Controlled Mixing in Microfluidic Systems Using Bacterial Chemotaxis

Vortex Pattern Stabilization in Thin Films Resulting from Shear Thickening of Active Suspensions

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path toward functionalization through patterning of thin films and membranes.

Diffusive dynamics of elongated particles in active colloidal suspensions of motile algae

Swimming microorganisms can influence the diffusion of passive particles. The effect of this swimmer-particle interaction depends on different properties, such as the hydrodynamic field of the swimmer and the relative sizes of microorganisms and particles. We investigated an enhancement of the diffusion of silica doublets in a suspension of microalgae Chlamydomonas reinhardtii in a flat capillary. Depending on the concentration of microswimmers, the translational and rotational diffusion constants increase by several orders of magnitude in the presence of the swimming algae. For low concentrations of algae, the doublets exhibit Brownian motion in a fluctuating flow field generated by multiple swimmers. One can observe strong, diffusive transport caused by occasional large displacements. At high swimmer concentration, the algae form dense clusters, where the rotational motion of the doublets shows a subdiffusive behaviour while the translational motion remains diffusive.

Rectification of twitching bacteria through narrow channels: A numerical simulations study

Bacteria living on surfaces use different types of motility mechanisms to move on the surface in search of food or to form microcolonies. Twitching is one such form of motility employed by bacteria such as Neisseria gonorrhoeae, in which the polymeric extensions known as type IV pili mediate its movement. Pili extending from the cell body adhere to the surface and pull the bacteria by retraction. The bacterial movement is decided by the two-dimensional tug-of-war among the pili attached to the surface. Natural surfaces on which these microcrawlers dwell are generally spatially inhomogeneous and have varying surface properties. Their motility is known to be affected by the topography of the surfaces. Therefore, it is possible to control bacterial movement by designing structured surfaces which can be potentially utilized for controlling biofilm architecture. In this paper, we numerically investigate the twitching motility in a two-dimensional corrugated channel. The bacterial movement is simulated by two different models: (a) a detailed tug-of-war model which extensively describe the twitching motility of bacteria assisted by pili and (b) a coarse-grained run-and-tumble model which depicts the motion of wide-ranging self-propelled particles. The simulation of bacterial motion through asymmetric corrugated channels using the above models show rectification. The bacterial transport depends on the geometric parameters of the channel and inherent system parameters such as persistence length and self-propelled velocity. In particular, the variation of the particle current with the geometric parameters of the microchannels shows that one can optimize the particle current for specific values of these parameters.

Phototactic Algae-Driven Unidirectional Transport of Submillimeter-Sized Cargo in a Microchannel

The sensing and actuation capabilities of biological cells integrated with artificial components have been used to create autonomous microsystems. For creating autonomous microsystems, the unidirectional transport of a submillimeter-sized cargo with stimuli responsive bio-motors should be developed as a fundamental motion. This study aims to use Volvox as a light-controlled microrobot to achieve the unidirectional transport of a submillimeter-sized cargo. We show the fabrication of a guide structure, cargo, and light irradiation platform for a unidirectional actuation. The fundamental performances of each component were investigated, and the motions of Volvox were controlled in a microchamber with the developed light irradiation platform. All components were integrated to demonstrate the unidirectional actuation of a block by Volvox. We discuss the dynamics of the mechanical motions.

Pair dispersion in dilute suspension of active swimmers

Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in a dramatic increase in diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. Although each tracer is subject to strong fluctuations resulting in large absolute diffusivity, the small-scale relative dispersion is suppressed due to the correlations in fluid velocity which are relevant when the inter-tracer separation is below the persistence length of the swimmer's motion. Our results suggest that the reorientation of swimming direction plays an important role in biological mixing and should be accounted in the design of potential active matter devices capable of effective fluid mixing at microscale.

Nutrient Transport Driven by Microbial Active Carpets

We demonstrate that active carpets of bacteria or self-propelled colloids generate coherent flows towards the substrate, and propose that these currents provide efficient pathways to replenish nutrients that feed back into activity. A full theory is developed in terms of gradients in the active matter density and velocity, and applied to bacterial turbulence, topological defects and clustering. Currents with complex spatiotemporal patterns are obtained, which are tunable through confinement. Our findings show that diversity in carpet architecture is essential to maintain biofunctionality.

Magnetocapillary self-assemblies: Locomotion and micromanipulation along a liquid interface

This paper presents an overview and discussion of magnetocapillary self-assemblies. New results are presented, in particular concerning the possible development of future applications. These self-organizing structures possess the notable ability to move along an interface when powered by an oscillatory, uniform magnetic field. The system is constructed as follows. Soft magnetic particles are placed on a liquid interface, and submitted to a magnetic induction field. An attractive force due to the curvature of the interface around the particles competes with an interaction between magnetic dipoles. Ordered structures can spontaneously emerge from these conditions. Furthermore, time-dependent magnetic fields can produce a wide range of dynamic behaviours, including non-time-reversible deformation sequences that produce translational motion at low Reynolds number. In other words, due to a spontaneous breaking of time-reversal symmetry, the assembly can turn into a surface microswimmer. Trajectories have been shown to be precisely controllable. As a consequence, this system offers a way to produce microrobots able to perform different tasks. This is illustrated in this paper by the capture, transport and release of a floating cargo, and the controlled mixing of fluids at low Reynolds number.

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a "swimmer efficiency" functional η is introduced. It is proven that in order to obtain maximum swimmer efficiency, the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.

Chemotaxis of bio-hybrid multiple bacteria-driven microswimmers

In this study, in a bio-hybrid microswimmer system driven by multiple Serratia marcescens bacteria, we quantify the chemotactic drift of a large number of microswimmers towards L-serine and elucidate the associated collective chemotaxis behavior by statistical analysis of over a thousand swimming trajectories of the microswimmers. The results show that the microswimmers have a strong heading preference for moving up the L-serine gradient, while their speed does not change considerably when moving up and down the gradient; therefore, the heading bias constitutes the major factor that produces the chemotactic drift. The heading direction of a microswimmer is found to be significantly more persistent when it moves up the L-serine gradient than when it travels down the gradient; this effect causes the apparent heading preference of the microswimmers and is the crucial reason that enables the seemingly cooperative chemotaxis of multiple bacteria on a microswimmer. In addition, we find that their chemotactic drift velocity increases superquadratically with their mean swimming speed, suggesting that chemotaxis of bio-hybrid microsystems can be enhanced by designing and building faster microswimmers. Such bio-hybrid microswimmers with chemotactic steering capability may find future applications in targeted drug delivery, bioengineering, and lab-on-a-chip devices.

Protist-facilitated particle transport using emulated soil micromodels

Microbial processes in the subsurface can be visualized directly using micromodels to emulate pore-scale geometries. Here, emulated soil micromodels were used to measure transport of fluorescent beads in the presence and absence of the soil ciliate Colpoda sp. under quiescent conditions. Beads alone or beads with protists were delivered to the input wells of replicate micromodels that contained three 20 mm(2) channels emulating a sandy loam microstructure. Bead abundance in microstructured channels was measured by direct counts of tiled confocal micrographs. For channels with protists, average bead abundances were approximately 320, 560, 710, 830, and 790 mm(-2) after 1, 2, 3, 5, and 10 days, respectively, versus 0, 0, 0.3, 7.8, and 45 mm(-2) without protists. Spatial and temporal patterns of bead abundance indicate that protist-facilitated transport is not a diffusive-type process but rather a function of more complex protist behaviors, including particle uptake and egestion and motility in a microstructured habitat. Protist-facilitated transport may enhance particle mixing in the soil subsurface and could someday be used for targeted delivery of nanoparticles, encapsulated chemicals, or bacteria for remediation and agriculture applications.

Dynamic force patterns of an undulatory microswimmer

We probe the viscous forces involved in the undulatory swimming of the model organism C. elegans. Using micropipette deflection, we attain direct measurements of lateral and propulsive forces produced in response to the motion of the worm. We observe excellent agreement of the results with resistive force theory, through which we determine the drag coefficients of this organism. The drag coefficients are in accordance with theoretical predictions. Using a simple scaling argument, we obtain a relationship between the size of the worm and the forces that we measure, which well describes our data.

Analytical modeling and experimental characterization of chemotaxis in Serratia marcescens

This paper presents a modeling and experimental framework to characterize the chemotaxis of Serratia marcescens (S. marcescens) relying on two-dimensional and three-dimensional tracking of individual bacteria. Previous studies mainly characterized bacterial chemotaxis based on population density analysis. Instead, this study focuses on single-cell tracking and measuring the chemotactic drift velocity V(C) from the biased tumble rate of individual bacteria on exposure to a concentration gradient of l-aspartate. The chemotactic response of S. marcescens is quantified over a range of concentration gradients (10^{-3} to 5 mM/mm) and average concentrations (0.5 × 10(-3) to 2.5 mM). Through the analysis of a large number of bacterial swimming trajectories, the tumble rate is found to have a significant bias with respect to the swimming direction. We also verify the relative gradient sensing mechanism in the chemotaxis of S. marcescens by measuring the change of V(C) with the average concentration and the gradient. The applied full pathway model with fitted parameters matches the experimental data. Finally, we show that our measurements based on individual bacteria lead to the determination of the motility coefficient μ (7.25 × 10(-6) cm(2)/s) of a population. The experimental characterization and simulation results for the chemotaxis of this bacterial species contribute towards using S. marcescens in chemically controlled biohybrid systems.

Fluid mixing by curved trajectories of microswimmers

We consider the tracer diffusion D(rr) that arises from the run-and-tumble motion of low Reynolds number swimmers, such as bacteria. Assuming a dilute suspension, where the bacteria move in uncorrelated runs of length λ, we obtain an exact expression for D(rr) for dipolar swimmers in three dimensions, hence explaining the surprising result that this is independent of λ. We compare D(rr) to the contribution to tracer diffusion from entrainment.

Recent developments in microfluidics-based chemotaxis studies

Microfluidic devices can better control cellular microenvironments compared to conventional cell migration assays. Over the past few years, microfluidics-based chemotaxis studies showed a rapid growth. New strategies were developed to explore cell migration in manipulated chemical gradients. In addition to expanding the use of microfluidic devices for a broader range of cell types, microfluidic devices were used to study cell migration and chemotaxis in complex environments. Furthermore, high-throughput microfluidic chemotaxis devices and integrated microfluidic chemotaxis systems were developed for medical and commercial applications. In this article, we review recent developments in microfluidics-based chemotaxis studies and discuss the new trends in this field observed over the past few years.

Non-Newtonian viscosity of Escherichia coli suspensions

The viscosity of an active suspension of E. coli bacteria is determined experimentally as a function of the shear rate using a Y-shaped microfluidic channel. From the relative suspension viscosity, we identify rheological thickening and thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the microchannel.

Bacterial microsystems and microrobots

Microorganisms and specifically motile bacteria have been recently added to the list of micro-actuators typically considered for the implementation of microsystems and microrobots. Such trend has been motivated by the fact these microorganisms are self-powered actuators with overall sizes at the lower end of the micrometer range and which have proven to be extremely effective in low Reynolds number hydrodynamic regime of usually less than 10(-2). Furthermore, the various sensors or taxes in bacteria influencing their movements can also be exploited to perform tasks that were previously considered only for futuristic artificial microrobots. Bacterial implementations and related issues are not only reviewed, but this paper also proposes many techniques and approaches that can be considered as building blocks for the implementations of more sophisticated microsystems and microrobots.

Collective chemotactic dynamics in the presence of self-generated fluid flows

In microswimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers." Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually repelling due to the nontrivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.

Targeted cargo delivery using a rotating nickel nanowire

This paper reports an approach to perform basic noncontact and contact manipulation tasks using rotating nickel nanowires driven by a rotating magnetic field. A rotating nanowire is capable of propulsion and steering near a solid surface by a tumbling motion. The FEM simulation shows that fluid flow is induced around the rotating nanowire, which was applied to manipulate micro-objects in a noncontact fashion. Pushing, pulling, and rotation tests of individual polystyrene microbeads are conducted on a solid surface. In addition, targeted delivery tasks of biological samples, e.g., individual flagellated microorganisms and human blood cells, are demonstrated. The results imply that rotating magnetic nanowires are good tools for handling cellular and subcellular objects in an aqueous low-Reynolds-number environment and have potential for single-cell analysis.

FROM THE CLINICAL EDITOR

In this study, the authors report the ability to push, pull, and rotate individual polystyrene microbeads on a solid surface. Furthermore, they demonstrate targeted delivery of biological samples, implying that rotating magnetic nanowires are good tools for handling cellular and subcellular objects.

Chemotaxis driven instability of a confined bacterial suspension

A suspension of bacteria in a thin channel or film subject to a gradient in the concentration of a chemoattractant, will develop, in the absence of an imposed fluid flow, a steady bacteria concentration field that depends exponentially on cross-stream position. Above a critical bacteria concentration, this quiescent base state is unstable to a steady convective motion driven by the active stresses induced by the bacteria's swimming. Unlike previously identified long-wavelength instabilities of active fluids, this instability results from coupling of the bacteria concentration field with the disturbance flow.

Transverse mixing enhancement due to bacterial random motility in porous microfluidic devices

Bacterial swimming in groundwater may create flow disturbances in the surrounding microenvironment thereby enhancing contaminant mixing. Porous microfluidic devices (MFDs) were fabricated in three different pore geometry designs: uniform grain size with large pore throats (MFD-I), nonuniform grain size with restricted pore space (MFD-II), and uniform grain size with small pore throats (MFD-III). Escherichia coli HCB33 was used to assess the effect of bacterial random motility on transverse mixing of a tracer, fluorescent labeled dextran, under three experimental conditions in which motile bacteria, nonmotile bacteria, and plain buffer suspensions were flown through the MFDs at four different flow rates. Mixing was quantified in terms of the best-fit effective transverse dispersion coefficient ((D(cy))(eff)). A mixing enhancement index (MEI) was defined as the ratio of the (D(cy))(eff) of tracer in experiments with motile bacteria and without bacteria. Motile bacteria caused a maximum 5-6 fold increase in MEI in MFD-II, a nearly 4-fold increase in MFD-I, and very little observed change in MFD-III. The apparent transverse dispersivities (α(app)) of MFD-II and MFD-I increased by 3 and 2.3 times, respectively, with no change in MFD-III. These observations indicate that both pore throat size and pore arrangement are critical factors for contaminant mixing in porous media.

Enhancement of biomixing by swimming algal cells in two-dimensional films

Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and presents a fascinating stochastic process. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-two-dimensional liquid films by simultaneously tracking the motion of the cells and that of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the concentration of swimmers, which is explored over a wide range. The mean square displacements are well described by a stochastic Langevin model, which is used to parameterize the mixing. The effective diffusion coefficient D grows rapidly with the swimmer concentration Φ as D ∼ Φ(3/2), as a result of the increasing frequency of tracer-swimmer interactions and the long-range hydrodynamic disturbances created by the swimmers. Conditional sampling of the tracer data based on the instantaneous swimmer position shows that the rapid growth of the diffusivity enhancement with concentration must be due to particle interactions with multiple swimmers simultaneously. Finally, the anomalous probability distributions of tracer displacements become Gaussian at high concentration, but manifest strong power-law tails at low concentration, while the tracer displacements always grow diffusively in time.

Miniaturization and parallelization of biological and chemical assays in microfluidic devices

Microfluidic systems are an attractive solution for the miniaturization of biological and chemical assays. The typical sample volume can be reduced up to 1 million-fold, and a superb level of spatiotemporal control is possible, facilitating highly parallelized assays with drastically increased throughput and reduced cost. In this review, we focus on systems in which multiple reactions are spatially separated by immobilization of reagents on two-dimensional arrays, or by compartmentalization in microfabricated reaction chambers or droplets. These systems have manifold applications, and some, such as next-generation sequencing are already starting to transform biology. This is likely the first step in a biotechnological transformation comparable to that already brought about by the microprocessor in electronics. We discuss both current applications and likely future impacts in areas such as the study of single cells/single organisms and high-throughput screening.

Microfluidic gradient platforms for controlling cellular behavior

Concentration gradients play an important role in controlling biological and pathological processes, such as metastasis, embryogenesis, axon guidance, and wound healing. Microfluidic devices fabricated by photo- and soft lithography techniques can manipulate the fluidic flow and diffusion profile to create biomolecular gradients in a temporal and spatial manner. Furthermore, microfluidic devices enable the control of cell-extracellular microenvironment interactions, including cell-cell, cell-matrix, and cell-soluble factor interaction. In this paper, we review the development of microfluidic-based gradient devices and highlight their biological applications.

Full 3D translational and rotational optical control of multiple rod-shaped bacteria

The class of rod-shaped bacteria is an important example of non-spherical objects where defined alignment is desired for the observation of intracellular processes or studies of the flagella. However, all available methods for orientational control of rod-shaped bacteria are either limited with respect to the accessible rotational axes or feasible angles or restricted to one single bacterium. In this paper we demonstrate a scheme to orientate rod-shaped bacteria with holographic optical tweezers (HOT) in any direction. While these bacteria have a strong preference to align along the direction of the incident laser beam, our scheme provides for the first time full rotational control of multiple bacteria with respect to any arbitrary axis. In combination with the translational control HOT inherently provide, this enables full control of all three translational and the two important rotational degrees of freedom of multiple rod-shaped bacteria and allows one to arrange them in any desired configuration.

High-throughput design of microfluidics based on directed bacterial motility

Use of motile cells as sensors and actuators in microfabricated devices requires precise design of interfaces between living and non-living components, a process that has relied on slow revision of device architectures as prototypes are sequentially evaluated and re-designed. In this report, we describe a microdesign and fabrication approach capable of iteratively refining three-dimensional bacterial interfaces in periods as short as 10 minutes, and demonstrate its use to drive fluid transport by harnessing flagellar motion. In this approach, multiphoton excitation is used to promote protein photocrosslinking in a direct-write procedure mediated by static and dynamic masking, with the resultant microstructures serving to capture motile bacteria from the surrounding fluidic environment. Reproducible steering and patterning of flagellated E. coli cells drive microfluidic currents capable of guiding micro-objects on predictable trajectories with velocities reaching 150 microm s(-1) and achieving bulk flow through microchannels. We show that bacteria can be dynamically immobilized at specified positions, an approach that frees such devices from limitations imposed by the functional lifetime of cells. These results provide a foundation for the development of sophisticated microfluidic devices powered by cells.

Polypeptide-mediated switchable microarray of bacteria

This paper describes a feasible solution for the bacterial cell death and contamination from cell division that occurs in microfluidic applications. The method adopts a smart thermoresponsive surface, highly resolved micropatterns, and surface-functionalized bacteria tagged with thermoresponsive molecules. We developed a method for controllable bacterial attachment and detachment using an elastin-like polypeptide (ELP). To create a smart surface with switchable properties, the surface of a glass substrate was conjugated with thermoresponsive ELP molecules. The attachment of bacterial cells to the ELP surface was induced by the hydrophobic affinity of the ELPs on the glass surface to tagged ELPs on the bacterial surface. A cell-repellent polymer was micropatterned to create a highly resolved space for specific bacterial adhesion. Reversible bacterial attachment and detachment was achieved by controlling the thermoresponsive phase transition of ELP molecules. Five different types of bacteria were successfully conjugated with ELPs and arrayed on the surface. The viability of the bacteria that had attached to the surface was evaluated by determining colony forming units of released bacteria on an agar plate.

Three-dimensional two-component velocity measurement of the flow field induced by the Vorticella picta microorganism using a confocal microparticle image velocimetry technique

Understanding the biological feeding strategy and characteristics of a microorganism as an actuator requires the detailed and quantitative measurement of flow velocity and flow rate induced by the microorganism. Although some velocimetry methods have been applied to examine the flow, the measured dimensions were limited to at most two-dimensional two-component measurements. Here we have developed a method to measure three-dimensional two-component flow velocity fields generated by the microorganism Vorticella picta using a piezoscanner and a confocal microscope. We obtained the two-component velocities of the flow field in a two-dimensional plane denoted as the XY plane, with an observation area of 455x341 mum(2) and the resolution of 9.09 mum per each velocity vector by a confocal microparticle image velocimetry technique. The measurement of the flow field at each height took 37.5 ms, and it was repeated in 16 planes with a 2.50 mum separation in the Z direction. We reconstructed the three-dimensional two-component flow velocity field. From the reconstructed data, the flow velocity field [u((x,y,z)),v((x,y,z))] in an arbitrary plane can be visualized. The flow rates through YZ and ZX planes were also calculated. During feeding, we examined a suction flow to the mouth of the Vorticella picta and measured it to be to 300 pls.

Injection and transport of bacteria in nanotube-vesicle networks

The microinjection of bacteria (the MG1655 strain of E. coli) into unilamellar lipid vesicles contained in surface-immobilized nanotube-vesicle networks is demonstrated. The density of bacteria can be controlled from a single bacterium up to several thousands of bacteria per injected vesicle. The bacteria retain flagellar motion and propulsion. The bacteria (approximately 2 × 0.8 μm) cannot escape from one vesicle to another as the size of the nanotubes is too small (∼200 nm in diameter) to allow for entry. Bacteria can, however, be moved from one vesicle to another in a nanotube-vesicle network by using Marangoni flows. Thus, single or several species can be transferred to a neighboring vesicle at will. The technique offers new possibilities for live matter functionalization into synthetic host networks, and may provide means for studying the effect of compartmentalization and perfusion of chemical species on a single bacterium. Furthermore, it may serve as an experimental model to study how vesicle-encapsulated bacteria evade destruction in macrophages or how bacteria surf along thin membrane nanotubes toward connected macrophage cell bodies.

Microfluidic pump powered by self-organizing bacteria

Results are presented that demonstrate the successful use of live bacteria as mechanical actuators in microfabricated fluid systems. The flow deposition of bacteria is used to create a motile bacterial carpet that can generate local fluid motion inside a microfabricated system. By tracking the motion of tracer particles, we demonstrate that the bacterial cells that comprise the carpet self-organize, generating a collective fluid motion that can pump fluid autonomously through a microfabricated channel at speeds as high as 25 microm s(-1). The pumping performance of the system can also be augmented by changing the chemical environment. The addition of glucose to the working buffer raises the metabolic activity of the bacterial carpet, resulting in increased pumping performance. The performance of the bacterial pump is also shown to be strongly influenced by the global geometry of the pump, with narrower channels achieving a higher pumping velocity with a faster rise time.