Semiflexible Polymer Chains Research Articles

Phase behavior of semiflexible polymer chains

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10<or=N(b)<30. Both the density at which the IN transition occurs and the location of the gas-liquid coexistence go through a maximum with increasing N(b). For longer chains, behavior expected from theory is found and both of these coexisting densities decrease with increasing length.

Viscoelastic Behavior of a Single Semiflexible Polymer Chain

The dynamical response of a semiflexible polymer chain is studied based on the theory developed by Hallatschek et al. for the worm-like chain model. The linear viscoelastic response under oscillato...

Nonnative Protein Polymers: Structure, Morphology, and Relation to Nucleation and Growth

Thermally induced aggregates of α-chymotrypsinogen A and bovine granulocyte-colony stimulating factor in acidic solutions were characterized by a combination of static and dynamic light scattering, spectroscopy, transmission electron microscopy, and monomer loss kinetics. The resulting soluble, high-molecular weight aggregates (∼10 3–10 5 kDa) are linear, semiflexible polymer chains that do not appreciably associate with one another under the conditions at which they were formed, with classic power-law scaling of the radius of gyration and hydrodynamic radius with weight-average molecular weight ( M w). Aggregates in both systems are composed of nonnative monomers with elevated levels of β-sheet secondary structure, and bind thioflavine T. In general, the aggregate size distributions showed low polydispersity by light scattering. Together with the inverse scaling of M w with protein concentration, the results clearly indicate that aggregation proceeds via nucleated (chain) polymerization. For α-chymotrypsinogen A, the scaling behavior is combined with the kinetics of aggregation to deduce separate values for the characteristic timescales for nucleation ( τ n) and growth ( τ g), as well as the stoichiometry of the nucleus ( x). The analysis illustrates a general procedure to noninvasively and quantitatively determine τ n, τ g, and x for soluble (chain polymer) aggregates, as well as the relationship between τ n/ τ g and aggregate M w.

Forces and extensions in semiflexible and rigid polymer chains and filaments

We present a revised theoretical study of statistical properties of semiflexible filaments. Using a single auxiliary field and mean-field theory, we succeed in obtaining the exact analytical results for force–extension relations for a chain with arbitrary stiffness, and compare it with earlier theories and experiment. At a small persistence-to-contour length ratio, lp/L ≪ 1 the chain behaves classically, as an entropic spring. However, we find a critical value for L/lp ≈ 3.0 in 3D (or L/lp ≈ 5.4 in 2D) above which the restoring force of the chain becomes negative for the end-to-end distance (or ). That is, very stiff (or very short) chains and filaments resist an attempt to reduce their preferred end-to-end distance as much as to stretch it.

Monte Carlo simulation of polymer wrapping of nanotubes

We study the behavior of a dilute solution of semiflexible polymer chains near a weakly attractive cylindrical surface using Monte Carlo simulation. The competition between monomer–monomer interactions and adsorption energy on the one hand, and bending energy and entropic penalty of adsorption on the other, leads to ordered conformations of the chains around the tube. Above a critical cylinder radius, the chains are found to be fully adsorbed in a monolayer. The preferred adsorbed conformations under such conditions are single and multiple helices. Our findings may shed light on the experimentally observed ordered polymer wrapping of carbon nanotubes.

Functions of fenugreek gum with various molecular weights on the gelatinization and retrogradation behaviors of corn starch—1: Characterizations of fenugreek gum and investigations of corn starch/fenugreek gum composite system at a relatively high starch concentration; 15 w/v%

Gelatinization and retrogradation behaviors of corn starch were investigated in an aqueous system in the presence or absence of fenugreek gum with various molecular weights. Weight-average molecular weight M w of fenugreek gum samples ranged from 7.5×10 4 to 20.7×10 5 g/mol, whereas z-average root-mean-square radius of gyration R g ranged between 16.3 and 122.3 nm. The Flory exponent of 0.59 determined by the relationship between M w and R g and the Mark–Houwink–Sakurada exponent of 0.67 determined by the relationship between M w and intrinsic viscosity [ η] suggested semi-flexible polymer chains with some chain stiffness for the molecules of fenugreek gum. The addition of fenugreek gum (0.5 w/v%) increased peak viscosity of the composite system (15% starch) during gelatinization when C[ η] ( C: concentration of the gum) and the M w of the gum were larger than 2.38 and 87.0×10 4 g/mol, respectively. It rather shifted the onset of viscosity increase to higher temperatures without altering the endothermic enthalpy change during gelatinization detected by differential scanning calorimetry. The addition of fenugreek gum decreased the rate constant of the composite system, representing the relationship between rheological creep compliance and storage time at 4 °C for 14 days. This effect of the gum to inhibit the structural hardening of the composite system during long-term retrogradation (14-days time scale) was enhanced markedly when C[ η] and the M w of the gum were equal to or larger than 4.05 and 18.3×10 5 g/mol, respectively. These critical C[ η] and M w values for fenugreek gum were compared with corresponding data for guar gum, an alternative galactomannan with a different galactose/mannose ratio, and the functions of galactomannans were discussed on the gelatinization and retrogradation behaviors of corn starch in an aqueous system.

Role of Conformational Entropy in Force-Induced Biopolymer Unfolding

A statistical mechanical description of flexible and semiflexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a crossover length which increases linearly with the chain length. Below this crossover length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time sawtoothlike behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.

Surface-Induced Liquid Crystal Transitions of Wormlike Polymers Confined in a Narrow Slit. A Mean-Field Theory

On the basis of a mean-field treatment of semiflexible polymer chains, we analyze the structure of long wormlike polymers sterically confined between two parallel, structureless walls separated by a distance W. With the Onsager excluded-volume interaction between polymer segments, the system displays three phases, uniaxial, biaxial, and condensed, depending on the polymer density and W. We have also determined the induced attractive force acting on the walls, mediated by the Onsager excluded-volume interaction between polymer segments.

Memory of fluctuating Brownian dipolar chains

Nonmagnetic particles in suspension in a ferrofluid act as magnetic holes when an external magnetic field is exerted: They acquire an effective dipolar moment opposing the surrounding one, which induces dipolar magnetic interactions. For a large enough imposed field and particle size, the induced interactions dominate the thermal forces, dipolar chains form. At equilibrium, these chains fluctuate under the effect of brownian noise. When the imposed magnetic field is suddenly decreased, these chains roughen dynamically. We study the time and size scaling of these fluctuations and roughening, and the relationships between the equilibrium and out of equilibrium behavior. We compare the experimental data both to Brownian dynamics simulations, and to a simple theory of semiflexible polymer chains, a generalization of the Rouse model. The scaling behavior of the experiments agree with the predictions of both theory and simulations over 5 orders of magnitudes. The roughening follows three successive regimes: The root mean square width of the chain initially evolves as W approximately t1/2, then it enters a subdiffusive regime where W approximately t1/4 and eventually it saturates to a level W approximately N, where N is the number of particles in the chain. The exact prefactors as a function of the applied field, particle diameter, and temperature are also derived analytically. We also show that this phenomenon can be described equivalently as a non-Markovian diffusion process for a particle in an environment with memory effects. Within this framework, our system is shown to confirm the predictions of theories for anomalous diffusion in systems with memory.

Dynamics of Prestressed Semiflexible Polymer Chains as a Model of Cell Rheology

We report on a model of a prestressed nonlinear semiflexible polymer chain that links thermally driven dynamics to the creep behavior of living cells. Numerical simulations show that the chain's creep follows a power law with an exponent that decreases with increasing prestress. This is related to the propagation of free energy through the chain in response to stretching, where the propagation speed is regulated by the prestress via the chain's nonlinear elasticity. These results indicate that the main aspects of cell rheology are consistent with the dynamics of single polymer chains under tension.

Monte Carlo simulations of a semi-flexible polymer chain: a first glance

We present preliminary results for Monte Carlo simulations of a three dimensional semi-flexible polymer chain with continuous monomer positions. In these simulations, standard Metropolis Monte Carlo methods are used to examine the basic properties of the model, such as equilibration configurations, overall size, and transition temperatures.

Direct Calculation of the Tube Potential Confining Entangled Polymers

We directly compute, for the first time, a confining “tube” potential acting on a flexible or semiflexible polymer chain entangled with like chains using equilibrium molecular dynamics simulations and compare these results to the conventional tube diameter inferred from the plateau in the time-dependent relaxation modulus G(t) and to an apparent tube diameter inferred from the crossover time τe from t1/2 to t1/4 scaling in the time-dependent monomer diffusivity g2(t). We find that the “narrow” tube diameter obtained at the equilibration time τe, where the monomer first “feels” that it is in a tube, widens with time as the tube potential softens and develops a nonquadratic tail. Our results help explain why the value of the entanglement spacing inferred by measurements at time scale τe is only half the conventional value obtained by measurements of the plateau modulus in the vicinity of the Rouse time τR.

Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

We establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O3 nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter c = (W2l)(L2pi)2. We also discuss the stability of the toroid states and propose the low-energy effective Green's function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.

Forced-Unfolding and Force-Quench Refolding of RNA Hairpins

Nanomanipulation of individual RNA molecules, using laser optical tweezers, has made it possible to infer the major features of their energy landscape. Time-dependent mechanical unfolding trajectories, measured at a constant stretching force (fS) of simple RNA structures (hairpins and three-helix junctions) sandwiched between RNA/DNA hybrid handles show that they unfold in a reversible all-or-none manner. To provide a molecular interpretation of the experiments we use a general coarse-grained off-lattice Gō-like model, in which each nucleotide is represented using three interaction sites. Using the coarse-grained model we have explored forced-unfolding of RNA hairpin as a function of fS and the loading rate (rf). The simulations and theoretical analysis have been done both with and without the handles that are explicitly modeled by semiflexible polymer chains. The mechanisms and timescales for denaturation by temperature jump and mechanical unfolding are vastly different. The directed perturbation of the native state by fS results in a sequential unfolding of the hairpin starting from their ends, whereas thermal denaturation occurs stochastically. From the dependence of the unfolding rates on rf and fS we show that the position of the unfolding transition state is not a constant but moves dramatically as either rf or fS is changed. The transition-state movements are interpreted by adopting the Hammond postulate for forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to the two ends, show that the value of the unfolding force increases (especially at high pulling speeds) as the length of the handles increases. The pathways for refolding of RNA from stretched initial conformation, upon quenching fS to the quench force fQ, are highly heterogeneous. The refolding times, upon force-quench, are at least an order-of-magnitude greater than those obtained by temperature-quench. The long fQ-dependent refolding times starting from fully stretched states are analyzed using a model that accounts for the microscopic steps in the rate-limiting step, which involves the trans to gauche transitions of the dihedral angles in the GAAA tetraloop. The simulations with explicit molecular model for the handles show that the dynamics of force-quench refolding is strongly dependent on the interplay of their contour length and persistence length and the RNA persistence length. Using the generality of our results, we also make a number of precise experimentally testable predictions.

Conformational statistics of ribbonlike semiflexible polymer chains

The conformational statistics of ribbonlike polymers possessing bending and twist rigidity are considered on the basis of a lattice model of directed self-correlated walks. It was assumed that local properties of the ribbonlike chain are strongly anisotropic: bending is possible only in the plane of the ribbon (the orientation of this plane can vary due to twist). The generating function for the distribution of a chain segment that is non-Gaussian is constructed. It is shown that in the isotropic environment the twist degree of freedom has no effect on the state of such macromolecules as a whole, and the consideration of rigidity alone in bending results in correct statistical features of a polymer chain. This model is suitable in accounting for the twist degree of freedom in the system with broken rotary symmetry.

Influence of Surface Interactions on Folding and Forced Unbinding of Semiflexible Chains

We have investigated the folding and forced unbinding transitions of adsorbed semiflexible polymer chains using theory and simulations. These processes describe, at an elementary level, a number of biologically relevant phenomena that include adhesive interactions between proteins and tethering of receptors to cell walls. The binding interface is modeled as a solid surface, and the wormlike chain (WLC) is used for the semiflexible chain (SC). Using Langevin simulations, in the overdamped limit we examine the ordering kinetics of racquet-like and toroidal structures in the presence of an attractive interaction between the surface and the polymer chain. For a range of interactions, temperature, and the persistence length, l(p), we obtained the monomer density distribution, n(x), (x is the perpendicular distance of a tagged chain end from the surface) for all of the relevant morphologies. There is a single peak in n(x) inside the range of attractive forces, b, for chains in the extended conformations, whereas in racquet and toroidal structures there is an additional peak at x approximately b. The simulated results for n(x) are in good agreement with theory. The formation of toroids on the surface appears to be a first-order transition as evidenced by the bimodal distribution in n(x). The theoretical result underestimates the simulated n(x) for x << b and follows n(x) closely for x >/= b; the calculated density agrees exactly with n(x) in the range x << b. The chain-surface interaction is probed by subjecting the surface structures to a pulling force, f. The average extension, x( f), as a function of f exhibits a sigmoidal profile with sharp all-or-none transition at the unfolding force threshold f = f(c) which increases for more structured states. Simulated x(f) compare well with the theoretical predictions. The critical force, f(c), is a function of l(s)/l(c) for a fixed temperature, where l(c) and l(s) are the length scales that express the strength of the intramolecular and SC-surface attraction, respectively. For a fixed l(s), f(c) increases as l(p) decreases.

Statics and Dynamics of Polymer-Wrapped Colloids

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.

The Glass Transition Temperature of Polymer Melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.

Morphological variation in a toroid generated from a single polymer chain

A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the cross-sectional area and stiffness of the chain together with the surface energy, which characterizes the segmental interaction parameter. Changes in the thickness and outer/inner radius on a toroid are interpreted in terms of these parameters. Our theoretical expectation corresponds to the actual morphological changes in a single giant DNA molecule as observed by electron microscopy.

Excluded Volume Effects on Polymer Chains Confined to Spherical Surfaces

We present results from extensive Monte Carlo simulations of flexible and semiflexible excluded-volume polymer chains confined to impenetrable spherical surfaces. Our results are compared with the ...