Realistic Simulations of Proton Transport along the Gramicidin Channel: Demonstrating the Importance of Solvation Effects

Proton exit pathways surrounding the oxygen evolving complex of photosystem II

Photosystem II allows water to be the primary electron source for the photosynthetic electron transfer chain. Water is oxidized to dioxygen at the Oxygen Evolving Complex (OEC), a Mn₄CaO₅ inorganic core embedded on the lumenal side of PSII. Water-filled channels surrounding the OEC must bring in substrate water molecules, remove the product protons to the lumen, and may transport the product oxygen. Three water-filled channels, denoted large, narrow, and broad, extend from the OEC towards the aqueous surface more than 15 Å away. However, the role of each pathway in the transport in and out of the OEC is yet to be established. Here, we combine Molecular Dynamics (MD), Multi Conformation Continuum Electrostatics (MCCE) and Network Analysis to compare and contrast the three potential proton transfer paths. Hydrogen bond network analysis shows that near the OEC the waters are highly interconnected with similar free energy for hydronium at all locations. The paths diverge as they move towards the lumen. The water chain in the broad channel is better connected than in the narrow and large channels, where disruptions in the network are observed approximately 10 Å from the OEC. In addition, the barrier for hydronium translocation is lower in the broad channel. Thus, a proton released from any location on the OEC can access all paths, but the likely exit to the lumen passes through PsbO via the broad channel.

Characterizing the Water Wire in the Gramicidin Channel Found by Monte Carlo Sampling Using Continuum Electrostatics and in Molecular Dynamics Trajectories with Conventional or Polarizable Force Fields

Water molecules play a key role in all biochemical processes. They help define the shape of proteins, and they are reactant or product in many reactions and are released as ligands are bound. They facilitate the transfer of protons through transmembrane proton channel, pump and transporter proteins. Continuum electrostatics (CE) force fields used by program Multiconformation CE (MCCE) capture electrostatic interactions in biomolecules with an implicit solvent, which captures the averaged solvent water equilibrium properties. Hybrid CE methods can use explicit water molecules within the protein surrounded by implicit solvent. These hybrid methods permit the study of explicit hydrogen bond networks within the protein and allow analysis of processes such as proton transfer reactions. Yet hybrid CE methods have not been rigorously tested. Here, we present an explicit treatment of water molecules in the Gramicidin A (gA) channel using MCCE and compare the resulting distributions of water molecules and key hydration features against those obtained with explicit solvent Molecular Dynamics (MD) simulations with the nonpolarizable CHARMM36 and polarizable Drude force fields. CHARMM36 leads to an aligned water wire in the channel characterized by a large absolute net water dipole moment; the MCCE and Drude analysis lead to a small net dipole moment as the water molecules change orientation within the channel. The correct orientation is not as yet known, so these calculations identify an open question.

Highlighting membrane protein structure and function: A celebration of the Protein Data Bank

Biological membranes define the boundaries of cells and compartmentalize the chemical and physical processes required for life. Many biological processes are carried out by proteins embedded in or associated with such membranes. Determination of membrane protein (MP) structures at atomic or near-atomic resolution plays a vital role in elucidating their structural and functional impact in biology. This endeavor has determined 1198 unique MP structures as of early 2021. The value of these structures is expanded greatly by deposition of their three-dimensional (3D) coordinates into the Protein Data Bank (PDB) after the first atomic MP structure was elucidated in 1985. Since then, free access to MP structures facilitates broader and deeper understanding of MPs, which provides crucial new insights into their biological functions. Here we highlight the structural and functional biology of representative MPs and landmarks in the evolution of new technologies, with insights into key developments influenced by the PDB in magnifying their impact.

A Review on Applications of Computational Methods in Drug Screening and Design

Drug development is one of the most significant processes in the pharmaceutical industry. Various computational methods have dramatically reduced the time and cost of drug discovery. In this review, we firstly discussed roles of multiscale biomolecular simulations in identifying drug binding sites on the target macromolecule and elucidating drug action mechanisms. Then, virtual screening methods (e.g., molecular docking, pharmacophore modeling, and QSAR) as well as structure- and ligand-based classical/de novo drug design were introduced and discussed. Last, we explored the development of machine learning methods and their applications in aforementioned computational methods to speed up the drug discovery process. Also, several application examples of combining various methods was discussed. A combination of different methods to jointly solve the tough problem at different scales and dimensions will be an inevitable trend in drug screening and design.

On the control of the proton current in the voltage-gated proton channel Hv1

The nature of the action of voltage-activated proton transport proteins is a conundrum of great current interest. Here we approach this issue by exploring the action of Hv1, a voltage-gated proton channel found in different cells in humans and other organisms. Our study focuses on evaluating the free energy of transporting a proton through the channel, as well as the effect of the proton transfer through D112, in both the closed and open channel conformations. It is found that D112 allows a transported proton to bypass the electrostatic barrier of the open channel, while not being able to help in passing the barrier in the closed form. This reflects the change in position of the gating arginine residues relative to D112, upon voltage activation. Significantly, the effect of D112 accounts for the observed trend in selectivity by overcoming the electrostatic barrier at its highest point. Thus, the calculations provide a structure/function correlation for the Hv1 system. The present work also clarifies that the action of Hv1 is not controlled by a Grotthuss mechanism but, as is always the case, by the protein electrostatic potential at the rate-limiting barriers.

Water mediated dielectric polarizability and electron charge transport properties of high resistance natural fibers

Recent studies showed that silk and human hair fibers develop thermoelectric properties at optimal water, temperature and light conditions. The nature of charge carriers and the role of water in mediating charge conduction in these fibers is an unexplored issue. By studying four different classes of natural fibers, viz., silk cocoon, human hair, jute and corn silk, we uncover their common electrical transport properties and its dependence on water concentration and temperature. All these fibers uniformly exhibit nonlinear, hysteretic current - voltage characteristics, which scale with water concentration. The optimal electrical conductivity shows thermally activated hopping transport mechanism. Scanning tunneling microscope (STM) and dielectric measurements of silk cocoon fibers showed the electronic density of states and dielectric properties of the hydrated medium enhances with water concentration. Electron paramagnetic resonance (EPR) study reveals that the charge carriers in these membranes are electronic in nature. Our results are explained through the mechanism of hopping of a Polaron, which is an electron surrounded by positive charge fluctuations created by water molecules. The mechanism unravels the peculiar role water plays in mediating electrical activity in these membranes and also opens the possibility for exploring such charge transport mechanism in other biological membranes.

Classical Molecular Dynamics with Mobile Protons

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Ultrafast proton transport in sub-1-nm diameter carbon nanotube porins

Proton transport plays an important role in many biological processes due to the ability of protons to rapidly translocate along chains of hydrogen-bonded water molecules. Molecular dynamics simulations have predicted that confinement in hydrophobic nanochannels should enhance the rate of proton transport. Here, we show that 0.8-nm-diameter carbon nanotube porins, which promote the formation of one-dimensional water wires, can support proton transport rates exceeding those of bulk water by an order of magnitude. The transport rates in these narrow nanotube pores also exceed those of biological channels and Nafion. With larger 1.5-nm-diameter nanotube porins, proton transport rates comparable to bulk water are observed. We also show that the proton conductance of these channels can be modulated by the presence of Ca(2+) ions. Our results illustrate the potential of small-diameter carbon nanotube porins as a proton conductor material and suggest that strong spatial confinement is a key factor in enabling efficient proton transport.

Biased Molecular Simulations for Free-Energy Mapping: A Comparison on the KcsA Channel as a Test Case

The calculation of free-energy landscapes in proteins is a challenge for modern numerical simulations. As to the case of potassium ion channels is concerned, it is particularly interesting because of the nanometric dimensions of the selectivity filter, where the complex electrostatics is highly relevant. The present study aims at comparing three different techniques used to bias molecular dynamics simulations, namely Umbrella Sampling, Steered Molecular Dynamics, and Metadynamics, never applied all together in the past to the same channel protein. Our test case is represented by potassium ions permeating the selectivity filter of the KcsA channel.

Role of the Membrane Dipole Potential for Proton Transport in Gramicidin A Embedded in a DMPC Bilayer

The membrane potential at the water/phospholipid interfaces may play a key role for proton conduction of gramicidin A (gA). Here we address this issue by Density Functional Theory-based molecular dynamics and metadynamics simulations. The calculations, performed on gA embedded in a solvated 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) model membrane environment (about 2,000 atoms), indicate that (i) the membrane dipole potential rises at the channel mouth by ∼0.4 V. A similar value has been measured for gA embedded in a DMPC monolayer; (ii) the calculated free energy barrier is located at the channel entrance, consistent with experiments comparing gA proton conduction in different bilayers. The electronic structures of the proton ligands (water molecules and peptide units) are similar to those in the bulk solvent. Based on these results, we suggest an important role of the membrane dipole potential for the free energy barrier of proton permeation of gA. This may provide a rationale for the large increase in the rate of proton conduction under application of a transmembrane voltage, as observed experimentally. Our calculations might suggest also a role for proton desolvation for the permeation process. This role has already emerged from EVB calculations on gA embedded in a model membrane.

Adenosine triphosphate hydrolysis mechanism in kinesin studied by combined quantum-mechanical/molecular-mechanical metadynamics simulations

Kinesin is a molecular motor that hydrolyzes adenosine triphosphate (ATP) and moves along microtubules against load. While motility and atomic structures have been well-characterized for various members of the kinesin family, not much is known about ATP hydrolysis inside the active site. Here, we study ATP hydrolysis mechanisms in the kinesin-5 protein Eg5 by using combined quantum mechanics/molecular mechanics metadynamics simulations. Approximately 200 atoms at the catalytic site are treated by a dispersion-corrected density functional and, in total, 13 metadynamics simulations are performed with their cumulative time reaching ~0.7 ns. Using the converged runs, we compute free energy surfaces and obtain a few hydrolysis pathways. The pathway with the lowest free energy barrier involves a two-water chain and is initiated by the Pγ-Oβ dissociation concerted with approach of the lytic water to PγO3-. This immediately induces a proton transfer from the lytic water to another water, which then gives a proton to the conserved Glu270. Later, the proton is transferred back from Glu270 to HPO(4)2- via another hydrogen-bonded chain. We find that the reaction is favorable when the salt bridge between Glu270 in switch II and Arg234 in switch I is transiently broken, which facilitates the ability of Glu270 to accept a proton. When ATP is placed in the ADP-bound conformation of Eg5, the ATP-Mg moiety is surrounded by many water molecules and Thr107 blocks the water chain, which together make the hydrolysis reaction less favorable. The observed two-water chain mechanisms are rather similar to those suggested in two other motors, myosin and F1-ATPase, raising the possibility of a common mechanism.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Quantum dynamics in continuum for proton transport--generalized correlation

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

Computational Study of the pKa Values of Potential Catalytic Residues in the Active Site of Monoamine Oxidase B

Monoamine oxidase (MAO), which exists in two isozymic forms, MAO A and MAO B, is an important flavoenzyme responsible for the metabolism of amine neurotransmitters such as dopamine, serotonin, and norepinephrine. Despite extensive research effort, neither the catalytic nor the inhibition mechanisms of MAO have been completely understood. There has also been dispute with regard to the protonation state of the substrate upon entering the active site, as well as the identity of residues that are important for the initial deprotonation of irreversible acetylenic inhibitors, in accordance with the recently proposed mechanism. Therefore, in order to investigate features essential for the modes of action of MAO, we have calculated pKa values of three relevant tyrosine residues in the MAO B active site, with and without dopamine bound as the substrate (as well as the pKa of the dopamine itself in the active site). The calculated pKa values for Tyr188, Tyr398, and Tyr435 in the complex are found to be shifted upward to 13.0, 13.7, and 14.7, respectively, relative to 10.1 in aqueous solution, ruling out the likelihood that they are viable proton acceptors. The altered tyrosine pKa values could be rationalized as an interplay of two opposing effects: insertion of positively charged bulky dopamine that lowers tyrosine pKa values, and subsequent removal of water molecules from the active site that elevates tyrosine pKa values, in which the latter prevails. Additionally, the pKa value of the bound dopamine (8.8) is practically unchanged compared to the corresponding value in aqueous solution (8.9), as would be expected from a charged amine placed in a hydrophobic active site consisting of aromatic moieties. We also observed potentially favorable cation-π interactions between the -NH3(+) group on dopamine and aromatic moieties, which provide a stabilizing effect to the charged fragment. Thus, we offer here theoretical evidence that the amine is most likely to be present in the active site in its protonated form, which is similar to the conclusion from experimental studies of MAO A (Jones et al. J. Neural Trans.2007, 114, 707-712). However, the free energy cost of transferring the proton from the substrate to the bulk solvent is only 1.9 kcal mol(-1), leaving open the possibility that the amine enters the chemical step in its neutral form. In conjunction with additional experimental and computational work, the data presented here should lead toward a deeper understanding of mechanisms of the catalytic activity and irreversible inhibition of MAO B, which can allow for the design of novel and improved MAO B inhibitors.

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model.

Simulating electrostatic energies in proteins: perspectives and some recent studies of pKas, redox, and other crucial functional properties

Electrostatic energies provide what is arguably the most effective tool for structure-function correlation of biological molecules. Here, we provide an overview of the current state-of-the-art simulations of electrostatic energies in macromolecules, emphasizing the microscopic perspective but also relating it to macroscopic approaches. We comment on the convergence issue and other problems of the microscopic models and the ways of keeping the microscopic physics while moving to semi-macroscopic directions. We discuss the nature of the protein dielectric "constants" reiterating our long-standing point that the dielectric "constants" in semi-macroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering different functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding, and protein stability. We emphasize the microscopic overcharging approach for studying pK(a) 's of internal groups in proteins and give a demonstration of power of this approach. We also emphasize recent advances in coarse grained models with a physically based electrostatic treatment and provide some examples including further directions in treating voltage activated ion channels.

Water wires in atomistic models of the Hv1 proton channel

The voltage-gated proton channel (Hv1) is homologous to the voltage-sensing domain (VSD) of voltage-gated potassium (Kv) channels but lacks a separate pore domain. The Hv1 monomer has dual functions: it gates the proton current and also serves as the proton conduction pathway. To gain insight into the structure and dynamics of the yet unresolved proton permeation pathway, we performed all-atom molecular dynamics simulations of two different Hv1 homology models in a lipid bilayer in excess water. The structure of the Kv1.2-Kv2.1 paddle-chimera VSD was used as template to generate both models, but they differ in the sequence alignment of the S4 segment. In both models, we observe a water wire that extends through the membrane, whereas the corresponding region is dry in simulations of the Kv1.2-Kv2.1 paddle-chimera. We find that the kinetic stability of the water wire is dependent upon the identity and location of the residues lining the permeation pathway, in particular, the S4 arginines. A measurement of water transport kinetics indicates that the water wire is a relatively static feature of the permeation pathway. Taken together, our results suggest that proton conduction in Hv1 may occur via Grotthuss hopping along a robust water wire, with exchange of water molecules between inner and outer ends of the permeation pathway minimized by specific water-protein interactions. This article is part of a Special Issue entitled: Membrane protein structure and function.

Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems

Recent years have witnessed an explosion in computational power, leading to attempts to model ever more complex systems. Nevertheless, there remain cases for which the use of brute-force computer simulations is clearly not the solution. In such cases, great benefit can be obtained from the use of physically sound simplifications. The introduction of such coarse graining can be traced back to the early usage of a simplified model in studies of proteins. Since then, the field has progressed tremendously. In this review, we cover both key developments in the field and potential future directions. Additionally, particular emphasis is given to two general approaches, namely the renormalization and reference potential approaches, which allow one to move back and forth between the coarse-grained (CG) and full models, as these approaches provide the foundation for CG modeling of complex systems.

Proton transport in biological systems can be probed by two-dimensional infrared spectroscopy

We propose a new method to determine the proton transfer (PT) rate in channel proteins by two-dimensional infrared (2DIR) spectroscopy. Proton transport processes in biological systems, such as proton channels, trigger numerous fundamental biochemical reactions. Due to the limitation in both spatial and time resolution of the traditional experimental approaches, describing the whole proton transport process and identifying the rate limiting steps at the molecular level is challenging. In the present paper, we focus on proton transport through the Gramicidin A channel. Using a kinetic PT model derived from all-atom molecular dynamics simulations, we model the amide I region of the 2DIR spectrum of the channel protein to examine its sensitivity to the proton transport process. We demonstrate that the 2DIR spectrum of the isotope-labeled channel contain information on the PT rate, which may be extracted by analyzing the antidiagonal linewidth of the spectral feature related to the labeled site. Such experiments in combination with detailed numerical simulations should allow the extraction of site dependent PT rates, providing a method for identifying possible rate limiting steps for proton channel transfer.

Multiscale modeling of biological functions

Recent years have witnessed a tremendous explosion in computational power, which in turn has resulted in great progress in the complexity of the biological and chemical problems that can be addressed by means of all-atom simulations. Despite this, however, our computational time is not infinite, and in fact many of the key problems of the field were resolved long before the existence of the current levels of computational power. This review will start by presenting a brief historical overview of the use of multiscale simulations in biology, and then present some key developments in the field, highlighting several cases where the use of a physically sound simplification is clearly superior to a brute-force approach. Finally, some potential future directions will be discussed.

Multiscale simulations of protein landscapes: using coarse-grained models as reference potentials to full explicit models

Evaluating the free-energy landscape of proteins and the corresponding functional aspects presents a major challenge for computer simulation approaches. This challenge is due to the complexity of the landscape and the enormous computer time needed for converging simulations. The use of simplified coarse-grained (CG) folding models offers an effective way of sampling the landscape but such a treatment, however, may not give the correct description of the effect of the actual protein residues. A general way around this problem that has been put forward in our early work (Fan et al., Theor Chem Acc 1999;103:77-80) uses the CG model as a reference potential for free-energy calculations of different properties of the explicit model. This method is refined and extended here, focusing on improving the electrostatic treatment and on demonstrating key applications. These applications include: evaluation of changes of folding energy upon mutations, calculations of transition-states binding free energies (which are crucial for rational enzyme design), evaluations of catalytic landscape, and evaluations of the time-dependent responses to pH changes. Furthermore, the general potential of our approach in overcoming major challenges in studies of structure function correlation in proteins is discussed.

Temperature dependence of proton permeation through a voltage-gated proton channel

Voltage-gated proton channels are found in many different types of cells, where they facilitate proton movement through the membrane. The mechanism of proton permeation through the channel is an issue of long-term interest, but it remains an open question. To address this issue, we examined the temperature dependence of proton permeation. Under whole cell recordings, rapid temperature changes within a few milliseconds were imposed. This method allowed for the measurement of current amplitudes immediately before and after a temperature jump, from which the ratios of these currents (Iratio) were determined. The use of Iratio for evaluating the temperature dependence minimized the contributions of factors other than permeation. Temperature jumps of various degrees (DeltaT, -15 to 15 degrees C) were applied over a wide temperature range (4-49 degrees C), and the Q10s for the proton currents were evaluated from the Iratios. Q10 exhibited a high temperature dependence, varying from 2.2 at 10 degrees C to 1.3 at 40 degrees C. This implies that processes with different temperature dependencies underlie the observed Q10. A novel resistivity pulse method revealed that the access resistance with its low temperature dependence predominated in high temperature ranges. The measured temperature dependence of Q10 was decomposed into Q10 of the channel and of the access resistances. Finally, the Q10 for proton permeation through the voltage-gated proton channel itself was calculated and found to vary from 2.8 at 5 degrees C to 2.2 at 45 degrees C, as expected for an activation enthalpy of 64 kJ/mol. The thermodynamic features for proton permeation through proton-selective channels were discussed for the underlying mechanism.

Functional role of Asp160 and the deprotonation mechanism of ammonium in the Escherichia coli ammonia channel protein AmtB

Molecular dynamics simulations on the wild-type AmtB protein and its D160A homology model have been performed. Although no significant structural changes due to the mutation of Asp160 were observed, calculations confirmed the critical role of Asp160 for the recognition and binding of NH(4)(+) in AmtB. The carboxyl group of Asp160 is approximately 8 A from NH(4)(+), but their favorable through-space electrostatic interaction is further enhanced by a hydrogen bond chain involving Ala162 (the backbone carbonyl group) and Gly163 (the backbone amide group). This explains the occurrence of the second binding site in AmtB which does not exist in the D160A mutant, as shown in the computed energy profiles. As the initially buried carboxyl group of Asp160 links to the ammonium ion in the periplasmic binding vestibule through a chain of water molecules, a likely deprotonation venue thus is from ammonium to Asp160. Combined QM(PM3)/MM molecular dynamics simulations showed that indeed Asp160 can serve as the proton acceptor and the overall proton transfer process needs to overcome a barrier of merely 7.7 kcal/mol, which is in good agreement with our previous QM(DFT)/MM optimizations. Significantly, the proton transfer adopts an unconventional mechanism by migrating the negative charge from the carboxyl group of Asp160 to NH(4)(+) via two water molecules, which can be illustrated as -CO(2)(-)...H(2)O...H(2)O...NH(4)(+) --> -COOH...H(2)O...OH(-)...NH(4)(+) --> -COOH...H(2)O...H(2)O...NH(3). Apparently, this is also a charge recombination process and thus is exothermic.

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.

A theoretical study on the detection of proton transfer pathways in some mutants of human carbonic anhydrase II

Structural and kinetic studies of mutants can give much insight into the function of an enzyme. We report the detection of possible proton transfer pathways into the active site of a number of mutants of the enzyme human carbonic anhydrase II (HCA II). Using a recently developed method of path search in the protein conformational space, we identify hydrogen-bonded networks (or proton paths) that can dynamically connect the protein surface to the active site through fluctuations in protein structure and hydration. The feasibility of establishing such dynamical connectivities is assessed by computing the change in free energy of conformational fluctuations and compared to those identified earlier in the wild type enzyme. It is found that the point mutation facilitates or suppresses one or more of the alternative pathways. Our results allow the use of a generic set of pathways to correlate qualitatively the residual activity in the mutants to the molecular mechanism of proton transfer in the absence of His at position 64. We also demonstrate how the detected pathways may be used to compare the efficiencies of the mutants His-64-Ala/Asn-62-His and His-64-Ala/Asn-67-His using the empirical valence bond theory.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.

Electrostatic basis for the unidirectionality of the primary proton transfer in cytochrome c oxidase

Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c oxidase (CcO) is one of the challenges of modern biophysics. Despite promising mechanistic proposals, most works have not related the activation barriers of the different assumed steps to the protein structure, and there has not been a physically consistent model that reproduced the barriers needed to create a working pump. This work reevaluates the activation barriers for the primary proton transfer (PT) steps by calculations that reflect all relevant free energy contributions, including the electrostatic energies of the generated charges, the energies of water insertion, and large structural rearrangements of the donor and acceptor. The calculations have reproduced barriers that account for the directionality and sequence of events in the primary PT in CcO. It has also been found that the PT from Glu-286 (E) to the propionate of heme a(3) (Prd) provides a gate for an initial back leakage from the high pH side of the membrane. Interestingly, the rotation of E that brings it closer to Prd appears to provide a way for blocking competing pathways in the primary PT. Our study elucidates and quantifies the nature of the control of the directionality in the primary PT in CcO and provides instructive insight into the role of the water molecules in biological PT, showing that "bridges" of several water molecules in hydrophobic regions present a problem (rather than a solution) that is minimized in the primary PT.

Effect of Membrane Environment on Proton Permeation through Gramicidin A Channels

Multistate empirical valence bond simulations were employed to study proton transport through gramicidin A channels embedded in two different lipid bilayers, glycerol 1-monooleate (GMO) and diphytanolphosphatidylcholine (DiPhPC). Free energy barriers to proton permeation were derived using a new internal reaction coordinate describing the proton permeation process. The large quantitative and qualitative differences between the two systems are discussed in terms of local bilayer structures, ordering of interfacial water, and channel flexibility in the two environments.

Proton transfer 200 years after von Grotthuss: insights from ab initio simulations

In the last decade, ab initio simulations and especially Car-Parrinello molecular dynamics have significantly contributed to the improvement of our understanding of both the physical and chemical properties of water, ice, and hydrogen-bonded systems in general. At the heart of this family of in silico techniques lies the crucial idea of computing the many-body interactions by solving the electronic structure problem "on the fly" as the simulation proceeds, which circumvents the need for pre-parameterized potential models. In particular, the field of proton transfer in hydrogen-bonded networks greatly benefits from these technical advances. Here, several systems of seemingly quite different nature and of increasing complexity, such as Grotthuss diffusion in water, excited-state proton-transfer in solution, phase transitions in ice, and protonated water networks in the membrane protein bacteriorhodopsin, are discussed in the realms of a unifying viewpoint.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Proton Transfer and Associated Molecular Rearrangements in the Photocycle of Photoactive Yellow Protein: Role of Water Molecular Migration on the Proton Transfer Reaction

The mechanism of the proton transfer and the concomitant molecular structural and hydrogen bond rearrangements after the photoisomerization of the chromophore in the photocycle of photoactive yellow protein are theoretically investigated by using the QM/MM method and molecular dynamics calculations. The free energy surface along this proton-transfer process is determined. This work suggests the important role of the water molecular migration into the moiety of chromophore, which facilitates proton transfer by the hydrogen bond rearrangement and the hydration of the pB' state.

Charge delocalization in proton channels, II: the synthetic LS2 channel and proton selectivity

In this study, the minimalist synthetic LS2 channel is used as a prototype to examine the selectivity of protons over other cations. The free-energy profiles along the transport pathway of LS2 are calculated for three cation species: a realistic delocalized proton (including Grotthuss shuttling)--H(+), a classical (nonshuttling) hydronium--H(3)O(+), and a potassium cation--K(+). The overall barrier for K(+) is approximately twice as large as that for H(+), explaining the >100 times larger maximal ion conductance for the latter, in qualitative agreement with the experimental result. The profile for the classical hydronium is quantitatively intermediate between those of H(+) and K(+) and qualitatively more similar to that of H(+), for which the locations of the peaks are well correlated with the troughs of the pore radius profile. There is a strong correlation between the free-energy profiles and the very different characteristic hydration structures of the three cation species. This work suggests that the passage of various cations through ion channels cannot always be explained by simple electrostatic desolvation considerations.

Detailed Structures and Mechanism of Polymer Solvation

In the present study, we simulated a model system, PE in biphenyl, to gain the insight into the detailed solvation structures and the molecular mechanism of polymer chain solvation. Using atomistic molecular dynamics (MD) simulation, it was found that when the biphenyl is far from PE chain or in the bulk, the dihedral angle of the two rings in the solvent molecule are approximately 32 degrees. But, the dihedral angel is about 27 degrees when the biphenyls are very close to the PE chain. In the first solvation shell, the orientation angle of the biphenyl long axis to the chain segment backbone was found to be enhanced around two values: approximately 0 and approximately 60 degrees. The detailed solvation structures found here include all dyad conformations (TT, TG, TG', GT, GG, GG', G'T, G'G, and G'G') and vary as a function of the distance between PE chain and biphenyls in the first solvation shell. The closer the the solvent molecule to the PE segment, the higher the TT conformation fraction response is. The other dyad conformations such as TG, GG', etc. undergo different decreases, respectively. This study shows that the solvation even in the Theta condition makes the overall size expansion or the chain stretched. Such a cooperative change was examined here and found not due to generating or losing a conformational state but due to a change in conformational distribution. This change occurs in the middle location of the chain instead of the chain end locations.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Chance and design—Proton transfer in water, channels and bioenergetic proteins

Proton transfer and transport in water, gramicidin and some selected channels and bioenergetic proteins are reviewed. An attempt is made to draw some conclusions about how Nature designs long distance, proton transport functionality. The prevalence of water rather than amino acid hydrogen bonded chains is noted, and the possible benefits of waters as the major component are discussed qualitatively.

Exploring the gating mechanism in the ClC chloride channel via metadynamics

Computer simulations have been used to probe the gating mechanism in the Salmonella serovar typhimurium chloride channel (st-ClC). Specifically, the recently developed metadynamics methodology has been exploited to construct free energy surfaces as a function of the positions of either one or two chloride ions inside the pore, the position and protonation state of the key E148 residue, and the number of water molecules coordinating the translocating ions. The present calculations confirm the multi-ion mechanism in which an ion-push-ion effect lowers the main barriers to chloride ion translocation. When a second anion is taken into account, the barrier for chloride passage through the E148 narrow region is computed to be 6 kcal/mol in the wild-type channel, irrespective of the protonation state of the E148 residue, which is shown to only affect the entrance barrier. In the E148A mutant, this barrier is much lower, amounting to 3 kcal/mol. The metadynamics calculations reported herein also demonstrate that before reaching the periplasmic solution, chloride ions have to overcome an additional barrier arising from two different effects, namely the rearrangement of their solvation shell and a flip in the backbone angles of the residues E148 and G149, which reside at the end of the alphaF helix.

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

The origin of the barrier for proton transport through the aquaporin channel is a problem of general interest. It is becoming increasingly clear that this barrier is not attributable to the orientation of the water molecules across the channel but rather to the electrostatic penalty for moving the proton charge to the center of the channel. However, the reason for the high electrostatic barrier is still rather controversial. It has been argued by some workers that the barrier is due to the so-called NPA motif and/or to the helix macrodipole or to other specific elements. However, our works indicated that the main reason for the high barrier is the loss of the generalized solvation upon moving the proton charge from the bulk to the center of the channel and that this does not reflect a specific repulsive electrostatic interaction but the absence of sufficient electrostatic stabilization. At this stage it seems that the elucidation and clarification of the origin of the electrostatic barrier can serve as an instructive test case for electrostatic models. Thus, we reexamine the free-energy surface for proton transport in aquaporins using the microscopic free-energy perturbation/umbrella sampling (FEP/US) and the empirical valence bond/umbrella sampling (EVB/US) methods as well as the semimacroscopic protein dipole Langevin dipole model in its linear response approximation version (the PDLD/S-LRA). These extensive studies help to clarify the nature of the barrier and to establish the "reduced solvation effect" as the primary source of this barrier. That is, it is found that the barrier is associated with the loss of the generalized solvation energy (which includes of course all electrostatic effects) upon moving the proton charge from the bulk solvent to the center of the channel. It is also demonstrated that the residues in the NPA region and the helix dipole cannot be considered as the main reasons for the electrostatic barrier. Furthermore, our microscopic and semimacroscopic studies clarify the problems with incomplete alternative calculations, illustrating that the effects of various electrostatic elements are drastically overestimated by macroscopic calculations that use a low dielectric constant and do not consider the protein reorganization. Similarly, it is pointed out that microscopic potential of mean force calculations that do not evaluate the electrostatic barrier relative to the bulk water cannot be used to establish the origin of the electrostatic barrier. The relationship between the present study and calculations of pK(a)s in protein interiors is clarified, pointing out that approaches that are applied to study the aquaporin barrier should be validated by pK(a)s calculations. Such calculations also help to clarify the crucial role of solvation energies in establishing the barrier in aquaporins.

Proton in the well and through the desolvation barrier

The concept of the membrane proton well was suggested by Peter Mitchell to account for the energetic equivalence of the chemical (DeltapH) and electrical (Deltapsi) components of the proton-motive force. The proton well was defined as a proton-conducting crevice passing down into the membrane dielectric and able to accumulate protons in response to the generation either of Deltapsi or of DeltapH. In this review, the concept of proton well is contrasted to the desolvation penalty of > 500 meV for transferring protons into the membrane core. The magnitude of the desolvation penalty argues against deep proton wells in the energy-transducing enzymes. The shallow DeltapH- and Deltapsi-sensitive proton traps, mechanistically linked to the functional groups in the membrane interior, seem more realistic. In such constructs, the draw of a trapped proton into the membrane core can happen at the expense of some exergonic reaction, e.g., release of another proton from the membrane into the aqueous phase. It is argued that the proton transfer in the ATP synthase and the cytochrome bc complex could proceed in this way.

Guanine Alkylation by Ethylene Oxide: Calculation of Chemical Reactivity

In this paper we report on calculations of the activation free energy for a chemical reaction between ethylene oxide and guanine. Ethylene oxide is biologically relevant per se and is also a model compound for numerous ultimate carcinogens. Calculations were performed on the medium-high ab initio, DFT, and semiempirical MO levels. Effects of solvation were considered using the Langevine dipole method and solvent reaction field method of Tomasi and co-workers. The calculated activation free energies are in reasonable agreement with the experimental value.

Protons @ interfaces: implications for biological energy conversion

The review focuses on the anisotropy of proton transfer at the surface of biological membranes. We consider (i) the data from "pulsed" experiments, where light-triggered enzymes capture or eject protons at the membrane surface, (ii) the electrostatic properties of water at charged interfaces, and (iii) the specific structural attributes of proton-translocating enzymes. The pulsed experiments revealed that proton exchange between the membrane surface and the bulk aqueous phase takes as much as about 1 ms, but could be accelerated by added mobile pH-buffers. Since the accelerating capacity of the latter decreased with the increase in their electric charge, it was concluded that the membrane surface is separated from the bulk aqueous phase by a barrier of electrostatic nature. The barrier could arise owing to the water polarization at the negatively charged membrane surface. The barrier height depends linearly on the charge of penetrating ions; for protons, it has been estimated as about 0.12 eV. While the proton exchange between the surface and the bulk aqueous phase is retarded by the interfacial barrier, the proton diffusion along the membrane, between neighboring enzymes, takes only microseconds. The proton spreading over the membrane is facilitated by the hydrogen-bonded networks at the surface. The membrane-buried layers of these networks can eventually serve as a storage/buffer for protons (proton sponges). As the proton equilibration between the surface and the bulk aqueous phase is slower than the lateral proton diffusion between the "sources" and "sinks", the proton activity at the membrane surface, as sensed by the energy transducing enzymes at steady state, might deviate from that measured in the adjoining water phase. This trait should increase the driving force for ATP synthesis, especially in the case of alkaliphilic bacteria.

Toward theoretical analysis of long-range proton transfer kinetics in biomolecular pumps

Motivated by the long-term goal of theoretically analyzing long-range proton transfer (PT) kinetics in biomolecular pumps, researchers made a number of technical developments in the framework of quantum mechanics-molecular mechanics (QM/MM) simulations. A set of collective reaction coordinates is proposed for characterizing the progress of long-range proton transfers; unlike previous suggestions, the new coordinates can describe PT along highly nonlinear three-dimensional pathways. Calculations using a realistic model of carbonic anhydrase demonstrated that adiabatic mapping using these collective coordinates gives reliable energetics and critical geometrical parameters as compared to minimum energy path calculations, which suggests that the new coordinates can be effectively used as reaction coordinate in potential of mean force calculations for long-range PT in complex systems. In addition, the generalized solvent boundary potential was implemented in the QM/MM framework for rectangular geometries, which is useful for studying reactions in membrane systems. The resulting protocol was found to produce water structure in the interior of aquaporin consistent with previous studies including a much larger number of explicit solvent and lipid molecules. The effect of electrostatics for PT through a membrane protein was also illustrated with a simple model channel embedded in different dielectric continuum environments. The encouraging results observed so far suggest that robust theoretical analysis of long-range PT kinetics in biomolecular pumps can soon be realized in a QM/MM framework.