Conformational Properties of Active Semiflexible Polymers

Structural dynamics and optimal transport of an active polymer

We study the spontaneous configuration transitions of an active semi-flexible polymer between spiral and non-spiral states, and show that the configuration dynamics is fully described by a subcritical pitchfork bifurcation. Exploiting the fact that an active polymer barely moves in spiral states and exhibits net displacements in non-spiral states, we theoretically prove that the motion of the active polymer is consistent with a run-and-tumble-like dynamics. Moreover, we find that there exists an optimal self-propelling force that maximizes the diffusion coefficient.

Delayed Excitations Induce Polymer Looping and Coherent Motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

A passive star polymer in a dense active bath: insights from computer simulations

Using computer simulations in two dimensions (2D), we explore the structure and dynamics of a star polymer with three arms made of passive monomers immersed in a bath of active Brownian particles (ABPs). We analyze the conformational and dynamical changes of the polymer as a function of activity and packing fraction. We also study the process of motility induced phase separation (MIPS) in the presence of a star polymer, which acts as a mobile nucleation center. The presence of the polymer increases the growth rate of the clusters in comparison to a bath without the polymer. In particular, for low packing fraction, both nucleation and cluster growth are affected by the inclusion of the star polymer. Clusters grow in the vicinity of the star polymer, resulting in the star polymer experiencing a caged motion similar to a tagged ABP in the dense phase. Due to the topological constraints of the star polymers and clustering nearby, the conformational changes of the star polymer lead to interesting observations. Inter alia, we observe the shrinking of the arm with increasing activity along with a short-lived hairpin structure of one arm formed. We also see the transient pairing of two arms of the star polymer, while the third is largely separated at high activity. We hope our findings will help in understanding the behavior of active-passive mixtures, including biopolymers of complex topology in dense active suspensions.

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.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

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.

Long-range ordering of velocity-aligned active polymers

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

Adsorption of active polymers on attractive nanoparticles

The adsorption of active polymers on an attractive nanoparticle (NP) is studied using Langevin dynamics simulations. The active polymers consist of an active Brownian particle (ABP) at the head and a subsequent passive polymer chain. The ABP experiences an active force of magnitude Fa. The interactions between the active polymer and NP are modeled as Lennard-Jones potential with a strength εpn. We find the critical adsorption point εpn* increases with increasing the active force Fa. The increment of εpn*, denoted as Δεpn*, due to Fa can be expressed approximately as Δεpn* ∝ Fa2.5 for the restricted rotating active polymer (RRAP) where the rotation of the head ABP is restricted and Δεpn* ∝ Fa1.7 for the freely rotating active polymer (FRAP) where the ABP rotates freely. Meanwhile, the conformation of the adsorbed polymer, such as adsorbed trains on NP and the tail near the ABP, are also dependent on Fa. When the tail near the ABP is short, the adsorption is significantly affected by the active force. However, when the tail is long, the whole polymer can be viewed as a long tail stretched by the active force and unperturbed adsorption monomers. Simulation results show that the active force has a direct and significant effect on εpn* and the structure of the adsorbed active polymers.

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.

Translocation Dynamics of an Active Filament through a Long-Length Scale Channel

Active filament translocation through a confined space is crucial for diverse biological processes. By using Langevin dynamics simulations, we investigate the translocation dynamics of an axially self-propelled chain through a channel. First, results show a suggestive reciprocal scaling of translocation time versus active force. Second, in the case of a long channel, we demonstrate a very intriguing nonmonotonic change of translocation time with increasing channel width. The driving force shows a similar trend, providing a consistent picture to understand the unexpected channel width effect. In particular, in a moderately broad channel, the disordered chain conformation results in a loss of driving force and thus inhibits translocation dynamics. Chain adsorption might occur in a wide channel, which accounts for a facilitated translocation. Lastly, we connect the translocation process to tension propagation (TP). A modified TP picture is proposed to interpret the waiting time distribution. Our work highlights the new phenomenology owing to the crucial interplay of activity and spacial confinement, which drives the translocation dynamics, going beyond the traditional entropic barrier scenario.

Structure and dynamics of an active polymer chain inside a nanochannel grafted with polymers

We use computer simulations to investigate the complex dynamics of a polymer, made of active Brownian particles, inside a channel grafted internally with passive polymer chains. Our simulations reveal that this probe-polymer, if passive, exhibits a compact structure when its interaction is repulsive with the grafted chains as it tends to stay within the hollow space created along the axis of the channel. On increasing the attractive interaction, the passive probe-polymer is pulled towards the grafted polymeric region and adopts an extended structure. By contrast, switching on the activity helps the probe-polymer to escape from the local traps caused by the sticky grafted chains. The interplay between the activity of the probe-polymer and its sticky interaction with the grafted chains results in shrinking, followed by swelling as the activity is increased. To elucidate the dynamics we compute the mean square displacement (MSD) of the center of mass of the probe-polymer, which increases monotonically with activity and displays superdiffusive behavior at an intermediate time and enhanced diffusion at a long time period. In addition, compared with the attractive interaction, the active probe-polymer shows faster dynamics when the interaction is repulsive to the grafted polymers. We believe that our current study will provide insights into the structural changes and dynamics of active polymers in heterogeneous media and will be useful in designing polymer-based drug delivery vehicles.

Effects of inertia on conformation and dynamics of tangentially driven active filaments

Active filamentlike systems propelling along their backbone exist across scales ranging from motor-driven biofilaments to worms and robotic chains. In macroscopic active filaments such as a chain of robots, in contrast to their microscopic counterparts, inertial effects on their motion cannot be ignored. Nonetheless, the consequences of the interplay between inertia and flexibility on the shape and dynamics of active filaments remain unexplored. Here we examine inertial effects on a flexible tangentially driven active polymer model pertinent to the above examples and we determine the conditions under which inertia becomes important. Performing Langevin dynamics simulations of active polymers with underdamped and overdamped dynamics for a wide range of contour lengths and activities, we uncover striking inertial effects on conformation and dynamics for high levels of activities. Inertial collisions increase the persistence length of active polymers and remarkably alter their scaling behavior. In stark contrast to passive polymers, inertia leaves its fingerprint at long times by an enhanced diffusion of the center of mass. We rationalize inertia-induced enhanced dynamics by analytical calculations of center-of-mass velocity correlations, applicable to any active polymer model, which reveal significant contributions from active force fluctuations convoluted by inertial relaxation.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

Conformation and dynamics of an active filament in crowded media

The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.

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.

Active and thermal fluctuations in multi-scale polymer structure and dynamics

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

Activity mediated globule to coil transition of a flexible polymer in a poor solvent

Understanding the role of self-propulsion on the conformational properties of active filamentous objects has relevance in biology. In this work, we consider a flexible bead-spring model for active polymers with both attractive and repulsive interactions among the non-bonded monomers. The activity for each monomer works along its intrinsic direction of self-propulsion which changes diffusively with time. We study its kinetics in the overdamped limit, following quenching from good to poor solvent conditions. We observe that with low activities, though the kinetic pathways remain similar, the scaling exponent for the relaxation time of globule formation becomes smaller than that for the case with no activity. Interestingly, for higher activities when self-propulsion dominates over interaction energy, the polymer conformation becomes extended coil-like. There, in the steady state, the variation of the spatial extension of the polymer, measured via its gyration radius, shows two completely different scaling regimes: the corresponding Flory exponent ν changes from 1/3 to 3/5 similar to a transition of the polymer from a globular state to a self-avoiding walk. This can be explained by an interplay among the three energy scales present in the system, viz., the "ballistic", thermal, and interaction energy.

Emergent collective behavior of active Brownian particles with visual perception

Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited maneuverability to an instantaneous visual input of the positions of neighbors within a vision cone and a cut-off radius. The system exhibits large-scale self-organized structures, which depend on selected parameter values, and, in particular, the presence of excluded-volume interactions. The emergent structures in two dimensions, such as worms, worm-aggregate coexistence, and hexagonally close-packed structures, are analysed and phase diagrams are constructed. The analysis of the particle's mean-square displacement shows ABP-like dynamics for dilute systems and the worm phase. In the limit of densely packed structures, the active diffusion coefficient is significantly smaller and depends on the number of particles in the cluster. Our analysis of the cluster-growth dynamics shows distinct differences to processes in systems of short-range attractive colloids in equilibrium. Specifically, the characteristic time for the growth and decay of clusters of a particular size is longer than that of isotropically attractive colloids, which we attribute to the non-reciprocal nature of the directed visual perception. Our simulations reveal a strong interplay between ABP-characteristic interactions, such as volume exclusion and rotational diffusion, and cognitive-based interactions and navigation.

Migration of active rings in porous media

Inspired by how the shape deformations in active organisms help them to migrate through disordered porous environments, we simulate active ring polymers in two-dimensional random porous media. Flexible and inextensible active ring polymers navigate smoothly through the disordered media. In contrast, semiflexible rings undergo transient trapping inside the pore space; the degree of trapping is inversely correlated with the increase in activity. We discover that flexible rings swell while inextensible and semiflexible rings monotonically shrink upon increasing the activity. Together, our findings identify the optimal migration of active ring polymers through porous media.

Dynamics of active polar ring polymers

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equation of motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.

Emergent conformational properties of end-tailored transversely propelling polymers

We study the dynamics and conformations of a single active semiflexible polymer whose monomers experience a propulsion force perpendicular to the local tangent, with the end beads being different from the inner beads ("end-tailored"). Using Langevin simulations, we demonstrate that, apart from sideways motion, the relative propulsion strength between the end beads and the polymer backbone significantly changes the conformational properties of the polymers as a function of bending stiffness, end-tailoring and propulsion force. Expectedly, for slower ends the polymer curves away from the moving direction, while faster ends lead to opposite curving, in both cases slightly reducing the center of mass velocity compared to a straight fiber. Interestingly, for faster end beads there is a rich and dynamic morphology diagram: the polymer ends may get folded together to 2D loops or hairpin-like conformations that rotate due to their asymmetry in shape and periodic flapping motion around a rather straight state during full propulsion is also possible. We rationalize the simulations using scaling and kinematic arguments and present the state diagram of the conformations. Sideways propelled fibers comprise a rather unexplored and versatile class of self-propellers, and their study will open novel ways for designing, e.g. motile actuators or mixers in soft robotics.

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.

Absolute negative mobility of active polymer chains in steady laminar flows

We investigate the transport of active polymer chains in steady laminar flows in the presence of thermal noise and an external constant force. In the model, the polymer chain is worm-like and is propelled by active forces along its tangent vectors. Compared with inertial Brownian particles, active polymer chains in steady laminar flows exhibit richer movement patterns due to their specific spatial structures. The simulation results show that the velocity-force relation is strongly dependent on the system parameters such as the chain length, bending rigidity, active force and so on. The polymer chain may move in some preferential movement directions and exhibits absolute negative mobility within appropriate parameter regimes, i.e., the polymer chain can move in a direction opposite to the external constant force. In particular, we can observe giant negative mobility in a broad range of parameter regimes.

Simulating wet active polymers by multiparticle collision dynamics

The conformational and dynamical properties of active Brownian polymers embedded in a fluid depend on the nature of the driving mechanism, e.g., self-propulsion or external actuation of the monomers. Implementations of self-propelled and actuated active Brownian polymers in a multiparticle collision (MPC) dynamics fluid are presented, which capture the distinct differences between the two driving mechanisms. The active force-free nature of self-propelled monomers requires adaptations of the MPC simulation scheme, with its streaming and collision steps, where the monomer self-propulsion velocity has to be omitted in the collision step. Comparison of MPC simulation results for active polymers in dilute solution with results of Brownian dynamics simulations accounting for hydrodynamics via the Rotne-Prager-Yamakawa tensor confirm the suitability of the implementation. The polymer conformational and dynamical properties are analyzed by the static and dynamic structure factor, and the scaling behavior of the latter with respect to the wave number and time dependence are discussed. The dynamic structure factor displays various activity-induced temporal regimes, depending on the considered wave number, which reflect the persistent diffusive motion of the whole polymer at small wave numbers, and the activity-enhanced internal dynamics at large wave numbers. The obtained simulation results are compared with theoretical predictions.

Self-induced hydrodynamic coil-stretch transition of active polymers

We analyze the conformational dynamics and statistical properties of an active polymer model. The polymer is described as a freely jointed bead-rod chain subject to stochastic active force dipoles that act on the suspending solvent where they drive long-ranged fluid flows. Using Langevin simulations of isolated chains in unconfined domains, we show how the coupling of active flows with polymer conformations leads to emergent dynamics. Systems with contractile dipoles behave similarly to passive Brownian chains with enhanced fluctuations due to dipolar flows. In systems with extensile dipoles, however, our simulations uncover an active coil-stretch transition whereby the polymer spontaneously unfolds and stretches out in its own self-induced hydrodynamic flow, and we characterize this transition in terms of a dimensionless activity parameter comparing active dipolar forces to thermal fluctuations. We discuss our findings in the context of the classic coil-stretch transition of passive polymers in extensional flows and complement our simulations with a simple kinetic model for an active trimer.

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.

Active bath-induced localization and collapse of passive semiflexible polymers

The conformational and dynamical properties of a passive polymer embedded in a bath of active Brownian particles (ABPs) are studied by Langevin dynamics simulations. Various activities and ABP concentrations below and above the critical values for motility-induced phase separation (MIPS) are considered. In a homogeneous ABP fluid, the embedded polymer swells with increasing bath activity, with stronger swelling for larger densities. The polymer dynamics is enhanced, with the diffusion coefficient increasing by a power-law with increasing activity, where the exponent depends on the ABP concentration. For ABP concentrations in the MIPS regime, we observe a localization of the polymer in the low-density ABP phase associated with polymer collapse for moderate activities and a reswelling for high activities accompanied by a preferred localization in the high-density ABP phase. Localization and reswelling are independent of the polymer stiffness, with stiff polymers behaving similarly to flexible polymers. The polymer collapse is associated with a slowdown of its dynamics and a significantly smaller center-of-mass diffusion coefficient. In general, the polymer dynamics can only partially be described by an effective (bath) temperature. Moreover, the properties of a polymer embedded in a homogeneous active bath deviate quantitatively from those of a polymer composed of active monomers, i.e., linear chains of ABPs; however, such a polymer exhibits qualitatively similar activity-dependent features.

A single active ring model with velocity self-alignment

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

Surfactants and rotelles in active chiral fluids

Surfactant molecules migrate to interfaces, reduce interfacial tension, and form micelles. All of these behaviors occur at or near equilibrium. Here, we describe active analogs of surfactants that operate far from equilibrium in active chiral fluids. Unlike molecular surfactants, the amphiphilic character of surfactants in active chiral fluids is a consequence of their activity. Our fluid of choice is a mixture of spinners that demixes into left-handed and right-handed chiral fluid domains. We realize spinners in experiment with three-dimensionally printed vibrots. Vibrot surfactants are chains of vibrots containing both types of handedness. Experiments demonstrate the affinity of double-stranded chains to interfaces, where they glide along and act as mixing agents. Simulations access larger systems in which single-stranded chains form spinning vesicles, termed rotelles. Rotelles are the chiral analogs of micelles. Rotelle formation is a ratchet mechanism catalyzed by the vorticity of the chiral fluid and only exist far from equilibrium.

Activity-Induced Collapse and Arrest of Active Polymer Rings

We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that their behavior depends crucially on their size: Short rings (N≲100) swell, whereas longer rings (N≳200) collapse, at sufficiently high activity. By investigating the nonequilibrium process leading to the steady state, we find a universal route driving both outcomes; we highlight the central role of steric interactions, at variance with linear chains, and of topology conservation. We further show that the collapsed rings are arrested by looking at different observables, all underlining the presence of an extremely long timescales at the steady state, associated with the internal dynamics of the collapsed section. Finally, we found that in some circumstances the collapsed state spins about its axis.

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.

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.

Dynamics as a cause for the nanoscale organization of the genome

Chromatin ‘blobs’ were recently identified by live super-resolution imaging of labeled nucleosomes as pervasive but fleeting structural entities. However, the mechanisms leading to the formation of these blobs and their functional implications are unknown. We explore here whether causal relationships exist between parameters that characterize the chromatin blob dynamics and structure, by adapting a framework for spatio-temporal Granger-causality inference. Our analysis reveals that chromatin dynamics is a key determinant for both blob area and local density. Such causality, however, could be demonstrated only in 10–20% of the nucleus, suggesting that chromatin dynamics and structure at the nanometer scale are dominated by stochasticity. We show that the theory of active semiflexible polymers can be invoked to provide potential mechanisms leading to the organization of chromatin into blobs. Our results represent a first step toward elucidating the mechanisms that govern the dynamic and stochastic organization of chromatin in the cell nucleus.

Hydrodynamic interactions in squirmer dumbbells: active stress-induced alignment and locomotion

Hydrodynamic interactions are fundamental for the dynamics of swimming self-propelled particles. Specifically, bonds between microswimmers enforce permanent spatial proximity and, thus, enhance emergent correlations by microswimmer-specific flow fields. We employ the squirmer model to study the swimming behavior of microswimmer dumbbells by mesoscale hydrodynamic simulations, where the squirmers' rotational motion is geometrically unrestricted. An important aspect of the applied particle-based simulation approach-the multiparticle collision dynamics method-is the intrinsic account for thermal fluctuations. We find a strong effect of active stress on the motility of dumbbells. In particular, pairs of strong pullers exhibit orders of magnitude smaller swimming efficiency than pairs of pushers. This is a consequence of the inherent thermal fluctuations in combination with the strong coupling of the squirmers' rotational motion, which implies non-exponentially decaying auto- and cross-correlation functions of the propulsion directions, and active stress-dependent characteristic decay times. As a consequence, specific stationary-state relative alignments of the squirmer propulsion directions emerge, where pullers are preferentially aligned in an antiparallel manner along the bond vector, whereas pushers are preferentially aligned normal to the bond vector with a relative angle of approximately 60° at weak active stress, and one of the propulsion directions is aligned with the bond at strong active stress. The distinct differences between dumbbells comprised of pusher or pullers suggest means to control microswimmer assemblies for future microbot applications.

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.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

Anisotropic dynamics of a self-assembled colloidal chain in an active bath

Anisotropic macromolecules exposed to non-equilibrium (active) noise are very common in biological systems, and an accurate understanding of their anisotropic dynamics is therefore crucial. Here, we experimentally investigate the dynamics of isolated chains assembled from magnetic microparticles at a liquid-air interface and moving in an active bath consisting of motile E. coli bacteria. We investigate both the internal chain dynamics and the anisotropic center-of-mass dynamics through particle tracking. We find that both the internal and center-of-mass dynamics are greatly enhanced compared to the passive case, i.e., a system without bacteria, and that the center-of-mass diffusion coefficient D features a non-monotonic dependence as a function of the chain length. Furthermore, our results show that the relationship between the components of D parallel and perpendicular with respect to the direction of the applied magnetic field is preserved in the active bath compared to the passive case, with a higher diffusion in the parallel direction, in contrast to previous findings in the literature. We argue that this qualitative difference is due to subtle differences in the experimental geometry and conditions and the relative roles played by long-range hydrodynamic interactions and short-range collisions.

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.

Three-body problem for Langevin dynamics with different temperatures

A mixture of Brownian particles at different temperatures has been a useful model for studying the out-of-equilibrium properties of systems made up of microscopic components with differing levels of activity. This model was previously studied analytically for two-particle interactions in the dilute limit, yielding a Boltzmann-like two-particle distribution with an effective temperature. Like the Newtonian two- and three-body problems, we ask here whether the two-particle results can be extended to three-particle interactions to get the three-particle distributions. By considering the special solvable case of pairwise quadratic interactions, we show that, unlike the two-particle distribution, the three-particle distribution cannot in general be Boltzmann-like with an effective temperature. We instead find that the steady-state distribution of any two particles in a triplet depends on the properties of and interactions with the third particle, leading to some unexpected behaviors not present in equilibrium.

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).

Enhanced Rotational Motion of Spherical Squirmer in Polymer Solutions

The rotational diffusive motion of a self-propelled, attractive spherical colloid immersed in a solution of self-avoiding polymers is studied by mesoscale hydrodynamic simulations. A drastic enhancement of the rotational diffusion by more than an order of magnitude in the presence of activity is obtained. The amplification is a consequence of two effects, a decrease of the amount of adsorbed polymers by active motion and an asymmetric encounter with polymers on the squirmer surface, which yields an additional torque and random noise for the rotational motion. Our simulations suggest a way to control the rotational dynamics of squirmer-type microswimmers by the degree of polymer adsorption and system heterogeneity.