Dynamic Looping of a Free-Draining Polymer

Ye, Felix X.-F.; Stinis, Panos; Qian, Hong

doi:10.1137/17m1127260

Cited by 9 publications

(3 citation statements)

References 34 publications

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“…The basic idea of this approximation is given by S̅ ( R , t ) – S̅ eq ( R ) B ( t ), where S̅ eq ( R ) = S̅ ( R ,0), which describes the system in thermal equilibrium at t = 0. With this initial condition, the formal solution of the reaction-diffusion equation (eq ) can be written as ,− ,, where G ( R , t – t ′| R ′, 0) is Green’s function, which satisfies the following equation, given by The solution of eq is known as which in the limit of t → ∞ defines S̅ eq ( R ) given below To determine the survival probability, we substitute the Wilemski–Fixman approximation into the right-hand side of eq , which on subsequent integration over R yields Considering and in the above equation, the subsequent calculations lead to where k 1 = k ′ Nb 2 and A = β(Δ G av – F Δ x av ). On the other hand, if both sides of eq are multiplied by k ( R ) and then integrated over R , we get the following expression where and The Laplace transform of eq results in B ( s ) in eq can further be substituted with an expression obtained from the Laplace transform of eq , given by This yields the following expression for the survival probability in the Laplace domain The explicit expression for ⟨ S ( s )⟩ can be deduced when k a and C ( t ) are evaluated from their definitions.…”

Section: Dynamic Disorder Model Of Single Polyubiquitin Unfolding Kin...mentioning

confidence: 99%

“…The basic idea of this approximation is given by S̅ (R,t) − S̅ eq (R)B(t), where S̅ eq (R) = S̅ (R,0), which describes the system in thermal equilibrium at t = 0. With this initial condition, the formal solution of the reaction-diffusion equation (eq 9) can be written as 10,[12][13][14]43,44 ∫ ∫ 11) where G(R, t − t′|R′, 0) is Green's function, which satisfies the following equation, given by…”

Section: ■ Introductionmentioning

confidence: 99%

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Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder

2020

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Mechanical unfolding of single polyubiquitin molecules subjected to a constant stretching force showed nonexponentiality in the measured probability density of unfolding (waiting time distribution) and the survival probability of the folded state during the course of the measurements. These observations explored the relevance of disorder present in the system under study with implications for a static disorder approach to rationalize the experimental results. Here, an approach for dynamic disorder is presented based on Zwanzig’s fluctuating bottleneck (FB) model, in which the rate of the reaction is controlled by the passage through the cross-sectional area of the bottleneck. The radius of the latter undergoes stochastic fluctuations that in turn is described in terms of the end-to-end distance fluctuations of the Rouse-like dynamics using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our results are comprised of analytical expressions for the survival probability and waiting time distribution, which show excellent agreement with the experimental data throughout the range of the applied forces. In addition, by fitting the survival probabilities at different stretching forces, we quantify two system parameters, namely, the average free energy ΔG av and the average distance to the transition state Δx av, both perfectly recovered the experimental estimates. These agreements validate the present model of polymer dynamics, which captures the very essence of dynamic disorder in single-molecule pulling experiments.

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Section: Dynamic Disorder Model Of Single Polyubiquitin Unfolding Kin...mentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder

2020

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“…Therefore, it is practical to adopt an approximation technique using the self-consistent closure scheme suggested by Wilemski and Fixman [24,25] in which S(R ij , t) is written as S(R ij , t) ∼ S eq (R ij )φ(t) where S eq (R ij ) = S(R ij , 0) that describes the system in thermal equilibrium at t = 0. With this initial condition the formal solution of equation ( 9) can be written as [10,12,[24][25][26][27][28][29]]…”

Section: Dynamic Disorder Model Of Escape Kineticsmentioning

confidence: 99%

Kinetics of escape of ssDNA molecules fromα-hemolysin nanopores: a dynamic disorder study

Kundu¹,

Saha²,

Gangopadhyay³

2020

J. Stat. Mech.

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Experimental studies of the escape events of single-stranded DNA (ssDNA) molecules from the membrane embedded α-hemolysin nanopores exhibited the non-exponential kinetics. The data for homopolymers of adenine (dA27) and cytosine (dC27) revealed the profound influence of the sequence dependent DNA-pore interactions and the applied potentials on the escape kinetics. The non-exponential behavior is a signature of the presence of disorder in biochemical reactions. Here, we rationalize the experimental results with a dynamic disorder approach based on Zwanzig's fluctuating bottleneck (FB) model as a general mechanism where the rate of the reaction is controlled by the passage of a molecule through the cross-sectional area of the vestibule of the α-hemolysin channel (the bottleneck). The stochastic fluctuations of the radius of the latter is represented by the fluctuations of the intersegment distance of a Rouse chain, the dynamics of which is described using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our analytical results essentially capture the effects of underlying energetics due to the sequence-dependent nature and applied potentials in reproducing the measured survival probabilities for dA27 and dC27 in an excellent way, thereby validating

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Effects of solvent quality on contact formation dynamics of polymer chain

Bian

Zhao

2018

Chemical Physics Letters

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Dynamic Looping of a Free-Draining Polymer

Cited by 9 publications

References 34 publications

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder

Kinetics of escape of ssDNA molecules fromα-hemolysin nanopores: a dynamic disorder study

Effects of solvent quality on contact formation dynamics of polymer chain

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