Lateral diffusion of ions near membrane surface.

Biological membranes isolate living cells from their environment, while allowing selective molecular transport between the inner and outer realms. For example, Na+ and K+ permeability through ionic channels contributes to neural conduction. Whether the ionic currents arise directly from cations in the bulk, or from the interface, is currently unclear. There are only scant results concerning lateral diffusion of ions on aquated membrane surfaces (and strong belief that this occurs through binding to a diffusing lipid). We performed classical molecular dynamics (MD) simulations of monovalent ions, Na+, K+, and Cl-, near the surface of the zwitterionic palmitoyl-oleoyl-phosphatidylcholine (POPC) membrane. Realistic force-fields for lipids (Amber's Lipid17 and Lipid21) and water (TIP4P-Ew) are tested for the mass and charge densities and the electrostatic potential across the membrane. These calculations reveal that the chloride can bind to the choline moiety through an intervening water molecule by forming a CH⋯OH hydrogen bond, while cations bind to both the phosphatic and carbonyl oxygens of phosphatidylcholine moieties. Upon transitioning from the bulk to the interface, a cation sheds some of its hydration water, which are replaced by headgroup atoms. Notably, an interfacial cation can bind 1-4 headgroup atoms, which is a key to understanding its surface hopping mechanism. We find that cation binding to three headgroup atoms immobilizes it, while binding to four energizes it. Consequently, the lateral cation diffusion rate is only 15-25 times slower than in the bulk, and 4-5 times faster than lipid self-diffusion. K+ diffusion is notably more anomalous than Na+, switching from sub- to super-diffusion after about 2 ns.

Collagen Structured Hydration.

Collagen is a triple-helical protein unique to the extracellular matrix, conferring rigidity and stability to tissues such as bone and tendon. For the [(PPG)10]3 collagen-mimetic peptide at room temperature, our molecular dynamics simulations show that these properties result in a remarkably ordered first hydration layer of water molecules hydrogen bonded to the backbone carbonyl (bb-CO) oxygen atoms. This originates from the following observations. The radius of gyration attests that the PPG triplets are organized along a straight line, so that all triplets (excepting the ends) are equivalent. The solvent-accessible surface area (SASA) for the bb-CO oxygens shows a repetitive regularity for every triplet. This leads to water occupancy of the bb-CO sites following a similar regularity. In the crystal-phase X-ray data, as well as in our 100 K simulations, we observe a 0-2-1 water occupancy in the P-P-G triplet. Surprisingly, a similar (0-1.7-1) regularity is maintained in the liquid phase, in spite of the sub-nsec water exchange rates, because the bb-CO sites rarely remain vacant. The manifested ordered first-shell water molecules are expected to produce a cylindrical electrostatic potential around the peptide, to be investigated in future work.

Temperature and Nuclear Quantum Effects on the Stretching Modes of the Water Hexamer.

The water hexamer has many low-lying isomers, e.g., ring, book, cage, and prism, shifting from two- to three-dimensional structures. We show that this dimensionality change is accompanied by a drop in the quantum nature of the cluster, as manifested in the red shift of the quantal OH stretching modes as compared with their classical counterparts. We obtain this "nuclear quantum effect" (NQE) as the mean deviation between the OH stretch frequencies from velocity autocorrelation Fourier transforms from classical trajectories on a high-level water potential (MB-pol) as compared with scaled harmonic frequencies from high-level quantum chemistry calculations. With a universal scaling factor, the predicted OH frequencies agree with experiment to a mean absolute deviation ≤10 cm-1, which allows unequivocal isomer assignments. By assuming temperature-independent NQEs, we produce the temperature dependence of the cage isomer OH stretch spectrum below 70 K, where it is the dominant structure. All bands widen and blue-shift with increasing temperature, most conspicuously the reddest mode, which thus constitutes a "vibrational thermometer".

Temperature Dependence of Intramolecular Vibrational Bands in Small Water Clusters.

Cyclic water clusters are pivotal for understanding atmospheric reactions as well as liquid water, yet the temperature (T) dependence of their dynamics and spectroscopy is poorly studied. The development of highly accurate water potentials, such as MB-pol, partly rectifies this. It remains to account for the quantum nuclear effects (NQE), because quantum nuclear dynamics become increasingly inaccurate at low temperatures. From a practical point of view, we find that NQE can be accounted for simply by subtracting a constant from the frequencies obtained from the velocity autocorrelation functions (VACF) of classical nuclear dynamics, resulting in unprecedented agreement with experiment, mostly within 5 cm-1. We have performed classical simulations of (H2O)n clusters (n = 2-5) from 20 K and up to their melting temperature, calculating both all-atom and partial VACF, thus generating the temperature dependence of the vibrational frequencies (IR and Raman bands). Focusing on the hydrogen-bonded (HBed) OH stretch and HOH bend, we find opposing T dependencies. The HBed OH modes blue shift linearly with T, attributed to ring expansion rather than any specific conformational change. The lowest-frequency Raman concerted mode is predicted to show the largest such shift. In contrast, the HOH bend undergoes a red-shift, with the highest frequency concerted band undergoing the largest red-shift. These results can be explained by a coupled-oscillator model for n hydrogen atoms on a ring, constrained to move either tangentially (stretch) or perpendicularly (bend) to the ring. With increasing temperature and weakening of HBs, the intrinsic force constant increases (stretch) or remains constant (bend), while the nearest-neighbor coupling constant decreases, and this results in the interesting behavior revealed herein. T-dependent Raman studies are required for testing some of these predictions.

Ionic radii of hydrated sodium cation from QTAIM.

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na+(H2O)n clusters, as a function of the sodium coordination number (CN = 2-6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4-12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na+-O distances into Na+ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na+ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases.

Thermally Induced Hydrogen-Bond Rearrangements in Small Water Clusters and the Persistent Water Tetramer.

Small water clusters absorb heat and catalyze pivotal atmospheric reactions. Yet, experiments produced conflicting results on water cluster distribution under atmospheric conditions. Additionally, it is unclear which "phase transitions" such clusters exhibit, at what temperatures, and what are their underlying molecular mechanisms. We find that logarithmically small tails in the radial probability densities of (H2O) n clusters (n = 2 - 6) provide direct testimony for such transitions. Using the best available water potential (MB-pol), an advanced thermostating algorithm (g-BAOAB), and sufficiently long trajectories, we map the "bifurcation", "melting", and (hitherto unexplored) "vaporization" transitions, finding that both melting and vaporization proceed via a "monomer on a ring" conformer, exhibiting huge distance fluctuations at the vaporization temperatures (T v). T v may play a role in determining the atmospheric cluster size distribution such that the dimer and tetramer, with their exceptionally low/high T v values, are under/over-represented in these distributions, as indeed observed in nondestructive mass spectrometric measurements.

Structure, spectroscopy, and dynamics of the phenol-(water)2 cluster at low and high temperatures.

Aqueous solutions are complex due to hydrogen bonding (HBing). While gas-phase clusters could provide clues on the solution behavior, most neutral clusters were studied at cryogenic temperatures. Recent results of Shimamori and Fujii provide the first IR spectrum of warm phenol-(H2O)2 clusters. To understand the temperature (T) effect, we have revisited the structure and spectroscopy of phenol-(H2O)2 at all T. While older quantum chemistry work concluded that the cyclic isomers are the most stable, the inclusion of dispersion interactions reveals that they are nearly isoenergetic with isomers forming π-HBs with the phenyl ring. Whereas the OH-stretch bands were previously assigned to purely local modes, we show that at low T they involve a concerted component. We have calculated the (static) anharmonic IR spectra for all low-lying isomers, showing that at the MP2 level, one can single out one isomer (udu) as accounting for the low-T spectrum to 3 cm-1 accuracy. Yet no isomer can explain the substantial blueshift of the phenyl-OH band at elevated temperatures. We describe the temperature effect using ab initio molecular dynamics with a density functional and basis-set (B3LYP-D3/aug-cc-pVTZ) that provide a realistic description of OH⋯O vs. OH⋯π HBing. From the dipole moment autocorrelation function, we obtain good description for both low- and high-T spectra. Trajectory visualization suggests that the ring structure remains mostly intact even at high T, with intermittent switching between OH⋯O and OH⋯π HBing and lengthening of all 3 HBs. The phenyl-OH blueshift is thus attributed to strengthening of its OH bond. A model for three beads on a ring suggests that this shift is partly offset by the elimination of coupling to the other OH bonds in the ring, whereas for the two water molecules these two effects nearly cancel.

Isoelectronic Theory for Cationic Radii.

Ionic radii play a central role in all branches of chemistry, in geochemistry, solid-state physics, and biophysics. While authoritative compilations of experimental radii are available, their theoretical basis is unclear, and no quantitative derivation exists. Here we show how a quantitative calculation of ionic radii for cations with spherically symmetric charge distribution is obtained by charge-weighted averaging of outer and inner radii. The outer radius is the atomic (covalent) radius, and the inner is that of the underlying closed-shell orbital. The first is available from recent experimental compilations, whereas the second is calculated from a "modified Slater theory", in which the screening (S) and effective principal quantum number (n*) were previously obtained by fitting experimental ionization energies in isoelectronic series. This reproduces the experimental Shannon-Prewitt "effective ionic radii" (for coordination number 6) with mean absolute deviation of 0.025 Å, approximately the accuracy of the experimental data itself. The remarkable agreement suggests that the calculation of other cationic attributes might be based on similar principles.

Origin of proton affinity to membrane/water interfaces.

Proton diffusion along biological membranes is vitally important for cellular energetics. Here we extended previous time-resolved fluorescence measurements to study the time and temperature dependence of surface proton transport. We determined the Gibbs activation energy barrier ΔG ‡r that opposes proton surface-to-bulk release from Arrhenius plots of (i) protons' surface diffusion constant and (ii) the rate coefficient for proton surface-to-bulk release. The large size of ΔG ‡r disproves that quasi-equilibrium exists in our experiments between protons in the near-membrane layers and in the aqueous bulk. Instead, non-equilibrium kinetics describes the proton travel between the site of its photo-release and its arrival at a distant membrane patch at different temperatures. ΔG ‡r contains only a minor enthalpic contribution that roughly corresponds to the breakage of a single hydrogen bond. Thus, our experiments reveal an entropic trap that ensures channeling of highly mobile protons along the membrane interface in the absence of potent acceptors.

Reinvestigation of the Infrared Spectrum of the Gas-Phase Protonated Water Tetramer.

Gas-phase H9O4+ has been considered an archetypal Eigen cation, H3O+(H2O)3. Yet ab initio molecular dynamics (AIMD) suggested that its infrared spectrum is explained by a linear-chain Zundel isomer, alone or in a mixture with the Eigen cation. Recently, hole-burning experiments suggested a single isomer, with a second-order vibrational perturbation theory (VPT2) spectrum agreeing with the Eigen cation. To resolve this discrepancy, we have extended both calculations to more advanced DFT functionals, better basis sets, and dispersion correction. For Zundel-isomers, we find VPT2 anharmonic frequencies for four low-frequency modes involving the excess proton unreliable, including the 1750 cm-1 band that is pivotal for differentiating between Zundel and Eigen isomers. Because the analogous bands of the H5O2+ cation show little effect of anharmonicity, we utilize the harmonic frequencies for these modes. With this caveat, both AIMD and VPT2 agree on the spectrum as originating from a Zundel isomer. VPT2 also shows that both isomers have the same spectrum in the high frequency region, so that the hole burning experiments should be extended to lower frequencies.

Proton Wire Dynamics in the Green Fluorescent Protein.

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the "bottom" of the GFP barrel with a "water pool" (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP.

Reversible Excited-State Proton Geminate Recombination: Revisited.

About three decades ago, Pines and Huppert found that the excited-state proton transfer to water from a photoacid (8-hydroxy-1,3,6-pyrene trisulfonate (HPTS)) is followed by an efficient diffusion-assisted reversible geminate-recombination of the proton. To model the reaction, Pines, Huppert, and Agmon used the Debye-Smoluchowski equation with boundary conditions appropriate for reversible contact reaction kinetics. This reaction model has been used successfully to quantitatively fit the experimental data of the time-resolved fluorescence of HPTS and several commonly used photoacids. A consequence of the reversibility of this reaction is an apparent long-time tail of the photoacid fluorescence signal, obeying (after lifetime correction) a t-3/2 power law asymptotics. Recently, Lawler and Fayer reported that in bulk water the observed power-law decay of the long-time fluorescence tail of HPTS is -1.1 rather than -1.5, as expected from the spherically symmetric diffusion model. In the current study, we reaffirm our previous reports of the power-law behavior of HPTS fluorescence. We also demonstrate that molecular-level complications such as the deviation from spherical symmetry, rotational dynamics, competitive proton binding to the sulfonate moieties of HPTS, distance-dependent diffusion coefficient, and the initial starting point of the proton can affect the observed kinetics only at intermediate times, but not at asymptotically long times. Theoretically, we analyze the rebinding kinetics in terms of the number of extrema of the logarithmic derivative, showing subtle effects on the direction of approach to the asymptotic line (whether from above or below), which also appears to be corroborated experimentally.

Protons and Hydroxide Ions in Aqueous Systems.

Understanding the structure and dynamics of water's constituent ions, proton and hydroxide, has been a subject of numerous experimental and theoretical studies over the last century. Besides their obvious importance in acid-base chemistry, these ions play an important role in numerous applications ranging from enzyme catalysis to environmental chemistry. Despite a long history of research, many fundamental issues regarding their properties continue to be an active area of research. Here, we provide a review of the experimental and theoretical advances made in the last several decades in understanding the structure, dynamics, and transport of the proton and hydroxide ions in different aqueous environments, ranging from water clusters to the bulk liquid and its interfaces with hydrophobic surfaces. The propensity of these ions to accumulate at hydrophobic surfaces has been a subject of intense debate, and we highlight the open issues and challenges in this area. Biological applications reviewed include proton transport along the hydration layer of various membranes and through channel proteins, problems that are at the core of cellular bioenergetics.

Complete Assignment of the Infrared Spectrum of the Gas-Phase Protonated Ammonia Dimer.

The infrared (IR) spectrum of the ammoniated ammonium dimer is more complex than those of the larger protonated ammonia clusters due to close-lying fundamental and combination bands and possible Fermi resonances (FR). To date, the only theoretical analysis involved partial dimensionality quantum nuclear dynamic simulations, assuming a symmetric structure (D3d) with the proton midway between the two nitrogen atoms. Here we report an extensive study of the less symmetric (C3v) dimer, utilizing both second order vibrational perturbation theory (VPT2) and ab initio molecular dynamics (AIMD), from which we calculated the Fourier transform (FT) of the dipole-moment autocorrelation function (DACF). The resultant IR spectrum was assigned using FTed velocity autocorrelation functions (VACFs) of several interatomic distances and angles. At 50 K, we have been able to assign all 21 AIMD fundamentals, in reasonable agreement with MP2-based VPT2, about 30 AIMD combination bands, and a difference band. The combinations involve a wag or the NN stretch as one of the components, and appear to follow symmetry selection rules. On this basis, we suggest possible assignments of the experimental spectrum. The VACF-analysis revealed two possible FR bands, one of which is the strongest peak in the computed spectrum. Raising the temperature to 180 K eliminated the "proton transfer mode" (PTM) fundamental, and reduced the number of observed combination bands and FRs. With increasing temperature, fundamentals red-shift, and the doubly degenerate wags exhibit larger anharmonic splittings in their VACF bending spectra. We have repeated the analysis for the H3ND(+)NH3 isotopologue, finding that it has a simplified spectrum, with all the strong peaks being fundamentals. Experimental study of this isotopologue may thus provide a good starting point for disentangling the N2H7(+) spectrum.

Structure and Spectroscopy of Hydrated Sodium Ions at Different Temperatures and the Cluster Stability Rules.

The sodium cation plays an important role in several physiological processes. Understanding its solvation may help understanding ion selectivity in sodium channels that are pivotal for nerve impulses. This paper presents a thorough investigation of over 75 isomers of gas-phase Na(+)(H2O)(n=1-8) clusters, whose optimized structures, energies, and (harmonic) vibrational frequencies were computed quantum mechanically at the full MP2/6-31++G(d,p) level of theory. From these data, we have calculated the temperature effects on the cluster thermodynamic functions, and thus the equilibrium Boltzmann distribution for each n. For a selected number of isomers, we have corrected the calculations for basis set superposition error (BSSE) to obtain accurate clustering energies, in excellent agreement with experiment. The computed clusters are overwhelmingly 4-coordinated, as opposed to bulk liquid water, where sodium cations are believed to be mostly 5- or 6-coordinated. To explain this, we suggest the "cluster stability rules", a set of coordination-number-dependent hydrogen-bond (HB) strengths that can be obtained using a single BSSE correction. Assuming additivity and transferability, these reproduce the relative stability of most of our computed isomers. These rules enable us to elucidate the trends in HB strengths, outlining the major determinants of cluster stability. For n = 4 and 5, we have also performed anharmonic vibrational calculations (VPT2) to compare with available photodissociation infrared spectra of these gas-phase clusters. The comparison suggests that the experiments actually monitor a mixture of predominantly 3-coordinated isomers, which is quite remote from the computed Boltzmann distribution, particularly at low temperatures. Surprisingly, for these experiments, water evaporation pathways can rationalize the non-equilibrium isomer distribution. The equilibrium isomer distribution is, in turn, rationalized by the entropy of internal rotations of "dangling" water molecules.

The hole in the barrel: water exchange at the GFP chromophore.

Internal water molecules in proteins are conceivably part of the protein structure, not exchanging easily with the bulk. We present a detailed molecular dynamics study of the water molecule bound to the green fluorescent protein (GFP) chromophore that conducts its proton following photoexcitation. It readily exchanges above 310 K through a hole that forms between strands 7 and 10, due to fluctuations in the 6-7 loop. As the hole widens, rapid succession of water exchange events occur. The exiting water molecule passes three layers of atoms, constituting the binding, internal, and surface sites. Along this pathway, hydrogen bonding protein residues are replaced with water molecules. The mean squared displacement along this pathway is initially subdiffusive, becomes superdiffusive as the water traverses the protein wall in a flip-flop motion, and reverts to normal diffusion in the bulk. The residence correlation function for the bound state decays biexponentially, supporting this three-site scenario. For a favorable orientation of the Thr203 side-chain, the hole often fills with a single file of water molecules that could indeed rapidly conduct the photodissociated proton outside the protein. The activation enthalpy for its formation, 26 kJ/mol, agrees with the experimental value for a protein conformation change suggested to gate proton escape.

Protonated water dimer on benzene: standing Eigen or crouching Zundel?

Protonated water clusters that are hydrogen-bonded to a neutral benzene molecule are a reductionist model for protons at hydrophobic surfaces, which are of fundamental importance in biological energy transduction processes. Of particular interest is the protonated water dimer ("Zundel ion") on benzene, whose gas-phase messenger IR spectrum has been previously interpreted in terms of an asymmetric binding of the protonated water dimer to the benzene ring through a single water molecule. This "standing Eigen" isomer has a hydronium core. We have found an alternative "crouching Zundel" isomer, which attaches to the benzene ring symmetrically via both of its water molecules. When Ar-tagged, it has an IR spectrum in much better agreement with experiment than the standing Eigen isomer, particularly at the lower frequencies. These conclusions are based on static harmonic (and anharmonic) normal-mode analysis using density functional theory with various (dispersion corrected) functionals and particularly on dynamic anharmonic spectra obtained from the dipole autocorrelation functions from classical ab initio molecular dynamics with the BLYP, PBE, and B3LYP functionals. Possible implications to protons on water/organic-phase interfaces are discussed.

Network analysis of proton transfer in liquid water.

Proton transfer in macromolecular systems is a fascinating yet elusive process. In the last ten years, molecular simulations have shown to be a useful tool to unveil the atomistic mechanism. Notwithstanding, the large number of degrees of freedom involved make the accurate description of the process very hard even for the case of proton diffusion in bulk water. Here, multi-state empirical valence bond molecular dynamics simulations in conjunction with complex network analysis are applied to study proton transfer in liquid water. Making use of a transition network formalism, this approach takes into account the time evolution of several coordinates simultaneously. Our results provide evidence for a strong dependence of proton transfer on the length of the hydrogen bond solvating the Zundel complex, with proton transfer enhancement as shorter bonds are formed at the acceptor site. We identify six major states (nodes) on the network leading from the "special pair" to a more symmetric Zundel complex required for transferring the proton. Moreover, the second solvation shell specifically rearranges to promote the transfer, reiterating the idea that solvation beyond the first shell of the Zundel complex plays a crucial role in the process.

Deciphering the infrared spectrum of the protonated water pentamer and the hybrid Eigen-Zundel cation.

Traditionally, infrared band assignment for the protonated water clusters, such as H(+)(H2O)5, is based on their lowest energy isomer. Recent experiments extend the observation spectral window to lower frequencies, for which such assignment appears to be inadequate. Because this hydrogen-bonded system is highly anharmonic, harmonic spectral calculations are insufficient for reliable interpretation. Consequently, we have calculated the IR spectrum of several isomers of the protonated water pentamer using an inherently anharmonic methodology, utilizing dipole and velocity autocorrelation functions computed from ab initio molecular dynamic trajectories. While the spectrum of H(+)(H2O)5 is universally assumed to represent the branched Eigen isomer, we find a better agreement for a mixture of a ring and linear isomers. The first has an Eigen core and contributes at high frequencies, whereas the latter accounts for all prominent low-frequency bands. Interestingly, its core is neither a classical Eigen nor a Zundel cation, but rather has hybrid geometry. Such an isomer may play a role in proton conductance along short proton wires.