Session Y48: Focus Session: Statistical Physics of Active Systems Away From Detailed Balance: Swimmers and All That

Flow-controlled densification of E. Coli through a constriction

Bacterial suspensions are examples of ``active matter.'' Each bacteria can be regarded as a self-propelled particle that interacts hydrodynamically with its environment, including the surrounding ``passive'' fluid, the boundaries and other bacteria. In this presentation, we show a new phenomenon concerning E. Coli suspensions flowing through a funnel-like constrictions in micro-fluidic channels. The dynamics of bacterial suspensions flowing in confined spaces is relevant to understand their behavior in scenarios such as porous materials, soil, microbiology, water purification, and biomedical research. The applied flow induces a counter-intuitive symmetry breaking in the bulk bacteria concentration, which is found to increase past the funnel. The concentration enhancement persists over large distances and its amplitude increases linearly with the flow rate and disappears at large flow values. We show that the effect is reversible when the flow direction is reversed. We explain the observed effects on the interactions between the active bacteria and the channel boundaries. This experiment opens the possibility to control the concentration bacterial suspensions in microfluidic channels by simply tuning the flow of liquid.   

Bidirectional sorting of flocking particles in the presence of asymmetric barriers

We numerically demonstrate bidirectional sorting of flocking particles interacting with an array of funnel-shaped barriers. The particles choose a swimming direction by averaging the headings of their neighbors according to the Vicsek model, and experience additional steric interactions as well as repulsion from the fixed barriers. We show that particles preferentially localize to one side of the barrier array over time, and that the direction of this rectification can be reversed by adjusting the particle-particle exclusion radius or the noise term in the equations of motion. These results provide a conceptual basis for isolation and sorting of single- and multi-cellular organisms which move collectively according to flocking-type interaction rules.   

Microfluidic one-way streets for algae

Controlling locomotion and transport of microorganisms is a key challenge in the development of future biotechnological applications. Here, we demonstrate the use of optimized microfluidic ratchets to rectify the mean swimming direction in suspensions of the unicellular green alga Chlamydomonas reinhardtii, which is a promising candidate for the photosynthetic production of hydrogen. To assess the potential of microfluidic barriers for the manipulation of algal swimming, we studied first the scattering of individual C. reinhardtii from solid boundaries. High-speed imaging reveals the surprising result that these quasi-spherical ``puller''-type microswimmers primarily interact with surfaces via direct flagellar contact, whereas hydrodynamic effects play a subordinate role. A minimal theoretical model, based on run-and-turn motion and the experimentally measured surface-scattering law, predicts the existence of optimal wedge-shaped ratchets that maximize rectification of initially uniform suspensions. We confirm this prediction in experimental measurements with different geometries. Since the mechano-elastic properties of eukaryotic flagella are conserved across many genera, we expect that our results and methods are applicable to a broad class of biflagellate microorganisms.   

Concentrating bacterial cells using a ratchet system: a lattice Monte Carlo simulation study

Rectification of motile E. coli bacteria has been observed in the presence of funnel-like channels. We present a lattice Monte Carlo model which takes into account both the size and the mechanical and thermodynamic properties of autonomous bacterial cells. The motion of the cells is composed of alternating run and tumble periods. We show that the rectification effect of the funnels is strongly dependent upon the effective random walk step length of the run/tumble cycle as well as the size of the funnel's aperture. Our results agree with experimental observations, and also confirm some conclusions from a previous simulation model of point-like bacteria. We also explore series of funnels as a means to pump and concentrate cells. We observe deviations from theoretical predictions when the size of the cells is comparable to that of the aperture of the funnel. The current model can be extended to study cells with different shapes, e.g. cigar-shape bacteria.   

Spontaneous Segregation of Self-Propelled Particles with Different Motilities

We study mixtures of self-propelled and passive rod-like particles in two dimensions using Brownian dynamics simulations. The simulations demonstrate that the two species spontaneously segregate to generate a rich array of dynamical domain structures whose properties depend on the propulsion velocity, density, and composition. In addition to presenting phase diagrams as a function of the system parameters, we investigate the mechanisms driving segregation. We show that the difference in collision frequencies between self-propelled and passive rods provides a driving force for segregation, which is amplified by the tendency of the self-propelled rods to swarm or cluster. Finally, both self-propelled and passive rods exhibit giant number fluctuations for sufficient propulsion velocities.   

Active Brownian Particles with Active Fluctuations

We study the effect of different types of noise on the dynamics of self-propelled particles with variable speed (active Brownian particles). We distinguish between passive and active fluctuations. Passive fluctuations are considered independent of the direction of particle's motion (e.g., thermal fluctuations). In contrast, active ones are assumed to be intrinsically connected with the propulsion mechanism of the active particle and, as a result, correlated with its time-dependent orientation. We calculate the stationary speed and velocity probability density functions of non-interacting active Brownian particles in the presence of both fluctuation types and discuss the generic signature of active fluctuations [1]. Furthermore, we discuss a model of active Brownian particles interacting via a velocity-alignment force [2]. We show, based on the results of a corresponding mean-field theory, how the type of fluctuations has a strong impact on the onset and stability of collective motion. \\[4pt] [1] P. Romanczuk and L. Schimansky-Geier, {\em Phys Rev Lett}, {\bf 106}, 230601 (2011) \\[0pt] [2] P. Romanczuk and L. Schimansky-Geier, {\em Ecol Compl}, in press, doi:10.1016/j.ecocom.2011.07.008 (2011)   

Run and tumble, run and reverse, or run reverse and flick - who wins the chemotaxis race?

Run and tumble of {\em E.coli} bacteria is a well understood example of the stochastic cell motion that is alternated in the presence of signaling chemicals. By regulating the tumbling frequency bacteria are able to navigate toward the food sources. Another bacteria that use twitching to move on a surface, {\em M. xanthus}, utilize a different strategy - at the end of the run they completely reverse the direction of motion and continue moving in the opposite direction. The frequency of reversals was shown to be connected to the chemotactic response of the cell. Recently yet another pattern was discovered in marine bacteria {\em V. alginolyticus} which alternate sharp reversals with flicks -- making a turn to an angle with a broad distribution and centered around 90 degrees. In this work we are presenting a theoretical framework that describes all above motion patterns. As a highlight of the developed approach we find the exact analytical expressions for the mean squared displacement of moving cells for arbitrary distribution of run times. That allows us to quantitatively compare the performance of bacteria exploring the environment with and without signaling chemicals and, therefore, to find the winner of the chemotactic race.   

Kinetic theory for systems of self-propelled particles

Models of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] are studied by means of kinetic theory. In these non-equilibrium models, particles try to align their travel directions with the average direction of their neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are non-additive and are typically of genuine multi-body nature. The theory [1] is based on a Master equation in 3N-dimensional phase space, which is made tractable by means of the molecular chaos approximation. The phase diagram for the transition to collective motion is calculated and compared to direct numerical simulations. A stability analysis of a homogeneous ordered state is performed, which reveals a long wave length instability for some of the considered models. The mean-field calculations of one of the models show a tricritical point where the flocking transition changes its character from continuous to discontinuous. \\[4pt] [1] T. Ihle, Phys. Rev. E 83 (2011) 030901   

Diffusional Variation in Autonomously Motile Catalytic Janus Particles

Recently, we and others have studied the motion of Janus particles that undergo catalytically-induced motion in an appropriate chemical environment. Published studies indicate particles move with reduced rotational diffusion, resulting in enhanced effective diffusion coefficient -- motile particles move longer distances between each random rotation, resulting in much greater overall motion. We undertook to study the effective diffusion coefficient of janus particles with various structural designs (symmetric and asymmetric anisotropy, angular dislocation of catalytic regimes) and under environmental stresses (external fields, imposed gradients). We find that structural features have a strong effect on the characteristics of observed motion and effective diffusion, and that environmental stresses can change particle dynamics, suppressing rotational diffusion and enhancing correlated motion. These results are consistent, with some caveats, as particles grow smaller, and the effects of Brownian motion become more pronounced. Deeper understanding of the statistical behavior of the systems results in particles with practical applications in transport on a microfluidic scale.   

Emergent Collective Behavior of Microscopic Swimmers

The individual components of a biological system often express simple behaviors that lead to the spontaneous emergence of order and high levels of complexity; the whole is greater than the sum of its parts. Emergent complexity may arise spontaneously or, more interestingly, in response to external forces present in the surrounding environment. Here, we study the emergence of the emergent collective behavior of swimming {\em Escherichia coli} bacteria inside microfabricated environments. We first demonstrate how the swimming dynamics of single bacterium cells inside jagged, funnel-shaped geometries leads to the emergence of complex migratory patterns. In particular, by creating ratchet-like barriers that redirect the motion of single E. coli cells, we demonstrate that while a single bacterium is unable to ``escape'' an array of ratchets, a {\em population} of cells are able to collectively navigate against these motion-rectifying barriers. We then investigate the collective behavior of cells at increasing densities and witness the emergence of multicellularity in bacteria. As the local density of cell increases to reach physiologically relevant concentrations, individual swimming cells respond to the cell-cell interactions and collectively assemble into biofilms. We describe the physiological development of such biofilms inside microfluidics devices and, using in situ measurements, study the physical properties of various biofilms from their motion and deformation.   

Active crystallization of Artificial Microswimmers

A novel type of light activated microswimmers is used to drive the system far from equilibrium. For sufficient concentrations they spontaneously assemble in crystalline clusters of particles. These clusters are mobile, with complex dynamics --explosion, self healing...-- and can reversibly melt down if the activity is shut down. The origin of the attraction between the active particles as well as the crystallization mechanism and the complex dynamics will be presented and rationalized quantitatively.   

Collective motility of cells on deformable substrates

We consider a simple model for motile cells on deformable substrates. The cells interact through contact interactions and medium-mediated elastic interactions arising due to the adhesion of the cells to the substrate. Using Brownian dynamics simulations and systematic coarse graining of the microscopic model, we characterize the collective velocity field of such a collection of cells by calculating the velocity autocorrelation function and identify the role of elastic interactions in the emergent motility of cell sheets. Our findings include suppression of diffusivity due to the attractive part of the elastic interaction and a growing length scale in the velocity correlations.