An official website of the United States government
Abstract It has been suggested before that small-scale magnetic flux rope (SMFR) structures in the solar wind can temporarily trap energetic charged particles. We present the derivation of a new fractional Parker equation for energetic-particle interaction with SMFRs from our pitch-angle-dependent fractional diffusion-advection equation that can account for such trapping effects. The latter was derived previously in le Roux & Zank from the first principles starting with the standard focused transport equation. The new equation features anomalous advection and diffusion terms. It suggests that energetic-particle parallel transport occurs with a decaying efficiency of advection effects as parallel superdiffusion becomes more dominant at late times. Parallel superdiffusion can be linked back to underlying anomalous pitch-angle transport, which might be subdiffusive during interaction with quasi-helical coherent SMFRs. We apply the new equation to time-dependent superdiffusive shock acceleration at a parallel shock. The results show that the superdiffusive-shock-acceleration timescale is fractional, the net fractional differential particle flux is conserved across the shock ignoring particle injection at the shock, and the accelerated particle spectrum at the shock converges to the familiar power-law spectrum predicted by standard steady-state diffusive-shock-acceleration theory at late times. Upstream, as parallel superdiffusion progressively dominates the advection of energetic particles, their spatial distributions decay on spatial scales that grow with time. Furthermore, superdiffusive parallel shock acceleration is found to be less efficient if parallel anomalous diffusion is more superdiffusive, while perpendicular particle escape from the shock, thought to be subdiffusive during SMFR interaction, is reduced when increasingly subdiffusive.
more »
« less
Motor-driven advection competes with crowding to drive spatiotemporally heterogeneous transport in cytoskeleton composites
The cytoskeleton–a composite network of biopolymers, molecular motors, and associated binding proteins–is a paradigmatic example of active matter. Particle transport through the cytoskeleton can range from anomalous and heterogeneous subdiffusion to superdiffusion and advection. Yet, recapitulating and understanding these properties–ubiquitous to the cytoskeleton and other out-of-equilibrium soft matter systems–remains challenging. Here, we combine light sheet microscopy with differential dynamic microscopy and single-particle tracking to elucidate anomalous and advective transport in actomyosin-microtubule composites. We show that particles exhibit multi-mode transport that transitions from pronounced subdiffusion to superdiffusion at tunable crossover timescales. Surprisingly, while higher actomyosin content increases the range of timescales over which transport is superdiffusive, it also markedly increases the degree of subdiffusion at short timescales and generally slows transport. Corresponding displacement distributions display unique combinations of non-Gaussianity, asymmetry, and non-zero modes, indicative of directed advection coupled with caged diffusion and hopping. At larger spatiotemporal scales, particles in active composites exhibit superdiffusive dynamics with scaling exponents that are robust to changing actomyosin fractions, in contrast to normal, yet faster, diffusion in networks without actomyosin. Our specific results shed important new light on the interplay between non-equilibrium processes, crowding and heterogeneity in active cytoskeletal systems. More generally, our approach is broadly applicable to active matter systems to elucidate transport and dynamics across scales.
more »
« less
- Award ID(s):
- 2203791
- PAR ID:
- 10406484
- Date Published:
- Journal Name:
- Frontiers in Physics
- Volume:
- 10
- ISSN:
- 2296-424X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The transport of macromolecules, such as DNA, through the cytoskeleton is critical to wide-ranging cellular processes from cytoplasmic streaming to transcription. The rigidity and steric hindrances imparted by the network of filaments comprising the cytoskeleton often leads to anomalous subdiffusion, while active processes such as motor-driven restructuring can induce athermal superdiffusion. Understanding the interplay between these seemingly antagonistic contributions to intracellular dynamics remains a grand challenge. Here, we use single-molecule tracking to show that the transport of large linear and relaxed circular DNA through motor-driven microtubule networks can be non-Gaussian and multimodal, with the degree and spatiotemporal scales over which these features manifest depending nontrivially on the state of activity and DNA topology. For example, active network restructuring increases caging and non-Gaussian transport modes of linear DNA, while dampening these mechanisms for circular DNA. We further discover that circular DNA molecules exhibit either markedly enhanced subdiffusion or superdiffusion compared to their linear counterparts, in the absence or presence of kinesin activity, indicative of microtubules threading circular DNA. This strong coupling leads to both stalling and directed transport, providing a direct route towards parsing distinct contributions to transport and determining the impact of coupling on the transport signatures. More generally, leveraging macromolecular topology as a route to programming molecular interactions and transport dynamics is an elegant yet largely overlooked mechanism that cells may exploit for intracellular trafficking, streaming, and compartmentalization. This mechanism could be harnessed for the design of self-regulating, sensing, and reconfigurable biomimetic matter. Published by the American Physical Society2025more » « less
-
The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.more » « less
-
Cytoskeletal crowding plays a key role in the diffusion of DNA molecules through the cell, acting as a barrier to effective intracellular transport and conformational stability required for processes such as transfection, viral infection, and gene therapy. Here, we elucidate the transport properties and conformational dynamics of linear and ring DNA molecules diffusing through entangled and crosslinked composite networks of actin and microtubules. We couple single-molecule conformational tracking with differential dynamic microscopy to reveal that ring and linear DNA exhibit unexpectedly distinct transport properties that are influenced differently by cytoskeleton crosslinking. Ring DNA coils are swollen and undergo heterogeneous and biphasic subdiffusion that is hindered by crosslinking. Conversely, crosslinking actually facilitates the single-mode subdiffusion that compacted linear chains exhibit. Our collective results demonstrate that transient threading by cytoskeleton filaments plays a key role in the dynamics of ring DNA, whereas the mobility of the cytoskeleton dictates transport of linear DNA.more » « less
-
Sharma, Pradeep (Ed.)Abstract The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable nonequilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton's versatile reconfigurability, programmed by interactions between its constituents, makes it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate—far from the composite cytoskeleton in cells. Here, we engineer actin–microtubule (MT) composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or MTs has an opposite effect. Our minimal advection–diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and demixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the nonequilibrium dynamics across all composites and timescales can be organized into three classes—slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fphy.2022.1055441
