Hydrophobic Interactions by Monte Carlo Simulations

Multiple Free Energy Calculations from Single State Point Continuous Fractional Component Monte Carlo Simulation Using Umbrella Sampling

We introduce an alternative method to perform free energy calculations for mixtures at multiple temperatures and pressures from a single simulation, by combining umbrella sampling and the continuous fractional component Monte Carlo method. One can perform a simulation of a mixture at a certain pressure and temperature and accurately compute the chemical potential at other pressures and temperatures close to the simulation conditions. This method has the following advantages: (1) Accurate estimates of the chemical potential as a function of pressure and temperature are obtained from a single state simulation without additional postprocessing. This can potentially reduce the number of simulations of a system for free energy calculations for a specific temperature and/or pressure range. (2) Partial molar volumes and enthalpies are obtained directly from the estimated chemical potentials. We tested our method for a Lennard-Jones system, aqueous mixtures of methanol at T = 298 K and P = 1 bar, and a mixture of ammonia, nitrogen, and hydrogen at T = 573 K and P = 800 bar. For pure methanol (N = 410 molecules), we observed that the estimated chemical potentials from umbrella sampling are in excellent agreement with the reference values obtained from independent simulations, for ΔT = ±15 K and ΔP = 100 bar (with respect to the simulated system). For larger systems, this range becomes smaller because the relative fluctuations of energy and volume become smaller. Without sufficient overlap, the performance of the method will become poor especially for nonlinear variations of the chemical potential.

Insights into the Molecular Mechanisms of Alzheimer's and Parkinson's Diseases with Molecular Simulations: Understanding the Roles of Artificial and Pathological Missense Mutations in Intrinsically Disordered Proteins Related to Pathology

Amyloid-β and α-synuclein are intrinsically disordered proteins (IDPs), which are at the center of Alzheimer's and Parkinson's disease pathologies, respectively. These IDPs are extremely flexible and do not adopt stable structures. Furthermore, both amyloid-β and α-synuclein can form toxic oligomers, amyloid fibrils and other type of aggregates in Alzheimer's and Parkinson's diseases. Experimentalists face challenges in investigating the structures and thermodynamic properties of these IDPs in their monomeric and oligomeric forms due to the rapid conformational changes, fast aggregation processes and strong solvent effects. Classical molecular dynamics simulations complement experiments and provide structural information at the atomic level with dynamics without facing the same experimental limitations. Artificial missense mutations are employed experimentally and computationally for providing insights into the structure-function relationships of amyloid-β and α-synuclein in relation to the pathologies of Alzheimer's and Parkinson's diseases. Furthermore, there are several natural genetic variations that play a role in the pathogenesis of familial cases of Alzheimer's and Parkinson's diseases, which are related to specific genetic defects inherited in dominant or recessive patterns. The present review summarizes the current understanding of monomeric and oligomeric forms of amyloid-β and α-synuclein, as well as the impacts of artificial and pathological missense mutations on the structural ensembles of these IDPs using molecular dynamics simulations. We also emphasize the recent investigations on residual secondary structure formation in dynamic conformational ensembles of amyloid-β and α-synuclein, such as β-structure linked to the oligomerization and fibrillation mechanisms related to the pathologies of Alzheimer's and Parkinson's diseases. This information represents an important foundation for the successful and efficient drug design studies.

How accurate are your simulations? Effects of confined aqueous volume and AMBER FF99SB and CHARMM22/CMAP force field parameters on structural ensembles of intrinsically disordered proteins: Amyloid-β42 in water

Amyloid-β₄₂ (Aβ₄₂) is an intrinsically disordered peptide intimately related to the pathogenesis of several neurodegenerative diseases. Molecular dynamics (MD) simulations are extensively utilized in the characterization of the structures and conformational dynamics of intrinsically disordered proteins (IDPs) including Aβ₄₂, with AMBER and CHARMM parameters being commonly used in these studies. Recently, comparison of the effects of force field parameters on the Aβ₄₂ structures has started to gain significant attention. In this study, the structures of Aβ₄₂ are simulated using AMBER FF99SB and CHARMM22/CMAP parameters via replica exchange MD simulations utilizing a widely used clustering algorithm. These analyses show that the structural properties (extent and positioning of the elements of secondary and tertiary structure), radius of gyration values, number and position of salt bridges are extremely dependent on the chosen force field parameters notably with the usage of clustering algorithms. For example, predicted secondary structure elements, which are of the great importance for better understanding of the molecular mechanisms of neurodegenerative diseases, deviate enormously in models generated using currently available force field parameters for proteins. Based on the derived models, chemical shift values are calculated and compared to the experimentally determined data. This comparison revealed that although both force field parameters yield results in agreement with experiments, the obtained structural properties were rather different using a clustering algorithm. In other words, these results show that the predicted structures depend heavily on the force field parameters. Importantly, since none of the force field parameters currently utilized in MD studies were developed specifically taking into account the disordered nature of IDPs, these findings clearly indicate that new force field parameters have to be developed for IDPs considering their rapid flexibility and dynamics with high amplitude. Furthermore, molecular simulations of IDPs are typically conducted using one water volume. We show that the confined aqueous volume impacts the predicted structural properties of Aβ₄₂ in water. Although up to date, confined aqueous volume effects have been ignored in the MD simulations of IDPs in water, our data indicate that these effects have to be taken into account in predicting the structural and thermodynamic properties of disordered proteins in solution.

Recent developments in the theoretical, simulational, and experimental studies of the role of water hydrogen bonding in hydrophobic phenomena

Hydrophobic effects (hydrophobic hydration and hydrophobic interaction) constitute an important element of a wide variety of phenomena relevant to biological, physical, chemical, environmental, engineering, and pharmaceutical sciences, such as the immiscibility of oil and water, self-assembly of amphiphiles leading to micelle and membrane formation, folding and stability and unfolding of the native structure of a biologically active protein, gating of ion channels, wetting, froth floatation, and adhesion. On the other hand, the hydrogen bonding ability of water plays a major (if not crucial) role in hydrophobic phenomena. We present a review of most important and relatively recent experimental, simulational, and theoretical research on hydrophobic phenomena in various systems. With a particular interest we survey investigations clarifying the role of water hydrogen bonding therein, because it has been the main object of our own recent research. We have developed a probabilistic hydrogen bond (PHB) model that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of its distance to a hydrophobe, hydrophobe radius, and temperature. Knowing that function, one can explicitly identify a water hydrogen bond contribution to the external potential whereto a water molecule is subjected near a hydrophobe. Combining the PHB model with the classical density functional theory (DFT), one can examine the contribution of water hydrogen bonding to the temperature and lengthscale effects on the hydration of particles and on their solvent-mediated interactions over the entire low-to-high temperature and small-to-large lengthscale ranges. We applied the combined DFT/PHB model to study a variety of hydrophobic phenomena such as (liquid) water in contact with a hydrophobic plate, solvation of spherical solutes of various radii in associated and non-associated liquids at various temperatures, the solvent-mediated interaction of spherical solutes and its temperature dependence, interaction of C60 fullerenes in water, temperature effect on the evaporation lengthscale of water confined between two hydrophobes, temperature dependence of the effective width of the solute-solvent transition layer and average density therein. These applications demonstrated that the DFT/PHB model can serve as a valuable tool in studying hydrophobic phenomena because it constitutes a balanced combination of simplicity, accuracy, and detail. The predictions of the combined DFT/PHB approach for the solvent density profiles and thermodynamic aspects of hydrophobic phenomena are generally in good agreement with experiments and simulations. For example, it predicts the small-to-large crossover lengthscale of its mechanism to be approximately in the range from 1nm to 4nm, and decreasing with increasing temperature. It also suggests that, in terms of the average fluid density in the solute-solvent transition layer, the transition layer for small hydrophobes (of radii ≲2 nm) becomes enriched with rather than depleted of fluid when both the solvent-solute affinity and hb-energy alteration ratio become large enough. The boundary values of these parameters, needed for the depletion-to-enrichment crossover, are predicted to decrease with increasing temperature.

Structures and free energy landscapes of the A53T mutant-type α-synuclein protein and impact of A53T mutation on the structures of the wild-type α-synuclein protein with dynamics

The A53T genetic missense mutation of the wild-type α-synuclein (αS) protein was initially identified in Greek and Italian families with familial Parkinson's disease. Detailed understanding of the structures and the changes induced in the wild-type αS structure by the A53T mutation, as well as establishing the direct relationships between the rapid conformational changes and free energy landscapes of these intrinsically disordered fibrillogenic proteins, helps to enhance our fundamental knowledge and to gain insights into the pathogenic mechanism of Parkinson's disease. We employed extensive parallel tempering molecular dynamics simulations along with thermodynamic calculations to determine the secondary and tertiary structural properties as well as the conformational free energy surfaces of the wild-type and A53T mutant-type αS proteins in an aqueous solution medium using both implicit and explicit water models. The confined aqueous volume effect in the simulations of disordered proteins using an explicit model for water is addressed for a model disordered protein. We also assessed the stabilities of the residual secondary structure component interconversions in αS based on free energy calculations at the atomic level with dynamics using our recently developed theoretical strategy. To the best of our knowledge, this study presents the first detailed comparison of the structural properties linked directly to the conformational free energy landscapes of the monomeric wild-type and A53T mutant-type α-synuclein proteins in an aqueous solution environment. Results demonstrate that the β-sheet structure is significantly more altered than the helical structure upon A53T mutation of the monomeric wild-type αS protein in aqueous solution. The β-sheet content close to the mutation site in the N-terminal region is more abundant while the non-amyloid-β component (NAC) and C-terminal regions show a decrease in β-sheet abundance upon A53T mutation. Obtained results utilizing our new theoretical strategy show that the residual secondary structure conversion stabilities resulting in α-helix formation are not significantly affected by the mutation. Interestingly, the residual secondary structure conversion stabilities show that secondary structure conversions resulting in β-sheet formation are influenced by the A53T mutation and the most stable residual transition yielding β-sheet occurs directly from the coil structure. Long-range interactions detected between the NAC region and the N- or C-terminal regions of the wild-type αS disappear upon A53T mutation. The A53T mutant-type αS structures are thermodynamically more stable than those of the wild-type αS protein structures in aqueous solution. Overall, the higher propensity of the A53T mutant-type αS protein to aggregate in comparison to the wild-type αS protein is related to the increased β-sheet formation and lack of strong intramolecular long-range interactions in the N-terminal region in comparison to its wild-type form. The specific residual secondary structure component stabilities reported herein provide information helpful for designing and synthesizing small organic molecules that can block the β-sheet forming residues, which are reactive toward aggregation.

Structures and free energy landscapes of aqueous zinc(II)-bound amyloid-β(1-40) and zinc(II)-bound amyloid-β(1-42) with dynamics

Binding of divalent metal ions with intrinsically disordered fibrillogenic proteins, such as amyloid-β (Aβ), influences the aggregation process and the severity of neurodegenerative diseases. The Aβ monomers and oligomers are the building blocks of the aggregates. In this work, we report the structures and free energy landscapes of the monomeric zinc(II)-bound Aβ40 (Zn:Aβ40) and zinc(II)-bound Aβ42 (Zn:Aβ42) intrinsically disordered fibrillogenic metallopeptides in an aqueous solution by utilizing an approach that employs first principles calculations and parallel tempering molecular dynamics simulations. The structural and thermodynamic properties, including the secondary and tertiary structures and conformational Gibbs free energies of these intrinsically disordered metallopeptide alloforms, are presented. The results show distinct differing characteristics for these metallopeptides. For example, prominent β-sheet formation in the N-terminal region (Asp1, Arg5, and Tyr10) of Zn:Aβ40 is significantly decreased or lacking in Zn:Aβ42. Our findings indicate that blocking multiple reactive residues forming abundant β-sheet structure located in the central hydrophobic core and C-terminal regions of Zn:Aβ42 via antibodies or small organic molecules might help to reduce the aggregation of Zn(II)-bound Aβ42. Furthermore, we find that helix formation increases but β-sheet formation decreases in the C-terminal region upon Zn(II) binding to Aβ. This depressed β-sheet formation in the C-terminal region (Gly33-Gly38) in monomeric Zn:Aβ42 might be linked to the formation of amorphous instead of fibrillar aggregates of Zn:Aβ42.

Molecular correlations and solvation in simple fluids

We study the molecular correlations in a lattice model of a solution of a low-solubility solute, with emphasis on how the thermodynamics is reflected in the correlation functions. The model is treated in the Bethe-Guggenheim approximation, which is exact on a Bethe lattice (Cayley tree). The solution properties are obtained in the limit of infinite dilution of the solute. With h(11)(r), h(12)(r), and h(22)(r) the three pair correlation functions as functions of the separation r (subscripts 1 and 2 referring to solvent and solute, respectively), we find for r > or = 2 lattice steps that h(22)(r)/h(12)(r) is identical with h(12)(r)/h(11)(r). This illustrates a general theorem that holds in the asymptotic limit of infinite r. The three correlation functions share a common exponential decay length (correlation length), but when the solubility of the solute is low the amplitude of the decay of h(22)(r) is much greater than that of h(12)(r), which in turn is much greater than that of h(11)(r). As a consequence the amplitude of the decay of h(22)(r) is enormously greater than that of h(11)(r). The effective solute-solute attraction then remains discernible at distances at which the solvent molecules are essentially no longer correlated, as found in similar circumstances in an earlier model. The second osmotic virial coefficient is large and negative, as expected. We find that the solvent-mediated part W(r) of the potential of mean force between solutes, evaluated at contact, r = 1, is related in this model to the Gibbs free energy of solvation at fixed pressure, DeltaG(p)(*), by (Z/2)W(1) + DeltaG(p)(*) is identical with pv(0), where Z is the coordination number of the lattice, p is the pressure, and v(0) is the volume of the cell associated with each lattice site. A large, positive DeltaG(p)(*) associated with the low solubility is thus reflected in a strong attraction (large negative W at contact), which is the major contributor to the second osmotic virial coefficient. In this model, the low solubility (large positive DeltaG(p)(*)) is due partly to an unfavorable enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in the hydrophobic effect, where the enthalpy of solvation itself favors high solubility, but is overweighed by the unfavorable solvation entropy.

Hydrophobic Interactions of Xenon by Monte Carlo Simulations

Hydrophobic interactions of xenon atoms dissolved in liquid water were studied by NpT Monte Carlo simulations in the temperature range 298.15 to 333K and at ambient pressure. Structural properties of dilute xenon solutions were calculated and compared to those of bulk water in order to show the influence of the hydrophobic solute. It was found that the xenon atoms tend to aggregate with increasing temperature. At low temperatures the aggregates are predominantly solvent-separated pairs; at higher temperatures the quota of contact pairs increases. Furthermore, the residual chemical potentials of xenon and water were calculated with different methods; it was found that the Widom insertion methods works best for this system. For the thermodynamic conditions of this work, the residual chemical potential of water in the presence of xenon was found to be a linear function of temperature.

Preferred conformation of the glycosidic linkage of methyl-β-mannose

The conformational preference of the glycosidic linkage of methyl-beta-mannose was studied in the gas phase and in aqueous solution by ab initio calculations, and by molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) simulations. MD simulations were performed with various water potential functions to study the impact of the chosen water potential on the predicted conformational preference of the glycosidic linkage of the carbohydrate in solution. This study shows that the trans (t) orientation of the glycosidic linkage of methyl-beta-mannose is preferred over its gauche clockwise (g+) orientation in solution. CPMD simulations clearly indicate that this preference is due to intermolecular hydrogen bonding with surrounding water molecules, whereas no such information could be demonstrated by MD simulations. This study demonstrates the importance of ab initio molecular dynamics simulations in studying the structural properties of carbohydrate-water interactions.