Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media

Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.

Nonequilibrium free energy during polymer chain growth

During fast diffusion-influenced polymerization, nonequilibrium behavior of the polymer chains and the surrounding reactive monomers has been reported recently. Based on the laws of thermodynamics, the emerging nonequilibrium structures should be characterizable by some “extra free energy” (excess over the equilibrium Helmholtz free energy). Here, we study the nonequilibrium thermodynamics of chain-growth polymerization of ideal chains in a dispersion of free reactive monomers, using off-lattice, reactive Brownian dynamics computer simulations in conjunction with approximative statistical mechanics and relative entropy (Gibbs–Shannon and Kullback–Leibler) concepts. In the case of fast growing polymers, we indeed report increased nonequilibrium free energies Δ Fneq of several kB T compared to equilibrium and near-equilibrium, slowly growing chains. Interestingly, Δ Fneq is a non-monotonic function of the degree of polymerization and thus also of time. Our decomposition of the thermodynamic contributions shows that the initial dominant extra free energy is stored in the nonequilibrium inhomogeneous density profiles of the free monomer gas (showing density depletion and wakes) in the vicinity of the active center at the propagating polymer end. At later stages of the polymerization process, we report significant extra contributions stored in the nonequilibrium polymer conformations. Finally, our study implies a nontrivial relaxation kinetics and “restoring” of the extra free energy during the equilibration process after polymerization.

The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions

We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.

Temperature Dependence of Internal Friction of Peptides

Internal friction is a valuable concept to describe the kinetics of proteins. As is well known, internal friction can be modulated by solvent features (such as viscosity). How can internal friction be affected by environmental temperature? The answer to this question is not evident. In the present work, we approach this problem with simulations on two model peptides. The thermodynamics and relaxation kinetics are characterized through long molecular dynamics simulations, with the viscosity modulated by varying the mass of solvent molecules. Based on the extrapolation to zero viscosity together with scaling of the relaxation time scales, we discover that internal friction is almost invariant at various temperatures. Controlled simulations further support the idea that internal friction is independent of environmental temperature. Comparisons between the two model peptides help us to understand the diverse phenomena in experiments.

Mapping a single-molecule folding process onto a topological space

Physics of protein folding has been dominated by conceptual frameworks including the nucleation-propagation mechanism and the diffusion-collision model, and none address the topological properties of a chain during a folding process. Single-molecule interrogation of folded biomolecules has enabled real-time monitoring of folding processes at an unprecedented resolution. Despite these advances, the topology landscape has not been fully mapped for any chain. Using a novel circuit topology approach, we map the topology landscape of a model polymeric chain. Inspired by single-molecule mechanical interrogation studies, we restrained the ends of a chain and followed fold nucleation dynamics. We find that, before the nucleation, transient local entropic loops dominate. Although the nucleation length of globules is dependent on the cohesive interaction, the ultimate topological states of the collapsed polymer are largely independent of the interaction but depend on the speed of the folding process. After the nucleation, transient topological rearrangements are observed that converge to a steady-state, where the fold grows in a self-similar manner.

Atypical effects of incorporated surfactants on stability and dissolution properties of amorphous polymeric dispersions

OBJECTIVES

To understand the impact of ionic and non-ionic surfactants on the dissolution and stability properties of amorphous polymeric dispersions using griseofulvin (GF) as a model for poorly soluble drugs.

METHODS

Solid dispersions of the poorly water-soluble drug, griseofulvin (GF) and the polymers, poly(vinylpyrrolidone) (PVP) and poly(2-hydroxypropyl methacrylate) (PHPMA), have been prepared by spray drying and bead milling and the effect of the ionic and non-ionic surfactants, namely sodium dodecyl sulphate (SDS) and Tween-80, on the physico-chemical properties of the solid dispersions studied.

KEY FINDINGS

The X-ray powder diffraction data and hot-stage microscopy showed a fast re-crystallisation of GF. While dynamic vapour sorption (DVS) measurements indicated an increased water uptake, slow dissolution rates were observed for the solid dispersions incorporating surfactants. The order by which surfactants free dispersions were prepared seemed critical as indicated by DVS and thermal analysis. Dispersions prepared by milling with SDS showed significantly better stability than spray-dried dispersions (drug remained amorphous for more than 6 months) as well as improved dissolution profile.

CONCLUSIONS

We suggest that surfactants can hinder the dissolution by promoting aggregation of polymeric chains, however that effect depends mainly on how the particles were prepared.

Internal tension in a collapsed polymer under shear flow and the connection to enzymatic cleavage of von Willebrand factor

By means of Brownian hydrodynamics simulations we show that the tension distribution along the contour of a single collapsed polymer in shear flow is inhomogeneous and above a threshold shear rate exhibits a double-peak structure when hydrodynamic interactions are taken into account. We argue that the tension maxima close to the termini of the polymer chain reflect the presence of polymeric protrusions. We establish the connection to shear-induced globule unfolding and determine the scaling behavior of the maximal tensile forces and the average protrusion length as a function of shear rate, globule size, and cohesive strength. A quasi-equilibrium theory is employed in order to describe the simulation results. Our results are used to explain experimental data for the shear-sensitive enzymatic degradation of von Willebrand factor.

How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory

It is currently the consensus belief that protective osmolytes such as trimethylamine N-oxide (TMAO) favor protein folding by being excluded from the vicinity of a protein, whereas denaturing osmolytes such as urea lead to protein unfolding by strongly binding to the surface. Despite there being consensus on how TMAO and urea affect proteins as a whole, very little is known as to their effects on the individual mechanisms responsible for protein structure formation, especially hydrophobic association. In the present study, we use single-molecule atomic force microscopy and molecular dynamics simulations to investigate the effects of TMAO and urea on the unfolding of the hydrophobic homopolymer polystyrene. Incorporated with interfacial energy measurements, our results show that TMAO and urea act on polystyrene as a protectant and a denaturant, respectively, while complying with Tanford-Wyman preferential binding theory. We provide a molecular explanation suggesting that TMAO molecules have a greater thermodynamic binding affinity with the collapsed conformation of polystyrene than with the extended conformation, while the reverse is true for urea molecules. Results presented here from both experiment and simulation are in line with earlier predictions on a model Lennard-Jones polymer while also demonstrating the distinction in the mechanism of osmolyte action between protein and hydrophobic polymer. This marks, to our knowledge, the first experimental observation of TMAO-induced hydrophobic collapse in a ternary aqueous system.

Shear-enhanced adsorption of a homopolymeric globule mediated by surface catch bonds

The adsorption of a single collapsed homopolymer onto a planar smooth surface in shear flow is investigated by means of Brownian hydrodynamics simulation. While cohesive intra-polymer forces are modeled by Lennard-Jones potentials, surface-monomer interactions are described by stochastic bonds whose two-state kinetics is characterized by three parameters: bond formation rate, bond dissociation rate and an effective catch bond parameter that describes how the force acting on a surface-monomer bond influences the dissociation rate. We construct adsorption state diagrams as a function of shear rate and all three surface-monomer bond parameters. We find shear-induced adsorption in a small range of parameters for low dissociation and association rates and only when the surface-monomer bond is near the transition between slip and catch bond behavior. By mapping on a simple surface-monomer interaction model with conservative pair potentials we try to estimate the conservative potential parameters necessary to observe shear-induced surface adsorption phenomena.

Confinement-dependent friction in peptide bundles

Friction within globular proteins or between adhering macromolecules crucially determines the kinetics of protein folding, the formation, and the relaxation of self-assembled molecular systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation number is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coefficient per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.