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Experiments have shown that cholesterol influences the membrane permeability of small molecules, amino acids, and cell-penetrating peptides. However, their exact translocation mechanisms under the influence of cholesterol remain poorly understood. Given the practical importance of cell-penetrating peptides and the existence of varied cholesterol contents in different cell types, it is necessary to examine the permeation of amino acids in cholesterol-containing membranes at atomic level of details. Here, bias-exchange metadynamics simulations were employed to investigate the molecular mechanism of the membrane permeation of two amino acids Arg and Trp important for cell-penetrating peptides in the presence of different concentrations of cholesterol. We found that the free energy barrier of Arg+ (the protonated form) permeation increased linearly as the cholesterol concentration increased, whereas the barrier of Trp permeation had a rapid increase from 0 mol. % to 20 mol. % cholesterol-containing membranes and nearly unchanged from 20 mol. % to 40 mol. % cholesterol-containing membranes. Arg0 becomes slightly more stable than Arg+ at the center of the dipalmitoylphosphatidylcholine (DPPC) membrane with 40 mol. % cholesterol concentrations. As a result, Arg+ has a similar permeability as Trp at 0 mol. % and 20 mol. % cholesterol, but a significantly lower permeability than Trp at 40 mol. % cholesterol. This difference is caused by the gradual reduction of water defects for Arg+ as the cholesterol concentration increases but lack of water defects for Trp in cholesterol-containing membranes. Strong but different orientation dependence between Arg+ and Trp permeations is observed. These results provide an improved microscopic understanding of amino-acid permeation through cholesterol-containing DPPC membrane systems. [ABSTRACT FROM AUTHOR]

This paper examines the folding mechanism of an individual β-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel β-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single β-hairpin in literature is confirmed to be useful in describing β-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, β1-β2 hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of β2-β3 hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent. [ABSTRACT FROM AUTHOR]

Protein topology, which refers to the arrangement of secondary structures of proteins, has been extensively investigated to examine its role in protein folding. However, recent studies show that topology alone cannot account for the variation of folding behaviors observed in some proteins of the same structural family. In a recent work, we showed that the native structure of the second β hairpin of protein G predicts a folding mechanism that is different from topology-based models. Here, we continue to examine how much one can learn about folding mechanism from native structure. This work focuses on fragment B of Staphylococcal protein A (BpA) - a three-helix (H[SUB1], H[SUB2], and H[SUB3]) bundle protein. Using a recently developed all-atom (except nonpolar hydrogen) Go model interacting with simple discontinuous potentials, the folding of the model BpA was observed in 112 out of 249 trajectories within 50 h of CPU times on a Pentium PC (1 GHz). The model successfully captured several specific properties of BpA that have been observed experimentally. These include the higher stability of H[SUB3] compared to H[SUB1] and H[SUB2], and the higher stability of the H[SUB2]-H[SUB3] microdomain compared to the H[SUB1]-H[SUB2] microdomain. These specific details were not produced by a topology-based square-well model of BpA. Thus, the result further supports the important role of sidechain packing in determining the specific pathway of protein folding. Additional 96000 short simulations were performed to locate the transition states of the two folding pathways. The limitation of the Go model and its possible improvement are also discussed. [ABSTRACT FROM AUTHOR]

We explore the distance fluctuation criterion (“Lindemann criterion”) for melting transitions. Distances from average positions in accord with Lindemann, or interparticle distances, in accord with Jellinek and Berry or Etters and Kaelberer, are examined. The primary goal is to determine which of these offers the more useful criterion. The choice of origin can sometimes effect the significance of the index. We study three systems with two kinds of potentials. They are all composed of 64 particles: (a) and (b), a homopolymer and a cluster that consist of beads interacting pairwise through square-well potentials, and (c) a cluster of particles interacting pairwise through Morse potentials. For each of the noncrystalline structures, in contrast to the crystals originally studied by Lindemann, the fluctuation parameter based on interparticle distances gives a clearer separability of liquid and solid phases than that based on fluctuations from average positions. The solid-like forms of the Morse cluster, the square-well cluster, and the square-well homopolymer have similar behavior, indicating that a broad class of systems can be evaluated with this index. In these systems, relative fluctuation parameters provide a suitable criterion for the melting transition. The critical values for the interparticle distance criterion, which are in the range of 0.03–0.05, are smaller than those for the Lindemann criterion (0.1–0.15). © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new method for calculating thermodynamics of any square-well systems by umbrella sampling of the corresponding hard-sphere systems is proposed. The removal of energetic barriers leads to an efficient configurational sampling. As an illustrative example, the method is applied to a square-well chain of freely-jointed 64 beads. Results indicate that it produces fast and more accurate thermodynamic results than either the direct molecular dynamics simulation or the umbrella sampling of the square-well chain. The new method, which provides a new route for accurate heat-capacity and free energy calculations, can be easily extended to a system interacting with the Lennard-Jones or any other continuous potentials. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies the equilibrium thermodynamics of homopolymers and clusters with square-well interactions through constant-temperature discontinuous molecular dynamics (DMD) and Monte Carlo simulations. Monte Carlo results for chains of fixed-bond lengths; DMD results for chains with flexible bond lengths; Square-well cluster of 64 square-well beads.

We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory–AB (GF–AB) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF–AB and GF–dimer–AC theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublík hard-disk dimer equation of state. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A multiplicative interpolation scheme (MIS) for the cavity function of associating hard-core particles is proposed and applied to the case of our shielded sticky-point model in which the particles associate into fused hard-sphere diatomic molecules (hard dumbbells). The results indicate that the MIS is a significant improvement over the simple interpolation scheme (SIS) of our earlier paper when the bonding length is much less than the hard-core diameter. The MIS is also applied to the case of a weak electrolyte modelled by shielded sticky-point particles that are charged, which associate into hard dipolar dumbbells. Using a near-exact hard-sphere cavity function along with the mean spherical approximation (MSA) for the electrostatic part of the activity coefficient, we find that the resulting version of the MIS is already in reasonable agreement with the experimental data for monochloroacetic acid, despite the equal-diameter restriction of the simple version of the model that we are using. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new method, which improves upon the mean spherical approximation (MSA), is developed by including the ionic-pairing contribution using a recent theory of association. The association constant of the new approximation is obtained through the second ionic virial coefficient. In the simplest version of our theory, which we call the pairing MSA 1 (PMSA1), we neglect the activity coefficient of the fully associated ionic-pairs, which are regarded as a separate dipolar species, and obtain the critical point (ρc*, Tc*) at (0.025, 0.075). In the second PMSA ( or PMSA2), we include the activity coefficient of these dipolar particles at the MSA level. The new critical point is located at (0.023, 0.073). In the third PMSA ( or PMSA3), we further include the effect of the presence of the dipolar-particle cores. The final critical point is located at (0.0245, 0.0745). These critical points are considerably closer than the MSA result (0.014, 0.079) to the most recent Monte Carlo estimates of ρc* from 0.025 to 0.04 and Tc* from 0.053 to somewhat over 0.057. Both PMSA2 and PMSA3 appear to improve the critical values of pressure and the degree of association significantly over PMSA1. All expressions for the thermodynamic properties in the PMSA1, PMSA2, and PMSA3 are of simple analytic form. The equation of state in the PMSA3 reduces to the very accurate Carnahan-Starling equation of state for hard spheres if the charges are turned off, and it reduces to an accurate equation of state for a mixture of hard spheres and hard dumbbells if the charges of the associated pairs are turned off. A comparison is made between our theory and that of a recent approach of Fisher and Levin, which is in good agreement with the simulation results if the hard-core contribution to the thermodynamics is neglected, but which falls out of agreement when an accurate core contribution is included. A discussion of the importance of an accurate core term in the treatment of the restrictive... [ABSTRACT FROM AUTHOR]

We report Monte Carlo simulation results for the bulk pressure of fused-hard-sphere (FHS) chain fluids with bond-length-to-bead-diameter ratios ≊ 0.4 at chain lengths n=4, 8 and 16. We also report density profiles for FHS chain fluids at a hard wall. The results for the compressibility factor are compared to results from extensions of the Generalized Flory (GF) and Generalized Flory Dimer (GFD) theories proposed by Yethiraj et al. and by us. Our new GF theory, GF-AB, significantly improves the prediction of the bulk pressure of fused-hard-sphere chains over the GFD theories proposed by Yethiraj et al. and by us although the GFD theories give slightly better low-density results. The GFD-A theory, the GFD-B theory and the new theories (GF-AB, GFD-AB, and GFD-AC) satisfy the exact zero-bonding-length limit. All theories considered recover the GF or GFD theories at the tangent hard-sphere chain limit. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The pairing mean spherical approximation (PMSA) developed in the previous paper of this series is applied to a binary mixture of hard spheres and ions of the restricted primitive model. The resulting equation of state is used to investigate the phase equilibrium for the binary mixture. It is found that the model exhibits type-III phase behavior. This work serves as the basis for more realistic models. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The exact asymptotic behavior of the particle–particle direct correlation function for dissociative dipolar dumbbells is discussed. It reveals the sense in which the complete association limit is like a critical point and suggests several approximations as well as the conditions under which they can be expected to be useful. The simplest of these is an extended mean spherical approximation (EMSA) that can be solved analytically for a model liquid of symmetric dissociative dipolar dumbbells with two centers (each bearing a point charge of opposite sign) a distance L apart, when σ/3≤L≤σ/2, where σ is the diameter of the spheres that consistute the dumbbells. The analytical expressions for the Born solvation free energy of a symmetric dipolar dumbbell in a symmetric dipolar dumbbell solvent and in a dipolar hard-sphere solvent are also obtained. Such expressions can be expected to be useful in investigating intramolecular electron-transfer reactions. Results for σ/2≤L≤σ that have a somewhat different conceptual status are obtained as well. They suggest a new interpretation of the Percus–Yevick solution to the sticky-sphere model considered by Baxter. [ABSTRACT FROM AUTHOR]

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ‘‘linear’’ approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier’s principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data. [ABSTRACT FROM AUTHOR]

A formally exact nonlocal density-functional expansion procedure for direct correlation functions developed earlier by Stell for a homogeneous system, and extended by Blum and Stell, Sullivan and Stell, and ourselves to various inhomogeneous systems, is used here to derive nonlocal integral-equation approximations. Two of the simplest of these approximations (zeroth order), which we shall characterize here as the hydrostatic Percus–Yevick (HPY) approximation and the hydrostatic hypernetted-chain (HHNC) approximation, respectively, are shown to be capable of accounting for wetting transitions on the basis of general theoretical considerations. Before turning to such transitions, we investigate in this first paper of a series the case of homogeneous hard-sphere fluids and hard spheres near a hard wall as well as the case of hard spheres inside a slit pore. Numerical results show that the HHNC approximation is better than the HNC approximation for both the homogeneous and inhomogeneous systems considered here while the HPY approximation appears to overcorrect the PY approximation. [ABSTRACT FROM AUTHOR]

The zeroth order (hydrostatic) nonlocal integral-equation approximation is applied here to Lennard-Jones (LJ) fluids. Systems of homogeneous LJ fluids are investigated, as well as LJ fluids near a hard wall, a model CO2 wall, and inside two model CO2 walls. The hydrostatic hypernetted chain (HHNC) approximation is shown to be better than both the Percus–Yevick and the hypernetted chain approximations when compared with computer simulations. The phenomena of solid wetting by liquid, solid wetting by gas, and capillary condensation are predicted by the HHNC approximation. [ABSTRACT FROM AUTHOR]

The observation that the intramolecular direct-correlation-function matrix is very closely approximated by its large-r form for rigid diatomics suggests an approximation such that the site–site Ornstein–Zernike equation becomes analytically solvable for several molecular models of interest. Alternatively, approximation of the particle–particle direct correlation function by its asymptotic form directly yields the same approximation, in particle–particle (in contrast to site–site) language. Applications of this approximation, which can be regarded as an extended mean spherical approximation when viewed in particle–particle terms, are made to rigid hard diatomics, dipolar diatomics, and a tetrahedral molecular model. The close but subtle connections between our approximation procedure and earlier approximations are discussed. [ABSTRACT FROM AUTHOR]

Analytical equations are obtained for the pair correlation functions in the mean spherical approximation (MSA) for two charged hard-sphere ions in a model molecular solvent. Model solvents of dipolar dumbbells (which may be partially dissociative) or charged hard-spheres fused in a tetrahedral configuration are treated in an extended MSA. The resulting expressions for the Born solvation free energy of an ion are very similar to that obtained earlier by Chan et al. for a charged hard-sphere ion in a dipolar hard-sphere solvent. The solvent averaged ion–ion potentials are obtained in the hypernetted chain approximation. Comparisons among results of various solvents are also made. In order of increasing oscillation amplitudes of the solvent averaged ion–ion potential for given molecular density and dipole moment we have continuum ≪dumbbell≤tetrahedral

The Born solvation free energy (BSFE) of two ions at a fixed distance from one another in a model polar solvent is obtained via two approaches. In the interaction-site approach, the two ions are modeled as a rigid extended dipolar dumbbell. Analytical expressions for the BSFE for such a dumbbell model in a dipolar dumbbell and a dipolar hard-sphere solvent are obtained under a mean spherical approximation (MSA). In the second approach, a thermodynamic cycle is established such that the BSFE for two ions a fixed distance apart can be expressed in terms of the solvent-averaged potential between the two ions and other known quantities. The results obtained via these two approaches are reasonably consistent, with the thermodynamic-cycle BSFE as a function of distance exhibiting more of the structure one expects to find in a molecular solvent. Both BSFE functions are substantially different from the corresponding continuum-solvent result. When the distance between two ions goes to infinity, our results reduce to earlier results for the single-ion BSFE obtained by us for a dipolar dumbbell solvent and by Chan et al. for a dipolar hard-sphere solvent. The BSFE of two ions in an ionic solution with a dielectric-continuum solvent is also obtained; it is found that the contribution of other ionic particles to the total BSFE is usually negligible if the dielectric constant of the solution is assumed to be unchanged. [ABSTRACT FROM AUTHOR]

The solvation dynamics of a pair of ions rigidly held a fixed distance from each other in either a dipolar hard-sphere solvent or a dipolar dumbbell solvent is investigated under the mean spherical approximation (MSA) applied to an interaction-site model in which the pair of ions is treated as a rigid extended dipolar dumbbell. An analytical expression for the reorganization free energy for a charge transfer reaction is obtained and compared with numerical results obtained via a thermodynamic cycle. Solvent effects on the rate of a charge transfer reaction are also investigated using the dielectric Green-function theory developed by Newton and Friedman. [ABSTRACT FROM AUTHOR]

A simple approximation scheme is given for the association constant of a family of models of associating particles introduced and considered by Cummings and Stell, Rasaiah et al., and Stell. The result correctly reduces to the law of mass action at low concentrations. For the ionic-species version, the theory requires accurate assessment of the cavity function of charged hard spheres, for which we develop a recipe. We show the close similarity (and some differences) between the above models and those considered by Wertheim, through a simple extensions of his models. We also note the equivalence of our approximation and Wertheim’s first-order thermodynamic perturbation theory. [ABSTRACT FROM AUTHOR]

The system of a fluid in the presence of a spherical semipermeable vesicle (SPV) with the freely mobile nonpermeating species inside the vesicle is investigated via an integral-equation approach. This system can be used to model certain feature of a biological cell, permeable to simple ions, in which solute proteins inside the cell are unable to permeate its walls. As an illustrative example of the use of our integral equations, the analytical solution for density profiles in the mean-spherical approximation/Debye–Hückel approximation (MSA/DH) is obtained, where the MSA is used to obtain the density profiles near a membrane and the DH approximation to obtain the bulk pair correlation functions. A method which applies to nonmobile protein fixed inside a cell is also considered. [ABSTRACT FROM AUTHOR]

An exact integral-equation formalism for a system of a binary hard-sphere mixture interacting with a spherical semipermeable vesicle (SPV) and plane semipermeable membrane (SPM) is derived by using the Ornstein–Zernike (OZ) equation with appropriate closures. The Percus–Yevick (PY) closure or the hypernetted chain (HNC) closure, in which the bulk correlation is obtained by the PY approximation, are considered as examples. We refer to these as the PY/PY and HNC/PY approximations, respectively. The mixture contains solvent particles, which are permeable to the membrane, and solute particles (‘‘protein’’ or ‘‘polymer’’ particles), which can not pass through the membrane. We develop an exact general formalism for this problem and as an illustration of its use give quantative results for solvent and solute particles modeled as hard spheres of different diameters. An analytical expression for the density ratio in the PY/PY and HNC/PY approximations between two sides of a plane SPM is obtained. Results obtained from these expressions agree very well with results obtained by equating chemical potentials in the region of interest. It turns out that the protein–membrane direct correlation function can be given by a simple analytic expression for the limit of a point solvent in the PY/PY approximation. The osmotic pressure and density profiles for the system containing an ideal spherical SPV or plane SPM in the PY/PY approximation are evaluated. Extension to the nonlocal density-functional closures previously introduced by Blum and Stell is discussed. Finally, we note that certain impenetrable-wall problems previously considered elsewhere can be regarded as semipermeable membrane problems treated via McMillan–Mayer formalism in the continuum–solvent approximation. [ABSTRACT FROM AUTHOR]

Integral equations that yield the charge and density profiles are derived for a Donnan system, in which an ionic solution is separated into two regions by a semipermeable membrane (SPM) or a spherical semipermeable vesicle (SPV). These equations are obtained from the Ornstein–Zernike (OZ) equation. We show how quantitative results can be obtained from either the mean spherical approximation (MSA) closure or the hypernetted-chain (HNC) closure for profiles. Use is made of bulk-correlation input obtained by means of the Debye–Hückel approximation, the MSA approximation, or the HNC approximation. The resulting approximations will be referred as MSA/DH, HNC/DH, MSA/MSA, etc. The system on which we focus contains three charged hard-sphere species: cation, anion, and a large ion (a protein or polymer ion) separated by a plane SPM, through which the large ion cannot pass, and to one side of which all large ions are confined, or a spherical SPV, outside of which the large ions are confined. Analytical expressions for the bulk density ratio between the two sides of a plane membrane as well as the membrane potential in various approximations are obtained. Results obtained from these expresssions are compared with the results obtained by equating electrochemical potentials. A new contact-value theorem is provided for the plane SPM system. Analytical solutions for the charge profile and the potential profile in the MSA/DH approximation are obtained. It turns out that results obtained in the HNC/DH approximation are exactly the same as those obtained by using 1D nonlinear Poisson–Boltzmann equations if the repulsive cores of the macroions are neglected. [ABSTRACT FROM AUTHOR]

We investigate the partition of ionic species in a system of two phases that are immiscible even in the limit of vanishing ionic concentrations. An analytic expression for the solvation free energy and for the standard free energy of transfer is obtained for dipolar hard-sphere solvents in the mean spherical approximation. We find that both dipolar hard-sphere solvents and continuum solvent models yield an electric potential difference (equilibrium junction potential) between two pure solvents in contact that is identically zero. Simple analytic expressions for partition coefficients and junction potentials are obtained in the ideal-solution limit for these solvent models. We note that for the junction potential the ideal solution limits differ in general from the pure-solvent values. For nonideal solutions, approximations based on the mean spherical approximation can be applied conveniently to calculate the activities of ionic species and to obtain the partition coefficients. [ABSTRACT FROM AUTHOR]

A simple interpolation scheme (SIS) suggested in an earlier paper is used to obtain the excess Helmholtz free energy and the equation of state for the shielded sticky-shell model and the shielded sticky-point model of associative fluids. It is found that the equation of state under the SIS for a fully associated homonuclear dumbbell fluid is quite accurate as long as L*=L/σ≥0.8. For ionic association, the excess Helmholtz free energy in this work reduces to that of Bjerrum’s theory in the ideal limit. An analytical equation of state for associative ions is evaluated. [ABSTRACT FROM AUTHOR]

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.