Raymond E. Goldstein

Biotechnology at low Reynolds numbers.

The shrinking of liquid handling systems to the micron and submicron size range entails moving into the area of small Reynolds numbers. The fluid dynamics in this regime are very different from the macroscale. We present an intuitive explanation of how the different physics of small Reynolds numbers flow, along with microscopic sizes, can influence device design, and give examples from our own work using fluid flow in microfabricated devices designed for biological processing.

Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering.

Bacterial processes ranging from gene expression to motility and biofilm formation are constantly challenged by internal and external noise. While the importance of stochastic fluctuations has been appreciated for chemotaxis, it is currently believed that deterministic long-range fluid dynamical effects govern cell–cell and cell–surface scattering—the elementary events that lead to swarming and collective swimming in active suspensions and to the formation of biofilms. Here, we report direct measurements of the bacterial flow field generated by individual swimming Escherichia coli both far from and near to a solid surface. These experiments allowed us to examine the relative importance of fluid dynamics and rotational diffusion for bacteria. For cell–cell interactions it is shown that thermal and intrinsic stochasticity drown the effects of long-range fluid dynamics, implying that physical interactions between bacteria are determined by steric collisions and near-field lubrication forces. This dominance of short-range forces closely links collective motion in bacterial suspensions to self-organization in driven granular systems, assemblages of biofilaments, and animal flocks. For the scattering of bacteria with surfaces, long-range fluid dynamical interactions are also shown to be negligible before collisions; however, once the bacterium swims along the surface within a few microns after an aligning collision, hydrodynamic effects can contribute to the experimentally observed, long residence times. Because these results are based on purely mechanical properties, they apply to a wide range of microorganisms.

Meso-scale turbulence in living fluids

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier–Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.

Flexive and Propulsive Dynamics of Elastica at Low Reynolds Number

A stiff one-armed swimmer in glycerine goes nowhere, but if its arm is elastic, exerting a restorative torque proportional to local curvature, the swimmer can go on its way. Considering this happy consequence and the principles of elasticity, we study a hyperdiffusion equation for the shape of the elastica in viscous flow, find solutions for impulsive or oscillatory forcing, and elucidate relevant aspects of propulsion. These results have application in a variety of physical and biological contexts, from dynamic biopolymer bending experiments to instabilities of elastic filaments.

Fluid Dynamics of Bacterial Turbulence

Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data.

Fluid-membrane tethers: Minimal surfaces and elastic boundary layers

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

Insights into the Evolution of Vitamin B12 Auxotrophy from Sequenced Algal Genomes

Vitamin B(12) (cobalamin) is a dietary requirement for humans because it is an essential cofactor for two enzymes, methylmalonyl-CoA mutase and methionine synthase (METH). Land plants and fungi neither synthesize or require cobalamin because they do not contain methylmalonyl-CoA mutase, and have an alternative B(12)-independent methionine synthase (METE). Within the algal kingdom, approximately half of all microalgal species need the vitamin as a growth supplement, but there is no phylogenetic relationship between these species, suggesting that the auxotrophy arose multiple times through evolution. We set out to determine the underlying cellular mechanisms for this observation by investigating elements of B(12) metabolism in the sequenced genomes of 15 different algal species, with representatives of the red, green, and brown algae, diatoms, and coccolithophores, including both macro- and microalgae, and from marine and freshwater environments. From this analysis, together with growth assays, we found a strong correlation between the absence of a functional METE gene and B(12) auxotrophy. The presence of a METE unitary pseudogene in the B(12)-dependent green algae Volvox carteri and Gonium pectorale, relatives of the B(12)-independent Chlamydomonas reinhardtii, suggest that B(12) dependence evolved recently in these lineages. In both C. reinhardtii and the diatom Phaeodactylum tricornutum, growth in the presence of cobalamin leads to repression of METE transcription, providing a mechanism for gene loss. Thus varying environmental conditions are likely to have been the reason for the multiple independent origins of B(12) auxotrophy in these organisms. Because the ultimate source of cobalamin is from prokaryotes, the selective loss of METE in different algal lineages will have had important physiological and ecological consequences for these organisms in terms of their dependence on bacteria.

Cytoplasmic streaming enables the distribution of molecules and vesicles in large plant cells

Recent studies of aquatic and land plants show that similar phenomena determine intracellular transport of organelles and vesicles. This suggests that aspects of cell signaling involved in development and response to external stimuli are conserved across species. The movement of molecular motors along cytoskeletal filaments directly or indirectly entrains the fluid cytosol, driving cyclosis (i.e., cytoplasmic streaming) and affecting gradients of molecular species within the cell, with potentially important metabolic implications as a driving force for cell expansion. Research has shown that myosin XI functions in organelle movement driving cytoplasmic streaming in aquatic and land plants. Despite the conserved cytoskeletal machinery propelling organelle movement among aquatic and land plants, the velocities of cyclosis in plant cells varies according to cell types, developmental stage of the cell, and plant species. Here, we synthesize recent insights into cytoplasmic streaming, molecular gradients, cytoskeletal and membrane dynamics, and expand current cellular models to identify important gaps in current research.

Competing patterns of signaling activity in dictyostelium discoideum.

Quantitative experiments are described on spatio-temporal patterns of coherent chemical signaling activity in populations of {\it Dictyostelium discoideum} amoebae. We observe competition between spontaneously firing centers and rotating spiral waves that depends strongly on the overall cell density. At low densities, no complete spirals appear and chemotactic aggregation is driven by periodic concentric waves, whereas at high densities the firing centers seen at early times nucleate and are apparently entrained by spiral waves whose cores ultimately serve as aggregation centers. Possible mechanisms for these observations are discussed.

Fluid flows created by swimming bacteria drive self-organization in confined suspensions

Significance The collective dynamics of swimming microorganisms exhibits a complex interplay with the surrounding fluid: the motile cells stir the fluid, which in turn can reorient and advect them. This feedback loop can result in long-range interactions between the cells, an effect whose significance remains controversial. We present a computational model that takes into account these cell–fluid interactions and cell–cell forces and that predicts counterintuitive cellular order driven by long-range flows. This prediction is confirmed with experimental studies that track the orientation of cells in a confined, dense bacterial suspension. Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatiotemporal patterns on scales that are large compared with those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we use the recent discovery of a spiral-vortex state in confined suspensions of Bacillus subtilis to study this issue in detail. Those experiments showed that if the radius of confinement in a thin cylindrical chamber is below a critical value, the suspension will spontaneously form a steady single-vortex state encircled by a counter-rotating cell boundary layer, with spiral cell orientation within the vortex. Left unclear, however, was the flagellar orientation, and hence the cell swimming direction, within the spiral vortex. Here, using a fast simulation method that captures oriented cell–cell and cell–fluid interactions in a minimal model of discrete particle systems, we predict the striking, counterintuitive result that in the presence of collectively generated fluid motion, the cells within the spiral vortex actually swim upstream against those flows. This prediction is then confirmed by the experiments reported here, which include measurements of flagella bundle orientation and cell tracking in the self-organized state. These results highlight the complex interplay between cell orientation and hydrodynamic flows in concentrated suspensions of microorganisms.