Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-microm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol(-1) K(-1), very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.

Sickle-cell haemoglobin polymerization: is it the primary pathogenic event of sickle-cell anaemia?

Sickle cell anaemia is associated with a mutant haemoglobin, HbS, which forms polymers in the red blood cells of patients. The primary role of the HbS polymerization for the pathophysiology has been questioned: observations in patients and model organisms contradict deterministic scenarios of sickling crises triggered by polymerization. However, results with knock-out sickle-cell mice, which were cured by delaying HbS polymerization, reconfirm polymerization's primary role. To reconcile the contradictory observations, this article reviews recent findings on two steps in polymerization: homogeneous nucleation of fibres, and their growth. The fibre growth is faster by far than for any other protein ordered structure. This is due to a negligible free-energy barrier for incorporation into a fibre, determined by an entropy gain, stemming from the release of water molecules structured around HbS. The kinetics of fibre nucleation have shown that the formation of the polymer nucleus is preceded by a metastable droplet of a dense liquid. The properties of the dense liquid are sensitive functions of solution composition, including components in micro- and nanomolar amounts. This mechanism allows low-concentration solution components to strongly affect the nucleation kinetics, accounting for the high variability of the disease. These insights can potentially be utilized for control of HbS polymerization and treatment of the disease.

Dynamics of Water in the Hydration Shells of C60: Molecular Dynamics Simulation Using a Coarse-Grained Model

Dynamics of water in the solvation shells of a fullerene molecule as obtained from a coarse-grained (CG) model for the C60-water interaction has been presented and compared with the same obtained from the atomistic model. While in the CG model the interaction between a fullerene and a water has been represented by a simple two-body central potential as obtained from a coarse-graining of the interactions of a C60 molecule with water, in the atomistic description all the interactions between the atoms of a C60 and a water molecule have been explicitly taken into account. Extensive molecular dynamics simulations of a C60 molecule in water have been performed in isothermal-isobaric ensembles. Translational and reorientational mobilities as well as residence time of water in the solvation shells of a fullerene molecule have been obtained by calculating the corresponding time correlation functions from simulation trajectories. Comparison of the dynamical behaviors obtained from the CG and the atomistic models shows overall good agreement. The nature of the relaxation and the trend that the dynamics becomes slower with the decreasing solute-water distance as obtained from the atomistic model have, in general, been reproduced by the CG model.

Methodology for the Calculation of the Potential of Mean Force for a Cation–π Complex in Water

We report potential of mean force (PMF) calculations on the interaction between the p-sulfonatocalix[4]arene and a monovalent cation (Cs(+)). It has been recently shown from microcalorimetry and (133)Cs NMR experiments that the association with Cs(+) is governed by favourable cation-pi interactions and is characterized by the insertion of the cation into the cavity of the macrocycle. We show that the PMF calculation based upon a classical model is not able to reproduce both the thermodynamic properties of association and the insertion of the cation. In order to take into account the different contributions of the cation-pi interactions, we develop a new methodology consisting of changing the standard PMF by an additional contribution resulting from quantum calculations. The calculated thermodynamic properties of association are thus in line with the microcalorimetry and (133)Cs NMR experiments and the structure of the complex at the Gibbs free-energy minimum shows the insertion of the cation into the cavity of the calixarene.

Hydrophobic association of alpha-helices, steric dewetting, and enthalpic barriers to protein folding

Efficient protein folding implies a microscopic funnel-like multidimensional free-energy landscape. Macroscopically, conformational entropy reduction can manifest itself as part of an empirical barrier in the traditional view of folding, but experiments show that such barriers can also entail significant unfavorable enthalpy changes. This observation raises the puzzling possibility, irrespective of conformational entropy, that individual microscopic folding trajectories may encounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate how nanoscale hydrophobic interactions might underpin this salient enthalpic effect in biomolecular assembly by computer simulations of the association of two preformed polyalanine or polyleucine helices in water. We observe a high, positive enthalpic signature at room temperature when the helix separation is less than a single layer of water molecules. Remarkably, this unfavorable enthalpy change, with a parallel increase in void volume, is largely compensated for by a concomitant increase in solvent entropy, netting only a small or nonexistent microscopic free-energy barrier. Thus, our findings suggest that high enthalpic folding barriers can be consistent with a funnel picture of folding and are mainly a desolvation phenomenon indicative of a cooperative mechanism of simultaneous formation of multiple side-chain contacts at the rate-limiting step.

The dewetting transition and the hydrophobic effect

A molecular-level description of the behavior of water in hydrophobic spaces is presented in terms of the coupled effects of solute size and atomic solute-solvent interactions. For model solutes with surface areas near those of protein contacts, we identify three different regions of solute-water interaction to be associated with three distinctly different structural characteristics of water in the intersolute region: dry, oscillating, and wet. A first orderlike phase transition is confirmed from the wet to dry state bridged by a narrow region with liquid-vapor oscillations in the intersolute region as the strength of the solute-water attractive dispersion interaction decreases. We demonstrate that the recent idea that cavitation in the intersolute region of nanoscopic solutes is preceded by the formation of a vapor layer around an individual solute is not the general case. The appearance of density waves pulled up around and outside of a nanoscopic plate occurs at lower interaction strengths than are required to obtain a wet state between such plates. We further show that chemically reasonable estimates of the interaction strength lead to a microscopically wet state and a hydrophobic interaction characterized by traps and barriers to association and not by vacuum induced collapse.

Effect of ions on the hydrophobic interaction between two plates

We use molecular dynamics simulations to investigate the solvent mediated attraction and drying between two nanoscale hydrophobic surfaces in aqueous salt solutions. We study these effects as a function of the ionic charge density, that is, the ionic charge per unit ionic volume, while keeping the ionic diameter fixed. The attraction is expressed by a negative change in the free energy as the plates are brought together, with enthalpy and entropy changes that both promote aggregation. We find a strong correlation between the strength of the hydrophobic interaction and the degree of preferential binding/exclusion of the ions relative to the surfaces. The results show that amplification of the hydrophobic interaction, a phenomenon analogous to salting-out, is a purely entropic effect and is induced by high-charge-density ions that exhibit preferential exclusion. In contrast, a reduction of the hydrophobic interaction, analogous to salting-in, is induced by low-charge-density ions that exhibit preferential binding, the effect being either entropic or enthalpic. Our findings are relevant to phenomena long studied in solution chemistry, as we demonstrate the significant, yet subtle, effects of electrolytes on hydrophobic aggregation and collapse.

Calculation of the absolute thermodynamic properties of association of host-guest systems from the intermolecular potential of mean force

The authors report calculations of the intermolecular potential of mean force (PMF) in the case of the host-guest interaction. The host-guest system is defined by a water soluble calixarene and a cation. With an organic cation such as the tetramethylammonium cation, the calixarene forms an insertion complex, whereas with the Lanthane cation, the supramolecular assembly is an outer-sphere complex. The authors apply a modified free energy perturbation method and the force constraint technique to establish the PMF profiles as a function of the separation distance between the host and guest. They use the PMF profile for the calculation of the absolute thermodynamic properties of association that they compare to the experimental values previously determined. They finish by giving some structural features of the insertion and outer-sphere complexes at the Gibbs free energy minimum.

Bursts in single-file motion mediated conduction

We present a cellular automaton (CA) model of particles in a single-file motion with free particle exchange at the boundaries of a one-dimensional channel connected to two infinite reservoirs in order to study the self-transmission of particles with excluded mutual passage. The parallel, local and homogeneous rule sets of the CA algorithm consider two different interactions of varying strength between particles, without any specific particle-channel interaction. CA model results suggest that one hallmark of single-file motion is the conduction bursts at a particular time scale, which have thus far only been discovered for hydrogen bond networked water translocation. The cumulative transport probabilities of particles through single-file channels of different length follow a single profile, which can be obtained through proper scaling of time. The universal features of our results suggest new experiments in single-file channel with fluids other than water.

Microtubule stability studied by three-dimensional molecular theory of solvation

We study microtubular supramolecular architectures of tubulin dimers self-assembling into linear protofilaments, in turn forming a closed tube, which is an important component of the cytoskeleton. We identify the protofilament arrangements with the lowest free energy using molecular dynamics to optimize tubulin conformations. We then use the three-dimensional molecular theory of solvation to obtain the hydration structure of protofilaments built of optimized tubulins and the solvent-mediated effective potential between them. The latter theoretical method, based on first principles of statistical mechanics, is capable of predicting the structure and thermodynamics of solvation of supramolecular architectures. We obtained a set of profiles of the potential of mean force between protofilaments in a periodic two-dimensional sheet in aqueous solution. The profiles were calculated for a number of amino acid sequences, tubulin conformations, and spatial arrangements of protofilaments. The results indicate that the effective interaction between protofilaments in aqueous solution depends little on the isotypes studied; however, it strongly depends on the M loop conformation of beta-tubulin. Based on the analysis of the potential of mean force between adjacent protofilaments, we found the optimal arrangement of protofilaments, which is in good agreement with other studies. We also decomposed the potential of mean force into its energetic and entropic components, and found that both are considerable in the free-energy balance for the stabilized protofilament arrangements.

A molecular dynamics simulation study of buckyballs in water: Atomistic versus coarse-grained models of C60

A simple coarse-grained water-C(60) model potential is proposed to study the solvation behavior of C(60) in water. Extensive molecular dynamics simulations are performed to compare the hydration behavior of the coarse-grained C(60) with that of its atomistic counterpart. In the coarse-grained description, we model the C(60) as a spherical solute and its interaction with water is represented by a simple two-body central potential as obtained from a coarse graining of the interactions of a water molecule with all the atoms of the C(60). On the other hand, the atomistic model takes into account a discrete nature of all the atoms of C(60) explicitly. Molecular dynamics simulations are carried out in an isothermal-isobaric ensemble at normal temperature and pressure. Various spatial and orientational correlations of the water around the two model C(60)s are compared. The coarse-grained model is shown to reproduce the hydration behavior of the C(60) quite well. The simplicity and the computational economy of the coarse-grained model will allow for simulations of self-assembly processes of a much larger system over a longer period of time.