493 research outputs found
Viscoelastic active diffusion governed by nonequilibrium fractional Langevin equations: underdamped dynamics and ergodicity breaking
In this work, we investigate the active dynamics and ergodicity breaking of a
nonequilibrium fractional Langevin equation (FLE) with a power-law memory
kernel of the form , where represents the Hurst
exponent. The system is subjected to two distinct noises: a thermal noise
satisfying the fluctuation-dissipation theorem and an active noise
characterized by an active Ornstein-Uhlenbeck process with a propulsion memory
time . We provide analytic solutions for the underdamped
active fractional Langevin equation, performing both analytical and
computational investigations of dynamic observables such as velocity
autocorrelation, the two-time position correlation, ensemble- and time-averaged
mean-squared displacements (MSDs), and ergodicity-breaking parameters. Our
results reveal that the interplay between the active noise and long-time
viscoelastic memory effect leads to unusual and complex nonequilibrium dynamics
in the active FLE systems. Furthermore, the active FLE displays a new type of
discrepancy between ensemble- and time-averaged observables. The active
component of the system exhibits ultraweak ergodicity breaking where both
ensemble- and time-averaged MSDs have the same functional form with unequal
amplitudes. However, the combined dynamics of the active and thermal components
of the active FLE system are eventually ergodic in the infinite-time limit.
Intriguingly, the system has a long-standing ergodicity-breaking state before
recovering the ergodicity. This apparent ergodicity-breaking state becomes
exceptionally long-lived as , making it difficult to observe ergodicity
within practical measurement times. Our findings provide insight into related
problems, such as the transport dynamics for self-propelled particles in
crowded or polymeric media
How dsDNA breathing enhances its flexibility and instability on short length scales
We study the unexpected high flexibility of short dsDNA which recently has
been reported by a number of experiments. Via the Langevin dynamics simulation
of our Breathing DNA model, first we observe the formation of bubbles within
the duplex and also forks at the ends, with the size distributions independent
of the contour length. We find that these local denaturations at a
physiological temperature, despite their rare and transient presence, can lower
the persistence length drastically for a short DNA segment in agreement with
experiment
Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional Langevin equation
In a viscoelastic environment, the diffusion of a particle becomes
non-Markovian due to the memory effect. An open question is to quantitatively
explain how self-propulsion particles with directional memory diffuse in such a
medium. Based on simulations and analytic theory, we address this issue with
active viscoelastic systems where an active particle is connected with multiple
semi-flexible filaments. Our Langevin dynamics simulations show that the active
cross-linker displays super- and sub-diffusive athermal motion with a
time-dependent anomalous exponent . In such viscoelastic feedback, the
active particle always has superdiffusion with at times shorter
than the self-propulsion time (). At times greater than , the
subdiffusion emerges with bounded between and . Remarkably,
the active subdiffusion is reinforced as the active propulsion (Pe) is more
vigorous. In the high-Pe limit, the athermal fluctuation in the stiff filament
eventually leads to , which can be misinterpreted with the thermal
Rouse motion in a flexible chain. We demonstrate that the motion of active
particles cross-linking a network of semi-flexible filaments can be governed by
a fractional Langevin equation combined with fractional Gaussian noise and an
Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation
function and mean-squared displacement of the model, explaining their scaling
relations as well as the prefactors. We find that there exist the threshold Pe
() and cross-over times ( and ) above
which the active viscoelastic dynamics emerge on the timescales of . Our study may provide a theoretical insight
into various nonequilibrium active dynamics in intracellular viscoelastic
environments
Neuronal messenger ribonucleoprotein transport follows an aging Lévy walk
Localization of messenger ribonucleoproteins (mRNPs) plays an essential role in the regulation of gene expression for long-term memory formation and neuronal development. Knowledge concerning the nature of neuronal mRNP transport is thus crucial for understanding how mRNPs are delivered to their target synapses. Here, we report experimental and theoretical evidence that the active transport dynamics of neuronal mRNPs, which is distinct from the previously reported motor-driven transport, follows an aging Levy walk. Such nonergodic, transient superdiffusion occurs because of two competing dynamic phases: the motor-involved ballistic run and static localization of mRNPs. Our proposed Levy walk model reproduces the experimentally extracted key dynamic characteristics of mRNPs with quantitative accuracy. Moreover, the aging status of mRNP particles in an experiment is inferred from the model. This study provides a predictive theoretical model for neuronal mRNP transport and offers insight into the active target search mechanism of mRNP particles in vivo.1111sciescopu
Protein Crowding in Lipid Bilayers Gives Rise to Non-Gaussian Anomalous Lateral Diffusion of Phospholipids and Proteins
Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios being around 1:50 - 1:100. Protein crowding has a decisive role in lateral membrane dynamics as shown by recent experimental and computational studies that have reported anomalous lateral diffusion of phospholipids and membrane proteins in crowded lipid membranes. Based on extensive simulations and stochastic modeling of the simulated trajectories, we here investigate in detail how increasing crowding by membrane proteins reshapes the stochastic characteristics of the anomalous lateral diffusion in lipid membranes. We observe that correlated Gaussian processes of the fractional Langevin equation type, identified as the stochastic mechanism behind lipid motion in noncrowded bilayer, no longer adequately describe the lipid and protein motion in crowded but otherwise identical membranes. It turns out that protein crowding gives rise to a multifractal, non-Gaussian, and spatiotemporally heterogeneous anomalous lateral diffusion on time scales from nanoseconds to, at least, tens of microseconds. Our investigation strongly suggests that the macromolecular complexity and spatiotemporal membrane heterogeneity in cellular membranes play critical roles in determining the stochastic nature of the lateral diffusion and, consequently, the associated dynamic phenomena within membranes. Clarifying the exact stochastic mechanism for various kinds of biological membranes is an important step towards a quantitative understanding of numerous intramembrane dynamic phenomena.Peer reviewe
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