Flagellar dynamics of a connected chain of active, polar, Brownian particles

Non-equilibrium structural and dynamic behaviors of active polymers in complex and crowded environments

Active matter systems, which convert internal chemical energy or energy from the environment into directed motion, are ubiquitous in nature and exhibit a range of emerging non-equilibrium behaviors. However, most of the current works on active matter have been devoted to particles, and the study of active polymers has only recently come into the spotlight due to their prevalence within living organisms. The intricate interplay between activity and conformational degrees of freedom gives rise to novel structural and dynamical behaviors of active polymers. Research in active polymers remarkably broadens diverse concepts of polymer physics, such as molecular architecture, dynamics, scaling and so on, which is of significant importance for the development of new polymer materials with unique performance. Furthermore, active polymers are often found in strongly interacting and crowded systems and in complex environments, so that the understanding of this behavior is essential for future developments of novel polymer-based biomaterials. This review thereby focuses on the study of active polymers in complex and crowded environments, and aims to provide insights into the fundamental physics underlying the adaptive and collective behaviors far from equilibrium, as well as the open challenges that the field is currently facing.

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

Escape dynamics of active ring polymers in a cylindrical nanochannel

We explore the escape dynamics of active ring polymers confined in a cylindrical nanochannel using Brownian dynamics. Our simulation results show that the escape time decreases with the increase of the Péclet number, which is not noticeable between the two stages of the escape process, based on whether the center of mass of the polymer is inside or outside the nanochannel. However, the monomer motion trajectory of the active polymer is very different from that of the passive polymer, similar to the snake-like motion with uniform velocity. The passive polymer, however, is in constant fugitive motion with increased velocity at the tail end of the escape. Our work is vital for understanding the escape dynamics of active ring polymers in the confined nanochannel, which provides new perspectives on their characterization and analysis.

Wave-like oscillations of clamped microtubules driven by collective dynein transport

Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a "gliding-assay" geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective "order parameter" based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.

Characteristic features of self-avoiding active Brownian polymers under linear shear flow

We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical properties, such as the stretching in the flow direction and compression in the gradient direction, shear-induced alignment, and shear viscosity. In the asymptotic limit of large activities and shear rates, the power-law scaling exponents of these quantities differ significantly from those of passive polymers. The chain's shear-induced stretching at a given shear rate is reduced by active noise, and it displays a non-monotonic behavior, where an initial polymer compression is followed by its stretching with increasing active force. The compression of the polymer in the gradient direction follows the relation ∼WiPe-3/4 as a function of the activity-dependent Weissenberg number WiPe, which differs from the scaling observed in passive systems ∼WiPe-1/2. The flow-induced alignment at large Péclet numbers Pe ≫ 1, where Pe is the Péclet number, and large shear rates WiPe ≫ 1 displays the scaling behavior WiPe-1/2, with an exponent differing from the passive value -1/3. Furthermore, the polymer's zero-shear viscosity displays a non-monotonic behavior, decreasing in an intermediate activity regime due to excluded-volume interactions and increasing again for large Pe. Shear thinning appears with increasing Weissenberg number with the power-laws WiPe-1/2 and WiPe-3/4 for passive and active polymers, respectively. In addition, our simulation results are compared with the results of an analytical approach, which predicts quantitatively similar behaviors for the various aforementioned physical quantities.

Emergent programmable behavior and chaos in dynamically driven active filaments

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Self-Oscillation and Synchronization Transitions in Elastoactive Structures

The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Among these, spontaneous self-oscillations of mechanical structures is perhaps the simplest and most widespread type of nonequilibrium phenomenon. Yet, we lack experimental model systems to investigate the various dynamical phenomena that may appear. Here, we introduce a centimeter-sized model system for one-dimensional elastoactive structures. We show that such structures exhibit flagellar motion when pinned at one end, self-snapping when pinned at two ends, and synchronization when coupled together with a sufficiently stiff link. We further demonstrate that these transitions can be described quantitatively by simple models of coupled pendula with follower forces. Beyond the canonical case considered here, we anticipate our work to open avenues for the understanding and design of the self-organization and response of active biological and synthetic solids, e.g., in higher dimensions and for more intricate geometries.

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

Rectification of polymer translocation through nanopores by nonchiral and chiral active particles

We study translocation of a flexible polymer chain through a membrane pore under the influence of active forces and steric exclusion using Langevin dynamics simulations within a minimal two-dimensional model. The active forces on the polymer are imparted by nonchiral and chiral active particles that are introduced on one side or both sides of a rigid membrane positioned across the midline of a confining box. We show that the polymer can translocate through the pore to either side of the dividing membrane in the absence of external forcing. Translocation of the polymer to a given side of the membrane is driven (hindered) by an effective pulling (pushing) exerted by the active particles that are present on that side. The effective pulling results from accumulation of active particles around the polymer. This crowding effect signifies persistent motion of active particles causing prolonged detention times for them close to the confining walls and the polymer. The effective pushing that hinders the translocation, on the other hand, results from steric collisions that occur between the polymer and active particles. As a result of the competition between these effective forces, we find a transition between two rectified cis-to-trans and trans-to-cis translocation regimes. This transition is identified by a sharp peak in the average translocation time. The effects of active particles on the transition is studied by analyzing how the translocation peak is regulated by the activity (self-propulsion) strength of these particles, their area fraction, and chirality strength.

Dynamics of a spherical self-propelled tracer in a polymeric medium: interplay of self-propulsion, stickiness, and crowding

We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity (self-propulsion) brings additional complexity to the tracer dynamics. Our simulations show that on increasing the stickiness of the tracer particle to the polymer beads, the dynamics of the tracer particle slows down as it gets stuck to the polymer chain and moves along with it. But with increasing self-propulsion velocity, the dynamics gets enhanced. In the case of increasing stickiness as well as activity, the non-Gaussian parameter (NGP) exhibits non-monotonic behavior, which also shows up in the re-scaled self part of the van-Hove function. Non-Gaussianity results owing to the enhanced binding events and the sticky motion of the tracer along with the chain with increasing stickiness. On the other hand, with increasing activity, initially non-Gaussianity increases as the tracer moves through the heterogeneous polymeric environment but for higher activity, the tracer escapes resulting in a negative NGP. For higher values of stickiness, the trapping time distributions of the passive tracer particle broaden and have long tails. On the other hand, for a given stickiness with increasing self-propulsion force, the trapping time distributions become narrower and have short tails. We believe that our current simulation study will be helpful in elucidating the complex motion of activity-driven probes in viscoelastic media.

Dynamics of a two-dimensional active polymer chain with a rotation-restricted active head

The dynamics of a two-dimensional active polymer composed of an active Brownian particle (ABP) at the head and a passive polymer chain is investigated using Langevin dynamics simulation. The ABP experiences a self-propulsion force f_s and a resistance torque M as the passive polymer chain is bonded to the edge of the ABP. M restricts the rotation of the ABP, and thus the dynamics of the ABP and that of the whole active polymer are influenced significantly. Due to this restriction, the persistence time τ_r, which characterizes the random rotation of the ABP, is increased significantly and changes non-monotonically with the rotational friction coefficient η_r. Our simulation results show that the effect of M on the dynamics of the active polymer can be characterized mainly by the change of τ_r. Moreover, the propulsive diffusion coefficient D_P of the whole polymer chain originated from the self-propulsion force can be described by a scaling relation D_P ∝ f_s²τ_r/N²η_t² with η_t the translational friction coefficient and N the polymer length. Our results show that the diffusion is promoted by the resistance torque M and τ_r is a key factor for the diffusion of active polymers.

Conformation and dynamics of a tethered active polymer chain

The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.

Effective forces between active polymers

The characterization of the interactions between two fully flexible self-avoiding polymers is one of the classic and most important problems in polymer physics. In this paper we measure these interactions in the presence of active fluctuations. We introduce activity into the problem using two of the most popular models in this field, one where activity is effectively embedded into the monomers' dynamics, and the other where passive polymers fluctuate in an explicit bath of active particles. We establish the conditions under which the interaction between active polymers can be mapped into the classical passive problem. We observe that the active bath can drive the development of strong attractive interactions between the polymers and that, upon enforcing a significant degree of overlap, they come together to form a single double-stranded unit. A phase diagram tracing this change in conformational behavior is also reported.

Active beating modes of two clamped filaments driven by molecular motors

Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.

Migration of active filaments under Poiseuille flow in a microcapillary tube

We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.

Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.

A semiflexible polymer in a gliding assay: reentrant transition, role of turnover and activity

We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a capture radius, and extend along the filament in a directed fashion before detaching. Both the extension and detachment rates are load-dependent and generate an active drive on the filament. The filament undergoes a first order phase transition from the open chain to spiral conformation and shows a reentrant behavior in both the active extension and the turnover, defined as the ratio of attachment-detachment rates. Associated with the phase transition, the size and shape of the polymer change non-monotonically, and the relevant autocorrelation functions display a double-exponential decay. The corresponding correlation times show a maximum signifying the dominance of spirals. The orientational dynamics captures the rotation of spirals, and its correlation time decays with activity as a power law.

Three-dimensional nonlinear dynamics of prestressed active filaments: Flapping, swirling, and flipping

Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.

Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays

Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient - even in the absence of inter-filament hydrodynamic interactions - to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics - specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.

The coil-globule transition in self-avoiding active polymers

We perform numerical simulations of an active fully flexible self-avoiding polymer as a function of the quality of the embedding solvent described in terms of an effective monomer-monomer interaction. Specifically, by extracting the Flory exponent of the active polymer under different conditions, we are able to pin down the location of the coil-globule transition for different strengths of the active forces. Remarkably, we find that a simple rescaling of the temperature is capable of qualitatively capturing the dependence of the Θ-point of the polymer on the amplitude of active fluctuations. We discuss the limits of this mapping and suggest that a negative active pressure between the monomers, not unlike the one that has already been found in suspensions of active hard spheres, may also be present in active polymers.

Periodic oscillations in a string of camphor infused disks

The rhythmic beating motion of autonomously motile filaments has many practical applications. Here, we present an experimental study on a filament made of camphor infused paper disks, stitched together adjacent to each other using nylon thread. The filament displays spontaneous translatory motion when it is placed on the surface of water due to the surface tension gradients created by camphor molecules on the water surface. When this filament is clamped on one end, we obtain regular oscillatory motion instead of translation. The filament shows qualitatively different dynamics at different activity levels, which is controlled by the amount of camphor infused into the paper disks. For a better physical understanding of the filament dynamics, we develop a minimal numerical model involving a semi-flexible filament made of active polar disks, where the polarity is coupled to the instantaneous velocity of the particle. This model qualitatively reproduces different oscillatory modes of the filament. Moreover, our model reveals a rich dynamical state diagram of the system, as a function of filament activity and the coupling strength.

Extensions of the worm-like-chain model to tethered active filaments under tension

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Translational and rotational dynamics of a self-propelled Janus probe in crowded environments

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non-viscoelastic disconnected monomers. Our simulations show that the translational as well as rotational mean square displacements have a distinctive three-step growth for fixed values of self-propulsion force, and steadily increase with self-propulsion, irrespective of the nature of the crowder. On the other hand, in the absence of crowders, the rotational dynamics of the Janus probe is independent of self-propulsion force. On replacing the repulsive polymers with sticky ones, translational and rotational mean square displacements of the Janus probe show a sharp drop. Since different faces of a Janus particle interact differently with the environment, we show that the direction of self-propulsion also affects its dynamics. The ratio of long-time translational and rotational diffusivities of the self-propelled probe with a fixed self-propulsion, when plotted against the area fraction of the crowders, passes through a minimum and at higher area fraction merges to its value in the absence of the crowder. This points towards the decoupling of the translational and rotational dynamics of the self-propelled probe at an intermediate area fraction of the crowders. However, such translational-rotational decoupling is absent for passive probes.

Hydrodynamics of polymers in an active bath

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

Buckling instabilities and spatio-temporal dynamics of active elastic filaments

Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. If the filament pushes a cargo, the friction on the cargo can be enough to deform the filament, thus affecting the transport properties of the cargo. Motivated by cytoskeletal filament motility assays, we study the dynamic buckling instabilities of a two-dimensional slender elastic filament driven through a dissipative medium by tangential propulsive forces in the presence of obstacles or cargo. We observe two distinct instabilities. When the filament's head is pinned or experiences significant translational but little rotational drag from its cargo, it buckles into a steadily rotating coiled state. When it is clamped or experiences both significant translational and rotational drag from its cargo, it buckles into a periodically beating, overall translating state. Using minimal analytically tractable models, linear stability theory and fully nonlinear computations, we study the onset of each buckling instability, characterize each buckled state, and map out the phase diagram of the system. Finally, we use particle-based Brownian dynamics simulations to show our main results are robust to moderate noise and steric repulsion. Overall, our results provide a unified framework to understand the dynamics of tangentially propelled filaments and filament-cargo assemblies.

How a local active force modifies the structural properties of polymers

We study the dynamics of a polymer, described as a variant of a Rouse chain, driven by an active terminal monomer (head). The local active force induces a transition from a globule-like to an elongated state, as revealed by the study of the end-to-end distance, the variance of which is analytically predicted under suitable approximations. The change in the relaxation times of the Rouse-modes produced by the local self-propulsion is consistent with the transition from globule to elongated conformations. Moreover, also the bond-bond spatial correlation for the chain head are affected by the self-propulsion and a gradient of over-stretched bonds along the chain is observed. We compare our numerical results both with the phenomenological stiff-polymer theory and several analytical predictions in the Rouse-chain approximation.

Conformation and dynamics of a self-avoiding active flexible polymer

We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ν_{a}≈1/2 for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law τ_{r}∼Pe^{-4/3} (Pe is Péclet number).

A Light-Driven Microgel Rotor

The current understanding of motility through body shape deformation of micro-organisms and the knowledge of fluid flows at the microscale provides ample examples for mimicry and design of soft microrobots. In this work, a 2D spiral is presented that is capable of rotating by non-reciprocal curling deformations. The body of the microswimmer is a ribbon consisting of a thermoresponsive hydrogel bilayer with embedded plasmonic gold nanorods. Such a system allows fast local photothermal heating and nonreciprocal bending deformation of the hydrogel bilayer under nonequilibrium conditions. It is shown that the spiral acts as a spring capable of large deformations thanks to its low stiffness, which is tunable by the swelling degree of the hydrogel and the temperature. Tethering the ribbon to a freely rotating microsphere enables rotational motion of the spiral by stroboscopic irradiation. The efficiency of the rotor is estimated using resistive force theory for Stokes flow. This research demonstrates microscopic locomotion by the shape change of a spiral and may find applications in the field of microfluidics, or soft microrobotics.

Beating to rotational transition of a clamped active ribbon-like filament

We present a detailed study of a clamped ribbon-like filament under a compressive active force using Brownian dynamics simulations. We show that a clamped ribbon-like filament is able to capture beating as well as rotational motion under the compressive force. The nature of oscillation is governed by the torsional rigidity of the filament. The frequency of oscillation is almost independent of the torsional rigidity. The beating of the filament gives a butterfly-shaped trajectory of the free-end monomer, whereas rotational motion yields a circular trajectory on a plane. The binormal correlation and the principal component analysis reveal the butterfly, elliptical, and circular trajectories of the free end monomer. We present a phase diagram for different kinds of motion in the parameter regime of compressive force and torsional rigidity.

Deviations from Blob Scaling Theory for Active Brownian Filaments Confined Within Cavities

Scaling arguments used to predict the radius of gyration of passive self-avoiding flexible polymers have been shown to hold for polymers under the influence of active fluctuations. In this Letter, we establish how the standard blob scaling theory representation of a polymer, capable of capturing the essential physics of passive polymers under a variety of settings, breaks down when dealing with active polymers under confinement. Using numerical simulations, we show how the predicted exponents associated to the forces applied by a polymer when restricted within cavities of different geometries hold only whenever the persistence length generated on the polymer by the active forces is much smaller than the size of the characteristic blob in the scaling theory.

Effect of external shear flow on sperm motility

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.

Active Brownian filaments with hydrodynamic interactions: conformations and dynamics

The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete linear chain composed of active Brownian particles is considered, analytically, a continuous linear semiflexible polymer with active velocities changing diffusively. The force-free nature of active monomers is accounted for-no Stokeslet fluid flow induced by active forces-and higher order hydrodynamic multipole moments are neglected. Hence, fluid-mediated interactions are assumed to arise solely due to intramolecular forces. The hydrodynamic interactions (HI) are taken into account analytically by the preaveraged Oseen tensor, and numerically by the Rotne-Prager-Yamakawa tensor. The nonequilibrium character of the active process implies a dependence of the stationary-state properties on HI via the polymer relaxation times. In particular, at moderate activities, HI lead to a substantial shrinkage of flexible and semiflexible polymers to an extent far beyond shrinkage of comparable free-draining polymers; even flexible HI-polymers shrink, while active free-draining polymers swell monotonically. Large activities imply a reswelling, however, to a less extent than for non-HI polymers, caused by the shorter polymer relaxation times due to hydrodynamic interactions. The polymer mean square displacement is enhanced, and an activity-determined ballistic regime appears. Over a wide range of time scales, flexible active polymers exhibit a hydrodynamically governed subdiffusive regime, with an exponent significantly smaller than that of the Rouse and Zimm models of passive polymers. Compared to simulations, the analytical approach predicts a weaker hydrodynamic effect. Overall, hydrodynamic interactions modify the conformational and dynamical properties of active polymers substantially.

Flagella-like Beating of a Single Microtubule

Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simultaneously on a microtubule. The tangential forces exerted by a cluster are mostly in the range 0-8 pN toward the microtubule minus end, indicating the action of 1 or 2 kinesin motors. The lateral forces are distributed symmetrically and mainly below 10 pN, while the lateral velocity has a strong peak around zero. Unlike well-known models for flapping filaments, kinesins are found to have a strong "pinning" effect on the beating filaments. Our results suggest new strategies to utilize molecular motors in dynamic roles that depend sensitively on the stress built-up in the system.

Morphological and dynamical properties of semiflexible filaments driven by molecular motors

We consider an explicit model of a semiflexible filament moving in two dimensions on a gliding assay of motor proteins, which attach to and detach from filament segments stochastically, with a detachment rate that depends on the local load experienced. Attached motor proteins move along the filament to one of its ends with a velocity that varies nonlinearly with the motor protein extension. The resultant force on the filament drives it out of equilibrium. The distance from equilibrium is reflected in the end-to-end distribution, modified bending stiffness, and a transition to spiral morphology of the polymer. The local stress dependence of activity results in correlated fluctuations in the speed and direction of the center of mass leading to a series of ballistic-diffusive crossovers in its dynamics.

Globulelike Conformation and Enhanced Diffusion of Active Polymers

We study the dynamics and conformation of polymers composed by active monomers. By means of Brownian dynamics simulations we show that, when the direction of the self-propulsion of each monomer is aligned with the backbone, the polymer undergoes a coil-to-globulelike transition, highlighted by a marked change of the scaling exponent of the gyration radius. Concurrently, the diffusion coefficient of the center of mass of the polymer becomes essentially independent of the polymer size for sufficiently long polymers or large magnitudes of the self-propulsion. These effects are reduced when the self-propulsion of the monomers is not bound to be tangent to the backbone of the polymer. Our results, rationalized by a minimal stochastic model, open new routes for activity-controlled polymers and, possibly, for a new generation of polymer-based drug carriers.

Active Brownian Filamentous Polymers under Shear Flow

The conformational and rheological properties of active filaments/polymers exposed to shear flow are studied analytically. Using the continuous Gaussian semiflexible polymer model extended by the activity, we derive analytical expressions for the dependence of the deformation, orientation, relaxation times, and viscosity on the persistence length, shear rate, and activity. The model yields a Weissenberg-number dependent shear-induced deformation, alignment, and shear thinning behavior, similarly to the passive counterpart. Thereby, the model shows an intimate coupling between activity and shear flow. As a consequence, activity enhances the shear-induced polymer deformation for flexible polymers. For semiflexible polymers/filaments, a nonmonotonic deformation is obtained because of the activity-induced shrinkage at moderate and swelling at large activities. Independent of stiffness, activity-induced swelling facilitates and enhances alignment and shear thinning compared to a passive polymer. In the asymptotic limit of large activities, a polymer length- and stiffness-independent behavior is obtained, with universal shear-rate dependencies for the conformations, dynamics, and rheology.

Internal dynamics of semiflexible polymers with active noise

The intramolecular dynamics of flexible and semiflexible polymers in response to active noise is studied theoretically. The active noise may either originate from interactions of a passive polymer with a bath of active Brownian particles or the polymer itself is comprised of active Brownian particles. We describe the polymer by the continuous Gaussian semiflexible-polymer model, taking into account the finite polymer extensibility. Our analytical calculations predict a strong dependence of the polymer dynamics on the activity. In particular, active semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics at weak activity to that of flexible polymers at strong activity. The end-to-end vector correlation function decays exponentially for times longer than the longest polymer relaxation time. Thereby, the polymer relaxation determines the decay of the correlation function for long and flexible polymers. For shorter and stiffer polymers, the relaxation behavior of individual active Brownian particles dominates the decay above a certain activity. The diffusive dynamics of a polymer is substantially enhanced by the activity. Three regimes can be identified in the mean square displacement for sufficiently strong activities: an activity-induced ballistic regime at short times, followed by a Rouse-type polymer-specific regime for any polymer stiffness, and free diffusion at long times, again determined by the activity.

Dynamically generated patterns in dense suspensions of active filaments

We use Langevin dynamics simulations to study dynamical behavior of a dense planar layer of active semiflexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several nonequilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that, for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterized by strong density fluctuations. Furthermore, we identify an activity-driven crossover from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analog in systems of active particles without internal degrees of freedom.

Spontaneous symmetry breaking induced unidirectional rotation of a chain-grafted colloidal particle in the active bath

Exploiting the energy of randomly moving active agents such as bacteria is a fascinating way to power a microdevice. Here we show, by simulations, that a chain-grafted disk-like colloidal particle can rotate unidirectionally and hence output work when immersed in a thin film of active particle suspension. The collective spontaneous symmetry breaking of chain configurations is the origin of the unidirectional rotation. Long persistence time, large propelling force and/or small rotating friction are keys to sustaining the collective broken symmetry and realizing the rotation. In the rotating state, we find very simple linear relations, e.g. between the mean angular speed and the propelling force. The time-evolving asymmetry of chain configurations reveals that there are two types of non-rotating state. The basic phenomena are also observed in the macroscopic granular experiments, implying the generic nature of these phenomena. Our findings provide new insights into the collective spontaneous symmetry breaking in active systems with flexible objects and also open the way to conceive new soft/deformable microdevices.

Identification of internal properties of fibres and micro-swimmers

In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.