Emergent mesoscale correlations in active solids with noisy chiral dynamics.

We present the linear response theory for an elastic solid composed of active Brownian particles with intrinsic individual chirality, deriving both a normal mode formulation and a continuum elastic formulation. Using this theory, we compute analytically the velocity correlations and energy spectra under different conditions, showing an excellent agreement with simulations. We generate the corresponding phase diagram, identifying chiral and achiral disordered regimes (for high chirality or noise levels), as well as chiral and achiral states with mesoscopic-range order (for low chirality and noise). The chiral ordered states display mesoscopic spatial correlations and oscillating time correlations, but no wave propagation. In the high chirality regime, we find a peak in the elastic energy spectrum that leads to a non-monotonic behavior with increasing noise strength that is consistent with the emergence of the 'hammering state' recently identified in chiral glasses. Finally, we show numerically that our theory, despite its linear response nature, can be applied beyond the idealized homogeneous solid assumed in our derivations. Indeed, by increasing the level of activity, we show that it remains a good approximation of the system dynamics until just below the melting transition. In addition, we show that there is still an excellent agreement between our analytical results and simulations when we extend our results to heterogeneous solids composed of mixtures of active particles with different intrinsic chirality and noise levels. The derived linear response theory is therefore robust and applicable to a broad range of real-world active systems. Our work provides a thorough analytical and numerical description of the emergent states in a densely packed system of chiral self-propelled Brownian disks, thus allowing a detailed understanding of the phases and dynamics identified in a minimal chiral active system.

F-box protein FBXB-65 regulates anterograde transport of the kinesin-3 motor UNC-104 through a PTM near its cargo-binding PH domain.

Axonal transport in neurons is essential for cargo movement between the cell body and synapses. Caenorhabditis elegans UNC-104 and its homolog KIF1A are kinesin-3 motors that anterogradely transport precursors of synaptic vesicles (pre-SVs) and are degraded at synapses. However, in C. elegans, touch neuron-specific knockdown of the E1 ubiquitin-activating enzyme, uba-1, leads to UNC-104 accumulation at neuronal ends and synapses. Here, we performed an RNAi screen and identified that depletion of fbxb-65, which encodes an F-box protein, leads to UNC-104 accumulation at neuronal distal ends, and alters UNC-104 net anterograde movement and levels of UNC-104 on cargo without changing synaptic UNC-104 levels. Split fluorescence reconstitution showed that UNC-104 and FBXB-65 interact throughout the neuron. Our theoretical model suggests that UNC-104 might exhibit cooperative cargo binding that is regulated by FBXB-65. FBXB-65 regulates an unidentified post-translational modification (PTM) of UNC-104 in a region beside the cargo-binding PH domain. Both fbxb-65 and UNC-104, independently of FBXB-65, regulate axonal pre-SV distribution, transport of pre-SVs at branch points and organismal lifespan. FBXB-65 regulates a PTM of UNC-104 and the number of motors on the cargo surface, which can fine-tune cargo transport to the synapse.

Noise-Induced Quenched Disorder in Dense Active Systems.

We report and characterize the emergence of a noise-induced state of quenched disorder in a generic model describing a dense sheet of active polar disks. In this state, self-propelled disks become jammed with random orientations, only displaying small fluctuations about their mean positions and headings. The quenched disorder phase appears at intermediate noise levels, between moving polar order and standard dynamic disorder. We show that it results from retrograde forces produced by angular fluctuations with Ornstein-Uhlenbeck dynamics, compute its critical noise, and argue that it could emerge in a variety of systems.

Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement.

We consider the influence of active speed fluctuations on the dynamics of a d-dimensional active Brownian particle performing a persistent stochastic motion. The speed fluctuation brings about a dynamical anisotropy even in the absence of shape anisotropy. We use the Laplace transform of the Fokker-Planck equation to obtain exact expressions for time-dependent dynamical moments. Our results agree with direct numerical simulations and show several dynamical crossovers determined by the activity, persistence, and speed fluctuation. The dynamical anisotropy leads to a subdiffusive scaling in the parallel component of displacement fluctuation at intermediate times. The kurtosis remains positive at short times determined by the speed fluctuation, crossing over to a negative minimum at intermediate times governed by the persistence before vanishing asymptotically. The probability distribution of particle displacement obtained from numerical simulations in two dimensions shows two crossovers between compact and extended trajectories via two bimodal distributions at intervening times. While the speed fluctuation dominates the first crossover, the second crossover is controlled by persistence like in the wormlike chain model of semiflexible polymers.

A semiflexible polymer in a gliding assay: reentrant transition, role of turnover and activity.

We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a capture radius, and extend along the filament in a directed fashion before detaching. Both the extension and detachment rates are load-dependent and generate an active drive on the filament. The filament undergoes a first order phase transition from the open chain to spiral conformation and shows a reentrant behavior in both the active extension and the turnover, defined as the ratio of attachment-detachment rates. Associated with the phase transition, the size and shape of the polymer change non-monotonically, and the relevant autocorrelation functions display a double-exponential decay. The corresponding correlation times show a maximum signifying the dominance of spirals. The orientational dynamics captures the rotation of spirals, and its correlation time decays with activity as a power law.

Active Brownian particles: mapping to equilibrium polymers and exact computation of moments.

It is well known that the path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers. Here we investigate the properties of the equilibrium polymer that corresponds to the trajectories of particles acted on simultaneously by both Brownian and active noise. Through this mapping we can see interesting crossovers in the mechanical properties of the polymer with changing contour length. The polymer end-to-end distribution exhibits Gaussian behaviour for short lengths, which changes to the form of semiflexible filaments at intermediate lengths, to finally go back to a Gaussian form for long contour lengths. By performing a Laplace transform of the governing Fokker-Planck equation of the active Brownian particle, we discuss a direct method to derive exact expressions for all the moments of the relevant dynamical variables, in arbitrary dimensions. These are verified via numerical simulations and used to describe interesting qualitative features such as, for example, dynamical crossovers. Finally we discuss the kurtosis of the ABP's position, which we compute exactly, and show that it can be used to differentiate between active Brownian particles and the active Ornstein-Uhlenbeck process.