Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

Basak, Sujit; Sengupta, Sombuddha; Chattopadhyay, Krishnananda

doi:10.1007/s12551-019-00580-9

“…with > 0, was solved by Pattle 174 (see also some recent "reincarnations" 175,176 ). Contemporary models of diffusion with space-dependent diffusion coefficients 154,[177][178][179][180][181][182][183][184] -with HDPs being a specific example that assumes the functional diffusivity form (17)can be used to describe (•) the non-Brownian diffusion in crowded, porous, and heterogeneous media [185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200][201][202] (such as densely macromolecularly crowded cell cytoplasm), (•) the reduction of a critical "patch size" required for survival of a population in the case of heterogeneous diffusion of its individuals 181 , (•) diffusion in heterogeneous comb-like and fractal structures 182 , (•) escalated polymerization of RNA nucleotides by a spatially confined thermal (and diffusivity) gradient in thermophoresis setups 203 , (•) motion of active particles with space-dependent friction in potentials [both of power-law forms] 204 , and (•) transient subdiffusion in disordered space-inhomogeneous quantum walks 205,206 . We mention also a class of diffusion models with (•) particle-spreading scenarios with concentration-dependent power-law-like diffusivity (20) 175,207 , (•) concentration-dependent dispersion in the population dynamics, with a nonlinear dependence of mobility on particle density, D(ρ) ∼ ρ κ (yielding a migration from more-to less-populated areas) [208]…”

Section: Some Applications Of Fbm and Hdpsmentioning

confidence: 99%

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Wang

¹

,

Cherstvy

²

,

Kantz

³

et al. 2021

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How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD-and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0|x| γ , and of their "combined" process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle' displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for "confined" processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

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“…Brownian motion (BM) features a linear spreading dynamics of the particles and a Gaussian distribution of their increments. Physical processes with non-Brownian spreading dynamics of the particles feature a nonlinear growth of the ensembleaveraged mean-squared displacement (MSD) [1][2][3][4][5][6][7][8][9][10][11][12][13]. In one spatial dimension, the MSD for anomalous-diffusion processes obeys a power law…”

Section: Anomalous Diffusion and Its Modelsmentioning

confidence: 99%

Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity: striking differences for massive versus massless particles

Cherstvy¹,

Safdari²,

Metzler³

2021

J. Phys. D: Appl. Phys.

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We investigate a diffusion process with a time-dependent diffusion coefficient, both exponentially increasing and decreasing in time, D ( t ) = D 0 e ± 2 α t . For this (hypothetical) nonstationary diffusion process we compute—both analytically and from extensive stochastic simulations—the behavior of the ensemble- and time-averaged mean-squared displacements (MSDs) of the particles, both in the over- and underdamped limits. Simple asymptotic relations derived for the short- and long-time behaviors are shown to be in excellent agreement with the results of simulations. The diffusive characteristics in the presence of ageing are also considered, with dramatic differences of the over- versus underdamped regime. Our results for D ( t ) = D 0 e ± 2 α t extend and generalize the class of diffusive systems obeying scaled Brownian motion featuring a power-law-like variation of the diffusivity with time, D ( t ) ∼ t α − 1 . We also examine the logarithmically increasing diffusivity, D ( t ) = D 0 log [ t / τ 0 ] , as another fundamental functional dependence (in addition to the power-law and exponential) and as an example of diffusivity slowly varying in time. One of the main conclusions is that the behavior of the massive particles is predominantly ergodic, while weak ergodicity breaking is repeatedly found for the time-dependent diffusion of the massless particles at short times. The latter manifests itself in the nonequivalence of the (both nonaged and aged) MSD and the mean time-averaged MSD. The current findings are potentially applicable to a class of physical systems out of thermal equilibrium where a rapid increase or decrease of the particles’ diffusivity is inherently realized. One biological system potentially featuring all three types of time-dependent diffusion (power-law-like, exponential, and logarithmic) is water diffusion in the brain tissues, as we thoroughly discuss in the end.

show abstract

“…with > 0, was solved by Pattle 174 (see also some recent "reincarnations" 175,176 ). Contemporary models of diffusion with space-dependent diffusion coefficients 154,[177][178][179][180][181][182][183][184] -with HDPs being a specific example that assumes the functional diffusivity form (17)can be used to describe (•) the non-Brownian diffusion in crowded, porous, and heterogeneous media [185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200][201][202] (such as densely macromolecularly crowded cell cytoplasm), (•) the reduction of a critical "patch size" required for survival of a population in the case of heterogeneous diffusion of its individuals 181 , (•) diffusion in heterogeneous comb-like and fractal structures 182 , (•) escalated polymerization of RNA nucleotides by a spatially confined thermal (and diffusivity) gradient in thermophoresis setups 203 , (•) motion of active particles with space-dependent friction in potentials [both of power-law forms] 204 , and (•) transient subdiffusion in disordered space-inhomogeneous quantum walks 205,206 . We mention also a class of diffusion models with (•) particle-spreading scenarios with concentration-dependent power-law-like diffusivity (20) 175,207 , (•) concentration-dependent dispersion in the population dynamics, with a nonlinear dependence of mobility on particle density, D(ρ) ∼ ρ κ (yielding a migration from more-to less-populated areas) [208]…”

Section: Some Applications Of Fbm and Hdpsmentioning

confidence: 99%

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Wang

¹

,

Cherstvy

²

,

Kantz

³

et al. 2021

Preprint

View full text Add to dashboard Cite

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0|x|γ and of their "combined" process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle' displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for "confined" processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB~ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

show abstract

Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

Cited by 15 publications

References 193 publications

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity: striking differences for massive versus massless particles

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

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