Patterns of bacterial motility in microfluidics-confining environments.

Understanding the motility behavior of bacteria in confining microenvironments, in which they search for available physical space and move in response to stimuli, is important for environmental, food industry, and biomedical applications. We studied the motility of five bacterial species with various sizes and flagellar architectures (Vibrio natriegens, Magnetococcus marinus, Pseudomonas putida, Vibrio fischeri, and Escherichia coli) in microfluidic environments presenting various levels of confinement and geometrical complexity, in the absence of external flow and concentration gradients. When the confinement is moderate, such as in quasi-open spaces with only one limiting wall, and in wide channels, the motility behavior of bacteria with complex flagellar architectures approximately follows the hydrodynamics-based predictions developed for simple monotrichous bacteria. Specifically, V. natriegens and V. fischeri moved parallel to the wall and P. putida and E. coli presented a stable movement parallel to the wall but with incidental wall escape events, while M. marinus exhibited frequent flipping between wall accumulator and wall escaper regimes. Conversely, in tighter confining environments, the motility is governed by the steric interactions between bacteria and the surrounding walls. In mesoscale regions, where the impacts of hydrodynamics and steric interactions overlap, these mechanisms can either push bacteria in the same directions in linear channels, leading to smooth bacterial movement, or they could be oppositional (e.g., in mesoscale-sized meandered channels), leading to chaotic movement and subsequent bacterial trapping. The study provides a methodological template for the design of microfluidic devices for single-cell genomic screening, bacterial entrapment for diagnostics, or biocomputation.

Synthetic quorum sensing in model microcapsule colonies.

Biological quorum sensing refers to the ability of cells to gauge their population density and collectively initiate a new behavior once a critical density is reached. Designing synthetic materials systems that exhibit quorum sensing-like behavior could enable the fabrication of devices with both self-recognition and self-regulating functionality. Herein, we develop models for a colony of synthetic microcapsules that communicate by producing and releasing signaling molecules. Production of the chemicals is regulated by a biomimetic negative feedback loop, the "repressilator" network. Through theory and simulation, we show that the chemical behavior of such capsules is sensitive to both the density and number of capsules in the colony. For example, decreasing the spacing between a fixed number of capsules can trigger a transition in chemical activity from the steady, repressed state to large-amplitude oscillations in chemical production. Alternatively, for a fixed density, an increase in the number of capsules in the colony can also promote a transition into the oscillatory state. This configuration-dependent behavior of the capsule colony exemplifies quorum-sensing behavior. Using our theoretical model, we predict the transitions from the steady state to oscillatory behavior as a function of the colony size and capsule density.

Using Chemical Pumps and Motors To Design Flows for Directed Particle Assembly.

Mechanical and electrical pumps are conventionally used to drive fluid flow in microfluidic devices; these pumps require external power supplies, thus limiting the portability of the devices. Harnessing catalytic reactions in solution allows pumping to be shifted into the chemical realm and alleviates the need for extraneous equipment. Chemical "pumps" involve surface-bound catalytic patches that decompose dissolved reagents into the products of the reaction. The catalytic reactions thereby produce chemical gradients that in turn generate pronounced flow fields. Such chemically-generated flows can be harnessed to transport particles in the solution and regulate their self-organization into complex structures within confined chambers. The challenge, however, is determining the reactions and conditions that will yield "programmable" flows, which permit control over the structure formation. In this Account, we review our modeling efforts to design chemical pumps (and "motors") to regulate the motion and assembly of microscopic particles in solution. In the first scenario, microcapsules release reagents in a microchamber with stationary catalytic patches and thereby act as "fuel" for the microcapsules' self-sustained motion. As the reagent is consumed, the capsules aggregate into "colonies" on the catalyst-covered sites. The shape of the assembled colonies can be tailored by patterning the distribution of the catalyst on the surface. Hence, these chemical pumps can be utilized to regulate the autonomous motion and targeted delivery of microcarriers in microfluidic devices. Notably, this fundamental physicochemical mechanism could have played a role in the self-organization of early biological cells (protocells). In the second example, the catalysts are localized on mobile, active particles, which are called "motors". Reactants dispersed in the solution are decomposed at the surface of the motors and produce a convective flow that transports both the active particles and nearby passive, non-coated particles. Depending on the numbers of active and passive particles and the structure of the self-organized cluster, these assemblies can translate or spin and thus act as self-assembled "conveyor belts" or gears in the microchamber. The latter examples involve the formation of two-dimensional structures. In the final scenario, we devise a mechanism for assembling three-dimensional towerlike structures using microcapsules in solution. Here, chemicals diffusing from a central patch on a surface generate a radially directed flow along the surface toward the center. This toroidal roll of fluid lifts the capsules above the patch and draws out the cluster into a tower, whose structure can be tailored by varying the attractive capsule-capsule and capsule-surface interaction strengths. Hence, our method of flow-directed assembly can permit the growth of reconfigurable 3D structures from simple subunits. Taken together, these findings facilitate the fabrication of stand-alone microfluidic devices that autonomously perform multistage chemical reactions and assays for portable biomedical applications and act as small-scale factories to autonomously build microscale components.

Convective flow reversal in self-powered enzyme micropumps.

Surface-bound enzymes can act as pumps that drive large-scale fluid flows in the presence of their substrates or promoters. Thus, enzymatic catalysis can be harnessed for "on demand" pumping in nano- and microfluidic devices powered by an intrinsic energy source. The mechanisms controlling the pumping have not, however, been completely elucidated. Herein, we combine theory and experiments to demonstrate a previously unreported spatiotemporal variation in pumping behavior in urease-based pumps and uncover the mechanisms behind these dynamics. We developed a theoretical model for the transduction of chemical energy into mechanical fluid flow in these systems, capturing buoyancy effects due to the solution containing nonuniform concentrations of substrate and product. We find that the qualitative features of the flow depend on the ratios of diffusivities δ=D(P)/D(S) and expansion coefficients ß=ß(P)/ß(S) of the reaction substrate (S) and product (P). If δ>1 and δ>ß (or if δ<1 and δ<ß ), an unexpected phenomenon arises: the flow direction reverses with time and distance from the pump. Our experimental results are in qualitative agreement with the model and show that both the speed and direction of fluid pumping (i) depend on the enzyme activity and coverage, (ii) vary with the distance from the pump, and (iii) evolve with time. These findings permit the rational design of enzymatic pumps that accurately control the direction and speed of fluid flow without external power sources, enabling effective, self-powered fluidic devices.

Flow-Driven Assembly of Microcapsules into Three-Dimensional Towers.

By harnessing biochemical signaling and chemotaxis, unicellular slime molds can aggregate on a surface to form a long, vertical stalk. Few synthetic systems can self-organize into analogous structures that emerge out of the plane. Through computational modeling, we devise a mechanism for assembling tower-like structures using microcapsules in solution as building blocks. In the simulations, chemicals diffusing from a central patch on a surface produce a concentration gradient, which generates a radially directed diffusioosmotic flow along the surface toward the center. This toroidal roll of a fluid pulls the microcapsules along the surface and lifts them above the patch. As more capsules are drawn toward the patch, some units are pushed off the surface but remain attached to the central microcapsule cluster. The upward-directed flow then draws out the cluster into a tower-like shape. The final three-dimensional (3D) structure depends on the flow field, the attractive capsule-capsule and capsule-surface interaction strengths, and the sedimentation force on the capsules. By tuning these factors, we can change the height of the structures that are produced. Moreover, by patterning the areas of the wall that are attractive to the capsules, we can form multiple vertical strands instead of a single tower. Our approach for flow-directed assembly can permit the growth of reconfigurable, 3D structures from simple subunits.

Convective Self-Sustained Motion in Mixtures of Chemically Active and Passive Particles.

We develop a model to describe the behavior of a system of active and passive particles in solution that can undergo spontaneous self-organization and self-sustained motion. The active particles are uniformly coated with a catalyst that decomposes the reagent in the surrounding fluid. The resulting variations in the fluid density give rise to a convective flow around the active particles. The generated fluid flow, in turn, drives the self-organization of both the active and passive particles into clusters that undergo self-sustained propulsion along the bottom wall of a microchamber. This propulsion continues until the reagents in the solution are consumed. Depending on the number of active and passive particles and the structure of the self-organized cluster, these assemblies can translate, spin, or remain stationary. We also illustrate a scenario in which the geometry of the container is harnessed to direct the motion of a self-organized, self-propelled cluster. The findings provide guidelines for creating autonomously moving active particles, or chemical "motors" that can transport passive cargo in microfluidic devices.

Solutal and thermal buoyancy effects in self-powered phosphatase micropumps.

Immobilized enzymes generate net fluid flow when exposed to specific reagents in solution. Thus, they function as self-powered platforms that combine sensing and on-demand fluid pumping. To uncover the mechanism of pumping, we examine the effects of solutal and thermal buoyancy on the behavior of phosphatase-based micropumps, using a series of reactants with known thermodynamic and kinetic parameters. By combining modeling and experiments, we perform the first quantitative comparison of thermal and solutal effects in an enzyme micropump system. Despite the significant exothermicity of the catalyzed reactions, we find that thermal effects play a minimal role in the observed fluid flow. Instead, fluid transport in phosphatase micropumps is governed by the density difference between the reactants and the products of the reaction. This surprising conclusion suggests new design principles for catalytic pumps.

Self-Propelled Nanomotors Autonomously Seek and Repair Cracks.

Biological self-healing involves the autonomous localization of healing agents at the site of damage. Herein, we design and characterize a synthetic repair system where self-propelled nanomotors autonomously seek and localize at microscopic cracks and thus mimic salient features of biological wound healing. We demonstrate that these chemically powered catalytic nanomotors, composed of conductive Au/Pt spherical Janus particles, can autonomously detect and repair microscopic mechanical defects to restore the electrical conductivity of broken electronic pathways. This repair mechanism capitalizes on energetic wells and obstacles formed by surface cracks, which dramatically alter the nanomotor dynamics and trigger their localization at the defects. By developing models for self-propelled Janus nanomotors on a cracked surface, we simulate the systems' dynamics over a range of particle speeds and densities to verify the process by which the nanomotors autonomously localize and accumulate at the cracks. We take advantage of this localization to demonstrate that the nanomotors can form conductive "patches" to repair scratched electrodes and restore the conductive pathway. Such a nanomotor-based repair system represents an important step toward the realization of biomimetic nanosystems that can autonomously sense and respond to environmental changes, a development that potentially can be expanded to a wide range of applications, from self-healing electronics to targeted drug delivery.

Designing Synthetic Microcapsules That Undergo Biomimetic Communication and Autonomous Motion.

Inspired by the collective behavior of slime molds and amoebas, we designed synthetic cell-like objects that move and self-organize in response to self-generated chemical gradients, thereby exhibiting autochemotaxis. Using computational modeling, we specifically focused on microcapsules that encompass a permeable shell and are localized on an adhesive surface in solution. Lacking any internal machinery, these spherical, fluid-filled shells might resemble the earliest protocells. Our microcapsules do, however, encase particles that can diffuse through the outer shell and into the surrounding fluid. The released particles play two important, physically realizable roles: (1) they affect the permeability of neighboring capsules and (2) they generate adhesion gradients on the underlying surface. Due to feedback mechanisms provided by the released particles, the self-generated adhesion gradients, and hydrodynamic interactions, the capsules undergo collective, self-sustained motion and even exhibit antlike tracking behavior. With the introduction of a chemically patterned stripe on the surface, a triad of capsules can be driven to pick up four-capsule cargo, transport this cargo, and drop off this payload at a designated site. We also modeled a system where the released particles give rise to a particular cycle of negative feedback loops (mimicking the "repressilator" network), which regulates the production of chemicals within the capsules and hence their release into the solution. By altering the system parameters, three capsules could be controllably driven to self-organize into a stable, close-packed triad that would either translate as a group or remain stationary. Moreover, the stationary triads could be made to switch off after assembly and thus produce minimal quantities of chemicals. Taken together, our models allow us to design a rich variety of self-propelled structures that achieve complex, cooperative behavior through fundamental physicochemical phenomena. The studies can also shed light on factors that enable individual protocells to communicate and self-assemble into larger communities.

Self-assembly of microcapsules regulated via the repressilator signaling network.

One of the intriguing challenges in designing active matter is devising systems that not only self-organize, but also exhibit self-regulation. Inspired by biological regulatory networks, we design a collection of self-organizing, self-regulating microcapsules that move in response to self-generated chemical signals. Three microcapsules act as localized sources of distinct chemicals that diffuse through surrounding fluid. Production rates are modulated by the "repressilator" regulatory network motif: each chemical species represses the production of the next in a cycle. Depending on the maximum production rates and capsule separation distances, we show that immobile capsules either exhibit steady or oscillatory chemical production. We then consider movement of the microcapsules over the substrate, induced by gradients in surface energy due to adsorbed chemicals. We numerically simulate this advection-diffusion-reaction system with solid-fluid interactions by combining lattice Boltzmann, immersed boundary and finite difference methods, and thereby, construct systems where the three capsules spontaneously assemble to form a close-packed triad. Chemical oscillations are shown to be critical to this assembly. By adjusting parameters, the triad can either remain stationary or translate as a cohesive group. Stationary triads can also be made to "turn off", producing chemicals at minimal rates after assembly. These findings provide design rules for creating synthetic material systems that encompass biomimetic feedback loops, which enable dynamic collective behavior.

Fluid-driven motion of passive cilia enables the layer to expel sticky particles.

Inspired by marine organisms that utilize active cilia to prevent the biofouling of their surfaces, we use computational and theoretical modeling to determine if passive cilia, which are driven to undulate by an oscillatory shear flow, can be harnessed for antifouling applications. By modeling the oscillating shear flow near a ciliated wall within a channel, we show that the fluid-driven motion of cilia enables the layer to repel adhesive particles away from the surface. Compared to the behavior of the system in a non-oscillating shear, the oscillations also help transport the particles more rapidly along the flow direction. Moreover, the oscillations allow "stickier" particles to be conveyed by the flow relative to the case involving non-oscillatory flow. A simple theoretical model that considers the motion of an adhesive particle interacting with an oscillating, elastic layer captures the behavior observed in the simulations and indicates that the adhesive particle can be repelled away for a wide range of oscillation frequencies. The findings suggest that passive cilia can be used to create self-cleaning surfaces, utilizing oscillations in the flow to prevent the attachment of microparticles and biological cells.

Active ciliated surfaces expel model swimmers.

Continually moving cilia on the surface of marine organisms provide a natural defense against biofouling. To probe the physical mechanisms underlying this antifouling behavior, we integrate the lattice Boltzmann and immersed boundary methods and undertake the first computational studies of the interactions between actuated, biomimetic cilia and a model swimmer. We find that swimmers are effectively "knocked away" from the ciliated surface through a combination of steric repulsion and locally fluctuating flows. In addition, the net flow generated by the collective motion of the entire ciliary array was important for significantly reducing the times spent by relatively slow swimmers near the surface. The results reveal that active ciliated layers can offer a means to resist a wide range of species with a single surface.

Boundary-bound reactions: Pattern formation with and without hydrodynamics.

We study chemical pattern formation in a fluid between two flat plates and the effect of such patterns on the formation of convective cells. This patterning is made possible by assuming the plates are chemically reactive or release reagents into the fluid, both of which we model as chemical fluxes. We consider this as a specific example of boundary-bound reactions. In the absence of coupling with fluid flow, we show that the two-reagent system with nonlinear reactions admits chemical instabilities equivalent to diffusion-driven Turing instabilities. In the other extreme, when chemical fluxes at the two bounding plates are constant, diffusion-driven instabilities do not occur but hydrodynamic phenomena analogous to Rayleigh-Bénard convection are possible. Assuming we can influence the chemical fluxes along the domain and select suitable reaction systems, this presents a mechanism for the control of chemical and hydrodynamic instabilities and pattern formation. We study a generic class of models and find necessary conditions for a bifurcation to pattern formation. Afterwards, we present two examples derived from the Schnakenberg-Selkov reaction. Unlike the classical Rayleigh-Bénard instability, which requires a sufficiently large unstable density gradient, a chemohydrodynamic instability based on Turing-style pattern formation can emerge from a state that is uniform in density. We also find parameter combinations that result in the formation of convective cells whether gravity acts upwards or downwards relative to the reactive plate. The wave number of the cells and the direction of the flow at regions of high/low concentration depend on the orientation, hence, different patterns can be elicited by simply inverting the device. More generally, our results suggest methods for controlling pattern formation and convection by tuning reaction parameters. As a consequence, we can drive and alter fluid flow in a chamber without mechanical pumps by influencing the chemical instabilities.

The N -Link Swimmer in Three Dimensions: Controllability and Optimality Results.

The controllability of a fully three-dimensional N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the N -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.

Microswimmer Propulsion by Two Steadily Rotating Helical Flagella.

Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by experimental observations of a group of magnetotactic bacterial strains, we extended the model by considering two flagella attached to the cell body and rotating about their respective axes. Using numerical simulations, we analyzed the motion of such a microswimmer in bulk fluid and close to a solid surface. We show that positioning the two flagella far apart on the cell body reduces the rate of rotation of the body and increases the swimming speed. Near surfaces, we found that swimmers with two flagella can swim in relatively straight trajectories or circular orbits in either direction. It is also possible for the swimmer to escape from surfaces, unlike a model swimmer of similar shape but with only a single flagellum. Thus, we conclude that there are important implications of swimming with two flagella or flagellar bundles rather than one. These considerations are relevant not only for understanding differences in bacterial morphology but also for designing microrobotic swimmers.

Fight the flow: the role of shear in artificial rheotaxis for individual and collective motion.

To navigate in complex fluid environments, swimming organisms like fish or bacteria often reorient their bodies antiparallel or against the flow, more commonly known as rheotaxis. This reorientation motion enables the organisms to migrate against the fluid flow, as observed in salmon swimming upstream to spawn. Rheotaxis can also be realized in artificial microswimmers - self-propelled particles that mimic swimming microorganisms. Here we study experimentally and by computer simulations the rheotaxis of self-propelled gold-platinum nanorods in microfluidic channels. We observed two distinct modes of artificial rheotaxis: a high shear domain near the bottom wall of the microfluidic channel and a low shear regime in the corners. Reduced fluid drag in the corners promotes the formation of many particle aggregates that rheotax collectively. Our study provides insight into the biomimetic functionality of artificial self-propelled nanorods for dynamic self-assembly and the delivery of payloads to targeted locations.

Harnessing catalytic pumps for directional delivery of microparticles in microchambers.

The directed transport of microparticles in microfluidic devices is vital for efficient bioassays and fabrication of complex microstructures. There remains, however, a need for methods to propel and steer microscopic cargo that do not require modifying these particles. Using theory and experiments, we show that catalytic surface reactions can be used to deliver microparticle cargo to specified regions in microchambers. Here reagents diffuse from a gel reservoir and react with the catalyst-coated surface. Fluid density gradients due to the spatially varying reagent concentration induce a convective flow, which carries the suspended particles until the reagents are consumed. Consequently, the cargo is deposited around a specific position on the surface. The velocity and final peak location of the cargo can be tuned independently. By increasing the local particle concentration, highly sensitive assays can be performed efficiently and rapidly. Moreover, the process can be repeated by introducing fresh reagent into the microchamber.

Harnessing surface-bound enzymatic reactions to organize microcapsules in solution.

By developing new computational models, we examine how enzymatic reactions on an underlying surface can be harnessed to direct the motion and organization of reagent-laden microcapsules in a fluid-filled microchannel. In the presence of appropriate reagents, surface-bound enzymes can act as pumps, which drive large-scale fluid flows. When the reagents diffuse through the capsules' porous shells, they can react with enzymatic sites on the bottom surface. The ensuing reaction generates fluid density variations, which result in fluid flows. These flows carry the suspended microcapsules and drive them to aggregate into "colonies" on and near the enzyme-covered sites. This aggregation continues until the reagent has been depleted and the convection stops. We show that the shape of the assembled colonies can be tailored by patterning the distribution of enzymes on the surface. This fundamental physicochemical mechanism could have played a role in the self-organization of early biological cells (protocells) and can be used to regulate the autonomous motion and targeted delivery of microcarriers in microfluidic devices.

Hydrodynamic analysis of flagellated bacteria swimming in corners of rectangular channels.

The influence of nearby solid surfaces on the motility of bacteria is of fundamental importance as these interactions govern the ability of the microorganisms to explore their environment and form sessile colonies. Reducing biofouling in medical implants and controlling the transport of bacterial cells in a microfluidic device are two applications that could benefit from a detailed understanding of swimming in microchannels. In this study, we investigate the self-propelled motion of a model bacterium, driven by rotating a single helical flagellum, in such an environment. In particular, we focus on the corner region of a large channel modeled as two perpendicular sections of no-slip planes joined with a rounded corner. We numerically solve the equations of Stokes flow using the boundary element method to obtain the swimming velocities at different positions and orientations relative to the channel corner. From these velocities, we construct many trajectories to ascertain the general behavior of the swimmers. Considering only hydrodynamic interactions between the bacterium and the channel walls, we show that some swimmers can become trapped near the corner while moving, on average, along the axis of the channel. This result suggests that such bacteria may be found at much higher densities in corners than in other parts of the channel. Another implication is that these corner accumulating bacteria may travel quickly through channels since they are guided directly along the corner and do not turn back or swim transversely across the channel.

Hydrodynamic analysis of flagellated bacteria swimming near one and between two no-slip plane boundaries.

The motility of swimming bacteria near solid surfaces has implications in a wide range of scenarios, including water treatment facilities, microfluidics, and biomedical implants. Using the boundary element method to numerically solve the equations of low Reynolds number fluid flow, we investigate the dynamics of a model swimmer propelled by rotating a single helical flagellum. Building on previous simulation results for swimmers near a single plane boundary, we introduce a second, parallel boundary and show that the bacterial trajectories change as the two plates are brought closer together. Analysis of this dynamical system shows that the configuration in the center of the channel and parallel to the walls is an unstable equilibrium state for large plate separations, but it becomes the only stable position for swimmers when the plate separation is reduced to three to four times the cell width. Our model also predicts that transient trajectories, i.e., those not at steady states, can exhibit curvature in the opposite sense to that expected from the well-known explanation for circular bacterial paths near a single wall.