Collective hydrogen-bond rearrangement dynamics in liquid water.

We investigate barrier-crossing processes corresponding to collective hydrogen-bond rearrangements in liquid water using Markov state modeling techniques. The analysis is based on trajectories from classical molecular dynamics simulations and accounts for the full dynamics of relative angular and separation coordinates of water clusters and requires no predefined hydrogen bond criterium. We account for the complete 12-dimensional conformational subspace of three water molecules and distinguish five well-separated slow dynamic processes with relaxation times in the picosecond range, followed by a quasi-continuum spectrum of faster modes. By analysis of the Markov eigenstates, these processes are shown to correspond to different collective interchanges of hydrogen-bond donors and acceptors. Using a projection onto hydrogen-bond states, we also analyze the switching of one hydrogen bond between two acceptor water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along alternative routes that involve different intermediate states with short-lived alternative hydrogen bonds or weakly bound states.

Nanoscale Structure of the Oil-Water Interface.

X-ray reflectivity (XR) and atomistic molecular dynamics (MD) simulations, carried out to determine the structure of the oil-water interface, provide new insight into the simplest liquid-liquid interface. For several oils (hexane, dodecane, and hexadecane) the XR shows very good agreement with a monotonic interface-normal electron density profile (EDP) broadened only by capillary waves. Similar agreement is also found for an EDP including a sub-Å thick electron depletion layer separating the oil and the water. The XR and MD derived depletions are much smaller than reported for the interface between solid-supported hydrophobic monolayers and water.

Unfolding and folding internal friction of ß-hairpins is smaller than that of α-helices.

By the forced unfolding of polyglutamine and polyalanine homopeptides in competing α-helix and ß-hairpin secondary structures, we disentangle equilibrium free energetics from nonequilibrium dissipative effects. We find that α-helices are characterized by larger friction or dissipation upon unfolding, regardless of whether they are free energetically preferred over ß-hairpins or not. Our analysis, based on MD simulations for atomistic peptide models with explicit water, suggests that this difference is related to the internal friction and mostly caused by the different number of intrapeptide hydrogen bonds in the α-helix and ß-hairpin states.

Reentrant melting of RNA with quenched sequence randomness.

The effect of quenched sequence disorder on the thermodynamics of RNA secondary structure formation is investigated for two- and four-letter alphabet models using the constrained annealing approach, from which the temperature behavior of the free energy, specific heat, and helicity is analytically obtained. For competing base pairing energies, the calculations reveal reentrant melting at low temperatures, in excellent agreement with numerical results. Our results suggest an additional mechanism for the experimental phenomenon of RNA cold denaturation.

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

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: implications for DNA hybridization.

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy -c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low-temperature/low-force compact (folded) structure and a high-temperature/high-force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c ≲ 2.479 a melting transition is possible; for c ≤ 2 the chain is always in the folded phase and for 2.479 ≲ c always in the unfolded phase. A force-induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single-molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double-stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ≈ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent [Formula: see text], which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.

Micro-rheology on (polymer-grafted) colloids using optical tweezers.

Optical tweezers are experimental tools with extraordinary resolution in positioning (± 1 nm) a micron-sized colloid and in the measurement of forces (± 50 fN) acting on it-without any mechanical contact. This enables one to carry out a multitude of novel experiments in nano- and microfluidics, of which the following will be presented in this review: (i) forces within single pairs of colloids in media of varying concentration and valency of the surrounding ionic solution, (ii) measurements of the electrophoretic mobility of single colloids in different solvents (concentration, valency of the ionic solution and pH), (iii) similar experiments as in (i) with DNA-grafted colloids, (iv) the nonlinear response of single DNA-grafted colloids in shear flow and (v) the drag force on single colloids pulled through a polymer solution. The experiments will be described in detail and their analysis discussed.

Viscous compressible hydrodynamics at planes, spheres and cylinders with finite surface slip.

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency omega approximately c2rho0/eta, with c the speed of sound, rho0 the fluid density and eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.

How the diffusivity profile reduces the arbitrariness of protein folding free energies.

The concept of a protein diffusing in its free-energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free-energy profiles for different RCs exhibit significant variations, some having an activation barrier, while others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free-energy and diffusivity effects into a single function, the rescaled free-energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.

Single flexible and semiflexible polymers at high shear: non-monotonic and non-universal stretching response.

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [Formula: see text] is only observed for low shear [Formula: see text] < [Formula: see text] , where [Formula: see text] is the shear rate at maximum polymer extension. For intermediate shear rates [Formula: see text] < [Formula: see text] < [Formula: see text] the radius of gyration decreases with increasing shear with minimum chain extension at [Formula: see text] . For even higher shear [Formula: see text] < [Formula: see text] the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [Formula: see text] approximately N (-1.4) and [Formula: see text] approximately N (0.7) as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [Formula: see text] [Formula: see text] anymore, where [Formula: see text] is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [Formula: see text] to reach the compression regime is experimentally realizable.

Ion specific correlations in bulk and at biointerfaces.

Ion specific effects are ubiquitous in any complex colloidal or biological fluid in bulk or at interfaces. The molecular origins of these 'Hofmeister effects' are not well understood and their theoretical description poses a formidable challenge to the modeling and simulation community. On the basis of the combination of atomistically resolved molecular dynamics (MD) computer simulations and statistical mechanics approaches, we present a few selected examples of specific electrolyte effects in bulk, at simple neutral and charged interfaces, and on a short α-helical peptide. The structural complexity in these strongly Coulomb-correlated systems is highlighted and analyzed in the light of available experimental data. While in general the comparison of MD simulations to experiments often lacks quantitative agreement, mostly because molecular force fields and coarse-graining procedures remain to be optimized, the consensus as regards trends provides important insights into microscopic hydration and binding mechanisms.

Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces.

The hydrophobic effect, i.e., the poor solvation of nonpolar parts of molecules, plays a key role in protein folding and more generally for molecular self-assembly and aggregation in aqueous media. The perturbation of the water structure accounts for many aspects of protein hydrophobicity. However, to what extent the dispersion interaction between molecular entities themselves contributes has remained unclear. This is so because in peptide folding interactions and structural changes occur on all length scales and make disentangling various contributions impossible. We address this issue both experimentally and theoretically by looking at the force necessary to peel a mildly hydrophobic single peptide molecule from a flat hydrophobic diamond surface in the presence of water. This setup avoids problems caused by bubble adsorption, cavitation, and slow equilibration that complicate the much-studied geometry with two macroscopic surfaces. Using atomic-force spectroscopy, we determine the mean desorption force of a single spider-silk peptide chain as F = 58 +/- 8 pN, which corresponds to a desorption free energy of approximately 5 k(B)T per amino acid. Our all-atomistic molecular dynamics simulation including explicit water correspondingly yields the desorption force F = 54 +/- 15 pN. This observation demonstrates that standard nonpolarizable force fields used in classical simulations are capable of resolving the fine details of the hydrophobic attraction of peptides. The analysis of the involved energetics shows that water-structure effects and dispersive interactions give contributions of comparable magnitude that largely cancel out. It follows that the correct modeling of peptide hydrophobicity must take the intimate coupling of solvation and dispersive effects into account.

Specific ion adsorption and surface forces in colloid science.

Mean-field theories that include nonelectrostatic interactions acting on ions near interfaces have been found to accommodate many experimentally observed ion specific effects. However, it is clear that this approach does not fully account for the liquid molecular structure and hydration effects. This is now improved by using parametrized ionic potentials deduced from recent nonprimitive model molecular dynamics (MD) simulations in a generalized Poisson-Boltzmann equation. We investigate how ion distributions and double layer forces depend on the choice of background salt. There is a strong ion specific double layer force set up due to unequal ion specific short-range potentials acting between ions and surfaces.

Shear-induced unfolding triggers adhesion of von Willebrand factor fibers.

von Willebrand factor (VWF), a protein present in our circulatory system, is necessary to stop bleeding under high shear-stress conditions as found in small blood vessels. The results presented here help unravel how an increase in hydrodynamic shear stress activates VWF's adhesion potential, leading to the counterintuitive phenomena of enhanced adsorption rate under strong shear conditions. Using a microfluidic device, we were able to mimic a wide range of bloodflow conditions and directly visualize the conformational dynamics of this protein under shear flow. In particular, we find that VWF displays a reversible globule-stretch transition at a critical shear rate gamma(crit) in the absence of any adsorbing surface. Computer simulations reproduce this sharp transition and identify the large size of VWF's repeating units as one of the keys for this unique hydrodynamic activation. In the presence of an adsorbing collagen substrate, we find a large increase in the protein adsorption at the same critical shear rate, suggesting that the globule unfolding in bulk triggers the surface adsorption in the case of a collagen substrate, which provides a sufficient density of binding sites. Monitoring the adsorption process of multiple VWF fibers, we were able to follow the formation of an immobilized network that constitutes a "sticky" grid necessary for blood platelet adhesion under high shear flow. Because areas of high shear stress coincide with a higher chance for vessel wall damage by mechanical forces, we identified the shear-induced increase in the binding probability of VWF as an effective self-regulating repair mechanism of our microvascular system.

Surfaces with quenched and annealed disordered charge distributions.

We consider surfaces with disordered charge distribution. The disorder can be caused by mobile charges, as for example in mixed lipid bilayers, or by weakly charged surfaces where charge regulation takes place (e.g. carboxyl groups). Using Monte-Carlo simulation methods we find for quenched as well as annealed disordered charge distributions counterion densities close to the surface that are significantly larger than for ordered regularly spaced surface ions. Our field-theoretic results agree well with results obtained from Monte-Carlo simulations of the system. Furthermore, we obtain expressions for the effective interaction between charged colloids and charged rods close to a charged surface and discuss the effect of the surface-ion mobility and polarization charges on the interaction. In general, polarization effects as well as surface-ion mobility lead to a weakening of the effective interaction between charged objects.

Density depletion at solid-liquid interfaces: a neutron reflectivity study.

Neutron reflectivity experiments conducted on self-assembled monolayers (SAMs) against polar (water) and nonpolar (organic) liquid phases reveal further evidence for a density reduction at hydrophobic-hydrophilic interfaces. The density depletion is found at the interface between hydrophobic dodecanethiol (C12) and hexadecanethiol (C16) SAMs and water and also between hydrophilic SAMs (C12/C11OH) and nonpolar fluids. The results show that the density deficit of a fluid in the boundary layer is not unique to aqueous solid-liquid interfaces but is more general and correlated with the affinity of the liquid to the solid surface. In water the variation of pH has only minor influence, while different electrolytes taken from the Hofmeister series seem to increase the depletion. On hydrophobic SAMs an increase in density depletion with temperature was observed, in agreement with Monte Carlo simulations performed on corresponding model systems. The increase in the water density depletion layer is governed by two effects: the surface energy difference between water and the substrate and the chemical potential of the aqueous phase.

Shear-flow-induced unfolding of polymeric globules.

The behavior of a single collapsed polymer under shear flow is examined using hydrodynamic simulations and scaling arguments. Below a threshold shear rate gamma[.]{*}, the chain remains collapsed and only deforms slightly, while above gamma[.]{*} the globule exhibits unfolding/refolding cycles. Hydrodynamics are crucial: In the free draining case, gamma[.]{*} scales with the globule radius R as gamma[.]{*} approximately R{-1}, while in the presence of hydrodynamic interactions gamma[.]{*} approximately R. Experiments on the globular von Willebrand protein confirm the presence of an unfolding transition at a well-defined critical shear rate.

Probing surfaces with single-polymer atomic force microscope experiments.

In the past 15 years atomic force microscope (AFM) based force spectroscopy has become a versatile tool to study inter- and intramolecular interactions of single polymer molecules. Irreversible coupling of polymer molecules between the tip of an AFM cantilever and the substrate allows one to study the stretching response up to the high force regime of several nN. For polymers that glide or slip laterally over the surface with negligible friction, on the other hand, the measured force profiles exhibit plateaus which allow one to extract the polymer adsorption energies. Long-term stable polymer coatings of the AFM tips allow for the possibility of repeating desorption experiments from solid supports with individual molecules many times, yielding good sampling statistics and thus reliable estimates for adsorption energies. In combination with recent advances in theoretical modeling, a detailed picture of the conformational statistics, backbone elasticity, and the adsorption characteristics of single polymer molecules is obtained.

Structural investigations of DNA-polycation complexes.

The internal structure of DNA-polycation complexes is investigated by synchrotron small-angle X-ray scattering (SAXS). Hexagonal packing of DNA is observed for DNA complexed with poly-L-lysine (PL), poly-L-arginine (PA), spermine (Sp), and linear and branched polyethyleneimine (lPEI and bPEI, respectively). Variations in the internal spacings and degree of long-range ordering are dependent on both polycation type and concentration of added salt. With increasing concentration of monovalent salt, a discontinuous phase transition is observed from compact to loose bundles and finally to an isotropic network phase. This salt-induced melting transition was found to be universal for all polyplexes studied and is in quantitative agreement with a simple free energy model based solely on electrostatic and entropic contributions. Using the osmotic stress method, bulk modulus (K) is measured for PL-DNA and PA-DNA polyplexes at various salt concentrations. With increasing osmotic force, we show that the salt-induced melting transition is shifted and compression in the loose bundle regime is in qualitative agreement with our model.