arXiv subjects

A. Farutin

Publications and source records attributed to A. Farutin.

5 recordsLinked to original sources

arXiv2021

Universal Trajectories of Motile Particles Driven by Chemical Activity

Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Motile cells display trajectories of intriguing complexity, from regular (e.g. circular, helical, and so on) to irregular motions (run-tumble), the origin of which has remained elusive for over a century. This dynamics versatility is conventionally attributed to the shape asymmetry of the motile entity, to the suspending media, and/or to stochastic regulation. We propose here a universal approach highlighting that these movements are generic, occurring for a large class of cells and artificial microswimmers, without the need of invoking shape asymmetry nor stochasticity, but are encoded in their inherent nonlinear evolution. We show, in particular, that for a circular and spherical particle moving in a simple fluid, circular, helical and chaotic motions (akin to a persistent random walk) emerge naturally in different regions of parameter space. This establishes the operating principles for complex trajectories manifestation of motile systems, and offers a new vision with minimal ingredients. The reduced evolution equations based on symmetries are consistent with those derived for a model of an autophoretic particle including diffusion, emission/absorption at the particle surface and hydrodynamics, and provide qualitative and quantitative agreement.

cond-mat.soft↗

arXiv2021

Motility and Swimming: Universal Description and Generic Trajectories

Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the ability of these entities to follow complex trajectories, ranging from straight, curved (circular, helical...), to random-like ones. The non-straight nature of these trajectories is often explained as a consequence of the asymmetry of the particle or the medium in which it moves, or due to the presence of bounding walls, etc... Here, we show that straight, circular and helical trajectories emerge naturally in the absence of asymmetry of the swimmer or that of suspending medium. Our first proof is based on general considerations, without referring to an explicit form of a model. We show that these three trajectories correspond to self-congruent solutions. Self-congruency means that the states of the system at different moments of time can be made identical by an appropriate combination of rotation and translation of the coordinate space. We show that these solutions are exhibited by spherically symmetric particles as a result of a series of pitchfork bifurcations as the activity is increased. Self-congruent dynamics in one and two dimensions are analyzed as well. Finally, we present a simple explicit nonlinear exactly solvable model of fully isotropic phoretic particle that shows the transitions from a non-motile state to straight motion to circular motion to helical motion as a series of spontaneous symmetry-breaking bifurcations. Whether a system exhibits or not a given trajectory only depends on the numerical values of parameters entering the model, while asymmetry of swimmer shape, or anisotropy of the suspending medium , or influence of bounding walls are not necessary.

cond-mat.soft↗

arXiv2021

A Reduced Model for a Phoretic Swimmer

We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses and is advected by the suspending fluid. Beyond a certain emission/absorption rate (characterized by a dimensionless Péclet number, $Pe$) the particle is known to undergo a bifurcation from a non motile to a motile state, with different trajectories, going from a straight to circular and to a chaotic motion by progressively increasing $Pe$. From the full model involving solute diffusion and advection, we derive a reduced closed model which involves only two time-dependent amplitudes $C_1(t)$ and $C_2(t)$ corresponding to the first two Fourier modes of the solute concentration field. This model consists of two coupled nonlinear ordinary differential equations for $C_1$ and $C_2$ and presents several great advantages:(i) the straight and circular motions can be handled fully analytically, (ii) complex motions such as chaos can be analyzed numerically very efficiently in comparison to the numerically expensive full model involving partial differential equations, (iii) the reduced model has a universal form dictated only by symmetries, (iv) the model can be extended to higher Fourier modes. The derivation method is exemplified for a 2D model, for simplicity, but can easily be extended to 3D, not only for the presently selected phoretic model, but also for any model in which chemical activity triggers locomotion. A typical example can be found, for example, in the field of cell motility involving acto-myosin kinetics. This strategy offers an interesting way to cope with swimmers on the basis of ordinary differential equations, allowing for analytical tractability and efficient numerical treatment.

cond-mat.soft↗

arXiv2016

Amoeboid swimming in a channel

Several micro-organisms, such as bacteria, algae, or spermatozoa, use flagella or cilia to swim in a fluid, while many other micro-organisms instead use ample shape deformation, described as amoeboid, to propel themselves by either crawling on a substrate or swimming. Many eukaryotic cells were believed to require an underlying substratum to migrate (crawl) by using membrane deformation (like blebbing or generation of lamellipodia) but there is now increasing evidence that a large variety of cells (including those of the immune system) can migrate without the assistance of focal adhesion, allowing them to swim as efficiently as they can crawl. This paper details the analysis of amoeboid swimming in a confined fluid by modeling the swimmer as an inextensible membrane deploying local active forces. The swimmer displays a rich behavior: it may settle into a straight trajectory in the channel or navigate from one wall to the other depending on its confinement. The nature of the swimmer is also found to be affected by confinement: the swimmer can behave, on the average over one swimming cycle, as a pusher at low confinement, and becomes a puller at higher confinement. The swimmer's nature is thus not an intrinsic property. The scaling of the swimmer velocity V with the force amplitude A is analyzed in detail showing that at small enough A, $V\sim A^2/η^2$, whereas at large enough A, V is independent of the force and is determined solely by the stroke frequency and swimmer size. This finding starkly contrasts with currently known results found from swimming models where motion is based on flagellar or ciliary activity, where $V\sim A/η$. To conclude, two definitions of efficiency as put forward in the literature are analyzed with distinct outcomes. We find that one type of efficiency has an optimum as a function of confinement while the other does not. Future perspectives are outlined.

physics.bio-ph↗

arXiv2015

Amoeboid motion in confined geometry

Many eukaryotic cells undergo frequent shape changes (described as amoeboid motion) that enable them to move forward. We investigate the effect of confinement on a minimal model of amoeboid swimmer. Complex pictures emerge: (i) The swimmer's nature (i.e., either pusher or puller) can be modified by confinement, thus suggesting that this is not an intrinsic property of the swimmer. This swimming nature transition stems from intricate internal degrees of freedom of membrane deformation. (ii) The swimming speed might increase with increasing confinement before decreasing again for stronger confinements. (iii) A straight amoeoboid swimmer's trajectory in the channel can become unstable, and ample lateral excursions of the swimmer prevail. This happens for both pusher- and puller-type swimmers. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. In this study, we combine numerical and theoretical analyses.

physics.bio-ph↗