Anomalous surface diffusion of protons on lipid membranes

Hydronium Ion Transport across the Liquid/Liquid Interface Assisted by a Phase-Transfer Catalyst: Structure and Thermodynamics Using Molecular Dynamics Simulation

Molecular dynamics simulations are used to examine the thermodynamic and structural aspects of the transfer of the classical hydronium ion (H3O+) across a water/1,2-dichloroethane (DCE) interface assisted by the phase-transfer catalyst (PTC) tetrakis(pentafluorophenyl) borate anion (TPFB-). The free energy of transfer from water to DCE of the H3O+-TPFB- ion pair is calculated to be 6 ± 1 kcal/mol, significantly less than that of the free hydronium ion (17 ± 1 kcal/mol). The ion pair is relatively stable at the interface and in the organic phase when it is accompanied by three water molecules with a small barrier to dissociation that supports its utility as a PTC. An examination of the hydration structure that accompanies the transfer of the ion pair shows that the ion pair, like the free hydronium ion, is transferred with the assistance of a finger-like water structure.

Dressing a Nonpolarizable Force Field for OH- in TIP4P/2005 Aqueous Solutions with Corrected Hirshfeld Charges

We present a rigid model for the OH- ion parametrized for binary mixtures with TIP4P/2005-type water molecules. Li+, Na+ and K+ were selected as counterions, hence mimicking the important and widely used solutions of soluble alkaline hydroxides. The optimized atomic charge distributions were obtained by scaling in a factor of 0.85 those derived from the atomic dipole corrected Hirshfeld approach. The agreement between experimental and Molecular Dynamics simulation results is remarkable for a set of properties, namely, the dependence of the density of the solutions on the hydroxide concentration and on temperature, the structure (i.e., positions of the atom-to-atom radial distribution functions and coordination numbers), the viscosity coefficients, the surface tension, or the freezing point depression. The proposed optimized potential parameters for OH- thus enlarge the set of models comprised within the Madrid-2019 force field and widen the potential applicability of the TIP4P/2005 water model in basic environments.

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.

Proton diffusion on the surface of mixed lipid membranes highlights the role of membrane composition

Proton circuits within biological membranes, the foundation of natural bioenergetic systems, are significantly influenced by the lipid compositions of different biological membranes. In this study, we investigate the influence of mixed lipid membrane composition on the proton transfer (PT) properties on the surface of the membrane. We track the excited-state PT (ESPT) process from a tethered probe to the membrane with timescales and length scales of PT relevant to bioenergetic systems. Two processes can happen during ESPT: the initial PT from the probe to the membrane at short timescales, followed by diffusion of dissociated protons around the probe on the membrane, and the possible geminate recombination with the probe at longer timescales. Here, we use membranes composed of mixtures of phosphatidylcholine (PC) and phosphatidic acid (PA). We show that the changes in the ESPT properties are not monotonous with the concentration of the lipid mixture; at a low concentration of PA in PC, we find that the membrane is a poor proton acceptor. Molecular dynamics simulations indicate that the membrane is more structured at this specific lipid mixture, with the least number of defects. Accordingly, we suggest that the structure of the membrane is an important factor in facilitating PT. We further show that the composition of the membrane affects the geminate proton diffusion around the probe, whereas, on a timescale of tens of nanoseconds, the dissociated proton is mostly lateral restricted to the membrane plane in PA membranes, while in PC, the diffusion is less restricted by the membrane.

Cobra Venom Cytotoxins as a Tool for Probing Mechanisms of Mitochondrial Energetics and Understanding Mitochondrial Membrane Structure

In this paper, we provide an overview of mitochondrial bioenergetics and specific conditions that lead to the formation of non-bilayer structures in mitochondria. Secondly, we provide a brief overview on the structure/function of cytotoxins and how snake venom cytotoxins have contributed to increasing our understanding of ATP synthesis via oxidative phosphorylation in mitochondria, to reconcile some controversial aspects of the chemiosmotic theory. Specifically, we provide an emphasis on the biochemical contribution of delocalized and localized proton movement, involving direct transport of protons though the Fo unit of ATP synthase or via the hydrophobic environment at the center of the inner mitochondrial membrane (proton circuit) on oxidative phosphorylation, and how this influences the rate of ATP synthesis. Importantly, we provide new insights on the molecular mechanisms through which cobra venom cytotoxins affect mitochondrial ATP synthesis, mitochondrial structure, and dynamics. Finally, we provide a perspective for the use of cytotoxins as novel pharmacological tools to study membrane bioenergetics and mitochondrial biology, how they can be used in translational research, and their potential therapeutic applications.

Solid-State Molecular Protonics Devices of Solid-Supported Biological Membranes Reveal the Mechanism of Long-Range Lateral Proton Transport

Lateral proton transport (PT) on the surface of biological membranes is a fundamental biochemical process in the bioenergetics of living cells, but a lack of available experimental techniques has resulted in a limited understanding of its mechanism. Here, we present a molecular protonics experimental approach to investigate lateral PT across membranes by measuring long-range (70 μm) lateral proton conduction via a few layers of lipid bilayers in a solid-state-like environment, i.e., without having bulk water surrounding the membrane. This configuration enables us to focus on lateral proton conduction across the surface of the membrane while decoupling it from bulk water. Hence, by controlling the relative humidity of the environment, we can directly explore the role of water in the lateral PT process. We show that proton conduction is dependent on the number of water molecules and their structure and on membrane composition, where we explore the role of the headgroup, the tail saturation, the membrane phase, and membrane fluidity. The measured PT as a function of temperature shows an inverse temperature dependency, which we explain by the desorption and adsorption of water molecules into the solid membrane platform. We explain our findings by discussing the role of percolating hydrogen bonding within the membrane structure in a Grotthuss-like mechanism.

A New Theory about Interfacial Proton Diffusion Revisited: The Commonly Accepted Laws of Electrostatics and Diffusion Prevail

The high propensity of protons to stay at interfaces has attracted much attention over the decades. It enables long-range interfacial proton diffusion without relying on titratable residues or electrostatic attraction. As a result, various phenomena manifest themselves, ranging from spillover in material sciences to local proton circuits between proton pumps and ATP synthases in bioenergetics. In an attempt to replace all existing theoretical and experimental insight into the origin of protons' preference for interfaces, TELP, the "Transmembrane Electrostatically-Localized Protons" hypothesis, has been proposed. The TELP hypothesis envisions static H+ and OH- layers on opposite sides of interfaces that are up to 75 µm thick. Yet, the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy is more than two orders of magnitude smaller and, as a result, the H+ and OH- layers cannot mutually stabilize each other, rendering proton accumulation at the interface energetically unfavorable. We show that (i) the law of electroneutrality, (ii) Fick's law of diffusion, and (iii) Coulomb's law prevail. Using them does not hinder but helps to interpret previously published experimental results, and also helps us understand the high entropy release barrier enabling long-range proton diffusion along the membrane surface.

Comparison of classical and ab initio simulations of hydronium and aqueous proton transfer

Proton transport in aqueous systems occurs by making and breaking covalent bonds, a process that classical force fields cannot reproduce. Various attempts have been made to remedy this deficiency, by valence bond theory or instantaneous proton transfers, but the ability of such methods to provide a realistic picture of this fundamental process has not been fully evaluated. Here we compare an ab initio molecular dynamics (AIMD) simulation of an excess proton in water to a simulation of a classical H3O+ in TIP3P water. The energy gap upon instantaneous proton transfer from H3O+ to an acceptor water molecule is much higher in the classical simulation than in the AIMD configurations evaluated with the same classical potential. The origins of this discrepancy are identified by comparing the solvent structures around the excess proton in the two systems. One major structural difference is in the tilt angle of the water molecules that accept an hydrogen bond from H3O+. The lack of lone pairs in TIP3P produces a tilt angle that is too large and generates an unfavorable geometry after instantaneous proton transfer. This problem can be alleviated by the use of TIP5P, which gives a tilt angle much closer to the AIMD result. Another important factor that raises the energy gap is the different optimal distance in water-water vs H3O+-water H-bonds. In AIMD the acceptor is gradually polarized and takes a hydronium-like configuration even before proton transfer actually happens. Ways to remedy some of these problems in classical simulations are discussed.

Diffusion coefficients and MSD measurements on curved membranes and porous media

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

Proton Migration on Top of Charged Membranes

Proton relay between interfacial water molecules allows rapid two-dimensional diffusion. An energy barrier, ΔGr‡, opposes proton-surface-to-bulk release. The ΔGr‡-regulating mechanism thus far has remained unknown. Here, we explored the effect interfacial charges have on ΔGr‡'s enthalpic and entropic constituents, ΔGH‡ and ΔGS‡, respectively. A light flash illuminating a micrometer-sized membrane patch of a free-standing planar lipid bilayer released protons from an adsorbed hydrophobic caged compound. A lipid-anchored pH-sensitive dye reported protons' arrival at a distant membrane patch. Introducing net-negative charges to the bilayer doubled ΔGH‡, while positive net charges decreased ΔGH‡. The accompanying variations in ΔGS‡ compensated for the ΔGH‡ modifications so that ΔGr‡ was nearly constant. The increase in the entropic component of the barrier is most likely due to the lower number and strength of hydrogen bonds known to be formed by positively charged residues as compared to negatively charged moieties. The resulting high ΔGr‡ ensured interfacial proton diffusion for all measured membranes. The observation indicates that the variation in membrane surface charge alone is a poor regulator of proton traffic along the membrane surface.

Local Attraction of Substrates and Co-Substrates Enhances Weak Acid and Base Transmembrane Transport

The transmembrane transport of weak acid and base metabolites depends on the local pH conditions that affect the protonation status of the substrates and the availability of co-substrates, typically protons. Different protein designs ensure the attraction of substrates and co-substrates to the transporter entry sites. These include electrostatic surface charges on the transport proteins and complexation with seemingly transport-unrelated proteins that provide substrate and/or proton antenna, or enzymatically generate substrates in place. Such protein assemblies affect transport rates and directionality. The lipid membrane surface also collects and transfers protons. The complexity in the various systems enables adjustability and regulation in a given physiological or pathophysiological situation. This review describes experimentally shown principles in the attraction and facilitation of weak acid and base transport substrates, including monocarboxylates, ammonium, bicarbonate, and arsenite, plus protons as a co-substrate.

Using Proton Geminate Recombination as a Probe of Proton Migration on Biological Membranes

Proton migration on biological membranes plays a major role in cellular respiration and photosynthesis, but it is not yet fully understood. Here we show that proton dissociation kinetics and related geminate recombination can be used as a probe of such proton migration mechanisms. We develop a simple model for the process and apply it to analyze the results obtained using a photo-induced proton release probe (chemically modified photoacid) tethered to phosphatidylcholine membranes. In our theoretical model, we apply approximate treatment for the diffusional cloud of the geminate proton around the dissociated photoacid and consider arbitrary dimension of the system, 1 < d < 3. We observe that in d > 2, there is a kinetic phase transition between an exponential and a power-law kinetic phases. The existence of an exponential decay phase at the beginning of the proton dissociation is a signature of d > 2 systems. In most other cases, the exponential decay phase is not present, and the kinetics follows a diffusional power-law P(t) ∼ t^-d/2 that develops after a short initiation time. Specifically, in a 1D case, which corresponds to the desorption of a proton from the surface, the dissociation occurs by the slow power-law ∼1/t and explains the abnormally slow desorption rate reported recently in experiments.

Imaging Fluorescence Blinking of a Mitochondrial Localization Probe: Cellular Localization Probes Turned into Multifunctional Sensors

Mitochondrial membranes and their microenvironments directly influence and reflect cellular metabolic states but are difficult to probe on site in live cells. Here, we demonstrate a strategy, showing how the widely used mitochondrial membrane localization fluorophore 10-nonyl acridine orange (NAO) can be transformed into a multifunctional probe of membrane microenvironments by monitoring its blinking kinetics. By transient state (TRAST) studies of NAO in small unilamellar vesicles (SUVs), together with computational simulations, we found that NAO exhibits prominent reversible singlet-triplet state transitions and can act as a light-induced Lewis acid forming a red-emissive doublet radical. The resulting blinking kinetics are highly environment-sensitive, specifically reflecting local membrane oxygen concentrations, redox conditions, membrane charge, fluidity, and lipid compositions. Here, not only cardiolipin concentration but also the cardiolipin acyl chain composition was found to strongly influence the NAO blinking kinetics. The blinking kinetics also reflect hydroxyl ion-dependent transitions to and from the fluorophore doublet radical, closely coupled to the proton-transfer events in the membranes, local pH, and two- and three-dimensional buffering properties on and above the membranes. Following the SUV studies, we show by TRAST imaging that the fluorescence blinking properties of NAO can be imaged in live cells in a spatially resolved manner. Generally, the demonstrated blinking imaging strategy can transform existing fluorophore markers into multiparametric sensors reflecting conditions of large biological relevance, which are difficult to retrieve by other means. This opens additional possibilities for fundamental membrane studies in lipid vesicles and live cells.

A critique of the capacitor-based "Transmembrane Electrostatically Localized Proton" hypothesis

In his Transmembrane Electrostatically Localized Proton hypothesis (TELP), James W. Lee has modeled the bioenergetic membrane as a simple capacitor. According to this model, the surface concentration of protons is completely independent of proton concentration in the bulk phase, and is linearly proportional to the transmembrane potential. Such a proportionality runs counter to the results of experimental measurements, molecular dynamics simulations, and electrostatics calculations. We show that the TELP model dramatically overestimates the surface concentration of protons, and we discuss the electrostatic reasons why a simple capacitor is not an appropriate model for the bioenergetic membrane.

Phenolic compounds alter the ion permeability of phospholipid bilayers via specific lipid interactions

This study aims to understand the role of specific phenolic-lipid interactions in the membrane-altering properties of phenolic compounds. We combine tethered lipid bilayer (tBLM) electrical impedance spectroscopy (EIS) with all-atom molecular dynamics (MD) simulations to study the membrane interactions of six phenolic compounds: caffeic acid methyl ester, caffeic acid, 3,4 dihydroxybenzoic acid, chlorogenic acid, syringic acid and p-coumaric acid. tBLM/EIS experiments showed that caffeic acid methyl ester, caffeic acid and 3,4 dihydroxybenzoic acid significantly increase the permeability of phospholipid bilayers to Na⁺ ions. In contrast, chlorogenic acid, syringic acid and p-coumaric acid showed no effect. Experiments with lipids lacking the phosphate group show a significant decrease in the membrane-altering effects indicating that specific phenolic-lipid interactions are critical in altering ion permeability. MD simulations confirm that compounds that alter ion permeability form stable interactions with the phosphate oxygen. In contrast, inactive phenolic compounds are superficially bound to the membrane surface and primarily interact with interfacial water. Our combined results show that compounds with similar structures can have very different effects on ion permeability in membranes. These effects are governed by specific interactions at the water-lipid interface and show no correlation with lipophilicity. Furthermore, none of the compounds alter the overall structure of the phospholipid bilayer as determined by area per lipid and order parameters. Based on data from this study and previous findings, we propose that phenolic compounds can alter membrane ion permeability by causing local changes in lipid packing that subsequently reduce the energy barrier for ion-induced pores.

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.

The aerobic mitochondrial ATP synthesis from a comprehensive point of view

Most of the ATP to satisfy the energetic demands of the cell is produced by the F₁F_o-ATP synthase (ATP synthase) which can also function outside the mitochondria. Active oxidative phosphorylation (OxPhos) was shown to operate in the photoreceptor outer segment, myelin sheath, exosomes, microvesicles, cell plasma membranes and platelets. The mitochondria would possess the exclusive ability to assemble the OxPhos molecular machinery so to share it with the endoplasmic reticulum (ER) and eventually export the ability to aerobically synthesize ATP in true extra-mitochondrial districts. The ER lipid rafts expressing OxPhos components is indicative of the close contact of the two organelles, bearing different evolutionary origins, to maximize the OxPhos efficiency, exiting in molecular transfer from the mitochondria to the ER. This implies that its malfunctioning could trigger a generalized oxidative stress. This is consistent with the most recent interpretations of the evolutionary symbiotic process whose necessary prerequisite appears to be the presence of the internal membrane system inside the eukaryote precursor, of probable archaeal origin allowing the engulfing of the α-proteobacterial precursor of mitochondria. The process of OxPhos in myelin is here studied in depth. A model is provided contemplating the biface arrangement of the nanomotor ATP synthase in the myelin sheath.

Molecular Dynamics Studies on the Effect of Surface Roughness and Surface Tension on the Thermodynamics and Dynamics of Hydronium Ion Transfer Across the Liquid/Liquid Interface

Molecular dynamics simulations are used to examine the effect of surface roughness and surface tension on the transfer of the classical hydronium ion (H₃O⁺) across the water/1,2-dichloroethane interface. Free energy of transfer, hydration structure, and dynamics as a function of the ion location along the interface normal are calculated with six different values of a control parameter whose variation modifies the surface tension without impacting the bulk properties of the two solvents. Transfer of the classical hydronium ion across the water/1,2-dichloroethan interface involves the cotransfer of three hydration shell water molecules, independent of the surface tension. However, as the interaction between the two liquids weakens, a rise in interfacial tension and decrease in intrinsic water fingering and capillary fluctuations result in fewer water molecules cotransported with the ion in the second shell and a reduction in the length of the finger that the ion is attached to, consistent with the reduced size of the second hydration shell. First shell water residence time and lateral ion diffusion constants vary with the surface tension in a way that is consistent with the abovementioned structural insight.

Interfacial solvation and slow transport of hydrated excess protons in non-ionic reverse micelles

This work employs molecular dynamics simulations to investigate the solvation and transport properties of hydrated excess protons (with a hydronium-like core structure) in non-ionic Igepal CO-520 reverse micelles of various sizes in a non-polar solvent. Multiscale Reactive Molecular Dynamics (MS-RMD) simulations were used to describe vehicular and hopping diffusion during the proton transport process. As detailed herein, an excess proton shows a marked tendency to localize in the interfacial region of micellar water pools. Slow proton transport was observed which becomes faster with increasing micellar size. Further analysis reveals that the slow diffusion of an excess proton is a combined result of slow water diffusion and the low proton hopping rate. This study also confirms that a low proton hopping rate in reverse micelles stems from the interfacial solvation of hydrated excess protons and the immobilization of interfacial water. The low water density in the interfacial region makes it difficult to form a complete hydrogen bond network near the hydrated excess proton, and therefore locks in the orientation of hydrated proton cations. The immobilization of the interfacial water also slows the relaxation of the overall hydrogen bond network.

An update of the chemiosmotic theory as suggested by possible proton currents inside the coupling membrane

Understanding how biological systems convert and store energy is a primary purpose of basic research. However, despite Mitchell's chemiosmotic theory, we are far from the complete description of basic processes such as oxidative phosphorylation (OXPHOS) and photosynthesis. After more than half a century, the chemiosmotic theory may need updating, thanks to the latest structural data on respiratory chain complexes. In particular, up-to date technologies, such as those using fluorescence indicators following proton displacements, have shown that proton translocation is lateral rather than transversal with respect to the coupling membrane. Furthermore, the definition of the physical species involved in the transfer (proton, hydroxonium ion or proton currents) is still an unresolved issue, even though the latest acquisitions support the idea that protonic currents, difficult to measure, are involved. Moreover, F_oF₁-ATP synthase ubiquitous motor enzyme has the peculiarity (unlike most enzymes) of affecting the thermodynamic equilibrium of ATP synthesis. It seems that the concept of diffusion of the proton charge expressed more than two centuries ago by Theodor von Grotthuss is to be taken into consideration to resolve these issues. All these uncertainties remind us that also in biology it is necessary to consider the Heisenberg indeterminacy principle, which sets limits to analytical questions.

Competing for the same space: protons and alkali ions at the interface of phospholipid bilayers

Maintaining gradients of solvated protons and alkali metal ions such as Na⁺ and K⁺ across membranes is critical for cellular function. Over the last few decades, both the interactions of protons and alkali metal ions with phospholipid membranes have been studied extensively and the reported interactions of these ions with phospholipid headgroups are very similar, yet few studies have investigated the potential interdependence between proton and alkali metal ion binding at the water-lipid interface. In this short review, we discuss the similarities between the proton-membrane and alkali ion-membrane interactions. Such interactions include cation attraction to the phosphate and carbonyl oxygens of the phospholipid headgroups that form strong lipid-ion and lipid-ion-water complexes. We also propose potential mechanisms that may modulate the affinities of these cationic species to the water-phospholipid interfacial oxygen moieties. This review aims to highlight the potential interdependence between protons and alkali metal ions at the membrane surface and encourage a more nuanced understanding of the complex nature of these biologically relevant processes.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Exploring fast proton transfer events associated with lateral proton diffusion on the surface of membranes

Proton diffusion (PD) across biological membranes is a fundamental process in many biological systems, and much experimental and theoretical effort has been employed for deciphering it. Here, we report on a spectroscopic probe, which can be tightly tethered to the membrane, for following fast (nanosecond) proton transfer events on the surface of membranes. Our probe is composed of a photoacid that serves as our light-induced proton source for the initiation of the PD process. We use our probe to follow PD, and its pH dependence, on the surface of lipid vesicles composed of a zwitterionic headgroup, a negative headgroup, a headgroup that is composed only from the negative phosphate group, or a positive headgroup without the phosphate group. We reveal that the PD kinetic parameters are highly sensitive to the nature of the lipid headgroup, ranging from a fast lateral diffusion at some membranes to the escape of protons from surface to bulk (and vice versa) at others. By referring to existing theoretical models for membrane PD, we found that while some of our results confirm the quasi-equilibrium model, other results are in line with the nonequilibrium model.

The effect of H3O+ on the membrane morphology and hydrogen bonding of a phospholipid bilayer

At the 2017 meeting of the Australian Society for Biophysics, we presented the combined results from two recent studies showing how hydronium ions (H₃O⁺) modulate the structure and ion permeability of phospholipid bilayers. In the first study, the impact of H₃O⁺ on lipid packing had been identified using tethered bilayer lipid membranes in conjunction with electrical impedance spectroscopy and neutron reflectometry. The increased presence of H₃O⁺ (i.e. lower pH) led to a significant reduction in membrane conductivity and increased membrane thickness. A first-order explanation for the effect was assigned to alterations in the steric packing of the membrane lipids. Changes in packing were described by a critical packing parameter (CPP) related to the interfacial area and volume and shape of the membrane lipids. We proposed that increasing the concentraton of H₃O⁺ resulted in stronger hydrogen bonding between the phosphate oxygens at the water-lipid interface leading to a reduced area per lipid and slightly increased membrane thickness. At the meeting, a molecular model for these pH effects based on the result of our second study was presented. Multiple μs-long, unrestrained molecular dynamic (MD) simulations of a phosphatidylcholine lipid bilayer were carried out and showed a concentration dependent reduction in the area per lipid and an increase in bilayer thickness, in agreement with experimental data. Further, H₃O⁺ preferentially accumulated at the water-lipid interface, suggesting the localised pH at the membrane surface is much lower than the bulk bathing solution. Another significant finding was that the hydrogen bonds formed by H₃O⁺ ions with lipid headgroup oxygens are, on average, shorter in length and longer-lived than the ones formed in bulk water. In addition, the H₃O⁺ ions resided for longer periods in association with the carbonyl oxygens than with either phosphate oxygen in lipids. In summary, the MD simulations support a model where the hydrogen bonding capacity of H₃O⁺ for carbonyl and phosphate oxygens is the origin of the pH-induced changes in lipid packing in phospholipid membranes. These molecular-level studies are an important step towards a better understanding of the effect of pH on biological membranes.

Fluorescence-based monitoring of electronic state and ion exchange kinetics with FCS and related techniques: from T-jump measurements to fluorescence fluctuations

In this review, we give a historical view of how our research in the development and use of fluorescence correlation spectroscopy (FCS) and related techniques has its roots and how it originally evolved from the pioneering work of Manfred Eigen, his colleagues, and coworkers. Work on temperature-jump (T-jump) experiments, conducted almost 50 years ago, led on to the development of the FCS technique. The pioneering work in the 1970s, introducing and demonstrating the concept for FCS, in turn formed the basis for the breakthrough use of FCS more than 15 years later. FCS can be used for monitoring reaction kinetics, based on fluctuations at thermodynamic equilibrium, rather than on relaxation measurements following perturbations. In this review, we more specifically discuss FCS measurements on photodynamic, electronic state transitions in fluorophore molecules, and on proton exchange dynamics in solution and on biomembranes. In the latter case, FCS measurements have proven capable of casting new light on the mechanisms of proton exchange at biological membranes, of central importance to bioenergetics and signal transduction. Finally, we describe the transient-state (TRAST) spectroscopy/imaging technique, sharing features with both relaxation (T-jump) and equilibrium fluctuation (FCS) techniques. TRAST is broadly applicable for cellular and molecular studies, and we briefly outline how TRAST can provide unique information from fluorophore blinking kinetics, reflecting e.g., cellular metabolism, rare molecular encounters, and molecular stoichiometries.

Interfacial water molecules at biological membranes: Structural features and role for lateral proton diffusion

Proton transport at water/membrane interfaces plays a fundamental role for a myriad of bioenergetic processes. Here we have performed ab initio molecular dynamics simulations of proton transfer along two phosphatidylcholine bilayers. As found in previous theoretical studies, the excess proton is preferably located at the water/membrane interface. Further, our simulations indicate that it interacts not only with phosphate head groups, but also with water molecules at the interfaces. Interfacial water molecules turn out to be oriented relative to the lipid bilayers, consistently with experimental evidence. Hence, the specific water-proton interaction may help explain the proton mobility experimentally observed at the membrane interface.

Orientation of non-spherical protonated water clusters revealed by infrared absorption dichroism

Infrared continuum bands that extend over a broad frequency range are a key spectral signature of protonated water clusters. They are observed for many membrane proteins that contain internal water molecules, but their microscopic mechanism has remained unclear. Here we compute infrared spectra for protonated and unprotonated water chains, discs, and droplets from ab initio molecular dynamics simulations. The continuum bands of the protonated clusters exhibit significant anisotropy for chains and discs, with increased absorption along the direction of maximal cluster extension. We show that the continuum band arises from the nuclei motion near the excess charge, with a long-ranged amplification due to the electronic polarizability. Our experimental, polarization-resolved light–dark difference spectrum of the light-driven proton pump bacteriorhodopsin exhibits a pronounced dichroic continuum band. Our results suggest that the protonated water cluster responsible for the continuum band of bacteriorhodopsin is oriented perpendicularly to the membrane normal.

Protein-bound water clusters play a key role for proton transport and storage in molecular biology. Here, the authors show by simulations and experiments that the orientation of non-spherical protonated water clusters in bacteriorhodopsin is unveiled by polarization-resolved infrared spectroscopy.

The effect of hydronium ions on the structure of phospholipid membranes

This work studies the mechanisms by which hydronium ions modulate the structure of phospholipid bilayers.

Acid-Group-Content-Dependent Proton Conductivity Mechanisms at the Interlayer of Poly(N-dodecylacrylamide-co-acrylic acid) Copolymer Multilayer Nanosheet Films

The effect of the content of acid groups on the proton conductivity at the interlayer of polymer-nanosheet assemblies was investigated. For that purpose, amphiphilic poly(N-dodecylacrylamide-co-acrylic acid) copolymers [p(DDA/AA)] with varying contents of AA were synthesized by free radical polymerization. Surface pressure (π)-area (A) isotherms of these copolymers indicated that stable polymer monolayers are formed at the air/water interface for AA mole fraction (n) ≤ 0.49. In all cases, a uniform dispersion of the AA groups in the polymer monolayer was observed. Subsequently, polymer monolayers were transferred onto solid substrates using the Langmuir-Blodgett (LB) technique. X-ray diffraction (XRD) analyses of the multilayer films showed strong Bragg diffraction peaks, suggesting a highly uniform lamellar structure for the multilayer films. The proton conductivity of the multilayer films parallel to the direction of the layer planes were measured by impedance spectroscopy, which revealed that the conductivity increased with increasing values of n. Activation energies for proton conduction of ∼0.3 and 0.42 eV were observed for n ≥ 0.32 and n = 0.07, respectively. Interestingly, the proton conductivity of a multilayer film with n = 0.19 did not follow the Arrhenius equation. These results were interpreted in terms of the average distance between the AA groups (l_AA), and it was concluded that, for n ≥ 0.32, an advanced 2D hydrogen bonding network was formed, while for n = 0.07, l_AA is too long to form such hydrogen bonding networks. The l_AA for n = 0.19 is intermediate to these extremes, resulting in the formation of hydrogen bonding networks at low temperatures, and disruption of these networks at high temperatures due to thermally induced motion. These results indicate that a high proton conductivity with low activation energy can be achieved, even under weakly acidic conditions, by arranging the acid groups at an optimal distance.

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.

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.

Protonation Dynamics on Lipid Nanodiscs: Influence of the Membrane Surface Area and External Buffers

Lipid membrane surfaces can act as proton-collecting antennae, accelerating proton uptake by membrane-bound proton transporters. We investigated this phenomenon in lipid nanodiscs (NDs) at equilibrium on a local scale, analyzing fluorescence fluctuations of individual pH-sensitive fluorophores at the membrane surface by fluorescence correlation spectroscopy (FCS). The protonation rate of the fluorophores was ∼100-fold higher when located at 9- and 12-nm diameter NDs, compared to when in solution, indicating that the proton-collecting antenna effect is maximal already for a membrane area of ∼60 nm². Fluorophore-labeled cytochrome c oxidase displayed a similar increase when reconstituted in 12 nm NDs, but not in 9 nm NDs, i.e., an acceleration of the protonation rate at the surface of cytochrome c oxidase is found when the lipid area surrounding the protein is larger than 80 nm², but not when below 30 nm². We also investigated the effect of external buffers on the fluorophore proton exchange rates at the ND membrane-water interfaces. With increasing buffer concentrations, the proton exchange rates were found to first decrease and then, at millimolar buffer concentrations, to increase. Monte Carlo simulations, based on a simple kinetic model of the proton exchange at the membrane-water interface, and using rate parameter values determined in our FCS experiments, could reconstruct both the observed membrane-size and the external buffer dependence. The FCS data in combination with the simulations indicate that the local proton diffusion coefficient along a membrane is ∼100 times slower than that observed over submillimeter distances by proton-pulse experiments (D_s ∼ 10⁻⁵cm²/s), and support recent theoretical studies showing that proton diffusion along membrane surfaces is time- and length-scale dependent.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Transport of lipophilic carboxylates is mediated by transmembrane helix 2 in multidrug transporter AcrB

The deployment of multidrug efflux pumps is a powerful defence mechanism for Gram-negative bacterial cells when exposed to antimicrobial agents. The major multidrug efflux transport system in Escherichia coli, AcrAB–TolC, is a tripartite system using the proton-motive force as an energy source. The polyspecific substrate-binding module AcrB uses various pathways to sequester drugs from the periplasm and outer leaflet of the inner membrane. Here we report the asymmetric AcrB structure in complex with fusidic acid at a resolution of 2.5 Å and mutational analysis of the putative fusidic acid binding site at the transmembrane domain. A groove shaped by the interface between transmembrane helix 1 (TM1) and TM2 specifically binds fusidic acid and other lipophilic carboxylated drugs. We propose that these bound drugs are actively displaced by an upward movement of TM2 towards the AcrB periplasmic porter domain in response to protonation events in the transmembrane domain.

The AcrB module of the AcrAB-TolC multidrug efflux pump sequesters drugs from the periplasm and outer leaflet of the inner membrane. Here, Oswald et al. provide evidence that lipophilic carboxylated substrates bind to a groove between transmembrane helices TM1 and TM2, for further transport by an upward movement of TM2.

Phospholipids and glycolipids mediate proton containment and circulation along the surface of energy-transducing membranes

Proton bioenergetics provides the energy for growth and survival of most organisms in the biosphere ranging from unicellular marine phytoplankton to humans. Chloroplasts harvest light and generate a proton electrochemical gradient (proton motive force) that drives the production of ATP needed for carbon dioxide fixation and plant growth. Mitochondria, bacteria and archaea generate proton motive force to energize growth and other physiologies. Energy transducing membranes are at the heart of proton bioenergetics and are responsible for catalyzing the conversion of energy held in high-energy electrons→electron transport chain→proton motive force→ATP. Whereas the electron transport chain is understood in great detail there are major gaps in understanding mechanisms of proton transfer or circulation during proton bioenergetics. This paper is built on the proposition that phospho- and glyco-glycerolipids form proton transport circuitry at the membrane's surface. By this proposition, an emergent membrane property, termed the hyducton, confines active/unbound protons or hydronium ions to a region of low volume close to the membrane surface. In turn, a von Grotthuß mechanism rapidly moves proton substrate in accordance with nano-electrochemical poles on the membrane surface created by powerful proton pumps such as ATP synthase.

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.

Long-Range Proton Conduction across Free-Standing Serum Albumin Mats

Free-standing serum-albumin mats can transport protons over millimetre length-scales. The results of photoinduced proton transfer and voltage-driven proton-conductivity measurements, together with temperature-dependent and isotope-effect studies, suggest that oxo-amino-acids of the protein serum albumin play a major role in the translocation of protons via an "over-the-barrier" hopping mechanism. The use of proton-conducting protein mats opens new possibilities for bioelectronic interfaces.

Non-Brownian diffusion in lipid membranes: Experiments and simulations

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.