arXiv subjects

Arvind Gopinath

Publications and source records attributed to Arvind Gopinath.

17 recordsLinked to original sources

arXiv2024

Kinetically arrested clusters in active filament arrays

We use Brownian dynamics simulations and theory to study the over-damped spatiotemporal dynamics and pattern formation in a fluid-permeated array of equally spaced, active, elastic filaments that are pinned at one end and free at the other. The filaments are modeled as connected colloidal chains with activity incorporated via compressive follower forces acting along the filament backbone. The length of the chains is smaller than the thermal persistence length. For a range of filament separation and activity values, we find that the filament array eventually self-assembles into a series of regularly spaced, kinetically arrested, compact clusters. Filament activity, geometry, elasticity, and grafting density are each seen to crucially influence the size, shape, and spacing of emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between clusters, to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to stabilize the clusters. Our simulations suggest design principles to realize filament-based clusters and similar self-assembling biomimetic materials using active colloids or synthetic microtubule-motor systems.

cond-mat.soft↗

arXiv2024

Elastic interactions compete with persistent cell motility to drive durotaxis

The directed migration of cells toward stiffer substrate regions or durotaxis is relevant to tissue development and tumor progression. Here, we introduce a phenomenological model for single cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates towards the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. Cell dynamics are governed by two critical parameters: the strength of the traction-induced boundary interaction (A) and the persistence of cell motility (Pe). The resulting elastic forces and torques align cells perpendicular (parallel) to the boundary and accumulate (deplete) them at clamped (free) boundaries. A clamped boundary induces an attractive potential, promoting durotaxis, while a free boundary generates a repulsive potential, preventing anti-durotaxis. By analyzing steady-state position and orientation probabilities, we show how accumulation and depletion depend on elastic potential strength and motility. We compare our findings with biological microswimmers and other active particles that accumulate at confining boundaries. The model defines metrics for boundary accumulation and durotaxis, presenting a phase diagram with three regimes: durotaxis, adurotaxis, and motility-induced accumulation. Our model predicts how durotaxis depends on cell contractility and motility, offering insights and testable predictions for future experiments.

cond-mat.soft↗

arXiv2022

Collective states of active particles with elastic dipolar interactions

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.

cond-mat.soft↗

arXiv2021

How do biofilms feel their environment?

The ability of bacteria to colonize and grow on different surfaces is an essential process for biofilm development and depends on complex biomechanical interactions between the biofilm and the underlying substrate. Changes in the physical properties of the underlying substrate are known to alter biofilm expansion, but the mechanisms by which biofilms sense and respond to physical features of their environment are still poorly understood. Here, we report the use of synthetic polyacrylamide hydrogels with tunable stiffness and controllable pore size to assess physical effects of the substrate on biofilm development. Using time lapse microscopy to track the growth of expanding Serratia marcescens colonies, we find that biofilm colony growth can increase with increasing substrate stiffness on purely elastic substrates, unlike what is found on traditional agar substrates. Using traction force microscopy, we find that biofilms exert transient stresses correlated over length scales much larger than a single bacterium. Our results are consistent with a model of biofilm development in which the interplay between osmotic pressure arising from the biofilm and the poroelastic response of the underlying substrate controls biofilm growth and morphology.

physics.bio-ph↗

arXiv2020

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Initially straight slender elastic rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is also known that beyond a critical value of the pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Recently, we showed that pre-stressed planar shapes when immersed in a dissipative fluid and animated by nonconservative follower forces exhibit stable large-amplitude flapping oscillations. Here, we use time-stepper methods to analyze the three-dimensional instabilities and dynamics of pre-stressed planar and non-planar filament configurations when subject to active follower forces and dissipative fluid drag. First, we find that type of boundary constraint determines the nature of the non-linear patterns following instability. When the filament is clamped at one end and pinned at the other with follower forces directed towards the clamped end, we observe only stable planar (flapping) oscillations termed flapping result. When both ends are clamped however, we observe a secondary instability wherein planar oscillations are destabilized by off-planar perturbations and result in fully three-dimensional swirling patterns characterized by two distinct time-scales. The first time scale characterizes continuous and unidirectional swirling rotation around the end-to-end axis. The second time scale captures the rate at which the direction of swirling reverses or flips. The overall time over which the direction of swirling flips is very short compared to the long times over which the filament swirls in the same direction. Computations indicate that the reversal of swirling oscillations resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations.

nlin.PS↗

arXiv2019

Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces

Elastically driven filaments subjected to animating compressive follower forces provide a synthetic way to mimic the oscillatory beating of active biological filaments such as eukaryotic cilia. The dynamics of such active filaments can, under favorable conditions, exhibit stable time-periodic responses that result due to the interplay of elastic buckling instabilities, geometric constraints, boundary conditions, and dissipation due to fluid drag. In this paper, we use a continuum elastic rod model to estimate the critical follower force required for the onset of the stable time-periodic flapping oscillations in pre-stressed rods subjected to fluid drag. The pre-stress is generated by imposing either clamped-clamped or clamped-pinned boundary constraints and the results are compared with those of clamped-free case, which is without pre-stress. We find that the critical value increases with the initial slack--that quantifies the pre-stress, and strongly depends on the type of the constraints at the boundaries. The frequency of oscillations far from the onset, however, depends primarily on the magnitude of the follower force, not on the boundary constraints. Interestingly, oscillations for the clamped-pinned case are observed only when the follower forces are directed towards the clamped end. This finding can be exploited to design a mechanical switch to initiate or quench the oscillations by reversing the direction of the follower force or altering the boundary conditions.

physics.bio-ph↗

arXiv2018

Persistence of strain in motor-filament assemblies

Crosslinked semi-flexible and flexible filaments that are actively deformed by molecular motors occur in various natural settings, such as the ordered eukaryotic flagellum, and the disordered cytoskeleton. The deformation of these composite systems is driven by active motor forces and resisted by passive filament elasticity, and structural constraints due to permanent cross-links. Using a mean field theory for a one-dimensional ordered system, we show that the combination of motor activity and finite filament extensibility yields a characteristic persistence length scale over which active strain decays. This decay length is set by the ability of motors to respond to combination of the weak extensional elasticity, passive shear resistance and the viscoelastic properties of the motor assembly, and generalizes the notion of persistence in purely thermal filaments to active systems.

physics.bio-ph↗

arXiv2018

Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for prestressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.

physics.comp-ph↗

arXiv2018

The propagation of active-passive interfaces in bacterial swarms

Propagating interfaces are ubiquitous in nature, underlying instabilities and pattern formation in biology and material science. Physical principles governing interface growth are well understood in passive settings; however, our understanding of interfaces in active systems is still in its infancy. Here, we study the evolution of an active-passive interface using a model active matter system, bacterial swarms. We use ultra-violet light exposure to create compact domains of passive bacteria within Serratia marcescens swarms, thereby creating interfaces separating motile and immotile cells. Post-exposure, the boundary re-shapes and erodes due to self-emergent collective flows. We demonstrate that the active-passive boundary acts as a diffuse interface with mechanical properties set by the flow. Intriguingly, interfacial velocity couples to local swarm speed and interface curvature, suggesting that an active analogue to classic Gibbs-Thomson-Stefan conditions controls boundary propagation. Our results generalize interface theories to mixing and segregation in active systems with collective flows.

physics.bio-ph↗

arXiv2016

Active colloids in complex fluids

We review recent work on active colloids or swimmers, such as self-propelled microorganisms, phoretic colloidal particles, and artificial micro-robotic systems, moving in fluid-like environments. These environments can be water-like and Newtonian but can frequently contain macromolecules, flexible polymers, soft cells, or hard particles, which impart complex, nonlinear rheological features to the fluid. While significant progress has been made on understanding how active colloids move and interact in Newtonian fluids, little is known on how active colloids behave in complex and non-Newtonian fluids. An emerging literature is starting to show how fluid rheology can dramatically change the gaits and speeds of individual swimmers. Simultaneously, a moving swimmer induces time dependent, three dimensional fluid flows, that can modify the medium (fluid) rheological properties. This two-way, non-linear coupling at microscopic scales has profound implications at meso- and macro-scales: steady state suspension properties, emergent collective behavior, and transport of passive tracer particles. Recent exciting theoretical results and current debate on quantifying these complex active fluids highlight the need for conceptually simple experiments to guide our understanding.

physics.bio-ph↗

arXiv2015

Particle diffusion in active fluids is non-monotonic in size

We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherichia coli. Using particles covering a range of sizes from 0.6 to 39 microns, we probe particle dynamics at both short and long time scales. In all cases, the particles exhibit super-diffusive ballistic behavior at short times before eventually transitioning to diffusive behavior. Surprisingly, we find a regime in which larger particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. We also find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Peclet number. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.

physics.bio-ph↗

arXiv2015

Flagellar Kinematics and Swimming of Algal Cells in Viscoelastic Fluids

The motility of microorganisms is influenced greatly by their hydrodynamic interactions with the fluidic environment they inhabit. We show by direct experimental observation of the bi-flagellated alga Chlamydomonas reinhardtii that fluid elasticity and viscosity strongly influence the beating pattern - the gait - and thereby control the propulsion speed. The beating frequency and the wave speed characterizing the cyclical bending are both enhanced by fluid elasticity. Despite these enhancements, the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. The origin of this complex response lies in the interplay between the elasticity-induced changes in the spatial and temporal aspects of the flagellar cycle and the buildup and subsequent relaxation of elastic stresses during the power and recovery strokes.

physics.bio-ph↗

arXiv2015

Persistence of activity in noisy motor-filament assemblies

Long, elastic filaments cross-linked and deformed by active molecular motors occur in various natural settings. The overall macroscopic mechanical response of such a composite network depends on the coupling between the active and the passive properties of the underlying constituents and nonlocal interactions between different parts of the composite. In a simple one dimensional system, using a mean field model, it has been shown that the combination of motor activity and finite filament extensibility yields a persistence length scale over which strain decays. Here we study a similar system, in the complementary limit of strong noise and moderate extensibility, using Brownian multi-particle collision dynamics-based numerical simulations that includes the coupling between motor kinetics and local filament extensibility. While the numerical model shows deviations from the mean field predictions due to the presence of strong active noise caused by the variations in individual motor activity, several qualitative features are still retained. Specifically, for fixed motor attachment and detachment rates, the decay is length is set by the ratio of the passive elasticity to the active shear resistance generated by attached motors. Our study generalizes the notion of persistence in passive thermal systems to actively driven systems with testable predictions.

physics.bio-ph↗

arXiv2012

Flagellar dynamics of a connected chain of active, Brownian particles

Eukaryotic flagella are active structures with a complex architecture of microtubules, motor proteins and elastic links. They are capable of whiplike motions driven by motors sliding along filaments that are themselves constrained at an end. Here, we show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. We use a combination of numerical simulations, scaling analysis and mean field continuum elastic theory to demarcate the phase diagram for this type of oscillatory motion as a function of the filament length, passive elasticity, propulsion force and longitudinal persistence of propulsion directions. Depending on the nature of the anchoring, we show that filament either undergoes flagella-like beating or assumes a steadily rotating coiled conformation. Our system is simpler than its biological inspiration, and thus could be experimentally realized using a variety of self-propelled particles.

cond-mat.soft↗

arXiv2011

Dynamical Self-regulation in Self-propelled Particle Flows

We study a continuum model of overdamped self-propelled particles with an aligning interaction in two dimensions. By combining analytical and numerical work, we map out the phase diagram for generic parameters. We find that the system self-organizes into two robust structures in different regions of parameter space: solitary waves of ordered swarms moving through a low density disordered background, and stationary asters. The self-regulating nature of the flow yields phase separation, ubiquitous in this class of systems, and controls the formation of solitary waves. Self-propulsion and the associated active convection play a crucial role in aster formation. A new result of our work is a phase diagram that displays these different regimes in a unified manner.

physics.bio-ph↗

arXiv2011

Viscoelastic flow transitions in abrupt planar contractions

We present experimental evidence of global viscoelastic flow transitions in 2:1, 8:1 and 32:1 planar contractions under inertia-less conditions. Light sheet visualization and laser Doppler velocimetry techniques are used to probe spatial structure and time scales associated with the onset of these instabilities. The results are reported in terms of critical Weissenberg numbers characterizing the fluid flow rates. For a given contraction ratio and polymer fluid, a two-dimensional, steady flow with converging streamlines transitions to a two-dimensional pattern with diverging streamlines beyond a critical Weissenberg number. At even higher Weissenberg numbers, spatial transition to three-dimensional flow is observed. A relationship between the upstream Weissenberg number for the onset of this spatial instability and the contraction ratio is derived. For contraction ratios substantially greater than unity, we observe that further increase in the flow rate results in a second temporal transition to a three-dimensional, time-dependent flow. This complex flow arises due to a combination of the effects of stress-curvature interaction and three dimensional perturbations induced by the walls bounding the neutral direction. Comparison with studies on other geometries indicates that boundary shapes deeply influence the sequence and nature of flow transitions.

cond-mat.soft↗

arXiv2010

Semi-permeable vesicles composed of natural clay

We report a simple route to form robust, inorganic, semi-permeable compartments composed of montmorillonite, a natural plate-like clay mineral that occurs widely in the environment. Mechanical forces due to shear in a narrow gap assemble clay nanoplates from an aqueous suspension onto air bubbles. Translucent vesicles suspended in a single-phase liquid are produced when the clay-covered air bubbles are exposed to a variety of water-miscible organic liquids. These vesicles of clay are mechanically robust and are stable in water and other liquids. The formation of clay vesicles can be described by a physical mechanism that recognizes changes in the wetting characteristics of clay-covered air bubbles in organic liquids. The clay vesicles are covered with small pores and so intrinsically exhibit size-selective permeability, which allows spontaneous compartmentalization of self-assembling molecules in aqueous environments. The results we report here expand our understanding of potential paths to micro-compartmentalization in natural settings and are of relevance to theories of colloidal aggregation, mineral cycles, and the origins of life.

cond-mat.soft↗