Session M07: Biological Active Matter III: Fluids and Filaments

Locomotion of flagellated bacteria: From the swimming of single bacteria to the collective motion of bacterial swarm

A flagellated bacterium exhibits fascinating swimming behaviors both as an individual cell and as a member of collectively moving swarm. I discuss two recent experimental works in my group on the swimming behaviors of Escherichia coli, a prominent example of flagellated bacteria. First, we study the motility of flagellated bacteria in colloidal suspensions of varying sizes and volume fractions. We find that bacteria in dilute colloidal suspensions display the quantitatively same motile behaviors as those in dilute polymer solutions, where a size-dependent motility enhancement up to 80% is observed accompanied by a strong suppression of bacterial wobbling. By virtue of the well-controlled size and the hard-sphere nature of colloids, this striking similarity not only resolves the long-standing controversy over bacterial motility enhancement in complex fluids, but also challenges all the existing theories using polymer dynamics in addressing the swimming of flagellated bacteria in dilute polymer solutions. We further develop a simple hydrodynamic model incorporating the colloidal nature of complex fluids, which quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Second, we study the collective motion of dense bacterial suspensions as a model of active fluids. Using light-powered E. coli, we map the detailed phase diagram of bacterial flows and image the transition kinetics of bacterial suspensions towards collective motions. In particular, we examine the unique configuration and dynamics of individual bacteria in collective motions. Together, our study sheds light onto the puzzling motile behaviors of bacteria in complex fluids and provides new insights into the collective swimming of bacterial suspensions relevant to a wide range of microbiological and biomedical processes.   

Formation of Active Two-Dimensional Fluids by Multicellular Magnetotactic Bacteria

We characterize a new phase of active matter composed of Multicellular Magnetotactic Bacteria (MMB).  After colliding with a surface in a weak magnetic field, MMB escape into the bulk fluid at random angles; MMB are exponentially distributed about the surface.  At high magnetic fields, MMB self organize as an active two-dimensional fluid on the surface.  Unlike previously reported microbial active fluids, contact with the surface enhances rotational diffusion by a factor of eight and velocity fluctuations are Laplace distributed.  The active fluid undergoes a percolation transition at a critical magnetic field.  Supercritical active fluids exhibit dynamic voids, which limit the relaxation of density fluctuations.   

Continuum kinetic modeling of active turbulence

Active fluids are continuously driven out of equilibrium due to the stresses generated by their microscopic constituents. These non-equilibrium dynamics, often called active turbulence, are characterized by jets, vortices, and topological defects that can span scales orders of magnitude larger than those of the constitutive particles. Many phenomenological active fluid models have been found to reproduce these dynamics, but such models typically lack a clear energetic structure. In this talk, we discuss active turbulence in a continuum kinetic model of a suspension of extensile particles -- an example of an active nematic fluid. We derive coarse-grained equations, based on the Bingham closure, that allow for efficient simulations at high particle activity while retaining the energetic structure of the kinetic theory. Simulations reveal a nonlinear length scale selection in the active force that drives self-similar dynamics at large scales, and we analytically characterize these dynamics through a balance of entropy production and dissipation that is uniquely accessible from the kinetic description.   

Statistical topology of streamlines in a time-invariant 2D flow

Two dimensional active flows are relevant in a number of areas in biology, particularly in the system of mucociliary clearance in the airway. In these systems, the flow may have a general direction but also exhibit significant patterns of disorder. The qualitative function of these systems may depend on the topology of the resultant flow patterns. Motivated by this, we ask the following question: what is the probability for a generic streamline in a two-dimensional random flow to be open or closed? To investigate this question, we introduce a framework for studying ensembles of two-dimensional time-invariant flow fields. We are able to establish two separate upper bounds on the trapped area a, one for a general ensemble and one for Gaussian ensembles, by leveraging different insights about the distribution of flow velocities on the closed and open streamlines. We also deduce an exact power series expression for a based on the asymptotic dynamics of flow field trajectories, although the terms in this series remain difficult to compute. Finally, we verify the validity of our bounds using numerical evidence, and comment on the implications of these numerical results on future investigations of this problem.   

Cilia Coordination

Cilia are cellular micro-organelles that organize and coordinate their activity to drive flows. Despite the importance of cilia coordination to biological function, a general understanding of this structure-to-function mapping remains lacking. For example, in microbes that use cilia for locomotion, the existence of multiple coordination states is important to perform distinct swimming and turning gaits. In contrast, ciliated tissues in the human lungs, brains, and reproductive tracts are specialized to pump fluids, and this specialization can be compromised if multiple states of cilia coordination co-exist.

Here, I will analyze cilia coordination in in-silico experiments and theoretical models reflecting two extremes of pairs and infinite numbers cilia. I will show results that suggest that functional specificity — and coordination states —  are interlaced with the architecture of the ciliary system.   

Cilia metasurfaces for electronically programmable surface-driven microfluidic manipulation

We report here active metasurfaces of electronically-actuated artificial cilia that can create arbitrary flow patterns in liquids near a surface. We first create voltage-actuated cilia that generate non-reciprocal motions to drive surface flows at tens of microns per second at actuation voltages of 1V. We then show a cilia unit cell that can locally create a range of elemental flow geometries. By combining these unit cells, we create an active cilia metasurface that can generate and switch between any desired surface flow pattern. Finally, we integrate the cilia with a light-powered CMOS clock circuit to demonstrate wireless operation. As a proof of concept, we use this circuit to output voltage pulses with various phase delays to demonstrate improved pumping efficiency using metachronal waves. These powerful results demonstrated experimentally and confirmed using theoretical computations, illustrate a new pathway to fine-scale microfluidic manipulations, with applications from microfluidic pumping to micro-robotic locomotion   

Self-similar clustering of beads in a bacterial suspension

Passive particles suspended in a bath of active swimmers are known to produce cooperative phenomena such as dynamic clustering or phase separation. However, such clusters have never been reported experimentally for particles in a bacterial suspension. Here we report experimental observations of two-dimensional clustering of micron-sized beads in a bath of Burkholderia contaminans bacteria. This clustering is induced by the short-range hydrodynamic attraction produced by the swimming of bacteria between neighboring beads. The characteristic cluster size, computed from the correlation length of the fluorescence intensity pattern, shows a self-similar growth in time. We explore this coarsening dynamics by varying the radius and surface fraction of the beads and the bacterial concentration.   

Metachronal coordination in the larvae of the coral Acropora millepora

Habitat selection is an important factor in the survival of reef corals. As the only motile stage of the reproductive cycle, coral larvae must choose a suitable location in which to settle and reach maturity. Larvae modify their swimming behaviour in response to cues such as light and chemicals, although the sensing and control mechanisms of this are poorly understood. Here, we present the first detailed biophysical study of motility in the multiciliated larvae of the common reef coral A. millepora. Using high-speed, high-resolution imaging, particle image velocimetry, and electron microscopy, we resolve individual cilium beat dynamics, their coordination patterns, and the resultant flow fields. We deduce that the cilia perform a diaplectic metachronal wave (MCW), whose orientation and periodicity are evident in the flows. While many recent models study the emergence and stability of MCWs based on the properties of individual cilia in idealized geometries, there have been few studies on real experimental systems, and almost no recent experiments on diaplectic MCWs. We compare and contrast our measured cilia and wave parameters with existing theoretical predictions. Our novel system with an unusual form of MCW exposes new challenges for fluid-dynamical and behavioural modelling.   

Ciliary chemosensitivity is enhanced by cilium geometry and motility

Cilia are hairlike organelles with roles in motility and sensing. We investigate whether locating chemoreceptors on cilia provides sensitivity advantages and whether motile sensory cilia have further advantages. Using a simple advection-diffusion model, we compute capture rates of diffusive molecules to a cilium. We find that due to its geometry, a non-motile cilium in a quiescent fluid has a capture rate equal to that of a circular absorbing region with quadruple the surface area, and when the same cilium is exposed to an external shear flow, the equivalent surface area is sextuple that of the quiescent case. Alternatively, if the cilium beats in a non-reciprocal manner in an otherwise quiescent fluid, its capture rate increases with the beating frequency to the power of 1/3, and this motility advantage is seen to apply even in simulated cilium bundles. Altogether, our results show that the geometry of cilia provide one reason why many receptors are found on cilia and point to the advantage of combining motility with chemoreception, for a singular cilium as well as groups of cilia.   

Local metachronal synchronization in cilia carpets

Carpets of actively bending cilia can exhibit self-organized metachronal coordination. Yet, active noise of the cilia beat is expected to perturb cilia synchronization. Using a multi-scale model calibrated by experimental cilia beat patterns, we find local multi-stability of traveling wave solutions. Yet, a single dexioplectic wave has predominant basin-of-attraction. Beyond a characteristic noise strength, we observe an abrupt loss of global synchronization even in finite systems, characterized by local synchronized patches. This theory prediction matches experimental observations in the ciliated nose pit in zebrafish.