can reduce the maximal enzyme activity 10fold.

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Operator algebraic methods in the theory ofdiffusion‐influencedreaction kinetics

Lee

2021

Bulletin Korean Chem Soc

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Operator algebra is a useful mathematical technique that provides formal analytic solutions to various time‐evolution equations, appearing in quantum and statistical mechanics. In particular, combined with the Laplace transformation and Green's function methods, the operator algebra has been found to be very useful in deriving analytic solutions to various kinetic equations such as the Smoluchowski equation. In this review, operator algebraic methods as applied in the theory of diffusion‐influenced bimolecular reaction kinetics will be briefly described.

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Concentration effects on the rates of irreversible diffusion-influenced reactions

Cited by 9 publications

References 51 publications

Excluded Volume Effects on the Kinetics of Diffusion‐influenced Reversible Bimolecular Reactions: A + B ⇄ C + B

Excluded Volume Effects on the Kinetics of Diffusion‐influenced Reversible Bimolecular Reactions: A + B ⇄ C + B

Particle-Based Simulation Reveals Macromolecular Crowding Effects on the Michaelis-Menten Mechanism

Operator algebraic methods in the theory ofdiffusion‐influencedreaction kinetics

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