Kinematic matrix theory and universalities in self-propellers and active swimmers

Modulating drift dynamics of circle swimmers by periodic potentials

We propose a method to modulate the drifting motion of overdamped circle swimmers in steady fluid flows by means of static sinusoidal potentials. Using Langevin formalism, we study drift velocity as a function of potential strength and wavelength with and without diffusional motion. Drift velocity is essentially quantized without diffusion, but in the presence of noise, the displacement per cycle has a continuous range. As a function of dimensionless potential wave number, domains of damped oscillatory and plateau regimes are observed in the drift velocity diagram. At weak potential and fluid velocity less than powered velocity, there is also a regime where drift velocity exceeds the fluid velocity. Methods based on these results can be used to separate biological and artificial circle swimmers based on their dynamical properties.

Memory effects in spiral diffusion of rotary self-propellers

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)10.1103/PhysRevE.94.030601] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell-cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell-cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell-cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta-Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.

How to connect time-lapse recorded trajectories of motile microorganisms with dynamical models in continuous time

We provide a tool for data-driven modeling of motility, data being time-lapse recorded trajectories. Several mathematical properties of a model to be found can be gleaned from appropriate model-independent experimental statistics, if one understands how such statistics are distorted by the finite sampling frequency of time-lapse recording, by experimental errors on recorded positions, and by conditional averaging. We give exact analytical expressions for these effects in the simplest possible model for persistent random motion, the Ornstein-Uhlenbeck process. Then we describe those aspects of these effects that are valid for any reasonable model for persistent random motion. Our findings are illustrated with experimental data and Monte Carlo simulations.

Spiral diffusion of rotating self-propellers with stochastic perturbation

Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion, and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.

Guiding chiral self-propellers in a periodic potential

Ingenious suggestions continue to be made for separation of racemic mixtures according to the inert structural chirality of the constituents. Recently discovered self-motile micro- or nanoparticles express dynamical chirality, i.e., that which originates in motion, not structure. Here, we predict how dynamically chiral objects, with overdamped dynamics in a soft periodic two-dimensional potential, can display not only separation into well-defined dynamical subclasses defined by motility characteristics, but also the ability to be steered to arbitrary locations in the plane by simply changing the amplitude of the external potential. Orientational and translational diffusion produce new types of drift absent in the noise-free case. As practical implementation seems feasible with acoustic or optical fields, these phenomena can be useful for laboratory microscales manipulations, possibly including reconfigurable microfluidic circuits with complex networks of unidirectional channels.

Gaussian memory in kinematic matrix theory for self-propellers

We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89, 062304 (2014)], which via simple matrix algebra accesses ensemble properties of self-propellers influenced by uncorrelated noise, to treat Gaussian correlated noises. This extension brings into reach many real-world biological and biomimetic self-propellers for which inertia is significant. Applying the formalism, we analyze in detail ensemble behaviors of a 2D self-propeller with velocity fluctuations and orientation evolution driven by an Ornstein-Uhlenbeck process. On the basis of exact results, a variety of dynamical regimes determined by the inertial, speed-fluctuation, orientational diffusion, and emergent disorientation time scales are delineated and discussed.