Session Z48: Focus Session: Statistical Physics of Active Systems Away from Detailed Balance; Motors, Swimmers and All That

Mechanical manipulation and bifurcation dynamics of stereociliary bundles

We propose a numerical model for the mechanical response of hair cells of the inner ear. These mechanically sensitive cells have been described previously using systems of nonlinear differential equations, that captured the main features of the experimental phenomena. Here we extend the study to include the effects of static and time-dependent forcing, and show it to induce transitions across different types of bifurcations. We compare the theory to the experimental measurements of the phase-locked response of spontaneously oscillating hair cells of the bullfrog sacculus, under varying mechanical deflections. For a static deflection, when adaptation phenomena play an important role, the offset generates a critical point where the frequency but not the amplitude vanishes, as opposed to the expected Hopf bifurcation where the amplitude vanishes. On the other hand, for a periodic deflection, mode-locking of the spontaneous oscilliations to the drive period can proceed via different types of bifurcations, depending on the degree of detuning. We will present a simple dynamic systems framework that captures the main features of the experimentally observed behavior in the form of an Arnold Tongue.   

Towards an active hydrodynamic theory of the metaphase spindle

he spindle is a dynamic steady-state structure composed of microtubules and a wide range of factors which control microtubule nucleation, growth, and motion. While many of the individual components of the spindle have been studied in detail, it is still unclear how these molecular constituents self-organize into this structure. Here I describe how we are using spatio-temporal correlations of microtubule density and orientation to formulate a continuum coarse grained theory for the spindle. Our results suggest that microtubule turnover plays a crucial role in stabilizing the giant density fluctuations predicted by traditional active hydrodynamic theories.   

A phase transition between collective and individual dynamics in suspension of swimming bacteria

We present the experimental study of the onset of collective behavior in suspension of swimming bacteria \textit{Bacillus Subtilis} in a liquid film. The system behavior is analyzed as the average swimming speed is varied in a wide range while the concentration of bacteria is constant. The average swimming speed was controlled by adjusting the concentration of dissolved oxygen in a fluid with bacteria. We obtained phase diagrams for the transition of the system between the state of collective swimming and the disordered state at different conditions.   

Chemotaxis of Phoretic Swimmers

An artificial phoretic swimmer in a uniform bath of reactant propels itself in a direction dictated by the polarity of the enzymatic and mobility patterning on its surface. We have have shown that a polar active particle of this type can also orient itself along an imposed gradient of reactant concentration. This amounts to a theoretical demonstration of a phoretic analogue of chemotaxis, that is, the ability of a self-propelled particle to align with respect to, and hence to move up or down, a chemical gradient. The nature of the chemotaxis depends on the shape of the particle, on the distribution of enzymatic sites on its surface, and on the surface mobility. We have also considered the type of motion that arises when the orientation time of the particle becomes comparable to the diffusion time of the cloud of reaction products around it. Lastly, we consider motion arising from the interaction of two or more such chemotactic particles.   

Active viscosity of E-Coli suspensions

Active suspension is the name borne by fluids laden with self-swimming entities such as bacteria, algae or artificial swimmers. Such fluids display emergent constitutive properties differing strongly from those of passive suspensions. Here, we present a recent work, were we measure the viscosity of a wild type E-Coli suspension in the dilute and semi-dilute limits. To this purpose, we use micro-fluidic device build as a Y shape micro-fluidic channel. On one side of the arm, the active suspension is injected and on the other arm, the suspending fluid in injected at the same flow rate. From the position of the interface between the pure fluid and the suspension, we extract the suspension relative viscosity. Varying bacteria density and flow rate, we show a regime specific to active fluids, where the relative viscosity is lower than the viscosity of the suspending viscous fluid. We discuss our results in the perspective of recent theoretical and experimental works.   

Molecular Dynamics Study of Self-propelled Droplets on Solid Substrates

We study, by molecular simulation, the statics and dynamics of chemically driven polymer droplets on regularly and finely corrugated substrates. Droplets are driven by a self-induced wettability gradient, which is formed under the droplet by changing the strength of the polymer-substrate interaction when the polymer get into contact with a reactive substrate with a pre-defined probability. The effect of reaction rate on droplet profile, slip and motion are investigated in the quasi steady-state. Moreover wetting properties of heterogeneous, partially reacted, systems are studied and a connection to experiments in the literature and thin film theoretical results on driven droplets are drawn, via exploring velocity profiles and dissipation mechanisms in the system.   

Self-assembled structures in immiscible systems of active, switchable nanocolloids

We consider the synthesis and fabrication of active building blocks that can dynamically switch between two or more states and assemble into novel structures. We present novel steady-state structures predicted by computer simulation to assemble in systems of switchable, immiscible building blocks. We discuss the dynamics that stabilize these structures, explore approaches to analyze the dissipative nature of the system, and provide a mapping to experimental colloidal systems where these concepts could be implemented.   

Collective motion in active solids and active crystals

We introduce a minimal model for self-propelled particles with strong attraction-repulsion interactions, but no explicit alignment rules, that displays collective polar or rotational motion. We describe a novel elasticity-based mechanism responsible for such collective motion and compute analytically its required conditions in the continuous elastic sheet approximation. By studying the mechanism's dynamics numerically and analytically, we show that it supports collective motion even for finite noise levels if the coupling between individual self-propulsion and elastic modes transfers energy towards larger and larger wavelengths. We hypothesize that this elasticity-based mechanism could provide an alternative explanation for collective motion in some biological groups without explicit alignment interactions, given their natural cohesion.   

Statistics and dynamics in an optical vortex

When two identical particles are driven along a straight line by an identical force there are no attractions forces between them. Surprisingly, when the same two particles are driven along a ring of light, with identical force, they attract and form a pair. The pairing mechanism is a pure non-equilibrium phenomena and is a result of symmetry breaking due to the path's curvature. We use experiment, simulation and theory to demonstrate and explain this effect. We show that dynamic limit-cycles and structure emerge due to this pseudo-potential in many particle systems, and demonstrate how they depend on temperature and trapping stiffness.   

Induced Motion by Asymmetric Enzymatic Degradation of Hydrogels

Biological hydrogels are continuously turned over through secretion and degradation. This non-equilibrium flux is critical to understanding cellular and molecular transport through biogels such as mucus and the extracellular matrix. Gel-digesting enzymes can drastically change the physical and chemical properties of the hydrogel environment. We report that a spatial gradient in the degradation of two gel/enzyme systems--gelatin/trypsin and hyaluronan/hyaluronidase--leads to directional motion of particles embedded in the gel in the direction of higher enzyme concentration. We study the rate at which the degradation front propagates through the gel and the ensuing velocity of the embedded particles, as functions of enzyme and gel concentrations. We propose that asymmetric degradation leads to asymmetric swelling, which transports particles up the enzyme concentration gradient.   

Possible mechanisms for initiating macroscopic left-right asymmetry in developing organisms

Systematic left-right (L/R) asymmetry in development --i.e. body axes satisfying a ``right-hand rule'' -- emerges at the organism level out of the microscopic handedness of biological molecules, not by the usual pattern-forming mechanisms of reactions (including regulation) plus diffusion, but rather (at the cell level) from the cytoskeleton and molecular motors -- usually in collective two-dimensional states associated with the cell membrane~\footnote{C. L. Henley, Landau 2008 conference\ (arxiv:0811.0055)}. I outline possible scenarios we are simulating for (i) snails and C. elegans, from a chiral shearing tendency in the actomyosin layer and/or (ii) for plant cells, from a precesson of the nematic order direction in the microtubule array.   

Activation of nanoscale allosteric protein domain motion revealed by neutron spin echo spectroscopy

NHERF1 is a multi-domain scaffolding protein that assembles the signaling complexes, and regulates the cell surface expression and endocytic recycling of a variety of membrane proteins. The ability of the two PDZ domains in NHERF1 to assemble protein complexes is allosterically modulated by a membrane-cytoskeleton linker protein ezrin, whose binding site is located as far as 110 angstroms away from the PDZ domains. Here, using neutron spin echo (\textbf{NSE}) spectroscopy, selective deuterium labeling, and theoretical analyses, we reveal the activation of interdomain motion in NHERF1 on nanometer length scales and on sub-microsecond time scales upon forming a complex with ezrin. We show that a much simplified coarse-grained model is sufficient to describe inter-domain motion of a multi-domain protein or protein complex. We expect that future NSE experiments will benefit by exploiting our approach of selective deuteration to resolve the specific domain motions of interest from a plethora of global translational and rotational motions. The results demonstrate that propagation of allosteric signals to distal sites involves the activation of long-range coupled domain motions on submicrosecond time scales, and that these coupled motions can be distinguished and characterized by NSE.   

Effector CD8$^+$ T cells migrate via chemokine-enhanced generalized L\'evy walks

Chemokines play a central role in regulating processes essential to the immune function of T cells, such as their migration within lymphoid tissues and targeting of pathogens in sites of inflammation. In order to understand the role of the chemokine CXCL10 during chronic infection by the parasite {\it T. gondii}, we analyze tracks of migrating CD8$^+$ T cells in brain tissue. Surprisingly, we find that T cell motility is not described by a Brownian walk, but instead is consistent with a generalized L\'evy walk consisting of L\'evy-distributed runs alternating with pauses of L\'evy-distributed durations. According to our model, this enables T cells to find rare targets more than an order of magnitude more efficiently than Brownian random walkers. The chemokine CXCL10 increases the migration speed without changing the character of the walk statistics. Thus, CD8$^+$ T cells use an efficient search strategy to facilitate an effective immune response, and CXCL10 aids them in shortening the average time to find rare targets.