Effect of Temperature and Capsid Tail on the Packing and Ejection of Viral DNA

We use a simulation technique based on molecular dynamics and stochastic rotation model to present the effect of temperature and capsid tail on the packaging and ejection processes of semiflexible polymers. We consider two types of solvents, a good solvent, where the polymer is neutral and repulsion interactions among its various sections are favored, and one where the polymer is charged, giving rise to extra electrostatic reaction. For tailless capsids, we find that packing a neutral polymer is slightly slower at higher temperatures whereas its ejection is slightly slower at lower temperatures. We find the same trend for a charged polymer but the effect is noticeably larger. At a high enough temperature, we notice that packing a charged polymer can be stopped. On the other hand, at fixed temperature and regardless whether the polymer is charged, packing is much easier for a capsid with a tail whereas ejection is much slower. The effect of including the tail on the dynamics of a charged polymer, in particular, is rather significant: more packing fraction is facilitated at higher temperatures due to more ordered polymer configuration inside the capsid. In contrast, during ejection the tail traps the last remaining beads for quite some time before allowing full ejection. We interpret these results in terms of entropic and electrostatic forces.     

Dynamics of Active Semiflexible Polymers

Active fluctuations, driven by processes that consume ATP, are prevalent in living cells and are mostly driven by different forms of molecular motors. Such motors often move and transmit forces along biopolymers, which in general can be treated as semiflexible chains. We present a theoretical analysis of the active (out of thermal equilibrium) fluctuation of semiflexible polymers, using both analytical and simulation methods. We find that enhanced diffusion, even superdiffusive, occurs in a well-defined temporal regime, defined by the thermal modes of the chain and the typical timescale of the activity. In addition, we find a dynamic resonance-like condition between the elastic modes of the chain and the duration of the active force, which leads to enhanced spatial correlation of local displacements. These results are in qualitative agreement with observations of cytoskeletal biopolymers, and were recently observed for the dynamics of chromatin in interphase cells. We therefore propose that the interplay between elasticity and activity is driving long-range correlations in our model system, and may also be manifest inside living cells.     

Dynamics of Active Semiflexible Polymers

Active fluctuations, driven by processes that consume ATP, are prevalent in living cells and are mostly driven by different forms of molecular motors. Such motors often move and transmit forces along biopolymers, which in general can be treated as semiflexible chains. We present a theoretical analysis of the active (out of thermal equilibrium) fluctuation of semiflexible polymers, using both analytical and simulation methods. We find that enhanced diffusion, even superdiffusive, occurs in a well-defined temporal regime, defined by the thermal modes of the chain and the typical timescale of the activity. In addition, we find a dynamic resonance-like condition between the elastic modes of the chain and the duration of the active force, which leads to enhanced spatial correlation of local displacements. These results are in qualitative agreement with observations of cytoskeletal biopolymers, and were recently observed for the dynamics of chromatin in interphase cells. We therefore propose that the interplay between elasticity and activity is driving long-range correlations in our model system, and may also be manifest inside living cells.     

Flexible polymer-induced condensation and bundle formation of DNA and F-actin filaments

A simple semi-empirical theory is developed for the ionic strength dependence of the flexible polymer-induced condensation of semiflexible polyelectrolytes such as DNA and F-actin filaments. Critical concentrations of flexible polymer needed for condensation are calculated by comparing the free energies of inserting the semiflexible polyelectrolytes in a solution of flexible polymers, respectively, in their free state, and in their condensed state. Predictions of the theory are compared to experimental data on the condensation of DNA and F-actin filaments induced by the flexible polymer poly(ethylene oxide). The theory also predicts that reentrant decollapse is possible at low ionic strength and high concentrations of flexible polymer, as observed for DNA.     

A Toy Model for the Generation of Homochirality during Polymerization

This article examines a toy model of polymerization which though artificial and unphysical has some interesting chiral features. Two key elements, enantiomeric cross inhibition and chiral feedback, are shown to lead to bifurcation, so that the end product can become homo-chiral. We find that the bifurcation is driven by the cross-inhibition but is not strongly dependant on its strength, which for perfect feedback fidelity mainly determines the time scale. We also find that bifurcation with a high degree of chiral polarization remains even when the fidelity of the chiral feedback is substantially less than unity. For small values of the feedback fidelity the polarization drops below unity and at a critical value falls sharply to zero in a `phase transition'. The value at which this happens depends on the cross-inhibition in a complex way. By comparing the behaviour of polymers differing only in their final length, N, we find that the bifurcation process is enhanced as N increases. The symmetry breaking which we find is clearly a particular manifestation of general bifurcation theory. In addition it has the specific interest that, at least in our model, long homochiral polymers are possible even in the presence of substantial enantiomeric cross-inhibition.     

Mechanical and structural properties of in vitro neurofilament hydrogels

Neurofilaments belong to the class of cytoskeletal intermediate filaments and are the predominant structural elements in axons. They are composed of a semiflexible backbone and highly charged anionic sidearms protruding from the surface of the filaments. Here, the rheology of in-vitro networks of neurofilaments purified from pig spinal cord was determined. The mechanical properties of these networks are qualitatively similar to other hydrogels of semiflexible polymers. The low-deformation storage modulus G'(omega) showed a concentration (c) dependence of G' approximately c (1.3) that is consistent with a model for semiflexible networks, but was also observed for polyelectrolyte brushes. A terminal relaxation was not observed in the frequency range investigated (0.007-5 Hz), supporting the notion that sidearms act as cross-links hindering slip between filaments on a time scale of many minutes. The mesh size distribution of the network was measured by analysis of Brownian motion of embedded beads. The concentration dependence of the mesh size follows the same power law behaviour as found for F-actin networks, but shows a significantly wider distribution attributable to the smaller persistence length of neurofilaments. The attractive interaction between filaments is increased by addition of Al(3+) ions resulting in a reduction of the linear response regime from strains bigger than 80% to less than 30%.     

Probe diffusion in aqueous poly(vinyl alcohol) solutions studied by fluorescence correlation spectroscopy

We report fluorescence correlation spectroscopy measurements of the translational diffusion coefficient of various probe particles in dilute and semidilute aqueous poly(vinyl alcohol) solutions. The range of sizes of the particles (fluorescent molecules, proteins, and polymers) was chosen to explore various length scales of the polymer solutions as defined by the polymer-polymer correlation length. For particles larger than the correlation length, we find that the diffusion coefficient, D, decreases exponentially with the polymer concentration. This can be explained by an exponential increase in the solution viscosity, consistent with the Stokes-Einstein equation. For probes on the order of the correlation length, the decrease of the diffusion coefficient cannot be accounted for by the Stokes-Einstein equation, but can be fit by a stretched exponential, D approximately exp(-alphacn), where we find n = 0.73-0.84 and alpha is related to the probe size. These results are in accord with a diffusion model of Langevin and Rondelez (Polymer 1978, 19, 1875), where these values of n indicate a good solvent quality.     

Energetics and dynamics of constrained actin filament bundling

The formation of filopodia-like bundles from a dendritic actin network has been observed to occur in vitro as a result of branching induced by Arp2/3 complex. We study both the energetics and dynamics of actin filament bundling in such a network to evaluate their relative importance in bundle formation processes. Our model considers two semiflexible actin filaments fixed at one end and free at the other, described using a normal-mode approximation. This model is studied by both Brownian dynamics and free-energy minimization methods. Remarkably, even short filaments can bundle at separations comparable to their lengths. In the dynamic simulations, we evaluate the time required for the filaments to interact and bind, and examine the dependence of this bundling time on the filament length, the distance between the filament bases, and the cross-linking energy. In most cases, bundling occurs in a second or less. Beyond a certain critical distance, we find that the bundling time increases very rapidly with increasing interfilament separation and/or decreasing filament length. For most of the cases we have studied, the energetics results for this critical distance are similar to those obtained from dynamics simulations run for 10 s, suggesting that beyond this timescale, energetics, rather than kinetic constraints, determine whether or not bundling occurs. Over a broad range of conditions, we find that the times required for bundling from a network are compatible with experimental observations.     

Multi-Platform Compatible Software for Analysis of Polymer Bending Mechanics

Cytoskeletal polymers play a fundamental role in the responses of cells to both external and internal stresses. Quantitative knowledge of the mechanical properties of those polymers is essential for developing predictive models of cell mechanics and mechano-sensing. Linear cytoskeletal polymers, such as actin filaments and microtubules, can grow to cellular length scales at which they behave as semiflexible polymers that undergo thermally-driven shape deformations. Bending deformations are often modeled using the wormlike chain model. A quantitative metric of a polymer''s resistance to bending is the persistence length, the fundamental parameter of that model. A polymer''s bending persistence length is extracted from its shape as visualized using various imaging techniques. However, the analysis methodologies required for determining the persistence length are often not readily within reach of most biological researchers or educators. Motivated by that limitation, we developed user-friendly, multi-platform compatible software to determine the bending persistence length from images of surface-adsorbed or freely fluctuating polymers. Three different types of analysis are available (cosine correlation, end-to-end and bending-mode analyses), allowing for rigorous cross-checking of analysis results. The software is freely available and we provide sample data of adsorbed and fluctuating filaments and expected analysis results for educational and tutorial purposes.     

Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.     

Use of molecularly imprinted polymers in a biotransformation process.

Molecularly imprinted polymers are highly stable and can be sterilised, making them ideal for use in biotransformation process. In this communication, we describe a novel application of molecularly imprinted polymers in an enzymatic reaction. The enzymatic condensation of Z-L-aspartic acid with L-phenylalanine methyl ester to give Z-L-Asp-L-Phe-OMe (Z-aspartame) was chosen as a model system to evaluate the applicability of using molecularly imprinted polymers to facilitate product formation. When the product-imprinted polymer is present, a considerable increase (40%) in product yield is obtained. Besides their use to enhance product yields, as demonstrated here, we suggest that imprinted polymers may also find use in the continuous removal of toxic compounds during biochemical reactions.     

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.     

Coarse-grained simulations of the salt dependence of the radius of gyration of polyelectrolytes as models for biomolecules in aqueous solution

The salt dependent radius of gyration of a polyelectrolyte in aqueous solution is calculated in an environment where the polyelectrolyte is surrounded by a permeable membrane that exchanges only solvent particles with the bulk. We obtain additionally the scaling exponent of the gyration radius as a function of the polymerization degree, and find that the polyelectrolyte retains a stretched conformation during the condensation and re-expansion process, indicating that these effects are of an electrostatic nature. The solvent quality is also shown to affect the polyelectrolyte conformation, especially for the poor solvent case. These results are obtained using a hybridized Monte Carlo technique with the coarse-grained, dissipative particle dynamics method with fluctuating number of solvent particles. The full range of the electrostatic interactions is included in the simulations, using the Ewald sum method, and the counterions and solvent molecules are included explicitly. In the complex systems mentioned above, the electrostatic interactions and the solvent quality play a key role in understanding phenomena that do not occur in uncharged systems. Our results are compared and validated with the behavior of some biomolecules under similar environments.     

Sequence effects on internal structure of droplets of associative polymers

Intrinsically disordered proteins (IDPs) can form liquid-like membraneless organelles, gels, and fibers in cells and in vitro. In this study, we propose a simple model of IDPs as associative polymers in poor solvent and explore the formation of transient liquid droplets and their transformation into solid-like aggregates. We use Langevin dynamics simulations of short polymers with two stickers placed symmetrically along their contour to study the effect of the primary sequence of these polymers on their organization inside condensed droplets. We observe that the shape, size, and number of sticker clusters inside the droplet change from a long cylindrical fiber to many compact clusters as one varies the location of stickers along the chain contour. Aging caused by the conversion of intramoleclular to intermolecular associations is observed in droplets of telechelic polymers but not for other sequences of associating polymers. The relevance of our results to condensates of IDPs is discussed.     

Crowding-induced membrane remodeling: Interplay of membrane tension,polymer density,architecture

The plasma membrane hosts a wide range of biomolecules, mainly proteins and carbohydrates, that mediate cellular interactions with its environment. The crowding of such biomolecules regulates cellular morphologies and cellular trafficking. Recent discoveries have shown that the structure and density of cell surface polymers and hence the signaling machinery change with the state of the cell, especially in cancer progression. The alterations in membrane-attached glycocalyx and glycosylation of proteins and lipids are common features of cancer cells. The overexpression of glycocalyx polymers, such as mucin and hyaluronan, strongly correlates with cancer metastasis. Here, we present a mesoscale biophysics-based model that accounts for the shape regulation of membranes by crowding of membrane-attached biopolymer-glycocalyx and actin networks. Our computational model is based on the dynamically triangulated Monte Carlo model for membranes and coarse-grained representations of polymer chains. The model allows us to investigate the crowding-induced shape transformations in cell membranes in a tension- and graft polymer density-dependent manner. Our results show that the number of membrane protrusions and their shape depend on membrane tension, with higher membrane tension inducing more tubular protrusions than the vesicular shapes formed at low tension at high surface coverage of polymers. The shape transformations occur above the threshold density predicted by the polymer brush theory, but this threshold also depends on the membrane tension. Increasing the size of the polymer, either by changing the length or by adding side chains, is shown to increase the crowding-induced curvature. The effect of crowding is more prominent for flexible polymers than for semiflexible rigid polymers. We also present an extension of the model that incorporates properties of the actin-like filament networks and demonstrate how tubular structures can be generated by biopolymer crowding on the cytosolic side of cell membranes.     

Polymer chain length effects on fibroblast attachment on nylon-3-modified surfaces

Nylon-3 polymers have a polyamide backbone reminiscent of that found in proteins (β- vs α-amino acid residues, respectively), which makes these materials interesting for biological applications. Because of the versatility of the ring-opening polymerization process and the variety of β-lactam starting materials available, the structure of nylon-3 copolymers is highly amenable to alteration. A previous study showed that relatively subtle changes in the structure or ratio of hydrophobic and cationic subunits that comprise these polymers can result in significant changes in the ability of nylon-3-bearing surfaces to support cell adhesion and spreading. In the present study, we have exploited the highly tailorable nature of these polymers to synthesize new versions possessing a wide range of chain lengths, with the intent of optimizing these materials for use as cell-supportive substrates. We find that longer nylon-3 chains lead to better fibroblast attachment on modified surfaces and that at the optimal chain lengths less hydrophobic subunits are superior. The best polymers we identified are comparable to an RGD-containing peptide in supporting fibroblast attachment. The results described here will help to focus future efforts aimed at refining nylon-3 copolymer substrates for specific tissue engineering applications.     

A comparison of DMPC- and DLPE-based lipid bilayers.

A 250 ps molecular dynamics simulation of the dimyristoylphosphatidylcholine (DMPC)-based lipid bilayer, including explicit water molecules, is reported. The solvent environment of the head groups and other structural properties of the bilayer have been analyzed and compared with experimental results as well as our previous simulation of the dilauroylphosphatidylethanolamine (DLPE)-based bilayer. From this comparison we find that the solvent structure around the DMPC head group (clathrate shell) is significantly different than that around the DLPE head group (typical hydrogen bonding interactions). We have modeled the probable relationship between the different solvent environments around the R-N(CH3)3+ (DMPC) and R-NH3+ (DLPE) head groups and the different interlammelar distances in these systems by performing potential of mean force (PMF) simulations on two N(CH3)4+ and NH4+ ions in water. From the PMF simulations it appears that the differences in the hydration of the DMPC and DLPE head groups is not responsible for the differences in the hydration force observed for these systems. We also find that the orientational polarization of DLPE and DMPC is similar, which suggests that solvent polarization is not responsible for the differences in the hydration repulsion behavior observed in these systems. We also examined the order parameters for DMPC and found them to be in reasonable agreement with experiment. Given the different characteristics of the DLPE and DMPC head groups, we suggest an explanation of the differences in the interlammellar spacings of bilayers composed of these like-charged lipids. From our DLPE simulations we find that the R-NH3+ head groups can interact with the nonesterified oxygens of the phosphate group in an intraleaflet or an interleaflet manner. For the latter a "cross link" between two leaflets can be formed, which causes a stabilization of the interlamellar spacings at fairly short distances. Moreover, due to the strong intraleaflet interaction we find that the DLPE interface is relatively "flat" (as opposed to DMPC-based bilayers), which results in a surface that has regions of positive and negative charge that reside in the same plane along the bilayer normal. Based on this we propose that the DLPE bilayer interface can correlate itself with another DLPE interface by alignment of the regions of positive (or negative) charge on one leaflet with the opposite charges on the opposing leaflet.     

Viscoelastic behavior of fractionated ovine submaxillary mucins.

Solution properties of fractionated ovine submaxillary mucin (OSM) and asialo OSM (aOSM) in aqueous guanidine hydrochloride have been investigated using light scattering and rheological methods. For the first time we present viscometric evidence in both dilute and concentrated solution that the molecular structure of OSM is that of a wormlike chain. The intrinsic viscosity shows molecular weight dependence consistent with the linear extended chain conformation observed by light scattering measurements. The viscoelastic behavior of the OSM fractions in aqueous guanidine hydrochloride was further examined above the overlap concentration as a function of molecular weight and temperature. Under these solvent conditions in which the role of nonbonding intermolecular interactions is minimized, OSM shows predominantly fluid like behavior. However, high molecular weight OSM shows evidence of the existence of an entanglement network at high concentration. The frequency-dependent shear storage and loss moduli at all concentrations and molecular weights can be scaled to yield a master curve by incorporating typical viscoelastic shift parameters. The entanglement molecular weight and concentration are consistent with literature data for extended, semiflexible wormlike chains. The behavior of aOSM is similar to that of intact OSM at comparable degrees of coil overlap, indicating that the terminal sialic acid residue on the carbohydrate side chain has no effect on the rheology of concentrated OSM solutions beyond that due to an increase in the hydrodynamic volume.     

α-Actinin and fimbrin cooperate with myosin II to organize actomyosin bundles during contractile-ring assembly

The actomyosin contractile ring assembles through the condensation of a broad band of nodes that forms at the cell equator in fission yeast cytokinesis. The condensation process depends on actin filaments that interconnect nodes. By mutating or titrating actin cross-linkers α-actinin Ain1 and fimbrin Fim1 in live cells, we reveal that both proteins are involved in node condensation. Ain1 and Fim1 stabilize the actin cytoskeleton and modulate node movement, which prevents nodes and linear structures from aggregating into clumps and allows normal ring formation. Our computer simulations modeling actin filaments as semiflexible polymers reproduce the experimental observations and provide a model of how actin cross-linkers work with other proteins to regulate actin-filament orientations inside actin bundles and organize the actin network. As predicted by the simulations, doubling myosin II Myo2 level rescues the node condensation defects caused by Ain1 overexpression. Taken together, our work supports a cooperative process of ring self-organization driven by the interaction between actin filaments and myosin II, which is progressively stabilized by the cross-linking proteins.