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Modern micromanipulation techniques typically involve trapping using electromagnetic, acoustic or flow fields that produce stresses on the trapped particles thereby precluding stress-free manipulations. Here, we show that by employing polyhedral symmetries in a multichannel microfluidic design, we can separate the tasks of displacing and trapping a particle into two distinct sets of flow operations, each characterized and protected by their unique groups of symmetries. By combining only the displacing uniform flow modes to entrain and move targeted particles in arbitrary directions, we were able to realize symmetry-protected, stress-free micromanipulation in 3D. Furthermore, we engineered complex, microscale paths by programming and controlling the flow within each channel in real-time, resulting in multiple particles simultaneously following desired paths in the absence of any supervision or feedback. Our work therefore provides a general symmetry-group-based framework for understanding and engineering microfluidics and a novel platform for 3D stress-free manipulations.

Intracellular transport of cargoes in the cell is essential for the organization and functioning cells, especially those that are large and elongated. The cytoskeletal networks inside large cells can be highly complex, and this cytoskeletal organization can have impacts on the distance and trajectories of travel. Here, we experimentally created microtubule networks with varying mesh sizes and examined the ability of kinesin-driven quantum dot cargoes to traverse the network. Using the experimental data, we deduced parameters for cargo detachment at intersections and away from intersections, allowing us to create an analytical theory for the run length as a function of mesh size. We also used these parameters to perform simulations of cargoes along paths extracted from the experimental networks. We find excellent agreement between the trends in run length, displacement, and trajectory persistence length comparing the experimental and simulated trajectories., Comment: 23 Pages, 7 Figures, 4 Tables

A common type of cytoskeletal morphology involves multiple converging microbutubules with their minus ends collected and stabilized by a microtubule organizing center (MTOC) in the interior of the cell. This arrangement enables the ballistic transport of cargo bound to microtubules, both dynein mediated transport towards the MTOC and kinesin mediated transport away from it, interspersed with diffusion for unbound cargo-motor complexes. Spatial and temporal positioning of the MTOC allows for bidirectional transport towards and away from specific organelles and locations within the cell and also the sequestering and subsequent dispersal of dynein transported cargo. The general principles governing dynamics, efficiency and tunability of such transport in the MTOC vicinity is not fully understood. To address this, we develop a one-dimensional model that includes advective transport towards an attractor (such as the MTOC), and diffusive transport that allows particles to reach absorbing boundaries (such as cellular membranes). We calculated the mean first passage time (MFPT) for cargo to reach the boundaries as a measure of the effectiveness of sequestering (large MFPT) and diffusive dispersal (low MFPT). The MFPT experiences a dramatic growth in magnitude, transitioning from a low to high MFPT regime (dispersal to sequestering) over a window of cargo attachment/detachment rates that is close to in vivo values. We find that increasing either the attachment or detachment rate, while fixing the other, can result in optimal dispersal when the attractor is placed asymmetrically. Finally, we describe a rare event regime, where the escape location is exponentially sensitive to the attractor positioning. Our results suggest that structures such as the MTOC allow for the sensitive control of the spatial and temporal features of transport and corresponding function under physiological conditions.

Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how inter-cellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation and fractal dimension, as well as local morphological features including junctions, branches, and rings depend on cell contractility and density, and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness-dependent, being optimal at intermediate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multi-cellular self-organization, leading to more robust and efficient realization of space-spanning networks than through just local inter-cellular interactions., Comment: 30 pages, 22 figures

Many types of mammalian cells exert active contractile forces and mechanically deform their elastic substrate, to accomplish biological functions such as cell migration. These substrate deformations provide a mechanism by which cells can sense other cells, leading to long range mechanical intercell interactions and possible self organization. Here, we treat cells as noisy motile particles that exert contractile dipolar stresses on elastic substrates as they move. By combining this minimal model for the motility of individual cells with a linear elastic model that accounts for substrate mediated cell cell interactions, we examine emergent collective states that result from the interplay of cell motility and long range elastic dipolar interactions. In particular, we show that particles self assemble into flexible, motile chains which can cluster to form diverse larger scale compact structures with polar order. By computing key structural and dynamical metrics, we distinguish between the collective states at weak and strong elastic interactions, as well as at low and high motility. We also show how these states are affected by confinement, an important characteristic of the complex mechanical microenvironment inhabited by cells. Our model predictions are generally applicable to active matter with dipolar interactions ranging from biological cells to synthetic colloids endowed with electric or magnetic dipole moments., Comment: 14 pages, 8 figures, Submitted to Frontiers in Physics: Soft Matter Physics - Special Issue

Variations of transport efficiency in structured environments between distinct individuals in actively self-propelled systems is both hard to study and poorly understood. Here, we study the transport of a non-tumbling {\ecoli} strain, an active-matter archetype with intrinsic size variation but fairly uniform speed, through a periodic pillar array. We show that long-term transport switches from a trapping dominated state for shorter cells to a much more dispersive state for longer cells above a critical bacterial size set by the pillar array geometry. Using a combination of experiments and modeling, we show that this anomalous size-dependence arises from an enhancement of the escape rate from trapping for longer cells caused by nearby pillars. Our results show that geometric effects can lead to size being a sensitive tuning knob for transport in structured environments, with implications in general for active matter systems and, in particular, for the morphological adaptation of bacteria to structured habitats, spatial structuring of communities and for anti-biofouling materials design., Comment: 4 figures

The spatial localization or sequestering of motile cargo and their dispersal within cells is an important process in a number of physiological contexts. The morphology of the cytoskeletal network, along which active, motor-driven intracellular transport takes place, plays a critical role in regulating such transport phases. Here, we use a computational model to address the existence and sensitivity of dynamic sequestering and how it depends on the parameters governing the cytoskeletal network geometry, with a focus on filament lengths and polarization away or toward the periphery. Our model of intracellular transport solves for the time evolution of a probability distribution of cargo that is transported by passive diffusion in the bulk cytoplasm and driven by motors on explicitly rendered, polar cytoskeletal filaments with random orientations. We show that depending on the lengths and polarizations of filaments in the network, dynamic sequestering regions can form in different regions of the cell. Furthermore, we find that, for certain parameters, the residence time of cargo is non-monotonic with increasing filament length, indicating an optimal regime for dynamic sequestration that is potentially tunable via filament length. Our results are consistent with {\it in vivo} observations and suggest that the ability to tunably control cargo sequestration via cytoskeletal network regulation could provide a general mechanism to regulate intracellular transport phases., Comment: 20 pages, 8 figures

Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of such growth, which we modeled as a quasi-static time evolution of a metric, with fast elastic relaxation of the shape. We consider regulation via coupling of the growth law, defined by the time derivative of the target metric, to purely local properties of the shape, such as the local curvature and stress. For cylindrical shells, motivated by rod-like E. \textit{coli}, we show that coupling to curvature alone is generically linearly unstable and that additionally coupling to stress can lead to stably elongating structures. Our approach can readily be extended to gain insights into the general classes of stable growth laws for different target geometries.

Collective motion of cells is common in many physiological processes, including tissue development, repair, and tumor formation. Recent experiments have shown that certain malignant cancer cells form clusters in a chemoattractant gradient, which display three different phases of motion: translational, rotational, and random. Intriguingly, all three phases are observed simultaneously, with clusters spontaneously switching between these modes of motion. The origin of this behavior is not understood at present, especially the robust appearance of cluster rotations. Guided by experiments on the motion of two-dimensional clusters in-vitro, we developed an agent based model in which the cells form a cohesive cluster due to attractive and alignment interactions but with potentially different behaviors based on their local environment. We find that when cells at the cluster rim are more motile, all three phases of motion coexist, in excellent agreement with the observations. Using the model we can identify that the transitions between different phases are driven by a competition between an ordered rim and a disordered core accompanied by the creation and annihilation of topological defects in the velocity field. The model makes definite predictions regarding the dependence of the motility phase of the cluster on its size and external chemical gradient, which agree with our experimental data. Our results suggest that heterogeneous behavior of individuals, based on local environment, can lead to novel, experimentally observed phases of collective motion., Comment: 14 pages, 5 figures

Microtubules are protein polymers that form "molecular highways" for long-range transport within living cells. Molecular motors actively step along microtubules to shuttle cellular materials between the nucleus and the cell periphery; this transport is critical for the survival and health of all eukaryotic cells. Structural defects in microtubules exist, but whether these defects impact molecular motor-based transport remains unknown. Here, we report a new, to our knowledge, approach that allowed us to directly investigate the impact of such defects. Using a modified optical-trapping method, we examined the group function of a major molecular motor, conventional kinesin, when transporting cargos along individual microtubules. We found that microtubule defects influence kinesin-based transport in vitro. The effects depend on motor number: cargos driven by a few motors tended to unbind prematurely from the microtubule, whereas cargos driven by more motors tended to pause. To our knowledge, our study provides the first direct link between microtubule defects and kinesin function. The effects uncovered in our study may have physiological relevance in vivo.

With their longest dimension typically being less than 100 nm, molecular motors are significantly below the optical-resolution limit. Despite substantial advances in fluorescence-based imaging methodologies, labeling with beads remains critical for optical-trapping-based investigations of molecular motors. A key experimental challenge in bead-based assays is that the number of motors on a bead is not well defined. Particularly for single-molecule investigations, the probability of single versus multiple-motor events has not been experimentally investigated. Here, we used bead travel distance as an indicator of multiple-motor transport and determined the lower-bound probability of bead transport by two or more motors. We limited the ATP concentration to increase our detection sensitivity for multiple- versus single-kinesin transport. Surprisingly, for all but the lowest motor number examined, our measurements exceeded estimations of a previous model by R2-fold. To bridge this apparent gap between theory and experiment, we derived a closed-form expression for the probability of bead transport by multiple motors, and constrained the only free parameter in this model using our experimental measurements. Our data indicate that kinesin extends to ~57 nm during bead transport, suggesting that kinesin exploits its conformational flexibility to interact with microtubules at highly curved interfaces such as those present for vesicle transport in cells. To our knowledge, our findings provide the first experimentally constrained guide for estimating the probability of multiple-motor transport in optical trapping studies. The experimental approach utilized here (limiting ATP concentration) may be generally applicable to studies in which molecular motors are labeled with cargos that are artificial or are purified from cellular extracts.

Within living cells, the transport of cargo is accomplished by groups of molecular motors. Such collective transport could utilize mechanisms which emerge from inter-motor interactions in ways that are yet to be fully understood. Here we combined experimental measurements of two-kinesin transport with a theoretical framework to investigate the functional ramifications of inter-motor interactions on individual motor function and collective cargo transport. In contrast to kinesin's low sidestepping frequency when present as a single motor, with exactly two kinesins per cargo, we observed substantial motion perpendicular to the microtubule. Our model captures a surface-associated mode of kinesin, which is only accessible via inter-motor interference in groups, in which kinesin diffuses along the microtubule surface and rapidly "hops" between protofilaments without dissociating from the microtubule. Critically, each kinesin transitions dynamically between the active stepping mode and this weak surface-associated mode enhancing local exploration of the microtubule surface, possibly enabling cellular cargos to overcome macromolecular crowding and to navigate obstacles along microtubule tracks without sacrificing overall travel distance.

Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific locations is accomplished through a combination of passive diffusion and active transport by molecular motors that ballistically move along a network of cytoskeletal filaments. Although motor-based transport is known to be necessary to overcome cytoplasmic crowding and the limited range of diffusion within reasonable time scales, the topological features of the cytoskeletal network that regulate transport efficiency and robustness have not been established. Using a continuum diffusion model, we observed that the time required for cellular transport was minimized when the network was localized near the nucleus. In simulations that explicitly incorporated network spatial architectures, total filament mass was the primary driver of network transit times. However, filament traps that redirect cargo back to the nucleus caused large variations in network transport. Filament polarity was more important than filament orientation in reducing average transit times, and transport properties were optimized in networks with intermediate motor on and off rates. Our results provide important insights into the functional constraints on intracellular transport under which cells have evolved cytoskeletal structures, and have potential applications for enhancing reactions in biomimetic systems through rational transport network design., Comment: 46 pages (20 pages main text, 4 main figures + supplement)

Collective and directed motility or swarming is an emergent phenomenon displayed by many self-organized assemblies of active biological matter such as clusters of embryonic cells during tissue development, cancerous cells during tumor formation and metastasis, colonies of bacteria in a biofilm, or even flocks of birds and schools of fish at the macro-scale. Such clusters typically encounter very heterogeneous environments. What happens when a cluster encounters an interface between two different environments has implications for its function and fate. Here we study this problem by using a mathematical model of a cluster that treats it as a single cohesive unit that moves in two dimensions by exerting a force/torque per unit area whose magnitude depends on the nature of the local environment. We find that low speed (overdamped) clusters encountering an interface with a moderate difference in properties can lead to refraction or even total internal reflection of the cluster. For large speeds (underdamped), where inertia dominates, the clusters show more complex behaviors crossing the interface multiple times and deviating from the predictable refraction and reflection for the low velocity clusters. We then present an extreme limit of the model in the absense of rotational damping where clusters can become stuck spiraling along the interface or move in large circular trajectories after leaving the interface. Our results show a wide range of behaviors that occur when collectively moving active biological matter moves across interfaces and these insights can be used to control motion by patterning environments., Comment: 15 pages, 7 figures

Foraging, either solitarily or collectively, is a necessary behavior for survival that is demonstrated by many organisms. Foraging can be collectively optimized by utilizing communication between the organisms. Examples of such communication range from high level strategic foraging by animal groups to rudimentary signaling among unicellular organisms. Here we systematically study the simplest form of communication via long range repulsive interactions between two diffusing Brownian searchers on a one-dimensional lattice. We show that the mean first passage time for either of them to reach a fixed target depends non-monotonically on the range of the interaction and can be optimized for a repulsive range that is comparable to the average spacing between searchers. Our results suggest that even the most rudimentary form of collective searching does in fact lower the search time for the foragers suggesting robust mechanisms for search optimization in cellular communities, Comment: 6 pages, 5 figures

The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial and temporal scales. Swarms that occur in natural environments typically have to contend with spatial disorder such as obstacles that hinder an individual's motion or communication with neighbors. We study swarming particles, with both aligning and repulsive interactions, on percolated networks where topological disorder is modeled by the random removal of lattice bonds. We find that an infinitesimal amount of disorder can completely suppress swarming for particles that utilize only alignment interactions suggesting that alignment alone is insufficient. The addition of repulsive forces between particles produces a critical phase transition from a collectively moving swarm to a disordered gas-like state. This novel phase transition is entirely driven by the amount of topological disorder in the particles environment and displays critical features that are similar to those of 2D percolation, while occurring at a value of disorder that is far from the percolation critical point.

Chiral polymers are ubiquitous in nature and in the cellular context they are often found in association with membranes. Here we show that surface bound polymers with an intrinsic twist and anisotropic bending stiffness can exhibit a sharp continuous phase transition between states with very different effective persistence lengths as the binding affinity is increased. Above a critical value for the binding strength, determined solely by the torsional modulus and intrinsic twist rate, the filament can exist in a zero twist, surface bound state with a homogeneous stiffness. Below the critical binding strength, twist walls proliferate and function as weak or floppy joints that sharply reduce the effective persistence length that is measurable on long lengthscales. The existence of such dramatically different conformational states has implications for both biopolymer function {\it in vivo} and for experimental observations of such filaments {\it in vitro}., Comment: 21 pages, 6 figures

We study the statistics of encounters of L\'evy flights by introducing the concept of vicious L\'evy flights - distinct groups of walkers performing independent L\'evy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time $t$ decays as $t^{-\alpha}$ at late times. We compute $\alpha$ up to the second order in $\epsilon$-expansion, where $\epsilon=\sigma-d$, $\sigma$ is the L\'evy exponent and $d$ is the spatial dimension. For $d=\sigma$, we find the exponent of the logarithmic decay exactly. Theoretical values of the exponents are confirmed by numerical simulations., Comment: 9 pages, 4 figures

The asymptotic behaviour of the survival or reunion probability of vicious walks with short-range interactions is generally well studied. In many realistic processes, however, walks interact with a long ranged potential that decays in $d$ dimensions with distance $r$ as $r^{-d-\sigma}$. We employ methods of renormalized field theory to study the effect of such long range interactions. We calculate, for the first time, the exponents describing the decay of the survival probability for all values of parameters $\sigma$ and $d$ to first order in the double expansion in $\epsilon=2-d$ and $\delta=2-d-\sigma$. We show that there are several regions in the $\sigma-d$ plane corresponding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections for the first time., Comment: 9 pages, 3 figures

We present a general method to study the non-equilibrium behavior of Casimir type fluctuation induced forces for classical free scalar field theories. In particular we analyze the temporal evolution of the force towards its equilibrium value when the field dynamics is given by a general class of over damped stochastic dynamics (including the model A and model B class). The steady state force is also analyzed for systems which have non-equilibrium steady states, for instance where they are driven by colored noise. The key to the method is that out of equilibrium force is computed by specifying an energy of interaction between the field and the surfaces in the problem. In general we find that there is a mapping of the dynamical problem onto a corresponding static one, and in the case where the latter can be solved the full dynamical behavior of the force can be extracted. The method is used how to compute the non-equilibrium Casimir force induced between two parallel plates by a fluctuating field, in the cases of Dirichlet, Neumann and mixed boundary conditions. Various other examples, such as the fluctuation induced force between inclusions in fluctuating media are discussed., Comment: 16 pages RevTex

While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise., Comment: 4 pages RevTex, 2 .eps figures

Chemotaxis is typically modeled in the context of cellular motion towards a static, exogenous source of chemoattractant. Here, we propose a time-dependent mechanism of chemotaxis in which a self-propelled particle ({\it e.g.}, a cell) releases a chemical that diffuses to fixed particles (targets) and signals the production of a second chemical by these targets. The particle then moves up concentration gradients of this second chemical, analogous to diffusive echolocation. When one target is present, we describe probe release strategies that optimize travel of the cell to the target. In the presence of multiple targets, the one selected by the cell depends on the strength and, interestingly, on the frequency of probe chemical release. Although involving an additional chemical signaling step, our chemical ``pinging'' hypothesis allows for greater flexibility in regulating target selection, as seen in a number of physical or biological realizations., Comment: 14 pages, 5 figures

Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system, and find excellent agreement with our analytic results., Comment: 11 pages, 5 figures, Phys. Rev. E (accepted)