Information transmission and signal permutation in active flow networks

© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel autonomous microfluidic devices. However, little is known about how information propagates through these far-from-equilibrium systems. Through a mathematical analogy with spin-ice vertex models, we investigate here the input-output characteristics of generic incompressible active flow networks (AFNs). Our analysis shows that information transport through an AFN is inherently different from conventional pressure or voltage driven networks. Active flows on hexagonal arrays preserve input information over longer distances than their passive counterparts and are highly sensitive to bulk topological defects, whose presence can be inferred from marginal input-output distributions alone. This sensitivity further allows controlled permutations on parallel inputs, revealing an unexpected link between active matter and group theory that can guide new microfluidic mixing strategies facilitated by active matter and aid the design of generic autonomous information transport networks

Topology-dependent density optima for efficient simultaneous network exploration

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimised at a searcher density that is well predicted by the spectral gap. Furthermore, we find that non-equilibrium processes, realised through the addition of bias, can support significantly increased density optima. Our results suggest novel hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.This work was supported by the EPSRC Systems Biology DTC Grant No. EP/G03706X/1 (D.B.W.), a Royal Society Wolfson Research Merit Award (R.E.B.), a Leverhulme Research Fellowship (R.E.B.), the BBSRC UK Multi-Scale Biology Network Grant No. BB/M025888/1 (R.E.B. and F.G.W.), and Trinity College, Cambridge (F.G.W.)

Active matter logic for autonomous microfluidics

Chemically or optically powered active matter plays an increasingly important role in materials design, but its computational potential has yet to be explored systematically. The competition between energy consumption and dissipation imposes stringent physical constraints on the information transport in active flow networks, facilitating global optimization strategies that are not well understood. Here, we combine insights from recent microbial experiments with concepts from lattice-field theory and non-equilibrium statistical mechanics to introduce a generic theoretical framework for active matter logic. Highlighting conceptual differences with classical and quantum computation, we demonstrate how the inherent non-locality of incompressible active flow networks can be utilized to construct universal logical operations, Fredkin gates and memory storage in set–reset latches through the synchronized self-organization of many individual network components. Our work lays the conceptual foundation for developing autonomous microfluidic transport devices driven by bacterial fluids, active liquid crystals or chemically engineered motile colloids.This work was supported by Trinity College, Cambridge (F.G.W.), an Alfred P. Sloan Research Fellowship (J.D.), an Edmund F. Kelly Research Award (J.D.), NSF Award CBET-1510768 (J.D.) and a Complex Systems Scholar Award of the James S. McDonnell Foundation (J.D.)

Topological sound in active-liquid metamaterials

Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal, or macroscopic constituents. These active liquids can flow spontaneously even in the absence of an external drive. Unlike spontaneous active flow, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials

Abnormal accumulation of autophagic vesicles correlates with axonal and synaptic pathology in young Alzheimer’s mice hippocampus

Dystrophic neurites associated with amyloid plaques precede neuronal death and manifest early in Alzheimer’s disease (AD). In this work we have characterized the plaque-associated neuritic pathology in the hippocampus of young (4- to 6-month-old) PS1M146L/APP751SL mice model, as the initial degenerative process underlying functional disturbance prior to neuronal loss. Neuritic plaques accounted for almost all fibrillar deposits and an axonal origin of the dystrophies was demonstrated. The early induction of autophagy pathology was evidenced by increased protein levels of the autophagosome marker LC3 that was localized in the axonal dystrophies, and by electron microscopic identification of numerous autophagic vesicles filling and causing the axonal swellings. Early neuritic cytoskeletal defects determined by the presence of phosphorylated tau (AT8-positive) and actin–cofilin rods along with decreased levels of kinesin-1 and dynein motor proteins could be responsible for this extensive vesicle accumulation within dystrophic neurites. Although microsomal Aβ oligomers were identified, the presence of A11-immunopositive Aβ plaques also suggested a direct role of plaque-associated Aβ oligomers in defective axonal transport and disease progression. Most importantly, presynaptic terminals morphologically disrupted by abnormal autophagic vesicle buildup were identified ultrastructurally and further supported by synaptosome isolation. Finally, these early abnormalities in axonal and presynaptic structures might represent the morphological substrate of hippocampal dysfunction preceding synaptic and neuronal loss and could significantly contribute to AD pathology in the preclinical stages

Active matter logic for autonomous microfluidics

Chemically or optically powered active matter plays an increasingly important role in materials design, but its computational potential has yet to be explored systematically. The competition between energy consumption and dissipation imposes stringent physical constraints on the information transport in active flow networks, facilitating global optimization strategies that are not well understood. Here, we combine insights from recent microbial experiments with concepts from lattice-field theory and non-equilibrium statistical mechanics to introduce a generic theoretical framework for active matter logic. Highlighting conceptual differences with classical and quantum computation, we demonstrate how the inherent non-locality of incompressible active flow networks can be utilized to construct universal logical operations, Fredkin gates and memory storage in set–reset latches through the synchronized self-organization of many individual network components. Our work lays the conceptual foundation for developing autonomous microfluidic transport devices driven by bacterial fluids, active liquid crystals or chemically engineered motile colloids

Mode selection in compressible active flow networks

Coherent, large-scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for compressible active flow networks. In contrast to thermally driven systems, we find that active friction selects discrete states with a limited number of oscillation modes activated at distinct fixed amplitudes. Using perturbation theory, we systematically predict the stationary states of noisy networks and find good agreement with a Bayesian state estimation based on a hidden Markov model applied to simulated time series data. Our results suggest that the macroscopic response of active network structures, from actomyosin force networks to cytoplasmic flows, can be dominated by a significantly reduced number of modes, in contrast to energy equipartition in thermal equilibrium. The model is also well suited to study topological sound modes and spectral band gaps in active matter

Displacement of transport processes on networked topologies

Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails to incorporate information of the actual path the particle traversed. In this work we consider another definition for the displacement of a particle on networked topologies. Using this definition, which we term the winding distance, we demonstrate that for Brownian particles, confinement to a network can induce a transition in the mean squared displacement from diffusive to ballistic behavior, \langle x2(t)\rangle \propto t2 for long times. A multiple scales approach is used to derive a macroscopic evolution equation for the displacement of a particle and uncover a topological condition for whether this transition in the mean squared displacement will occur. Furthermore, for networks satisfying this topological condition, we identify a prediction of the timescale upon which the displacement transitions to long-time behavior. Finally, we extend the investigation of displacement on networks to a class of anomalously diffusive transport processes, where we find that the mean squared displacement at long times is affected by both network topology and the character of the transport process