Inertial effect on evasion and pursuit dynamics of prey swarms: the emergence of a favourable mass ratio for the predator-prey arms race.

We show, based on a theoretical model, how inertia plays a pivotal role in the survival dynamics of a prey swarm while chased by a predator. With the varying mass of the prey and predator, diverse escape patterns emerge, such as circling, chasing, maneuvering, dividing into subgroups, and merging into a unitary group, similar to the escape trajectories observed in nature. Moreover, we find a transition from non-survival to survival of the prey swarm with increasing predator mass. The transition regime is also sensitive to the variation in prey mass. Further, the analysis of the prey group survival as a function of predator-to-prey mass ratio unveils the existence of three distinct regimes: (i) frequent chase and capture leading to the non-survival of the prey swarm, (ii) an intermediate regime where competition between pursuit and capture occurs, resembling an arms race, and (iii) the survival regime without the capture of prey. Interestingly, our study demonstrates the existence of a favourable predator-prey mass ratio for coexistence of both prey and predator in an ecosystem, which agrees well with the field studies.

Collective motion: Influence of local behavioural interactions among individuals.

Fascinating patterns are displayed in nature due to the collective coherent motion of many living organisms. The origin of collective behaviours is diverse as the group members benefit in various ways: large resources of food, mating choices, nesting, and protection from predators, to name a few. It is still not well understood how complex behaviours emerge from a collective group that are otherwise not displayed at the level of solitary individuals. In recent years, along with field studies, numerous theoretical approaches have been developed to obtain insights into the mechanisms of aggregations and the collective decision-making processes. This brief review focuses on the self-propelled particle models, which have played a significant role in deciphering the underlying dynamics of collective motion in various organisms. Here, we discuss how local behavioural interactions and coordinations among the individual members give rise to complex collective behaviours. We consider the examples of collective motion in the schooling of fishes, flocking of birds, and swarming of prey, and address the emergence of a variety of patterns, a transition from disorder to ordered motion, and survival chances of prey group when under predator attacks.

Cholate-conjugated cationic polymers for regulation of actin dynamics.

Cytoskeletal movement is a compulsory necessity for proper cell functioning and is largely controlled by actin filament dynamics. The actin dynamics can be fine-tuned by various natural and artificial materials including cationic proteins, polymers, liposomes, and lipids, although most of the synthetic substrates have toxicity issues. Herein, we show actin nucleation and stabilization with a synthetic family of cholic acid (CA)-conjugated cationic macromolecules. Architectural conjugation of CA is designed by attaching it to the polymer chain end, as well as to the side chain of the polymer. The side-chain cholate content is also varied in the copolymer, which results in self-aggregation in aqueous media above a certain critical aggregation concentration (CAC). Below the CAC, the in vitro actin dynamics modulation behaviour is studied using a pyrene actin fluorescence assay, actin co-sedimentation assay, dynamic light scattering (DLS), and transmission electron microscopy (TEM). These polymers are nontoxic to HeLa cells, and the 2% cholate conjugated cationic copolymer showed maximum enhancement of G-actin nucleation, as well as F-actin stabilization. We further develop a theoretical model to elucidate the underlying dynamics of the actin polymerization process under the influence of cationic copolymers with cholate pendants. Finally, we proposed macromolecular self-aggregation as a unique tool for modulating actin dynamics, as revealed from the experimental findings and theoretical modelling.

Fatty acid-based polymeric micelles to ameliorate amyloidogenic disorders.

To develop anti-amyloidogenic inhibitors for ameliorating the treatment of diabetes, herein, we have synthesised amphiphilic block copolymers with side-chain fatty acid (FA) moieties via reversible addition fragmentation chain-transfer (RAFT) polymerization. We addressed the unexplored role of FA pendants in the FA-tethered block copolymers (FABC) towards modulating the insulin fibrillation process with the aid of different biophysical techniques. Experimental findings established that FABC micelles can elongate the lag phase time to a greater extent and exhibit significant inhibitory potencies, with the more pronounced effect observed in stearic acid-based polymeric micelles (SABC475). Furthermore, conformational modulation using circular dichroism spectroscopic measurements demonstrates their potential role as effective inhibitors of insulin fibrils through reducing the ß-sheet contents. Interestingly, the FABC micelles can also disintegrate the matured fibrils and effectively diminish the fibril induced toxicity. Hydrophobic interaction and hydrogen (H) bonding are the two major driving forces that are equally responsible for the almost complete prevention of insulin aggregated species. Theoretical simulation results further support our experimental observations in explaining the inhibitory rate of the insulin fibrillation process in the presence of different FABC micelles. Overall, we envision that the reported study will provide a novel path to develop a new class of anti-amyloid polymeric inhibitors.

Growth kinetics and power laws indicate distinct mechanisms of cell-cell interactions in the aggregation process.

Cellular aggregation is a complex process orchestrated by various kinds of interactions depending on the environment. Different interactions give rise to different pathways of cellular rearrangement and the development of specialized tissues. To distinguish the underlying mechanisms, in this theoretical work, we investigate the spontaneous emergence of tissue patterns from an ensemble of single cells on a substrate following three leading pathways of cell-cell interactions, namely, direct cell adhesion contacts, matrix-mediated mechanical interaction, and chemical signaling. Our analysis shows that the growth kinetics of the aggregation process are distinctly different for each pathway and bear the signature of the specific cell-cell interactions. Interestingly, we find that the average domain size and the mass of the clusters exhibit a power law growth in time under certain interaction mechanisms hitherto unexplored. Further, as observed in experiments, the cluster size distribution can be characterized by stretched exponential functions showing distinct cellular organization processes.

Efficient flocking: metric versus topological interactions.

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; by contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.

Survival probability of a lazy prey on lattices and complex networks.

We develop a framework to analyse the survival probability of a prey following a minimal effort evasion strategy, that is being chased by N predators on finite lattices or complex networks. The predators independently perform random walks if the prey is not within their sighting radius, whereas, the prey only moves when a predator moves onto a node within its sighting radius. We verify the proposed framework on three different finite lattices with periodic boundaries through numerical simulations and find that the survival probability (Psur) decays exponentially with a decay rate proportional to P(N, k) (number of permutations), where k is the minimum number of predators required to capture a prey. We then extend the framework onto complex networks and verify its robustness on the networks generated by the Watts-Strogatz (W-S), Barabási-Albert (B-A) models and a few real-world networks. Our analysis predicts that, for the considered lattices, Psur reduces as the degree of the nodes of the lattice is increased. However, for networks, Psur initially increases with the average degree of the nodes, reaches a maximum, and then decreases. Furthermore, we analyse the effect of the long-range connections in networks on Psur in W-S networks. The proposed framework enables one to study the survival probability of such a prey being hunted by multiple predators on any given structure.

Survival chances of a prey swarm: how the cooperative interaction range affects the outcome.

A swarm of prey, when attacked by a predator, is known to rely on their cooperative interactions to escape. Understanding such interactions of collectively moving prey and the emerging patterns of their escape trajectories still remain elusive. In this paper, we investigate how the range of cooperative interactions within a prey group affects the survival chances of the group while chased by a predator. As observed in nature, the interaction range of prey may vary due to their vision, age, or even physical structure. Based on a simple theoretical prey-predator model, here, we show that an optimality criterion for survival can be established on the interaction range of prey. Very short-range or long-range interactions are shown to be inefficient for the escape mechanism. Interestingly, for an intermediate range of interaction, the survival probability of the prey group is found to be maximum. Our analysis also shows that the nature of the escape trajectories strongly depends on the range of interactions between prey and corroborates with the naturally observed escape patterns. Moreover, we find that the optimal survival interaction regime varies depending on the prey group size and also on the strength of the predator and the prey interactions.

Stick-slip dynamics of migrating cells on viscoelastic substrates.

Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviors have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip jumps but also predicts the existence of an optimal substrate viscosity corresponding to maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the time evolution of individual bond force that characterizes the stick-slip patterns on soft versus stiff substrates. Our analysis also elucidates how the duration of the stick-slip cycles are affected by various cellular parameters.

Aggregation dynamics of active cells on non-adhesive substrate.

Cellular self-assembly and organization are fundamental steps for the development of biological tissues. In this paper, within the framework of a cellular automata model, we address how an ordered tissue pattern spontaneously emerges from a randomly migrating single cell population without the influence of any external cues. This model is based on the active motility of cells and their ability to reorganize due to cell-cell cohesivity as observed in experiments. Our model successfully emulates the formation of nascent clusters and also predicts the temporal evolution of aggregates that leads to the compact tissue structures. Moreover, the simulations also capture several dynamical properties of growing aggregates, such as, the rate of cell aggregation and non-monotonic growth of the aggregate area which show a good agreement with the existing experimental observations. We further investigate the time evolution of the cohesive strength, and the compactness of aggregates, and also study the ruggedness of the growing structures by evaluating the fractal dimension to get insights into the complexity of tumorous tissue growth which were hitherto unexplored.

A general model of focal adhesion orientation dynamics in response to static and cyclic stretch.

Understanding cellular response to mechanical forces is immensely important for a plethora of biological processes. Focal adhesions are multimolecular protein assemblies that connect the cell to the extracellular matrix and play a pivotal role in cell mechanosensing. Under time-varying stretches, focal adhesions dynamically reorganize and reorient and as a result, regulate the response of cells in tissues. Here I present a simple theoretical model based on, to my knowledge, a novel approach in the understanding of stretch-sensitive bond association and dissociation processes together with the elasticity of the cell-substrate system to predict the growth, stability, and the orientation of focal adhesions in the presence of static as well as cyclically varying stretches. The model agrees well with several experimental observations; most importantly, it explains the puzzling observations of parallel orientation of focal adhesions under static stretch and nearly perpendicular orientation in response to fast varying cyclic stretch.

Theoretical concepts and models of cellular mechanosensing.

Recent discoveries have established that mechanical properties of the cellular environment such as its rigidity, geometry, and external stresses play an important role in determining the cellular function and fate. Mechanical properties have been shown to influence cell shape and orientation, regulate cell proliferation and differentiation, and even govern the development and organization of tissues. In recent years, many theoretical and experimental investigations have been carried out to elucidate the mechanisms and consequences of the mechanosensitivity of cells. In this review, we discuss recent theoretical concepts and approaches that explain and predict cell mechanosensitivity. We focus on the interplay of active and passive processes that govern cell-cell and cell-matrix interactions and discuss the role of this interplay in the processes of cell adhesion, regulation of cytoskeleton mechanics and the response of cells to applied mechanical stresses.

Nonlinear dynamics of cell orientation.

The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, tauc, for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, tauc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.

Dynamical theory of active cellular response to external stress.

We present a comprehensive, theoretical treatment of the orientational response to external stress of active, contractile cells embedded in a gel-like elastic medium. The theory includes both the forces that arise from the deformation of the matrix as well as forces due to the internal regulation of the stress fibers and focal adhesions of the cell. We calculate the time-dependent response of both the magnitude and the direction of the elastic dipole that characterizes the active forces exerted by the cell, for various situations. For static or quasistatic external stress, cells orient parallel to the stress while for high frequency dynamic external stress, cells orient nearly perpendicular. Both numerical and analytical calculations of these effects are presented. In addition we predict the relaxation time for the cellular response for both slowly and rapidly varying external stresses; several characteristic scaling regimes for the relaxation time as a function of applied frequency are predicted. We also treat the case of cells for which the regulation of the stress fibers and focal adhesions is controlled by strain (instead of stress) and show that the predicted dependence of the cellular orientation on the Poisson ratio of the matrix can differentiate strain vs stress regulation of cellular response.

Do cells sense stress or strain? Measurement of cellular orientation can provide a clue.

We predict theoretically the steady-state orientation of cells subject to dynamical stresses that vary more quickly than the cell relaxation time. We show that the orientation is a strong function of the Poisson's ratio, nu, of the matrix when cell activity is governed by the matrix strain; if cell activity is governed by the matrix stress, the orientation depends only weakly on nu. These results can be used to differentiate systems in which the strain or the stress determine the setpoint for the mechanosensitivity of cells.

Intermittent peel front dynamics and the crackling noise in an adhesive tape.

We report a comprehensive investigation of a model for peeling of an adhesive tape along with a nonlinear time series analysis of experimental acoustic emission signals in an effort to understand the origin of intermittent peeling of an adhesive tape and its connection to acoustic emission. The model represents the acoustic energy dissipated in terms of Rayleigh dissipation functional that depends on the local strain rate. We show that the nature of the peel front exhibits rich spatiotemporal patterns ranging from smooth, rugged, and stuck-peeled configurations that depend on three parameters, namely the ratio of inertial time scale of the tape mass to that of the roller, the dissipation coefficient, and the pull velocity. The stuck-peeled configurations are reminiscent of fibrillar peel front patterns observed in experiments. We show that while the intermittent peeling is controlled by the peel force function, the model acoustic energy dissipated depends on the nature of the peel front and its dynamical evolution. Even though the acoustic energy is a fully dynamical quantity, it can be quite noisy for a certain set of parameter values, suggesting the deterministic origin of acoustic emission in experiments. To verify this suggestion, we have carried out a dynamical analysis of experimental acoustic emission time series for a wide range of traction velocities. Our analysis shows an unambiguous presence of chaotic dynamics within a subinterval of pull speeds within the intermittent regime. Time-series analysis of the model acoustic energy signals is also found to be chaotic within a subinterval of pull speeds. Further, the model provides insight into several statistical and dynamical features of the experimental acoustic emission signals including the transition from burst-type acoustic emission to continuous-type with increasing pull velocity and the connection between acoustic emission and stick-slip dynamics. Finally, the model also offers an explanation for the recently observed feature that the duration of the slip phase can be less than that of the stick phase.

Dynamics of the peel front and the nature of acoustic emission during peeling of an adhesive tape.

We investigate the peel front dynamics and acoustic emission (AE) of an adhesive tape within the context of a recent model by including an additional dissipative energy that mimics bursts of acoustic signals. We find that the nature of the peeling front can vary from a smooth to a stuck-peeled configuration depending on the values of dissipation coefficient, inertia of the roller, and mass of the tape. Interestingly, we find that the distribution of AE bursts shows power law statistics with two scaling regimes with increasing pull velocity as observed in experiments. In these regimes, the stuck-peeled configuration is similar to the "edge of peeling" reminiscent of a system driven to a critical state.

Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape.

It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force function. By including the kinetic energy of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier equations. Our analysis also shows that the mass of the ribbon has a strong influence on the nature of the dynamics.

Dynamics of stick-slip in peeling of an adhesive tape.

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. We derive the equations of motion for the angular speed of the roller tape, the peel angle and the pull force used in earlier investigations using a Lagrangian. Due to the constraint between the pull force, peel angle and the peel force, it falls into the category of differential-algebraic equations requiring an appropriate algorithm for its numerical solution. Using such a scheme, we show that stick-slip jumps emerge in a purely dynamical manner. Our detailed numerical study shows that these set of equations exhibit rich dynamics hitherto not reported. In particular, our analysis shows that inertia has considerable influence on the nature of the dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a phenomenological peel force function which includes the influence of the pull speed. This reproduces the decreasing nature of the rupture force with the pull speed observed in experiments. This rich dynamics is made transparent by using a set of approximations valid in different regimes of the parameter space. The approximate solutions capture major features of the exact numerical solutions and also produce reasonably accurate values for the various quantities of interest.