Including Rebinding Reactions in Well-Mixed Models of Distributive Biochemical Reactions

Lawley, Sean D.; Keener, James P.

doi:10.1016/j.bpj.2016.10.008

Cited by 10 publications

(13 citation statements)

References 30 publications

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“…The kinetic schemes in Equations (50) and (51) are closely related to that of Lawley and Keener [ 15,16 ] :

\begin{array}{l} S_{0} goodbreak+ E ⇌_{(κ_{0}^{d} ϵ_{0})}^{κ_{0}^{a} ϵ_{0}} S_{0} E \overset{κ_{0}^{c} ((), 1 goodbreak- q^{*})}{\to} S_{1} goodbreak+ E^{*} \\ S_{1} goodbreak+ E ⇌_{(κ_{1}^{d} ϵ_{1})}^{κ_{1}^{a} ϵ_{1}} S_{1} E \overset{κ_{1}^{c}}{\to} S_{2} goodbreak+ E^{*} \\ S_{0} E \overset{κ_{0}^{c} q^{*}}{\to} S_{1} E \\ E^{*} \overset{k^{*}}{\to} E \end{array}

It can be obtained by replacing the last

E

in Equation (51) by

E^{*}

and adding the channel

E^{*} \to E

. Alternatively, this can be obtained by replacing

E

in the last reaction channel in Equation (50) by

E^{*}

.…”

Section: Resultsmentioning

confidence: 99%

“…We considered this problem previously [12] in the limit that the reactivation time was sufficiently short so that the concentration of E Ã was negligible and derived a diffusion-modified kinetic scheme (see Equation 51) using a many-particle approach. Then Lawley and Keener [15,16] studied the situation where the concentration of E Ã is arbitrary and presented a different kinetic scheme (see Equation 52), whose prediction was shown to be in excellent agreement with the results of many-particle simulations of Takahashi et al [11] When we subsequently investigated the general case, we were unable to rederive their results. Rather, as will be shown in this paper, we obtained a diffusion-modified kinetic scheme (see Equation 50) that unexpectedly contained a negative rate constant.…”

Section: Introductionmentioning

confidence: 91%

“…The kinetic schemes in Equations ( 50) and ( 51) are closely related to that of Lawley and Keener [15,16] :…”

Section: Diffusion-modified Kinetic Schemementioning

confidence: 99%

“…[11] We show that our diffusion-modified kinetic scheme quantitatively reproduces the simulation results to the same degree as the scheme proposed by Lawley and Keener. [15] 2 | METHODS…”

Section: Introductionmentioning

confidence: 99%

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Kinetics of diffusion‐influenced multisite phosphorylation with enzyme reactivation

Gopich

Szabó

2023

Biopolymers

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The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion‐modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non‐Markovian rate equations onto Markovian ones with time‐independent rate constants is not a good approximation at short times. We then developed a non‐Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion‐modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady‐state response in a phosphorylation‐dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation‐dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle‐based computer simulations.

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“…The kinetic schemes in Equations (50) and (51) are closely related to that of Lawley and Keener [ 15,16 ] :

\begin{array}{l} S_{0} goodbreak+ E ⇌_{(κ_{0}^{d} ϵ_{0})}^{κ_{0}^{a} ϵ_{0}} S_{0} E \overset{κ_{0}^{c} ((), 1 goodbreak- q^{*})}{\to} S_{1} goodbreak+ E^{*} \\ S_{1} goodbreak+ E ⇌_{(κ_{1}^{d} ϵ_{1})}^{κ_{1}^{a} ϵ_{1}} S_{1} E \overset{κ_{1}^{c}}{\to} S_{2} goodbreak+ E^{*} \\ S_{0} E \overset{κ_{0}^{c} q^{*}}{\to} S_{1} E \\ E^{*} \overset{k^{*}}{\to} E \end{array}

It can be obtained by replacing the last

E

in Equation (51) by

E^{*}

and adding the channel

E^{*} \to E

. Alternatively, this can be obtained by replacing

E

in the last reaction channel in Equation (50) by

E^{*}

.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

“…The kinetic schemes in Equations ( 50) and ( 51) are closely related to that of Lawley and Keener [15,16] :…”

Section: Diffusion-modified Kinetic Schemementioning

confidence: 99%

“…[11] We show that our diffusion-modified kinetic scheme quantitatively reproduces the simulation results to the same degree as the scheme proposed by Lawley and Keener. [15] 2 | METHODS…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kinetics of diffusion‐influenced multisite phosphorylation with enzyme reactivation

Gopich

Szabó

2023

Biopolymers

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show abstract

“…Such rebinding was the mechanism posited in [17] to explain the processive behavior of non-processive motors along microtubule bundles. Further, rebinding is very important in enzymatic reactions [46,19,33,34]. In that context, one incorporates rebinding by using an "effective" unbinding rate, which is the intrinsic unbinding rate multiplied by the probability that the particle does not rapidly rebind [32].…”

Section: Biological Applicationmentioning

confidence: 99%

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Miles¹,

Lawley²,

Keener³

2018

SIAM J. Appl. Math.

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We propose and analyze a mathematical model of cargo transport by non-processive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position follows a stochastic differential equation (SDE) that depends on the discrete states of the motors. The resulting system for the cargo position is consequently an SDE that randomly switches according to a Markov jump process governing motor dynamics. To study this system we (1) cast the cargo position in a renewal theory framework and generalize the renewal reward theorem and (2) decompose the continuous and discrete sources of stochasticity and exploit a resulting pair of disparate timescales. With these mathematical tools, we obtain explicit formulas for experimentally measurable quantities, such as cargo velocity and run length. Analyzing these formulas then yields some predictions regarding so-called non-processive clustering, the phenomenon that a single motor cannot transport cargo, but that two or more motors can. We find that having motor stepping, binding, and unbinding rates depend on the number of bound motors, due to geometric effects, is necessary and sufficient to explain recent experimental data on non-processive motors.

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Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network

Schmidt,

Gaetjens,

Leopin

et al. 2024

Biophysical Journal

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Including Rebinding Reactions in Well-Mixed Models of Distributive Biochemical Reactions

Cited by 10 publications

References 30 publications

Kinetics of diffusion‐influenced multisite phosphorylation with enzyme reactivation

Kinetics of diffusion‐influenced multisite phosphorylation with enzyme reactivation

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network

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