Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue.

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

Rheology of Suspensions of Flat Elastic Particles.

We consider a suspension of noninteracting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions.

Necking and failure of a particulate gel strand: signatures of yielding on different length scales.

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.

Equation of state for active matter.

We characterize the steady states of a suspension of two-dimensional active Brownian particles (ABPs). By approximating the first-order correction to the steady-state probability distribution to lowest order in Peclet number, we show that macroscopic quantities can be calculated in analogous way to equilibrium systems using this probability distribution. We then derive expressions for the macroscopic pressure and position-orientation correlation functions. We check our results by direct comparison with extensive numerical simulations. A key finding is the importance of many-body effective interactions even at very low densities.

Dynamics and interactions of Quincke roller clusters: From orbits and flips to excited states.

Active matter systems may be characterized by the conversion of energy into active motion, e.g., the self-propulsion of microorganisms. Artificial active colloids form models that exhibit essential properties of more complex biological systems but are amenable to laboratory experiments. While most experimental models consist of spheres, active particles of different shapes are less understood. Furthermore, interactions between these anisotropic active colloids are even less explored. Here, we investigate the motion of active colloidal clusters and the interactions between them. We focus on self-assembled dumbbells and trimers powered by an external dc electric field. For dumbbells, we observe an activity-dependent behavior of spinning, circular, and orbital motions. Moreover, collisions between dumbbells lead to the hierarchical self-assembly of tetramers and hexamers, both of which form rotational excited states. On the other hand, trimers exhibit flipping motion that leads to trajectories reminiscent of a honeycomb lattice.

Active Brownian particles in random and porous environments.

The transport of active particles may occur in complex environments, in which it emerges from the interplay between the mobility of the active components and the quenched disorder of the environment. Here, we explore the structural and dynamical properties of active Brownian particles (ABPs) in random environments composed of fixed obstacles in three dimensions. We consider different arrangements of the obstacles. In particular, we consider two particular situations corresponding to experimentally realizable settings. First, we model pinning particles in (non-overlapping) random positions and, second, in a percolating gel structure and provide an extensive characterization of the structure and dynamics of ABPs in these complex environments. We find that the confinement increases the heterogeneity of the dynamics, with new populations of absorbed and localized particles appearing close to the obstacles. This heterogeneity has a profound impact on the motility induced phase separation exhibited by the particles at high activity, ranging from nucleation and growth in random disorder to a complex phase separation in porous environments.

The nonlinear motion of cells subject to external forces.

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop.

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria.

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.

What good is maths in studies of wound healing?

Wound healing is an aspect of normal physiology that we all take for granted until it goes wrong, such as, for example, the scarring that results from a severe burn, or those patients who suffer from debilitating chronic wounds that fail to heal. Ever since wound repair research began as a discipline, clinicians and basic scientists have collaborated to try and understand the cell and molecular mechanisms that underpin healthy repair in the hope that this will reveal clues for the therapeutic treatment of pathological healing. In recent decades mathematicians and physicists have begun to join in with this important challenge. Here we describe examples of how mathematical modeling married to biological experimentation has provided insights that biology alone could not fathom. To date, these studies have largely focused on wound re-epithelialization and inflammation, but we also discuss other components of wound healing that might be ripe for similar interdisciplinary approaches.

Crystallisation and polymorph selection in active Brownian particles.

We explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work (Wysocki et al. in Europhys Lett 105:48004, 2014), we find that crystallisation is suppressed by activity and occurs at higher densities with increasing Péclet number ([Formula: see text]). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition, we observe the transition from a nucleation and growth regime at high [Formula: see text] to "spinodal nucleation" at low [Formula: see text]. Unlike the case of passive hard spheres, where preference for FCC over HCP polymorphs is weak, activity causes the annealing of HCP stacking faults, thus strongly favouring the FCC symmetry at high [Formula: see text]. When freezing occurs more slowly, in the nucleation and growth regime, this tendency is much reduced and we see a trend towards the passive case of little preference for either polymorph.

A Centrifuge-Based Method for Identifying Novel Genetic Traits That Affect Root-Substrate Adhesion in Arabidopsis thaliana.

The physical presence of roots and the compounds they release affect the cohesion between roots and their environment. However, the plant traits that are important for these interactions are unknown and most methods that quantify the contributions of these traits are time-intensive and require specialist equipment and complex substrates. Our lab developed an inexpensive, high-throughput phenotyping assay that quantifies root-substrate adhesion in Arabidopsis thaliana. We now report that this method has high sensitivity and versatility for identifying different types of traits affecting root-substrate adhesion including root hair morphology, vesicle trafficking pathways, and root exudate composition. We describe a practical protocol for conducting this assay and introduce its use in a forward genetic screen to identify novel genes affecting root-substrate interactions. This assay is a powerful tool for identifying and quantifying genetic contributions to cohesion between roots and their environment.

Competing active and passive interactions drive amoebalike crystallites and ordered bands in active colloids.

Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.

Steady-state distributions and nonsteady dynamics in nonequilibrium systems.

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.

Micro-scale interactions between Arabidopsis root hairs and soil particles influence soil erosion.

Soil is essential for sustaining life on land. Plant roots play a crucial role in stabilising soil and minimising erosion, although these mechanisms are still not completely understood. Consequently, identifying and breeding for plant traits to enhance erosion resistance is challenging. Root hair mutants in Arabidopsis thaliana were studied using three different quantitative methods to isolate their effect on root-soil cohesion. We present compelling evidence that micro-scale interactions of root hairs with surrounding soil increase soil cohesion and reduce erosion. Arabidopsis seedlings with root hairs were more difficult to detach from soil, compost and sterile gel media than those with hairless roots, and it was 10-times harder to erode soil from roots with than without hairs. We also developed a model that can consistently predict the impact root hairs make to soil erosion resistance. Our study thus provides new insight into the mechanisms by which roots maintain soil stability.

How many ways a cell can move: the modes of self-propulsion of an active drop.

Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime.

Exact results for sheared polar active suspensions with variable liquid crystalline order.

We consider a confined sheared active polar liquid crystal with a uniform orientation and study the effect of variations in the magnitude of polarization. Restricting our analysis to one-dimensional geometries, we demonstrate that with asymmetric boundary conditions, this system is characterized, macroscopically, by a linear shear stress vs. shear strain relationship that does not pass through the origin: At a zero strain rate, the fluid sustains a non-zero stress. Analytic solutions for the polarization, density, and velocity fields are derived for asymptotically large or small systems and are shown by comparison with precise numerical solutions to be good approximations for finite-size systems.

Tractionless Self-Propulsion of Active Drops.

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

The dynamical interplay between a megadalton peptide nanocage and solutes probed by microsecond atomistic MD; implications for design.

Understanding the assembly and dynamics of protein-based supramolecular capsids and cages is of fundamental importance and could lead to applications in synthetic biology and biotechnology. Here we present long and large atomistic molecular dynamics simulations of de novo designed self-assembling protein nanocages (SAGEs) in aqueous media. Microsecond simulations, comprised of ≈42 million atoms for three pre-formed SAGEs of different charges, in the presence of solutes and solvent have been completed. Here, the dynamics, stability and porosity of the peptide networks are explored along with their interactions with ions, small molecules and macromolecular solutes. All assemblies are stable over the µs timescale, and the solutes show a mixture of transport behaviour across or adherence to the fabric of the SAGE particles. Solute proteins largely retained native-like conformation on contact with SAGE. Certain residues of the SAGE peptides are identified as "repeat offenders" for contacting many different solutes, which suggest modifications to reduce non-specific binding. These studies highlight how molecular dynamics can aid the design process of SAGE and similar assemblies for potential applications as diverse as platforms for drug and vaccine delivery and nanoreactors to encapsulate enzyme pathways.

Active Suspensions have Nonmonotonic Flow Curves and Multiple Mechanical Equilibria.

We point out unconventional mechanical properties of confined active fluids, such as bacterial suspensions, under shear. Using a minimal model of an active liquid crystal with no free parameters, we predict the existence of a window of bacteria concentration for which a suspension of E. Coli effectively behaves, at steady-state, as a negative viscosity fluid and reach a quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a nonmonotonic local velocity profile, and it is associated with a nonmonotonic stress versus strain rate flow curve. This implies that fixed stress and fixed strain rate ensembles are not equivalent for active fluids.

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers.

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar-ordered phase appears because near-field lubrication rather than long-range hydrodynamics dominates the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.