Et tu, Grotthuss! and other unfinished stories

This review article is divided into three sections. In Section 1, a short biographical note on Freiherr von Grotthuss is followed by a detailed summary of the main findings and ideas present in his 1806 paper. Attempts to place Grotthuss contribution in the context of the science done at his time were also made. In Section 2, the modern version of the Grotthuss mechanism is reviewed. The classical Grotthuss model has been recently questioned and new mechanisms and ideas regarding proton transfer are briefly discussed. The last section discusses the significance of a classical Grotthuss mechanism for proton transfer in water chains inside protein cavities. This has been an interesting new twist in the ongoing history of the Grotthuss mechanism. A summary and discussion of what was learned from probably the simplest currently available experimental models of proton transfer in water wires in semi-synthetic ion channels are critically presented. This review ends discussing some of the questions that need to be addressed in the near future.     

The mechanism of the proton transfer: an outline

A brief summary of the principal notions of the quantum-mechanical theory of the charge transfer reactions has been presented. In the framework of this theory, the mechanism of the proton transfer consists in the classical medium reorganization that equalizes the proton energy levels in the initial and final states, and a consequent proton transfer via a quantum-mechanical underbarrier transition. On the basis of this mechanism, factors influencing the proton transfer probability, and hence kinetic isotope effect, have been discussed; among them are the optimum tunneling distance, the involvement of the excited vibrational states, etc. Semi-classical and quantum-mechanical treatments of the Swain-Schaad relations have been compared. Some applications to enzymatic proton-transfer reactions have been described.     

Charge delocalization in proton channels, I: the aquaporin channels and proton blockage

The explicit contribution to the free energy barrier and proton conductance from the delocalized nature of the excess proton is examined in aquaporin channels using an accurate all-atom molecular dynamics computer simulation model. In particular, the channel permeation free energy profiles are calculated and compared for both a delocalized (fully Grotthuss shuttling) proton and a classical (nonshuttling) hydronium ion along two aquaporin channels, Aqp1 and GlpF. To elucidate the effects of the bipolar field thought to arise from two alpha-helical macrodipoles on proton blockage, free energy profiles were also calculated for computational mutants of the two channels where the bipolar field was eliminated by artificially discharging the backbone atoms. Comparison of the free energy profiles between the proton and hydronium cases indicates that the magnitude of the free energy barrier and position of the barrier peak for the fully delocalized and shuttling proton are somewhat different from the case of the (localized) classical hydronium. The proton conductance through the two aquaporin channels is also estimated using Poisson-Nernst-Planck theory for both the Grotthuss shuttling excess proton and the classical hydronium cation.     

Protonation of excited state pyrene-1-carboxylate by phosphate and organic acids in aqueous solution studied by fluorescence spectroscopy

Pyrene-1-carboxylic acid has a pK of 4.0 in the ground state and 8.1 in the singlet electronic excited state. In the pH range of physiological interest (pH approximately 5-8), the ground state compound is largely ionized as pyrene-1-carboxylate, but protonation of the excited state molecule occurs when a proton donor reacts with the carboxylate during the excited state lifetime of the fluorophore. Both forms of the pyrene derivatives are fluorescent, and in this work the protonation reaction was measured by monitoring steady-state and time-resolved fluorescence. The rate of protonation of pyrene-COO(-) by acetic, chloroacetic, lactic, and cacodylic acids is a function of DeltapK, as predicted by Marcus theory. The rate of proton transfer from these acids saturates at high concentration, as expected for the existence of an encounter complex. Trihydrogen-phosphate is a much better proton donor than dihydrogen- and monohydrogen-phosphate, as can be seen by the pH dependence. The proton-donating ability of phosphate does not saturate at high concentrations, but increases with increasing phosphate concentration. We suggest that enhanced rate of proton transfer at high phosphate concentrations may be due to the dual proton donating and accepting nature of phosphate, in analogy to the Grotthuss mechanism for proton transfer in water. It is suggested that in molecular structures containing multiple phosphates, such as membrane surfaces and DNA, proton transfer rates will be enhanced by this mechanism.     

Water channel structures analysed by electron crystallography

Background

The mechanisms underlying water transport through aquaporin (AQP) have been debated for two decades. The water permeation phenomenon of AQP seems inexplicable because the Grotthuss mechanism does not allow for simultaneous fast water permeability and inhibition of proton transfer through the hydrogen bonds of water molecules.

Scope of review

The AQP1 structure determined by electron crystallography provided the first insights into the proton exclusion mechanism despite fast water permeation. Although several studies have provided clues about the mechanism based on the AQP structure, each proposed mechanism remains incomplete. The present review is focused on AQP function and structure solved by electron crystallography in an attempt to fill the gaps between the findings in the absence and presence of lipids.

Major conclusions

Many AQP structures can be superimposed regardless of the determination method. The AQP fold is preserved even under conditions lacking lipids, but the water arrangement in the channel pore differs. The differences might be explained by dipole moments formed by the two short helices in the lipid bilayer. In addition, structure analyses of double-layered two-dimensional crystals of AQP suggest an array formation and cell adhesive function.

General significance

Electron crystallography findings not only have contributed to resolve some of the water permeation mechanisms, but have also elucidated the multiple functions of AQPs in the membrane. The roles of AQPs in the brain remain obscure, but their multiple activities might be important in the regulation of brain and other biological functions. This article is part of a Special Issue entitled Aquaporins.     

Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel

The conduction of protons in the hydrogen-bonded chain of water molecules (or "proton wire") embedded in the lumen of gramicidin A is studied with molecular dynamics free energy simulations. The process may be described as a "hop-and-turn" or Grotthuss mechanism involving the chemical exchange (hop) of hydrogen nuclei between hydrogen-bonded water molecules arranged in single file in the lumen of the pore, and the subsequent reorganization (turn) of the hydrogen-bonded network. Accordingly, the conduction cycle is modeled by two complementary steps corresponding respectively to the translocation 1) of an ionic defect (H+) and 2) of a bonding defect along the hydrogen-bonded chain of water molecules in the pore interior. The molecular mechanism and the potential of mean force are analyzed for each of these two translocation steps. It is found that the mobility of protons in gramicidin A is essentially determined by the fine structure and the dynamic fluctuations of the hydrogen-bonded network. The translocation of H+ is mediated by spontaneous (thermal) fluctuations in the relative positions of oxygen atoms in the wire. In this diffusive mechanism, a shallow free-energy well slightly favors the presence of the excess proton near the middle of the channel. In the absence of H+, the water chain adopts either one of two polarized configurations, each of which corresponds to an oriented donor-acceptor hydrogen-bond pattern along the channel axis. Interconversion between these two conformations is an activated process that occurs through the sequential and directional reorientation of water molecules of the wire. The effect of hydrogen-bonding interactions between channel and water on proton translocation is analyzed from a comparison to the results obtained previously in a study of model nonpolar channels, in which such interactions were missing. Hydrogen-bond donation from water to the backbone carbonyl oxygen atoms lining the pore interior has a dual effect: it provides a coordination of water molecules well suited both to proton hydration and to high proton mobility, and it facilitates the slower reorientation or turn step of the Grotthuss mechanism by stabilizing intermediate configurations of the hydrogen-bonded network in which water molecules are in the process of flipping between their two preferred, polarized states. This mechanism offers a detailed molecular model for the rapid transport of protons in channels, in energy-transducing membrane proteins, and in enzymes.     

Enhancement of proton conductance by mutations of the selectivity filter of aquaporin-1

Prevention of cation permeation in wild-type aquaporin-1 (AQP1) is believed to be associated with the Asn-Pro-Ala (NPA) region and the aromatic/arginine selectivity filter (SF) domain. Previous work has suggested that the NPA region helps to impede proton permeation due to the protein backbone collective macrodipoles that create an environment favoring a directionally discontinuous channel hydrogen-bonded water chain and a large electrostatic barrier. The SF domain contributes to the proton permeation barrier by a spatial restriction mechanism and direct electrostatic interactions. To further explore these various effects, the free-energy barriers and the maximum cation conductance for the permeation of various cations through the AQP1-R195V and AQP1-R195S mutants are predicted computationally. The cations studied included the hydrated excess proton that utilizes the Grotthuss shuttling mechanism, a model “classical” charge localized hydronium cation that exhibits no Grotthuss shuttling, and a sodium cation. The hydrated excess proton was simulated using a specialized multi-state molecular dynamics method including a proper physical treatment of the proton shuttling and charge defect delocalization. Both AQP1 mutants exhibit a surprising cooperative effect leading to a reduction in the free-energy barrier for proton permeation around the NPA region due to altered water configurations in the SF region, with AQP1-R195S having a higher conductance than AQP1-R195V. The theoretical predictions are experimentally confirmed in wild-type AQP1 and the mutants expressed in Xenopus oocytes. The combined results suggest that the SF domain is a specialized structure that has evolved to impede proton permeation in aquaporins.     

The quinone chemistry of bc complexes

The quinone chemistry that gives rise to the rather unusual strict bifurcation of electron transfer at the Q(o) site of the cytochrome bc complexes remains controversial. In this article, I review recent ideas and propose a "logic-gated" binding mechanism that combines classical quinone electrochemistry with specific hydrogen bonding requirements and results in a reversible reaction that minimizes unwanted side-reactions that could otherwise undermine the efficiency of the Q-cycle proton/electron coupling mechanism.     

Lewis-inspired representation of dissociable water in clusters and Grotthuss chains

Proton transfer to and from water is critical to the function of water in many settings. However, it has been challenging to model. Here, we present proof-of-principle for an efficient yet robust model based on Lewis-inspired submolecular particles with interactions that deviate from Coulombic at short distances to take quantum effects into account. This “LEWIS” model provides excellent correspondence with experimental structures for water molecules and water clusters in their neutral, protonated and deprotonated forms; reasonable values for the proton affinities of water and hydroxide; a good value for the strength of the hydrogen bond in the water dimer; the correct order of magnitude for the stretch and bend force constants of water; and the expected time course for Grotthuss transport in water chains.     

The dynamics and energetics of water permeation and proton exclusion in aquaporins

Aquaporins and aquaglyceroporins are passive membrane channels that, in many species, facilitate highly efficient yet strictly selective permeation of water and small solutes across lipid bilayers. Their ability to block proton flux is particularly remarkable, because other aqueous pores and water efficiently conduct protons, via the so-called Grotthuss mechanism. How efficient water permeation is achieved and how it is reconciled with the seemingly contradictory task of strict proton exclusion have been long-standing puzzles. Because neither the dynamics of the water molecules nor the mobility of protons inside the aquaporin channel could be experimentally accessed so far, several groups addressed this challenge using a variety of atomistic computer simulation methods.     

Expanding the view of proton pumping in cytochrome c oxidase through computer simulation

In cytochrome c oxidase (CcO), a redox-driven proton pump, protons are transported by the Grotthuss shuttling via hydrogen-bonded water molecules and protonatable residues. Proton transport through the D-pathway is a complicated process that is highly sensitive to alterations in the amino acids or the solvation structure in the channel, both of which can inhibit proton pumping and enzymatic activity. Simulations of proton transport in the hydrophobic cavity showed a clear redox state dependence. To study the mechanism of proton pumping in CcO, multi-state empirical valence bond (MS-EVB) simulations have been conducted, focusing on the proton transport through the D-pathway and the hydrophobic cavity next to the binuclear center. The hydration structures, transport pathways, effects of residues, and free energy surfaces of proton transport were revealed in these MS-EVB simulations. The mechanistic insight gained from them is herein reviewed and placed in context for future studies.     

Proton transport in carbonic anhydrase: Insights from molecular simulation

This article reviews the insights gained from molecular simulations of human carbonic anhydrase II (HCA II) utilizing non-reactive and reactive force fields. The simulations with a reactive force field explore protein transfer and transport via Grotthuss shuttling, while the non-reactive simulations probe the larger conformational dynamics that underpin the various contributions to the rate-limiting proton transfer event. Specific attention is given to the orientational stability of the His64 group and the characteristics of the active site water cluster, in an effort to determine both of their impact on the maximal catalytic rate. The explicit proton transfer and transport events are described by the multistate empirical valence bond (MS-EVB) method, as are alternative pathways for the excess proton charge defect to enter/leave the active site. The simulation results are interpreted in light of experimental results on the wild-type enzyme and various site-specific mutations of HCA II in order to better elucidate the key factors that contribute to its exceptional efficiency.     

Sodium-translocating NADH:quinone oxidoreductase as a redox-driven ion pump

The Na⁺-translocating NADH:ubiquinone oxidoreductase (Na⁺-NQR) is a component of the respiratory chain of various bacteria. This enzyme is an analogous but not homologous counterpart of mitochondrial Complex I. Na⁺-NQR drives the same chemistry and also uses released energy to translocate ions across the membrane, but it pumps Na⁺ instead of H⁺. Most likely the mechanism of sodium pumping is quite different from that of proton pumping (for example, it could not accommodate the Grotthuss mechanism of ion movement); this is why the enzyme structure, subunits and prosthetic groups are completely special. This review summarizes modern knowledge on the structural and catalytic properties of bacterial Na⁺-translocating NADH:quinone oxidoreductases. The sequence of electron transfer through the enzyme cofactors and thermodynamic properties of those cofactors is discussed. The resolution of the intermediates of the catalytic cycle and localization of sodium-dependent steps are combined in a possible molecular mechanism of sodium transfer by the enzyme.     

Mechanism of nucleotide incorporation in DNA polymerase beta

DNA polymerases play a central role in the mechanisms of DNA replication and repair. Here, we report mechanisms of the beta-polymerase catalyzed phosphoryl transfer reactions corresponding to correct and incorrect nucleotide incorporations in the DNA. Based on energy minimizations, molecular dynamics simulations, and free energy calculations of solvated ternary complexes of pol beta and by employing a mixed quantum mechanics molecular mechanics Hamiltonian, we have uncovered the identities of transient intermediates in the phosphoryl transfer pathways. Our study has revealed that an intriguing Grotthuss hopping mechanism of proton transfer involving water and three conserved aspartate residues in pol beta's active site mediates the phosphoryl transfer in the correct as well as misincorporation of nucleotides. The significance of this catalytic step in serving as a kinetic check point of polymerase fidelity may be unique to DNA polymerase beta, and is discussed in relation to other known mechanisms of DNA polymerases.     

Forty years of Mitchell's proton circuit: From little grey books to little grey cells

It is more than forty years since Peter Mitchell published his first 'little grey book' laying out his chemiosmotic hypothesis. Although ideas about the molecular mechanisms of the proton pumps have evolved considerably since then, his concept of 'coupling through proton circuits' remains remarkably prescient, and has provided the inspiration for the research careers of this author and many others. This review is a personal account of how the proton circuit has been followed from the little grey book, via brown fat and calcium transport to investigations into the life and death of neurons, Hercule Poirot's 'little grey cells'.     

Role of internal water molecules in bacteriorhodopsin

Internal water molecules are considered to play a crucial role in the functional processes of proton pump proteins. They may participate in hydrogen-bonding networks inside proteins that constitute proton pathways. In addition, they could participate in the switch reaction by mediating an essential proton transfer at the active site. Nevertheless, little has been known about the structure and function of internal water molecules in such proteins. Recent progress in infrared spectroscopy and X-ray crystallography provided new information on water molecules inside bacteriorhodopsin, the light-driven proton pump. The accumulated knowledge on bacteriorhodopsin in the last decade of the 20th century will lead to a realistic picture of internal water molecules at work in the 21st century. In this review, I describe how the role of water molecules has been studied in bacteriorhodopsin, and what should be known about the role of water molecules in the future.     

Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the acetic acid dimer in the gas phase

In the paper are described studies of the double proton transfer (DPT) processes in the cyclic dimer of acetic acid in the gas phase using Car-Parrinello (CPMD) and path integral molecular dynamics (PIMD). Structures, energies and proton trajectories have been determined. The results show the double proton transfer in 450 K. In the classical dynamics (CPMD) a clear process mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. The DPT mechanism is also asynchronic when quantum tunneling has been allowed in the simulation. It has been found that the calculated values of barrier height for the proton transfer depends very strongly on the used approaches. Barrier received from the free-energy profile at the CPMD level is around 4.5 kcal mol^-1 whereas at the PIMD level is reduced to 1 kcal mol^-1. The nature of bonding in acetic acid dimer and rearrangement of electron density due to the proton movement has been also studied by the topological analysis of Electron Localization Function and Electron Localizability Indicator function.     

Hydroxide and proton migration in aquaporins

Hypothetical hydroxide and proton migration along the linear water chain in Aquaporin GlpF from Escherichia coli are studied by ab initio Car-Parrinello molecular dynamics simulations. It is found that the protein stabilizes a bipolar single file of water. The single file features a contiguous set of water-water hydrogen bonds in which polarization of the water molecules vary with position along the channel axis. Deprotonation of the water chain promotes the reorientation of water molecules while the hydroxide ion rapidly migrates by sequentially accepting protons from the neighboring water molecules. The hydroxide ion is not attracted by a conserved, channel-lining arginine residue, but is immobilized at two centrally located, conserved Asparagine-Proline-Alanine motifs where fourfold coordination stabilizes the ion. Hydroxide transition from the channel vestibules into the channel lumen is strongly influenced by electrostatic coupling to two conserved oppositely aligned macrodipoles. This suggests that the macrodipole's negative poles play a role in preventing hydroxide ions from entering into the channel's inner vestibules. Water protonation within the lumen facilitates water reorientation and subsequent proton expelling occurs. In the periplasmic half-channel, expelling occurs via the Grotthuss mechanism. Protonation within the cytoplasmic half-channel implies wire-breakage at the Asn-Pro-Ala motifs. The proton is here diffusively rejected as (H(5)O(2))(+).     

Framework Models of Ion Permeation Through Membrane Channels and the Generalized King–Altman Method

A modern approach to studying the detailed dynamics of biomolecules is to simulate them on computers. Framework models have been developed to incorporate information from these simulations in order to calculate properties of the biomolecules on much longer time scales than can be achieved by the simulations. They also provide a simple way to think about the simulated dynamics. This article develops a method for the solution of framework models, which generalizes the King–Altman method of enzyme kinetics. The generalized method is used to construct solutions of two framework models which have been introduced previously, the single-particle and Grotthuss (proton conduction) models. The solution of the Grotthuss model is greatly simplified in comparison with direct integration. In addition, a new framework model is introduced, generalizing the shaking stack model of ion conduction through the potassium channel.     

Molecular basis of proton blockage in aquaporins

Water transport channels in membrane proteins of the aquaporin superfamily are impermeable to ions, including H+ and OH-. We examine the molecular basis for the blockage of proton translocation through the single-file water chain in the pore of a bacterial aquaporin, GlpF. We compute the reversible thermodynamic work for the two complementary steps of the Grotthuss "hop-and-turn" relay mechanism: consecutive transfers of H+ along the hydrogen-bonded chain (hop) and conformational reorganization of the chain (turn). In the absence of H+, the strong preference for the bipolar orientation of water around the two Asn-Pro-Ala (NPA) motifs lining the pore over both unidirectional polarization states of the chain precludes the reorganization of the hydrogen-bonded network. Inversely, translocation of an excess proton in either direction is opposed by a free-energy barrier centered at the NPA region. Both hop and turn steps of proton translocation are opposed by the electrostatic field of the channel.