Self-regulated non-reciprocal motions in single-material microstructures.

Living cilia stir, sweep and steer via swirling strokes of complex bending and twisting, paired with distinct reverse arcs1,2. Efforts to mimic such dynamics synthetically rely on multimaterial designs but face limits to programming arbitrary motions or diverse behaviours in one structure3-8. Here we show how diverse, complex, non-reciprocal, stroke-like trajectories emerge in a single-material system through self-regulation. When a micropost composed of photoresponsive liquid crystal elastomer with mesogens aligned oblique to the structure axis is exposed to a static light source, dynamic dances evolve as light initiates a travelling order-to-disorder transition front, transiently turning the structure into a complex evolving bimorph that twists and bends via multilevel opto-chemo-mechanical feedback. As captured by our theoretical model, the travelling front continuously reorients the molecular, geometric and illumination axes relative to each other, yielding pathways composed from series of twisting, bending, photophobic and phototropic motions. Guided by the model, here we choreograph a wide range of trajectories by tailoring parameters, including illumination angle, light intensity, molecular anisotropy, microstructure geometry, temperature and irradiation intervals and duration. We further show how this opto-chemo-mechanical self-regulation serves as a foundation for creating self-organizing deformation patterns in closely spaced microstructure arrays via light-mediated interpost communication, as well as complex motions of jointed microstructures, with broad implications for autonomous multimodal actuators in areas such as soft robotics7,9,10, biomedical devices11,12 and energy transduction materials13, and for fundamental understanding of self-regulated systems14,15.

Integrating chemistry, fluid flow, and mechanics to drive spontaneous formation of three-dimensional (3D) patterns in anchored microstructures.

Enzymatic reactions in solution drive the convection of confined fluids throughout the enclosing chambers and thereby couple the processes of reaction and convection. In these systems, the energy released from the chemical reactions generates a force, which propels the fluids' spontaneous motion. Here, we use theoretical and computational modeling to determine how reaction-convection can be harnessed to tailor and control the dynamic behavior of soft matter immersed in solution. Our model system encompasses an array of surface-anchored, flexible posts in a millimeter-sized, fluid-filled chamber. Selected posts are coated with enzymes, which react with dissolved chemicals to produce buoyancy-driven fluid flows. We show that these chemically generated flows exert a force on both the coated (active) and passive posts and thus produce regular, self-organized patterns. Due to the specificity of enzymatic reactions, the posts display controllable kaleidoscopic behavior where one regular pattern is smoothly morphed into another with the addition of certain reactants. These spatiotemporal patterns also form "fingerprints" that distinctly characterize the system, reflecting the type of enzymes used, placement of the enzyme-coated posts, height of the chamber, and bending modulus of the elastic posts. The results reveal how reaction-convection provides concepts for designing soft matter that readily switches among multiple morphologies. This behavior enables microfluidic devices to be spontaneously reconfigured for specific applications without construction of new chambers and the fabrication of standalone sensors that operate without extraneous power sources.

Achieving controllable and reversible snap-through in pre-strained strips of liquid crystalline elastomers.

Deformable, elastic materials that buckle in response to external stimuli can display "snap-through", which involves a transition between different, stable buckled states. Snap-through produces a quick release of stored potential energy, and thus can provide fast actuation for soft robots and other flexible devices. Liquid crystalline elastomers (LCEs) exposed to light undergo a phase transition and a concomitant mechanical deformation, allowing control of snap-through for rapid, large amplitude actuation. Using both a semi-analytical model and finite element simulations, we focus on a thin LCE strip that is clamped at both ends and buckles due to an initially imposed strain. We show that when this clamped, strained sample is exposed to light, it produces controllable snap-through behavior, which can be regulated by varying the light intensity and the area of the sample targeted by light. In particular, this snap-through can be triggered in different directions, allowing the system to be reset and triggered multiple times. Removing the light source will cause the system to settle into one of two stable states, enabling the encoding and storage of information in the system. We also highlight a specific case where removing the light source removes the induced buckling and returns the material to an initially flat state. In this case, the system can be reset and form a new shape, allowing it to function as a rewriteable haptic interface.

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution.

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to "pump" the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid-structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets' initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

Self-Propelling Macroscale Sheets Powered by Enzyme Pumps.

Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano- and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self-propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter-scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

Chemically Driven Multimodal Locomotion of Active, Flexible Sheets.

The inhibitor-promoter feedback loop is a vital component in regulatory pathways that controls functionality in living systems. In this loop, the production of chemical A at one site promotes the production of chemical B at another site, but B inhibits the production of A. In solution, differences in the volumes of the reactants and products of this reaction can generate buoyancy-driven fluid flows, which will deform neighboring soft material. To probe the intrinsic interrelationship among chemistry, hydrodynamics, and fluid-structure interactions, we model a bio-inspired system where a flexible sheet immersed in solution encompasses two spatially separated catalytic patches, which drive the A-B inhibitor-promotor reaction. The convective rolls of fluid generated above the patches can circulate inward or outward depending on the chemical environment. Within the regime displaying chemical oscillations, the dynamic fluid-structure interactions morph the shape of the sheet to periodically "fly", "crawl", or "swim" along the bottom of the confining chamber, revealing an intimate coupling between form and function in this system. The oscillations in the sheet's motion in turn affect the chemical oscillations in the solution. In the regime with non-oscillatory chemistry, the induced flow still morphs the shape of the sheet, but now, the fluid simply translates the sheet along the length of the chamber. The findings reveal the potential for enzymatic reactions in the body to generate hydrodynamic behavior that modifies the shape of neighboring soft tissue, which in turn modifies both the fluid dynamics and the enzymatic reaction. The findings indicate that this non-linear dynamic behavior can be playing a critical role in the functioning of regulatory pathways in living systems.

Strain-Stiffening Hydrogels with Dynamic, Secondary Cross-Linking.

Hydrogels are water-swollen, typically soft networks useful as biomaterials and in other fields of biotechnology. Hydrogel networks capable of sensing and responding to external perturbations, such as light, temperature, pH, or force, are useful across a wide range of applications requiring on-demand cross-linking or dynamic changes. Thus far, although mechanophores have been described as strain-sensitive reactive groups, embedding this type of force-responsiveness into hydrogels is unproven. Here, we synthesized multifunctional polymers that combine a hydrophilic zwitterion with permanently cross-linking alkenes, and dynamically cross-linking disulfides. From these polymers, we created hydrogels that contain irreversible and strong thiol-ene cross-links and reversible disulfide cross-links, and they stiffened in response to strain, increasing hundreds of kPa in modulus under compression. We examined variations in polymer composition and used a constitutive model to determine how to balance the number of thiol-ene vs disulfide cross-links to create maximally force-responsive networks. These strain-stiffening hydrogels represent potential biomaterials that benefit from the mechanoresponsive behavior needed for emerging applications in areas such as tissue engineering.

Opto-chemo-mechanical transduction in photoresponsive gels elicits switchable self-trapped beams with remote interactions.

Next-generation photonics envisions circuitry-free, rapidly reconfigurable systems powered by solitonic beams of self-trapped light and their particlelike interactions. Progress, however, has been limited by the need for reversibly responsive materials that host such nonlinear optical waves. We find that repeatedly switchable self-trapped visible laser beams, which exhibit strong pairwise interactions, can be generated in a photoresponsive hydrogel. Through comprehensive experiments and simulations, we show that the unique nonlinear conditions arise when photoisomerization of spiropyran substituents in pH-responsive poly(acrylamide-co-acrylic acid) hydrogel transduces optical energy into mechanical deformation of the 3D cross-linked hydrogel matrix. A Gaussian beam self-traps when localized isomerization-induced contraction of the hydrogel and expulsion of water generates a transient waveguide, which entraps the optical field and suppresses divergence. The waveguide is erased and reformed within seconds when the optical field is sequentially removed and reintroduced, allowing the self-trapped beam to be rapidly and repeatedly switched on and off at remarkably low powers in the milliwatt regime. Furthermore, this opto-chemo-mechanical transduction of energy mediated by the 3D cross-linked hydrogel network facilitates pairwise interactions between self-trapped beams both in the short range where there is significant overlap of their optical fields, and even in the long range--over separation distances of up to 10 times the beam width--where such overlap is negligible.

Self-Generated Convective Flows Enhance the Rates of Chemical Reactions.

In chemical solutions, the products of catalytic reactions can occupy different volumes compared to the reactants and thus give rise to local density variations in the fluid. These density variations generate solutal buoyancy forces, which are exerted on the fluid and thus "pump" the fluid to flow. Herein, we examine if the reaction-induced pumping accelerates the chemical reaction by transporting the reactants to the catalyst at a rate faster than passive diffusion. Using both simulations and experiments, we show a significant increase in reaction rate when reaction-generated convective flow is present. In effect, through a feedback loop, catalysts speed up reactions not only by lowering the energy barrier but also by increasing the collision frequency between the reactants and the catalyst.

Control over emergence and alignment of transient blisters in thermo-responsive gels using hierarchically patterned substrates.

Surfaces with tunable microscale textures are vital in a large variety of technological applications, including heat transfer, antifouling and adhesion. To facilitate such broad-scale use, there is a need to create surfaces that undergo reconfigurable changes in topology and thus, enable switchable functionality. To date, there is a relative dearth of methods for engineering surfaces that can be actuated to change topography over a range of length scales, and hence, form tunable hierarchically structured layers. Combining modeling and experiments, we design a geometrically patterned, thermo-responsive poly (N-isopropylacrylamide) gel film that undergoes controllable hierarchical changes in topology with changes in temperature. At the bottom, the film is covalently bound to a solid, curved substrate; at the top, the film encompasses longitudinal rectangular ridges that are oriented perpendicular to the underlying cylindrical curves. At temperatures below lower critical solution temperature (LCST), the swollen gel exhibits 3D variations in polymer density and thickness defined by the gel's top and bottom topography. As the temperature rises above LCST, the interplay between the upper ridges and lower curves in the gel drives non-uniform, directional solvent transport, the nucleation and propagation of a phase-separated higher-density skin layer, and the resulting pressure buildup within the film. These different, interacting kinetic processes lead to an instability, which produces transient microscopic blisters in the film. Through simulations, we show how tuning the width of the ridges modifies the propagation of a skin layer and creates localized pressure build-up points, which enables control over the emergence, distribution, and alignment of the microscopic blisters. Additionally, we provide a simple argument to predict the size of such microscopic features. Experiments confirm our predictions and further highlight how our computational model enables the rational design of topographical transitions in these tunable films. The development of actuatable, hierarchically structured films provides new routes for achieving switchable functionality in actuators, drug release systems and adhesives.

Collaboration and competition between active sheets for self-propelled particles.

Biological species routinely collaborate for their mutual benefit or compete for available resources, thereby displaying dynamic behavior that is challenging to replicate in synthetic systems. Here we use computational modeling to design microscopic, chemically active sheets and self-propelled particles encompassing the appropriate synergistic interactions to exhibit bioinspired feeding, fleeing, and fighting. This design couples two different mechanisms for chemically generating motion in fluid-filled microchambers: solutal buoyancy and diffusiophoresis. Catalyst-coated sheets, which resemble crabs with four distinct claws, convert reactants in solution into products and thereby create local variations in the density and chemical composition of the fluid. Via the solutal buoyancy mechanism, the density variations generate fluid flows, which modify the shape and motility of the crabs. Concomitantly, the chemical variations propel the motion of the particles via diffusiophoresis, and thus, the crabs' and particles' motion becomes highly interconnected. For crabs with restricted lateral mobility, these two mechanisms can be modulated to either drive a crab to catch and appear to feed on all of the particles or enable the particles to flee from this sheet. Moreover, by adjusting the sheet's size and the catalytic coating, two crabs can compete and fight over the motile, diffusiophoretic particles. Alternatively, the crabs can temporally share resources by shuttling the particles back and forth between themselves. With completely mobile sheets, four crabs can collaborate to perform a function that one alone cannot accomplish. These findings provide design rules for creating chemically driven soft robotic sheets that significantly expand the functionality of microfluidic devices.

Dynamic behavior of chemically tunable mechano-responsive hydrogels.

Using theory and simulation, we model the mechanical behavior of gels that encompass loops and dangling chain ends. If the loops remain folded and dangling ends are chemically inert, then these topological features just serve as defects. If, however, the loops unfold to expose the hidden ("cryptic") binding sites and the ends of the dangling chains are reactive, these moieties can form bonds that improve the gel's mechanical properties. For gels with a lower critical solubility temperature (LCST), we systematically switch on the possible unfolding and binding events. To quantify the resulting effects, we derive equations for the gel's equilibrium and dynamic elastic moduli. We also use a finite element approach to simulate the gel's response to deformation and validate the analytic calculations. Herein, we show that the equilibrium moduli are highly sensitive to the presence of unfolding and binding transitions. The dynamical moduli are sensitive not only to these structural changes, but also to the frequency of deformation. For example, when reactive ends bind to exposed cryptic sites at T = 29 °C and relatively high frequency, the storage shear modulus is 119% greater than the corresponding equilibrium value, while the storage Young's modulus is 109% greater than at equilibrium. These findings provide guidelines for tuning the chemical reactivity of loops and dangling ends and the frequency of deformation to tailor the mechano-responsive behavior of polymer networks.

Controllable growth of interpenetrating or random copolymer networks.

Interpenetrating and random copolymer networks are vital in a number of industrial applications, including the fabrication of automotive parts, damping materials, and tissue engineering scaffolds. We develop a theoretical model for a process that enables the controlled growth of interpenetrating network (IPNs), or a random copolymer network (RCN) of specified size and mechanical properties. In this process, a primary gel "seed" is immersed into a solution containing the secondary monomer and crosslinkers. After the latter species are absorbed into the primary network, the absorbed monomers are polymerized to form the secondary polymer chains, which then can undergo further crosslinking to form an IPN, or undergo inter-chain exchange with the existing network to form a RCN. The swelling and elastic properties of the IPN and RCN networks can be tailored by modifying the monomer and crosslinker concentrations in the surrounding solution, or by tuning the enthalpic interactions between the primary polymer, secondary monomer and solvent through a proper choice of chemistry. This process can be used repeatedly to fabricate gels with a range of mechanical properties from stiff, rigid materials to soft, flexible networks, allowing the method to meet the materials requirements of a variety of applications.

Multiresponsive polymeric microstructures with encoded predetermined and self-regulated deformability.

Dynamic functions of biological organisms often rely on arrays of actively deformable microstructures undergoing a nearly unlimited repertoire of predetermined and self-regulated reconfigurations and motions, most of which are difficult or not yet possible to achieve in synthetic systems. Here, we introduce stimuli-responsive microstructures based on liquid-crystalline elastomers (LCEs) that display a broad range of hierarchical, even mechanically unfavored deformation behaviors. By polymerizing molded prepolymer in patterned magnetic fields, we encode any desired uniform mesogen orientation into the resulting LCE microstructures, which is then read out upon heating above the nematic-isotropic transition temperature (TN-I) as a specific prescribed deformation, such as twisting, in- and out-of-plane tilting, stretching, or contraction. By further introducing light-responsive moieties, we demonstrate unique multifunctionality of the LCEs capable of three actuation modes: self-regulated bending toward the light source at T < TN-I, magnetic-field-encoded predetermined deformation at T > TN-I, and direction-dependent self-regulated motion toward the light at T > TN-I We develop approaches to create patterned arrays of microstructures with encoded multiple area-specific deformation modes and show their functions in responsive release of cargo, image concealment, and light-controlled reflectivity. We foresee that this platform can be widely applied in switchable adhesion, information encryption, autonomous antennae, energy harvesting, soft robotics, and smart buildings.

Resonant amplification of enzymatic chemical oscillations by oscillating flow.

Using theory and simulation, we analyzed the resonant amplification of chemical oscillations that occur due to externally imposed oscillatory fluid flows. The chemical reactions are promoted by two enzyme-coated patches located sequentially on the inner surface of a pipe that transports the enclosed chemical solution. In the case of diffusion-limited systems, the period of oscillations in chemical reaction networks is determined by the rate of the chemical transport, which is diffusive in nature and, therefore, can be effectively accelerated by the imposed fluid flows. We first identify the natural frequencies of the chemical oscillations in the unperturbed reaction-diffusion system and, then, use the frequencies as a forcing input to drive the system to resonance. We demonstrate that flow-induced resonance can be used to amplify the amplitude of the chemical oscillations and to synchronize their frequency to the external forcing. In particular, we show that even 10% perturbations in the flow velocities can double the amplitude of the resulting chemical oscillations. Particularly, effective control can be achieved for the two-step chemical reactions where during the first half-period, the fluid flow accelerates the chemical flux toward the second catalytic patch, while during the second half-period, the flow amplifies the flux to the first patch. The results can provide design rules for regulating the dynamics of coupled reaction-diffusion processes and can facilitate the development of chemical reaction networks that act as chemical clocks.

Controlling the Spatiotemporal Transport of Particles in Fluid-Filled Microchambers.

The development of microscale devices that autonomously perform multistep processes is vital to advancing the use of microfluidics in industrial applications. Such advances can potentially be achieved through the use of "chemical pumps" that transduce the energy from inherent catalytic reactions into fluid flow within microchambers, without the need for extraneous external equipment. Using computational modeling, we focus on arrangements of multiple chemical pumps that are formed by anchoring patches of different enzymes onto the floor of a fluid-filled chamber. With the addition of the appropriate reactants, only one of the enzymatic patches is activated and thereby generates fluid flow centered about that patch. These flows drive the self-assembly of microparticles in the solution and localize the particles onto the activated patches. By varying the spatial arrangement of the enzymatic patches, and the sequence in which the appropriate reactants are added to the solution, we realize spatiotemporal control over the fluid flow and the sequential transport of microparticles from one patch to another. The order in which the particles visit the different patches can be altered by varying the sequence in which the reactants are added to the solution. By harnessing catalytic cascade reactions, where the product of one reaction is the reactant for the next, we achieve directed transport between the patches with the addition of just one reactant, which initiates the catalytic cascade. Through these studies, we show how the trajectory of the particles' motion among different "stations" can be readily regulated through intrinsic catalytic reactions and thus, provide guidelines for creating fluidic devices that perform multistep reactions in an autonomous, self-sustained manner.

Light-Induced Dynamic Control of Particle Motion in Fluid-Filled Microchannels.

The design of remotely programmable microfluidic systems with controlled fluid flow and particle transport is a significant challenge. Herein, we describe a system that harnesses the intrinsic thermal response of a fluid to spontaneously pump solutions and regulate the transport of immersed microparticles. Irradiating a silver-coated channel with ultraviolet (UV) light generates local convective vortexes, which, in addition to the externally imposed flow, can be used to guide particles along specific trajectories or to arrest their motion. The method provides the distinct advantage that the flow and the associated convective patterns can be dynamically altered by relocating the source of UV light. Moreover, the flow can be initiated and terminated "on-demand" by turning the light on or off.

Harnessing biomimetic cryptic bonds to form self-reinforcing gels.

Cryptic sites, which lay hidden in folded biomolecules, become exposed by applied force and form new bonds that reinforce the biomaterial. While these binding interactions effectively inhibit mechanical deformation, there are few synthetic materials that harness mechano-responsive cryptic sites to forestall damage. Here, we develop a computational model to design polymer gels encompassing cryptic sites and a lower critical solution temperature (LCST). LCST gels swell with a decrease in temperature, thereby generating internal stresses within the sample. The gels also encompass loops held together by the cryptic sites, as well as dangling chains with chemically reactive ends. A decrease in temperature or an applied force causes the loops to unfold and expose the cryptic sites, which then bind to the dangling chains. We show that these binding interactions act as "struts" that reinforce the network, as indicated by a significant decrease in the volume of the gel (from 44% to 80%) and shifts in the volume phase transition temperature. Once the temperature is increased or the deformation is removed, the latter "cryptic bonds" are broken, allowing the loops to refold and the gel to return to its original state. These findings provide guidelines for designing polymer networks with reversible, mechano-responsive bonds, which allow gels to undergo a self-stiffening behavior in response to a temperature-induced internal stress or external force. When applied as a coating, these gels can prevent the underlying materials from undergoing damage and thus, extend the lifetime of the system.

Patterning non-equilibrium morphologies in stimuli-responsive gels through topographical confinement.

Stimuli-responsive "smart" polymers have generated significant interest for introducing dynamic control into the properties of antifouling coatings, smart membranes, switchable adhesives and cell manipulation substrates. Switchable surface morphologies formed by confining stimuli-responsive gels to topographically structured substrates have shown potential for a variety of interfacial applications. Beyond patterning the equilibrium swelling behavior of gels, subjecting stimuli-responsive gels to topographical confinement could also introduce spatial gradients in the various timescales associated with gel deformation, giving rise to novel non-equilibrium morphologies. Here we show how by curing poly(N-isopropylacrylamide) (pNIPAAm)-based gel under confinement to a rigid, bumpy substrate, we can not only induce the surface curvature to invert with temperature, but also program the transient, non-equilibrium morphologies that emerge during the inversion process through changing the heating path. Finite element simulations show that the emergence of these transient morphologies is correlated with confinement-induced gradients in polymer concentration and position-dependent hydrostatic pressure within the gel. To illustrate the relevance of such morphologies in interfacial applications, we show how they enable us to control the gravity-induced assembly of colloidal particles and microalgae. Finally, we show how more complex arrangements in particle assembly can be created through controlling the thickness of the temperature-responsive gel over the bumps. Patterning stimuli-responsive gels on topographically-structured surfaces not only enables switching between two invertible topographies, but could also create opportunities for stimuli ramp-dependent control over the local curvature of the surface and emergence of unique transient morphologies. Harnessing these features could have potential in the design of multifunctional, actuatable materials for switchable adhesion, antifouling, cell manipulation, and liquid and particle transport surfaces.

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.