The long-time dynamics of two hydrodynamically-coupled swimming cells

Swimming micro-organisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system - of dimension two - describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of $t\to\infty$, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Twirling, whirling, and overwhirling revisited: Viscous dynamics of rotating filaments and ribbons

When an initially straight filament is immersed in a viscous fluid and rotated at one end, the fluid resists the rotational motion and causes a buildup of twist in the object. At a critical turning frequency, the object buckles due to the elastic stresses in the material. While this instability has been extensively studied over the past 25 years, these analyses have focused narrowly on filaments with circular cross sections near the onset of the instability. Here we explore the phase diagram for twirling filaments as a function of cross-sectional aspect ratio and rotational frequency. We find a large range of dynamic behaviors and even find that while filaments with circular cross sections transition directly from twirling to overwhirling, ribbonlike objects undergo a twirl-to-whirl transition, similar to what was originally predicted for rodlike objects. We show that the linear stability for rotating ribbons is equivalent to first order to that of cylindrical filaments. Hysteresis is also common, suggesting that there are multiple stable states in these systems. Finally, by comparing simulations using resistive force theory to immersed boundary methods, we identify the reason that these two methods have historically not agreed on the value of the critical turning frequency. © 2022 American Physical Society.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Continuum dynamics of suspensions at low Reynolds number

The dynamics of suspensions of particles has been an active area of research since Einstein first calculated the leading-order correction to the viscosity of a suspension of spherical particles (Einstein, Proc. R. Soc., vol. A102, 1906, pp. 161-179). Since then, researchers have strived to develop an accurate description of the behaviours of suspensions that goes beyond just leading order in the particle volume fraction. Here, we consider the low-Reynolds-number behaviour of a suspension of spherical particles. Working from the Green's functions for the flow due to a single particle, we derive a continuum-level description of the dynamics of suspensions. Our analysis corrects an error in the derivation of these equations in the work of Jackson (Chem. Engng Sci., vol. 52, 1997, pp. 2457-2469) and leads to stable equations of motion for the particles and fluid. In addition, our resulting equations naturally give the sedimentation speed for suspended particles and correct a separate error in the calculation by Batchelor (J. Fluid Mech., vol. 52, 1972, pp. 245-268). Using the pair-correlation function for hard spheres, we are able to compute the sedimentation speed out to seventh order in the volume fraction, which agrees with experimental data up to 30 %-35 %, and also get higher-order corrections to the suspension viscosity, which agree with experiments up to 15 %. Then, using the pair distribution for spheres in shear flow, we find alterations to both the first and second normal stresses. © The Author(s), 2023.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Bend or Twist What Plectonemes Reveal about the Mysterious Motility of Spiroplasma

Spiroplasma is a unique, helical bacterium that lacks a cell wall and swims using propagating helix hand inversions. These deformations are likely driven by a set of cytoskeletal filaments, but how remains perplexing. Here, we probe the underlying mechanism using a model where either twist or bend drive spiroplasma's chirality inversions. We show that Spiroplasma should wrap into plectonemes at different values of the length and external viscosity, depending on the mechanism. Then, by experimentally measuring the bending modulus of Spiroplasma and if and when plectonemes form, we show that Spiroplasma's helix hand inversions are likely driven by bending. © 2023 American Physical Society.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

EVL and MIM/MTSS1 regulate actin cytoskeletal remodeling to promote dendritic filopodia in neurons

Dendritic spines are the postsynaptic compartment of a neuronal synapse and are critical for synaptic connectivity and plasticity. A developmental precursor to dendritic spines, dendritic filopodia (DF), facilitate synapse formation by sampling the environment for suitable axon partners during neurodevelopment and learning. Despite the significance of the actin cytoskeleton in driving these dynamic protrusions, the actin elongation factors involved are not well characterized. We identified the Ena/VASP protein EVL as uniquely required for the morphogenesis and dynamics of DF. Using a combination of genetic and optogenetic manipulations, we demonstrated that EVL promotes protrusive motility through membrane-direct actin polymerization at DF tips. EVL forms a complex at nascent protrusions and DF tips with MIM/MTSS1, an I-BAR protein important for the initiation of DF. We proposed a model in which EVL cooperates with MIM to coalesce and elongate branched actin filaments, establishing the dynamic lamellipodia-like architecture of DF. © 2023 Parker et al.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]