Self-avoiding Polymer Research Articles

Effects of Linking Topology on the Shear Response of Connected Ring Polymers: Catenanes and Bonded Rings Flow Differently.

We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BRs develop a novel motif, termed gradient tumbling, rotating around the gradient axis. For the PCs the rings are stretched and display another new pattern, termed slip tumbling. The dynamics of BRs is continuous and oscillatory, whereas that of PCs is intermittent between slip-tumbling attempts. Our findings demonstrate the interplay between topology and hydrodynamics in dilute solutions of connected polymers.

Inertia and activity: spiral transitions in semi-flexible, self-avoiding polymers.

We consider a two-dimensional, tangentially active, semi-flexible, self-avoiding polymer to find a dynamical re-entrant transition between motile open chains and spinning achiral spirals with increasing activity. Utilizing probability distributions of the turning number, we ascertain the comparative stability of the spiral structure and present a detailed phase diagram within the activity inertia plane. The onset of spiral formation at low activity levels is governed by a torque balance and is independent of inertia. At higher activities, however, inertial effects lead to spiral destabilization, an effect absent in the overdamped limit. We further delineate alterations in size and shape by analyzing the end-to-end distance distribution and the radius of gyration tensor. The Kullback-Leibler divergence from equilibrium distributions exhibits a non-monotonic relationship with activity, reaching a peak at the most compact spirals characterized by the most persistent spinning. As inertia increases, this divergence from equilibrium diminishes.

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.

Scaling properties of a moving polymer

We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in (0,∞). Our main result states that the effective radius of the polymer is approximately J5/3; evidently for large J the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately J. For such a moving polymer taking values in R2, we offer a conjecture that the effective radius is approximately J5/4.

Stimuli-responsive polyelectrolyte brushes for regulating streaming current magnetic field and energy conversion efficiency in soft nanopores

The electrokinetic energy conversion, electroviscous effect, and induced internal and external magnetic fields in a smart polyelectrolyte grafted “soft” nanopore with pH responsiveness are studied here using an efficient molecular theory approach. The analysis is based on writing the total free energy of the system, including the conformational entropy of the flexible, self-avoiding polymer chains and the translational entropy of the mobile species, the electrostatic interactions, and the free energy due to chemical equilibrium reactions. Then, the free energy is minimized, while satisfying the necessary constraints to find the equilibrium state of the system. The predictions of the model are shown to be in excellent agreement with analytical solutions derived for special cases. We discuss the effect of different influential environmental and polymer brush parameters in detail and show that the electrokinetic energy conversion efficiency is optimal at moderate pH values and low background salt concentrations. It is also shown that the electrokinetic energy conversion efficiency is a complex function depending on both the environmental and polymer brush properties. Notably, high slip coefficients or high polymer grafting densities do not necessarily lead to a high energy conversion efficiency. Magnetic field readouts allow to measure streaming currents through nanopores without the need of electrodes and may be utilized as a secondary electronic signature in nanopore sensing techniques. It is shown that in nanopores modified with polyelectrolyte brushes, the induced magnetic fields can be tens of times larger than those in solid-state nanopores having only surface charges. We show that by tuning the pH, background salt concentration, surface charge, and polyelectrolyte grafting density, the magnitude of the internal and external magnetic fields can be significantly changed and controlled in a wide range.

Confinement anisotropy drives polar organization of two DNA molecules interacting in a nanoscale cavity

There is growing appreciation for the role phase transition based phenomena play in biological systems. In particular, self-avoiding polymer chains are predicted to undergo a unique confinement dependent demixing transition as the anisotropy of the confined space is increased. This phenomenon may be relevant for understanding how interactions between multiple dsDNA molecules can induce self-organized structure in prokaryotes. While recent in vivo experiments and Monte Carlo simulations have delivered essential insights into this phenomenon and its relation to bacteria, there are fundamental questions remaining concerning how segregated polymer states arise, the role of confinement anisotropy and the nature of the dynamics in the segregated states. To address these questions, we introduce an artificial nanofluidic model to quantify the interactions of multiple dsDNA molecules in cavities with controlled anisotropy. We find that two dsDNA molecules of equal size confined in an elliptical cavity will spontaneously demix and orient along the cavity poles as cavity eccentricity is increased; the two chains will then swap pole positions with a frequency that decreases with increasing cavity eccentricity. In addition, we explore a system consisting of a large dsDNA molecule and a plasmid molecule. We find that the plasmid is excluded from the larger molecule and will exhibit a preference for the ellipse poles, giving rise to a non-uniform spatial distribution in the cavity that may help explain the non-uniform plasmid distribution observed during in vivo imaging of high-copy number plasmids in bacteria.

Conformation of ring single-stranded DNA measured by DNA origami structures

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a complex challenge that has been addressed lately by different methods. We measured the persistence length of ring ssDNA using a combination of a special DNA origami structure, a self-avoiding ring polymer simulation model, and nonparametric estimation statistics. The method overcomes the complexities set forth by previously used methods. We designed the DNA origami nano structures and measured the ring ssDNA polymer conformations using atomic force microscopy. We then calculated their radius of gyration, which was used as a fitting parameter for finding the persistence length. As there is no simple formulation for the radius of gyration distribution, we developed a simulation program consisting of a self-avoiding ring polymer to fit the persistence length to the experimental data. ssDNA naturally forms stem-loops, which should be taken into account in fitting a model to the experimental measurement. To overcome that hurdle, we found the possible loops using minimal energy considerations and used them in our fitting procedure of the persistence length. Due to the statistical nature of the loops formation, we calculated the persistence length for different percentages of loops that are formed. In the range of 25–75% loop formation, we found the persistence length to be 1.9–4.4 nm, and for 50% loop formation we get a persistence length of 2.83 ± 0.63 nm. This estimation narrows the previously known persistence length and provides tools for finding the conformations of ssDNA.

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.

Driven injection of a polymer into a spherical cavity: A Langevin dynamics simulation study* *Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY20A040004) and the National Natural Science Foundation of China (Grant Nos. 11604232 and 11974305).

The injection of a self-avoiding flexible polymer into a spherical cavity under a driving force is studied by using Langevin dynamics simulation. For given polymer length (N) and driving force (f), the polymer can be completely injected into the cavity only when the radius of the cavity is larger than a transition radius (R eC). The dependence of R eC on N and f can be described by a scaling relation R eC ∝ N 1 / 3 f −δ . The value of δ changes from 4/15 in the small f region to 1/6 in the moderate f region due to the screening of the excluded-volume interaction between monomers. We find the complete injection time (τ) decreases monotonously with increasing the cavity radius or decreasing the polymer length. The simulation results are in good agreement with the theoretical predictions from the free energy analysis and a simple kinetic model.

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.

Aggregation of a macromolecule in a nano cube

We model a macromolecule as an infinitely long Gaussian semi-flexible polymer chain and the conformations of the chain were realized in the nano cube using a cubic lattice. A modified version of the recursion relations is used to calculate the grand canonical partition function of the chain to investigate distinct thermo-dynamical properties of the nano polymer aggregate than corresponding bulk behaviour of the macromolecule. Our analytical estimates on the thermo-dynamical properties of the macromolecule clearly show that the nano aggregate of the polymer chain has interesting and distinct conformational statistics than its corresponding bulk state, and the method described in the present report can be easily extend to investigate the thermodynamics of the self-avoiding polymer chain in the nano dimensions.

Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants

Without Borel or Padé techniques, we show that for a divergent series with n! large-order growth factor, the set of hypergeometric series pFp-2 represents suitable approximants. The divergent pFp-2 series are then resummed via their representation in terms of the Meijer-G function. The choice of pFp-2 accelerates the convergence even with only weak-coupling information as input. For more acceleration of the convergence, we employ the strong-coupling and large-order information. We obtained a new constraint that relates the difference between the sum of the numerator and the sum of denominator parameters in the hypergeometric approximant to one of the large-order parameters. To test the validity of that constraint, we employed it to obtain the exact partition function of the zero-dimensional ϕ4 scalar field theory. The algorithm is also applied for the resummation of the ground state energies of ϕ0+14 and iϕ0+13 scalar field theories. We get accurate results for the whole coupling space and the precision is improved systematically in using higher orders. Precise results for the critical exponents of the O(4)-symmetric field model in three dimensions have been obtained from resummation of the recent six-loops order of the corresponding perturbation series. The recent seven-loops order for the β-function of the ϕ3+14 field theory has been resummed which shows non-existence of fixed points. The first resummation result of the seven-loop series representing the fractal dimension of the two-dimensional self-avoiding polymer is presented here where we get a very accurate value of df=1.3307 compared to its exact value (4/3≈1.3333).

Phase separation of polymer-bound particles induced by loop-mediated one dimensional effective long-range interactions

The cellular cytoplasm is organized into compartments. Phase separation is a simple manner to create membrane-less compartments in order to confine and localize particles like proteins. In many cases these particles are bound to fluctuating polymers like DNA or RNA. We propose a general theoretical framework for such polymer-bound particles and derive an effective 1D lattice gas model with both nearest-neighbor and emergent long-range interactions arising from looped configurations of the fluctuating polymer. We argue that 1D phase transitions exist in such systems for both Gaussian and self-avoiding polymers and, using a variational method that goes beyond mean-field theory, we obtain the complete mean occupation-temperature phase diagram. To illustrate this model we apply it to the biologically relevant case of ParABS, a prevalent bacterial DNA segregation system.

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.

Comment on “Osmotic pressure of compressed lattice knots”

In a recent paper, E. J. Janse van Rensburg has presented computational data enumerating the conformations of closed circular self-avoiding lattice polymers with knots confined in a cubic box, and claimed to have observed a negative osmotic pressure in the system. The purpose of this comment is to state that osmotic pressure by a self-avoiding polymer, knotted or otherwise, is positive, which means a polymer pushes confining walls outwards, and the statement of the opposite is a mistake.

Statistics of Quenched Defects Containing Semi-Flexible Polymer Chain Exact Results (II)

We describe method to discuss thermodynamics of a defected semi-flexible homo-polymer chain in the two and three dimensions using fully directed self-avoiding walk lattice model. The defects are located along a line and these defects are not in the thermal equilibrium with the monomers of the semi-flexible polymer chain; i. e. we consider the case of defected semi-flexible polymer chain in the present manuscript for the case of quenched defects. There are m defects on the conformations of the N monomers long semi-flexible polymer chain and we exactly count the number of Q realizations of the defected conformations of N-monomers long self-avoiding semi-flexible polymer chain; and thus we derive the exact expression of the free energy of the defected semi-flexible polymer chain for the finite length (i. e. using the fixed particle ensemble method); and we also derive exact expression of the partition function for the defected self-avoiding semi-flexible polymer chain in the thermodynamic limit using the grand canonical ensemble theory. The method described in this manuscript may be easily extended to another case of the defected polymer chain for isotropic/directed walk lattice models.

Sequence specificity despite intrinsic disorder: How a disease-associated Val/Met polymorphism rearranges tertiary interactions in a long disordered protein.

The role of electrostatic interactions and mutations that change charge states in intrinsically disordered proteins (IDPs) is well-established, but many disease-associated mutations in IDPs are charge-neutral. The Val66Met single nucleotide polymorphism (SNP) in precursor brain-derived neurotrophic factor (BDNF) is one of the earliest SNPs to be associated with neuropsychiatric disorders, and the underlying molecular mechanism is unknown. Here we report on over 250 μs of fully-atomistic, explicit solvent, temperature replica-exchange molecular dynamics (MD) simulations of the 91 residue BDNF prodomain, for both the V66 and M66 sequence. The simulations were able to correctly reproduce the location of both local and non-local secondary structure changes due to the Val66Met mutation, when compared with NMR spectroscopy. We find that the change in local structure is mediated via entropic and sequence specific effects. We developed a hierarchical sequence-based framework for analysis and conceptualization, which first identifies “blobs” of 4-15 residues representing local globular regions or linkers. We use this framework within a novel test for enrichment of higher-order (tertiary) structure in disordered proteins; the size and shape of each blob is extracted from MD simulation of the real protein (RP), and used to parameterize a self-avoiding heterogenous polymer (SAHP). The SAHP version of the BDNF prodomain suggested a protein segmented into three regions, with a central long, highly disordered polyampholyte linker separating two globular regions. This effective segmentation was also observed in full simulations of the RP, but the Val66Met substitution significantly increased interactions across the linker, as well as the number of participating residues. The Val66Met substitution replaces β-bridging between V66 and V94 (on either side of the linker) with specific side-chain interactions between M66 and M95. The protein backbone in the vicinity of M95 is then free to form β-bridges with residues 31-41 near the N-terminus, which condenses the protein. A significant role for Met/Met interactions is consistent with previously-observed non-local effects of the Val66Met SNP, as well as established interactions between the Met66 sequence and a Met-rich receptor that initiates neuronal growth cone retraction.

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.

Cross-linker mediated compaction and local morphologies in a model chromosome

Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.