Temperature Dependence and Energetics of Single Ions at the Aqueous Liquid–Vapor Interface

We investigate temperature-dependence of free energetics with two single halide anions, I^– and Cl^–, crossing the aqueous liquid–vapor interface through molecular dynamics simulations. The result shows that I^– has a modest surface stability of 0.5 kcal/mol at 300 K and the stability decreases as the temperature increases, indicating the surface adsorption process for the anion is entropically disfavored. In contrast, Cl^– shows no such surface state at all temperatures. Decomposition of free energetics reveals that water–water interactions provide a favorable enthalpic contribution, while the desolvation of ion induces an increase in free energy. Calculations of surface fluctuations demonstrate that I^– generates significantly greater interfacial fluctuations compared to Cl^–. The fluctuation is attributed to the malleability of the solvation shells, which allows for more long-ranged perturbations and solvent density redistribution induced by I^– as the anion approaches the liquid–vapor interface. The increase in temperature of the solvent enhances the inherent thermally excited fluctuations and consequently reduces the relative contribution from anion to surface fluctuations, which is consistent with the decrease in surface stability of I^–. Our results indicate a strong correlation with induced interfacial fluctuations and anion surface stability; moreover, resulting temperature dependent behavior of induced fluctuations suggests the possibility of a critical level of induced fluctuations associated with surface stability

Free Energetics of Arginine Permeation into Model DMPC Lipid Bilayers: Coupling of Effective Counterion Concentration and Lateral Bilayer Dimensions

Mechanisms and underlying thermodynamic determinants of translocation of charged cationic peptides such as cell-penetrating peptides across the cellular membrane continue to receive much attention. Two widely held views include endocytotic and non-endocytotic (diffusive) processes of permeant transfer across the bilayer. Considering a purely diffusive process, we consider the free energetics of translocation of a monoarginine peptide mimic across a model DMPC bilayer. We compute potentials of mean force for the transfer of a charged monoarginine peptide unit from water to the center of a 1,2-dimyristoyl-<i>sn</i>-glycero-3-phosphocholine (DMPC) model lipid bilayer. We use fully atomistic molecular dynamics simulations coupled with the adaptive biasing force (ABF) method for free energy estimation. The estimated potential of mean force difference from bulk to bilayer center is 6.94 ± 0.28 kcal/mol. The order of magnitude of this prediction is consistent with past experimental estimates of arginine partitioning into physiological bilayers in the context of translocon-based experiments, though the correlation between the bench and computer experiments is not unambiguous. Moreover, the present value is roughly one-half of previous estimates based on all-atom molecular dynamics free energy calculations. We trace the differences between the present and earlier calculations to system sizes used in the simulations and the dependence of the contributions to the free energy from various system components (water, lipids, ions, peptide) on overall system size. By varying the bilayer lateral dimensions in simulations using only sufficient numbers of counterions to maintain overall system charge neutrality, we find the possibility of an inherent convergent transfer free energy value

Liquid–Vapor Interfacial Properties of Aqueous Solutions of Guanidinium and Methyl Guanidinium Chloride: Influence of Molecular Orientation on Interface Fluctuations

The guanidinium cation (C­(NH₂)₃⁺) is a highly stable cation in aqueous solution due to its efficient solvation by water molecules and resonance stabilization of the charge. Its salts increase the solubility of nonpolar molecules (“salting-in”) and decrease the ordering of water. It is one of the strongest denaturants used in biophysical studies of protein folding. We investigate the behavior of guanidinium and its derivative, methyl guanidinium (an amino acid analogue) at the air–water surface, using atomistic molecular dynamics (MD) simulations and calculation of potentials of mean force. Methyl guanidinium cation is less excluded from the air–water surface than guanidinium cation, but both cations show orientational dependence of surface affinity. Parallel orientations of the guanidinium ring (relative to the Gibbs dividing surface) show pronounced free energy minima in the interfacial region, while ring orientations perpendicular to the GDS exhibit no discernible surface stability. Calculations of surface fluctuations demonstrate that, near the air–water surface, the parallel-oriented cations generate significantly greater interfacial fluctuations compared to other orientations, which induces more long-ranged perturbations and solvent density redistribution. Our results suggest a strong correlation with induced interfacial fluctuations and ion surface stability. These results have implications for interpreting molecular-level, mechanistic action of this osmolyte’s interaction with hydrophobic interfaces as they impact protein denaturation (solubilization)

Free Energetics of Carbon Nanotube Association in Pure and Aqueous Ionic Solutions

Carbon nanotubes are a promising platform across a broad spectrum of applications ranging from separations technology, drug delivery, to bio­(electronic) sensors. Proper dispersion of carbon nanotube materials is important to retaining the electronic properties of nanotubes. Experimentally it has been shown that salts can regulate the dispersing properties of CNTs in aqueous system with surfactants (Niyogi, S.; Densmore, C. G.; Doorn, S. K. <i>J. Am. Chem. Soc.</i> <b>2009</b>, <i>131</i>, 1144–1153); details of the physicochemical mechanisms underlying such effects continue to be explored. We address the effects of inorganic monovalent salts (NaCl and NaI) on dispersion stability of carbon nanotubes.We perform all-atom molecular dynamics simulations using nonpolarizable interaction models to compute the potential of mean force between two (10,10) single-walled carbon nanotubes (SWNTs) in the presence of NaCl/NaI and compare to the potential of mean force between SWNTs in pure water. Addition of salts enhances stability of the contact state between two SWNT’s on the order of 4 kcal/mol. The ion-specific spatial distribution of different halide anions gives rise to starkly different contributions to the free energy stability of nanotubes in the contact state. Iodide anion directly stabilizes the contact state to a much greater extent than chloride anion. The enhanced stability arises from the locally repulsive forces imposed on nanotubes by the surface-segregated iodide anion. Within the time scale of our simulations, both NaI and NaCl solutions stabilize the contact state by equivalent amounts. The marginally higher stability for contact state in salt solutions recapitulates results for small hydrophobic solutes in NaCl solutions (Athawale, M. V.; Sarupria, S.; Garde, S. <i>J. Phys. Chem. B</i> <b>2008</b>, <i>112</i>, 5661–5670) as well as single-walled carbon nanotubes in NaCl and CaCl₂ aqueous solutions

Reconciling Structural and Thermodynamic Predictions Using All-Atom and Coarse-Grain Force Fields: The Case of Charged Oligo-Arginine Translocation into DMPC Bilayers

Using the translocation of short, charged cationic oligo-arginine peptides (mono-, di-, and triarginine) from bulk aqueous solution into model DMPC bilayers, we explore the question of the similarity of thermodynamic and structural predictions obtained from molecular dynamics simulations using all-atom and Martini coarse-grain force fields. Specifically, we estimate potentials of mean force associated with translocation using standard all-atom (CHARMM36 lipid) and polarizable and nonpolarizable Martini force fields, as well as a series of modified Martini-based parameter sets. We find that we are able to reproduce qualitative features of potentials of mean force of single amino acid side chain analogues into model bilayers. In particular, modifications of peptide–water and peptide–membrane interactions allow prediction of free energy minima at the bilayer–water interface as obtained with all-atom force fields. In the case of oligo-arginine peptides, the modified parameter sets predict interfacial free energy minima as well as free energy barriers in almost quantitative agreement with all-atom force field based simulations. Interfacial free energy minima predicted by a modified coarse-grained parameter set are −2.51, −4.28, and −5.42 for mono-, di-, and triarginine; corresponding values from all-atom simulations are −0.83, −3.33, and −3.29, respectively, all in units of kcal/mol. We found that a stronger interaction between oligo-arginine and the membrane components and a weaker interaction between oligo-arginine and water are crucial for producing such minima in PMFs using the polarizable CG model. The difference between bulk aqueous and bilayer center states predicted by the modified coarse-grain force field are 11.71, 14.14, and 16.53 kcal/mol, and those by the all-atom model are 6.94, 8.64, and 12.80 kcal/mol; those are of almost the same order of magnitude. Our simulations also demonstrate a remarkable similarity in the structural aspects of the ensemble of configurations generated using the all-atom and coarse-grain force fields. Both resolutions show that oligo-arginine peptides adopt preferential orientations as they translocate into the bilayer. The guiding theme centers on charged groups maintaining coordination with polar and charged bilayer components as well as local water. We also observe similar behaviors related with membrane deformations

Investigating Hydrophilic Pores in Model Lipid Bilayers Using Molecular Simulations: Correlating Bilayer Properties with Pore-Formation Thermodynamics

Cell-penetrating and antimicrobial peptides show a remarkable ability to translocate across physiological membranes. Along with factors such as electric-potential-induced perturbations of membrane structure and surface tension effects, experiments invoke porelike membrane configurations during the solute transfer process into vesicles and cells. The initiation and formation of pores are associated with a nontrivial free-energy cost, thus necessitating a consideration of the factors associated with pore formation and the attendant free energies. Because of experimental and modeling challenges related to the long time scales of the translocation process, we use umbrella sampling molecular dynamics simulations with a lipid-density-based order parameter to investigate membrane-pore-formation free energy employing Martini coarse-grained models. We investigate structure and thermodynamic features of the pore in 18 lipids spanning a range of headgroups, charge states, acyl chain lengths, and saturation. We probe the dependence of pore-formation barriers on the area per lipid, lipid bilayer thickness, and membrane bending rigidities in three different lipid classes. The pore-formation free energy in pure bilayers and peptide translocating scenarios are significantly coupled with bilayer thickness. Thicker bilayers require more reversible work to create pores. The pore-formation free energy is higher in peptide–lipid systems than in peptide-free lipid systems due to penalties to maintain the solvation of charged hydrophilic solutes within the membrane environment

Investigating Hydrophilic Pores in Model Lipid Bilayers Using Molecular Simulations: Correlating Bilayer Properties with Pore-Formation Thermodynamics

Cell-penetrating and antimicrobial peptides show a remarkable ability to translocate across physiological membranes. Along with factors such as electric-potential-induced perturbations of membrane structure and surface tension effects, experiments invoke porelike membrane configurations during the solute transfer process into vesicles and cells. The initiation and formation of pores are associated with a nontrivial free-energy cost, thus necessitating a consideration of the factors associated with pore formation and the attendant free energies. Because of experimental and modeling challenges related to the long time scales of the translocation process, we use umbrella sampling molecular dynamics simulations with a lipid-density-based order parameter to investigate membrane-pore-formation free energy employing Martini coarse-grained models. We investigate structure and thermodynamic features of the pore in 18 lipids spanning a range of headgroups, charge states, acyl chain lengths, and saturation. We probe the dependence of pore-formation barriers on the area per lipid, lipid bilayer thickness, and membrane bending rigidities in three different lipid classes. The pore-formation free energy in pure bilayers and peptide translocating scenarios are significantly coupled with bilayer thickness. Thicker bilayers require more reversible work to create pores. The pore-formation free energy is higher in peptide–lipid systems than in peptide-free lipid systems due to penalties to maintain the solvation of charged hydrophilic solutes within the membrane environment

Protein Denaturants at Aqueous–Hydrophobic Interfaces: Self-Consistent Correlation between Induced Interfacial Fluctuations and Denaturant Stability at the Interface

The notion of direct interaction between denaturing cosolvent and protein residues has been proposed in dialogue relevant to molecular mechanisms of protein denaturation. Here we consider the correlation between free energetic stability and induced fluctuations of an aqueous–hydrophobic interface between a model hydrophobically associating protein, HFBII, and two common protein denaturants, guanidinium cation (Gdm⁺) and urea. We compute potentials of mean force along an order parameter that brings the solute molecule close to the known hydrophobic region of the protein. We assess potentials of mean force for different relative orientations between the protein and denaturant molecule. We find that in both cases of guanidinium cation and urea relative orientations of the denaturant molecule that are parallel to the local protein–water interface exhibit greater stability compared to edge-on or perpendicular orientations. This behavior has been observed for guanidinium/methylguanidinium cations at the liquid–vapor interface of water, and thus the present results further corroborate earlier findings. Further analysis of the induced fluctuations of the aqueous–hydrophobic interface upon approach of the denaturant molecule indicates that the parallel orientation, displaying a greater stability at the interface, also induces larger fluctuations of the interface compared to the perpendicular orientations. The correlation of interfacial stability and induced interface fluctuation is a recurring theme for interface-stable solutes at hydrophobic interfaces. Moreover, observed correlations between interface stability and induced fluctuations recapitulate connections to local hydration structure and patterns around solutes as evidenced by experiment (Cooper et al., <i>J. Phys. Chem. A</i> <b>2014</b>, <i>118</i>, 5657.) and high-level ab initio/DFT calculations (Baer et al., <i>Faraday Discuss</i> <b>2013</b>, <i>160</i>, 89)

Investigating Hydrophilic Pores in Model Lipid Bilayers Using Molecular Simulations: Correlating Bilayer Properties with Pore-Formation Thermodynamics

Cell-penetrating and antimicrobial peptides show a remarkable ability to translocate across physiological membranes. Along with factors such as electric-potential-induced perturbations of membrane structure and surface tension effects, experiments invoke porelike membrane configurations during the solute transfer process into vesicles and cells. The initiation and formation of pores are associated with a nontrivial free-energy cost, thus necessitating a consideration of the factors associated with pore formation and the attendant free energies. Because of experimental and modeling challenges related to the long time scales of the translocation process, we use umbrella sampling molecular dynamics simulations with a lipid-density-based order parameter to investigate membrane-pore-formation free energy employing Martini coarse-grained models. We investigate structure and thermodynamic features of the pore in 18 lipids spanning a range of headgroups, charge states, acyl chain lengths, and saturation. We probe the dependence of pore-formation barriers on the area per lipid, lipid bilayer thickness, and membrane bending rigidities in three different lipid classes. The pore-formation free energy in pure bilayers and peptide translocating scenarios are significantly coupled with bilayer thickness. Thicker bilayers require more reversible work to create pores. The pore-formation free energy is higher in peptide–lipid systems than in peptide-free lipid systems due to penalties to maintain the solvation of charged hydrophilic solutes within the membrane environment

Translocation Thermodynamics of Linear and Cyclic Nonaarginine into Model DPPC Bilayer via Coarse-Grained Molecular Dynamics Simulation: Implications of Pore Formation and Nonadditivity

Structural mechanisms and underlying thermodynamic determinants of efficient internalization of charged cationic peptides (cell-penetrating peptides, CPPs) such as TAT, polyarginine, and their variants, into cells, cellular constructs, and model membrane/lipid bilayers (large and giant unilamellar or multilamelar vesicles) continue to garner significant attention. Two widely held views on the translocation mechanism center on endocytotic and nonendocytotic (diffusive) processes. Espousing the view of a purely diffusive internalization process (supported by recent experimental evidence, [Säälik, P.; et al. <i>J. Controlled Release</i> <b>2011</b>, <i>153</i>, 117–125]), we consider the underlying free energetics of the translocation of a nonaarginine peptide (Arg₉) into a model DPPC bilayer. In the case of the Arg₉ cationic peptide, recent experiments indicate a higher internalization efficiency of the cyclic structure (cyclic Arg₉) relative to the linear conformer. Furthermore, recent all-atom resolution molecular dynamics simulations of cyclic Arg₉ [Huang, K.; et al. <i>Biophys. J.</i>, <b>2013</b>, <i>104</i>, 412–420] suggested a critical stabilizing role of water- and lipid-constituted pores that form within the bilayer as the charged Arg₉ translocates deep into the bilayer center. Herein, we use umbrella sampling molecular dynamics simulations with coarse-grained Martini lipids, polarizable coarse-grained water, and peptide to explore the dependence of translocation free energetics on peptide structure and conformation via calculation of potentials of mean force along preselected reaction paths allowing and preventing membrane deformations that lead to pore formation. Within the context of the coarse-grained force fields we employ, we observe significant barriers for Arg₉ translocation from bulk aqueous solution to bilayer center. Moreover, we do not find free-energy minima in the headgroup–water interfacial region, as observed in simulations using all-atom force fields. The pore-forming paths systematically predict lower free-energy barriers (ca. 90 kJ/mol lower) than the non pore-forming paths, again consistent with all-atom force field simulations. The current force field suggests no preference for the more compact or covalently cyclic structures upon entering the bilayer. Decomposition of the PMF into the system’s components indicates that the dominant stabilizing contribution along the pore-forming path originates from the membrane as both layers of it deformed due to the formation of pore. Furthermore, our analysis revealed that although there is significant entropic stabilization arising from the enhanced configurational entropy exposing more states as the peptide moves through the bilayer, the enthalpic loss (as predicted by the interactions of this coarse-grained model) far outweighs any former stabilization, thus leading to significant barrier to translocation. Finally, we observe reduction in the translocation free-energy barrier for a second Arg₉ entering the bilayer in the presence of an initial peptide restrained at the center, again, in qualitative agreement with all-atom force fields