Four Dynamic Bacterial Clusters in a colony.

        In Bacillus subtilis colonies, motile bacteria move collectively, spontaneously forming dynamic clusters. These bacterial clusters share similarities with other systems exhibiting polarized collective motion, such as bird flocks or fish schools. Here we study experimentally how velocity and orientation fluctuations within clusters are spatially correlated. For a range of cell density and cluster size, the correlation length is shown to be 30% of the spatial size of clusters, and the correlation functions collapse onto a master curve after rescaling the separation with correlation length. Our results demonstrate that correlations of velocity and orientation fluctuations are scale invariant in dynamic bacterial clusters.

Collective bacterial cell motion observed in a colony.

        Flocking birds, fish schools, and insect swarms are familiar examplesof collective motion that plays a role in a range of problems, such as spreading of diseases. Models have provided a qualitative understanding of the collective motion, but progress has been hindered by the lack of detailed experimental data. Here we report simultaneous measurements of the positions, velocities, and orientations as a function of time for up to a thousand wild-type Bacillus subtilis bacteria in a colony. The bacteria spontaneously form closely packed dynamic clusters within which they move cooperatively. The number of bacteria in a cluster exhibits a power-law distribution truncated by an exponential tail. The probability of finding clusters with large numbers of bacteria grows markedly as the bacterial density increases. The number of bacteria per unit area exhibits fluctuations far larger than those for populations in thermal equilibrium. Such “giant number fluctuations” have been found in models and in experiments on inert systems but not observed previously in a biological system. Our results demonstrate that bacteria are an excellent system to study the general phenomenon of collective motion.

Bacterial colony grown from a C-shape inoculation.

        Bacteria are not the simple solitary creatures of limited capabilities they were long believed to be. When exposed to harsh environmental conditions such as starvation, extreme heat, and hazardous chemicals, the bacteria can collectively develop sophisticated strategies for adaptation and survival. To coordinate such cooperative ventures, bacteria have developed methods of cell-to-cell signaling. One of these methods is by secretion of extracellular materials. Recently, researchers have found chemical secretions capable of attacking sibling cells within the same colony.

        Here, we present experimental observations of competition between two sibling colonies of Paenibacillus dendritiformis grown on a low-nutrient agar gel. We find that neighboring colonies (growing from droplet inoculation) mutually inhibit growth through secretions that become lethal if the level exceeds a well-defined threshold. In contrast, within a single colony developing from a droplet inoculation, no growth inhibition is observed. However, growth inhibition and cell death are observed if material extracted from the agar between two growing colonies is introduced outside a growing single colony. To interpret the observations, we devised a simple mathematical model for the secretion of an antibacterial compound. Simulations of this model illustrate how secretions from neighboring colonies can be deadly, whereas secretions from a single colony growing from a droplet are not.

Trajectories of numerical tracers in a swarming colony

         Collective motion with extended spatiotemporal coherence can be found in systems of self-propelled objects at almost every length scale, from flocking birds and fish schools, to bacterial swarming  and cooperative behavior of molecular motors in the cell. This biologically originated phenomenon has been studied from perspectives of nonequilibrium statistical mechanics and nonlinear dynamics. The studies have used discrete-particle dynamics based on simple local-interaction laws, continuum ideas from liquid crystal physics, two-fluid models, and hydrodynamics, and have simulated numerically idealized swimmers.

     We determine and relate the characteristic velocity, length, and time scales for bacterial motion in swarming colonies of Paenibacillus dendritiformis growing on semi-solid agar substrates. The bacteria swim within a thin fluid layer, and they form long-lived jets and vortices. These coherent structures lead to anisotropy in velocity spatial correlations and to a two-step relaxation in velocity temporal correlations. The mean squared displacement of passive tracers exhibits a short-time regime with nearly ballistic transport and a diffusive long-time regime. We find that various definitions of the correlation length all lead to length scales that are, surprisingly, essentially independent of the mean bacterial speed, while the correlation time is linearly proportional to the ratio of the correlation length to the mean speed.

Kelvin-Helmholtz bellows created by internal waves

        Internal waves are a special kind of wave that can arise in any fluid that is stratified, meaning that the density of the fluid varies with height. The ocean is a classic example of a naturally occurring stratified fluid, being warmer and less salty near the surface, and colder and saltier in the deep sea. The ocean is stably stratified, meaning that a fluid parcel has a strong tendency to remain at its equilibrium height. Whenever a disturbance of any kind causes vertical motion of fluid, the fluid oscillates around its equilibrium height. This oscillatory disturbance propagates through the fluid as an internal wave. These waves are generally not visible from the surface, but are nearly ubiquitous throughout the ocean. Internal waves can generate turbulences at very small scales, which are extremely important for sustaining the global ocean circulation.

        We study internal wave generation by tidal flow over topography on the ocean floor in laboratory and numerical experiments. Waves are found to be generated most efficiently in a near-critical region where the slope of the bottom topography matches that of internal waves. If the near-critical region is sufficiently long, fluid motion with a velocity an order of magnitude larger than that of the forcing occurs within a thin boundary layer above the bottom surface. The resonant wave is unstable because of strong shear; Kelvin-Helmholtz billows (see figure on the left) precede wave breaking. Our work provides a new explanation for the intense boundary flows on continental slopes and how these flow may shape continental margins. We are currently investigating internal wave generation from a 3-D topography and nonlinear reflection of internal wave from a slope.

Instantaneous openings and particle velocity fields under two stretching conditions

     Fracture resistance is the property of materials that determines when and how they break. It can be defined as the energy per area required to create a new fracture surface. A very simple view would be that fracture resistance is essentially equal to the surface energy. However, this viewpoint is a severe over-simplification; studies have shown that adding small amounts, ~1% in volume fraction, of nanometer-sized fillers, such as rubber particles or nanotubes, can greatly improve the fracture resistance of a polymeric matrix. Many tough natural materials (usually of biological origin), such as nacre, bone, and spider silk, also contain nanostructures embedded in an amorphous matrix. Like their man-made counterparts, all these biological materials show greater resistance to fracture than one might expect from the mechanical properties of the component parts.

      We study fracture propagation in stretched natural rubber sheets. Experimental results in specimens stretched less than 3.8 times show a monotonic increase in the crack speed with stretch and can be explained by a numerical model based on neo-Hookean theory and Kelvin dissipation. In specimens stretched more than 3.8 times, strain-induced crystallites act as reinforcing and toughening fillers and significantly increase fracture resistance, like nanostructures in other polymeric or biological materials. Consequently, as we increase the amount of stretch, fractures travel slower and slower, and eventually halt altogether.

Experimental apparatus for friction studies

     The understanding of friction has evolved greatly in the last 70 years. Bowden and Tabor established that friction is due to populations of asperities and that the actual contact area of two solids in frictional sliding is much less than apparent. Dieterich showed that the population of frictional contacts evolves during dynamic sliding, and measured changes in force over time and at different steady speeds. Rice and Ruina  developed a standard theory for this phenomenon, known as ‘‘rate and state friction’’ in which a single state variable accounts for the population of asperities and its evolution in time. Baumberger and collaborators showed that the rate and state equations extend to low velocities, on the order of 1 µm/s, as a sliding object comes to a halt. During stick-slip motion, samples of Plexiglas and paper continue to creep during the ‘‘stick’’ phase.

    Here, we describe experiments where silicon and quartz are clamped on steel, motion is measured down to the nanometer scale, and velocities are measured down to 0.00001 µm/s. We see that static friction is not really static. Under conditions where objects are pressed into each other and are not normally expected to slide, the asperity population gives way a little bit and evolves before the contacts lock up and become motionless. The characteristic sliding distance is a fraction of a micrometer, which is the characteristic scale of asperities, and the motion remains regular down to the scale of nanometers. We show that the observations are described quantitatively by modifications of the standard equations of rate and state friction