Molecular dynamics simulation of the antiamoebin ion channel: linking structure and conductance

Joule heating involving ion currents through channel proteins

Ion currents associated with channel proteins in the presence of membrane potential are ubiquitous in cellular and organelle membranes. When an ion current occurs through a channel protein, Joule heating should occur. However, this Joule heating seems to have been largely overlooked in biology. Here we show theoretical investigation of Joule heating involving channel proteins in biological processes. We used electrochemical potential to derive the Joule's law for an ion current through an ion transport protein in the presence of membrane potential, and we suggest that heat production and absorption can occur. Simulation of temperature distribution around a single channel protein with the Joule heating revealed that the temperature increase was as small as <10-3 K, although an ensemble of channel proteins was suggested to exhibit a noticeable temperature increase. Thereby, we theoretically investigated the Joule heating of systems containing ensembles of channel proteins. Nerve is known to undergo rapid heat production followed by heat absorption during the action potential, and our simulation of Joule heating for a squid giant axon combined with the Hodgkin-Huxley model successfully reproduced the feature of the heat. Furthermore, we extended the theory of Joule heating to uncoupling protein 1 (UCP1), a solute carrier family transporter, which is important to the non-shivering thermogenesis in brown adipose tissue mitochondria (BATM). Our calculations showed that the Joule heat involving UCP1 was comparable to the literature calorimetry data of BATM. Joule heating of ion transport proteins is likely to be one of important mechanisms of cellular thermogenesis.

Multi-oligomeric states of alamethicin ion channel: Assemblies and conductance

Transmembrane assemblies of the peptaibol alamethicin (ALM) are among the most extensively studied ion channels not only because of their antimicrobial activity but also as models for channel structure and aggregation. In this study, several oligomeric states of ALM are investigated with molecular dynamics simulations to establish properties of the channel and obtain free energy profiles for ion transport and the corresponding values of conductance. The hexamer, heptamer, and octamer of ALM in phospholipid membrane are found to be stable but highly dynamic in barrel-stave structures, with calculated conductance equal to 18, 195, and 1270 pS, respectively, in 1 M KCl ion solution. The corresponding free energy profiles, reported for the first time, are reconstructed from simulations at applied voltage of 200 mV with the aid of the electrodiffusion model both with and without the knowledge of diffusivity. The calculated free energy barriers are equal to 2.5, 1.5, and 0.5 kcal/mol for K+ and 4.0, 2.2, and 1.5 kcal/mol for Cl-, for hexamer, heptamer, and octamer, respectively. The calculated conductance and the ratio between conductance in consecutive states are in good agreement with those measured experimentally. This suggests that the hexamer is the lowest conducting state, with measured conductance equal to 19 pS. The selectivity of K+ over Cl- is calculated as 1.5 and 2.3 for the octameric and heptameric channels, close to the selectivity measured for high-conductance states. Selectivity increases to 13 in the hexameric channel in which the narrowest Gln7 site has a pore radius of only ∼1.6 Å, again in accord with experiment. A good agreement found between calculated and measured conductance through a hexamer templated on cyclodextrin lands additional support for the results of our simulations, and the comparison with ALM reveals the dependence of conductance on the nature of phospholipid membrane.

Structure and Computational Electrophysiology of Ac-LS3, a Synthetic Ion Channel

Computer simulations are reported on Ac-LS3, a synthetic ion channel, containing 21 residues with a Leu-Ser-Ser-Leu-Leu-Ser-Leu heptad repeat, which forms ions channels upon application of voltage. A hexameric, coiled-coil bundle initially positioned perpendicular to the membrane settled into a stable, tilted structure after 1.5 μs, most likely to improve contacts between the non-polar exterior of the channel and the hydrophobic core of the membrane. Once tilted, the bundle remained in this state during subsequent simulations of nearly 10 μs at voltages ranging from 200 to -100 mV. In contrast, attempts to identify a stable pentameric structure failed, thus supporting the hypothesis that the channel is a hexamer. Results at 100 mV were used to reconstruct the free energy profiles for K⁺ and Cl^- in the channel. This was done by way of several methods in which results of molecular dynamics (MD) simulations were combined with the electrodiffusion model. Two of them developed recently do not require knowledge of the diffusivity. Instead, they utilize one-sided density profiles and committor probabilities. The consistency between different methods is very good, supporting the utility of the newly developed methods for reconstructing free energies of ions in channels. The flux of K⁺, which accounts for most of the current through the channel, calculated directly from MD matches well the total measured current. However, the current of Cl^- is somewhat overestimated, possibly due to a slightly unbalanced force field involving chloride. The current-voltage dependence was also reconstructed by way of a recently developed, efficient method that requires simulations only at a single voltage, yielding good agreement with the experiment. Taken together, the results demonstrate that computational electrophysiology has become a reliable tool for studying how channels mediate ion transport through membranes.

Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations

We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.

The Lorentz force on ions in membrane channels of neurons as a mechanism for transcranial static magnetic stimulation

Transcranial static magnetic stimulation is a novel noninvasive method of reduction of the cortical excitability in certain neurological diseases that makes use of static magnetic fields generated by permanent magnets. By contrast, ordinary transcranial magnetic stimulation makes use of pulsed magnetic fields generated by strong currents. Whereas the physical principle underlying ordinary transcranial magnetic stimulation is well known, that is, the Faraday´s law, the physical mechanism that explains the interaction between neurons and static magnetic fields in transcranial static magnetic stimulation remains unclear. In the present work, it is discussed the possibility that this mechanism might be the Lorentz force exerted on the ions flowing along the membrane channels of neurons. The overall effect of the static magnetic field would be to introduce an additional friction between the ions and the walls of the membrane channels, thus reducing its conductance. Calculations performed by using a Hodgkin-Huxley model demonstrate that even a slight reduction of the conductance of the membrane channels can lead to the suppression of the action potential, thus inhibiting neuronal activity.

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Structural Diversity and Bioactivities of Peptaibol Compounds From the Longibrachiatum Clade of the Filamentous Fungal Genus Trichoderma

This study examined the structural diversity and bioactivity of peptaibol compounds produced by species from the phylogenetically separated Longibrachiatum Clade of the filamentous fungal genus Trichoderma, which contains several biotechnologically, agriculturally and clinically important species. HPLC-ESI-MS investigations of crude extracts from 17 species of the Longibrachiatum Clade (T. aethiopicum, T. andinense, T. capillare, T. citrinoviride, T. effusum, T. flagellatum, T. ghanense, T. konilangbra, T. longibrachiatum, T. novae-zelandiae, T. pinnatum, T. parareesei, T. pseudokoningii, T. reesei, T. saturnisporum, T. sinensis, and T. orientale) revealed several new and recurrent 20-residue peptaibols related to trichobrachins, paracelsins, suzukacillins, saturnisporins, trichoaureocins, trichocellins, longibrachins, hyporientalins, trichokonins, trilongins, metanicins, trichosporins, gliodeliquescins, alamethicins and hypophellins, as well as eight 19-residue sequences from a new subfamily of peptaibols named brevicelsins. Non-ribosomal peptide synthetase genes were mined from the available genome sequences of the Longibrachiatum Clade. Their annotation and product prediction were performed in silico and revealed full agreement in 11 out of 20 positions regarding the amino acids predicted based on the signature sequences and the detected amino acids incorporated. Molecular dynamics simulations were performed for structural characterization of four selected peptaibol sequences: paracelsins B, H and their 19-residue counterparts brevicelsins I and IV. Loss of position R6 in brevicelsins resulted in smaller helical structures with higher atomic fluctuation for every residue than the structures formed by paracelsins. We observed the formation of highly bent, almost hairpin-like, helical structures throughout the trajectory, along with linear conformation. Bioactivity tests were performed on the purified peptaibol extract of T. reesei on clinically and phytopathologically important filamentous fungi, mammalian cells, and Arabidopsis thaliana seedlings. Porcine kidney cells and boar spermatozoa proved to be sensitive to the purified peptaibol extract. Peptaibol concentrations ≥0.3 mg ml-1 deterred the growth of A. thaliana. However, negative effects to plants were not detected at concentrations below 0.1 mg ml-1, which could still inhibit plant pathogenic filamentous fungi, suggesting that those peptaibols reported here may have applications for plant protection.

Synergistic combination of alkylphosphocholines with peptaibols in targeting Leishmania infantum in vitro

Anti-leishmanial treatment increasingly encounters therapeutic limitations due to drug toxicity and development of resistance. The effort for new therapeutic strategies led us to work on combinations of chemically different compounds that could yield enhanced leishmanicidal effect. Peptaibols are a special type of antimicrobial peptides that are able to form ion channels in cell membranes and potentially affect cell viability. We assayed the antileishmanial activity of two well studied helical peptaibols, the 16-residue antiamoebin and the 20-residue alamethicin-analogue suzukacillin, and we evaluated the biological effect of their combination with the alkylphosphocholine miltefosine and its synthetic analogue TC52. The peptaibols tested exhibited only moderate antileishmanial activity, however their combination with miltefosine had a super-additive effect against the intracellular parasite (combination index 0.83 and 0.43 for antiamoebin and suzukacillin respectively). Drug combinations altered the redox stage of promastigotes, rapidly dissipated mitochondrial membrane potential and induced concatenation of mitochondrial network promoting spheroidal morphology. These results evidenced a potent and specific antileishmanial effect of the peptaibols/miltefosine combinations, achieved with significantly lower concentrations of the compounds compared to monotherapy. Furthermore, they revealed the importance of exploring novel classes of bioactive compounds such as peptaibols and demonstrated for the first time that they can act in synergy with currently used antileishmanial drugs to improve the therapeutic outcome.

Flexible Proteins at the Origin of Life

Almost all modern proteins possess well-defined, relatively rigid scaffolds that provide structural preorganization for desired functions. Such scaffolds require the sufficient length of a polypeptide chain and extensive evolutionary optimization. How ancestral proteins attained functionality, even though they were most likely markedly smaller than their contemporary descendants, remains a major, unresolved question in the origin of life. On the basis of evidence from experiments and computer simulations, we argue that at least some of the earliest water-soluble and membrane proteins were markedly more flexible than their modern counterparts. As an example, we consider a small, evolved in vitro ligase, based on a novel architecture that may be the archetype of primordial enzymes. The protein does not contain a hydrophobic core or conventional elements of the secondary structure characteristic of modern water-soluble proteins, but instead is built of a flexible, catalytic loop supported by a small hydrophilic core containing zinc atoms. It appears that disorder in the polypeptide chain imparts robustness to mutations in the protein core. Simple ion channels, likely the earliest membrane protein assemblies, could also be quite flexible, but still retain their functionality, again in contrast to their modern descendants. This is demonstrated in the example of antiamoebin, which can serve as a useful model of small peptides forming ancestral ion channels. Common features of the earliest, functional protein architectures discussed here include not only their flexibility, but also a low level of evolutionary optimization and heterogeneity in amino acid composition and, possibly, the type of peptide bonds in the protein backbone.

Validity of the Electrodiffusion Model for Calculating Conductance of Simple Ion Channels

We examine the validity and utility of the electrodiffusion (ED) equation, i.e., the generalized Nernst-Planck equation, to characterize, in combination with molecular dynamics, the electrophysiological behavior of simple ion channels. As models, we consider three systems-two naturally occurring channels formed by α-helical bundles of peptaibols, trichotoxin, and alamethicin, and a synthetic, hexameric channel, formed by a peptide that contains only leucine and serine. All these channels mediate transport of potassium and chloride ions. Starting with equilibrium properties, such as the potential of mean force experienced by an ion traversing the channel and diffusivity, obtained from molecular dynamics simulations, the ED equation can be used to determine the full current-voltage dependence with modest or no additional effort. The potential of mean force can be obtained not only from equilibrium simulations, but also, with comparable accuracy, from nonequilibrium simulations at a single voltage. The main assumptions underlying the ED equation appear to hold well for the channels and voltages studied here. To expand the utility of the ED equation, we examine what are the necessary and sufficient conditions for Ohmic and nonrectifying behavior and relate deviations from this behavior to the shape of the ionic potential of mean force.

Pore size matters for potassium channel conductance

Ion channels are membrane proteins that mediate efficient ion transport across the hydrophobic core of cell membranes, an unlikely process in their absence. K⁺ channels discriminate K⁺ over cations with similar radii with extraordinary selectivity and display a wide diversity of ion transport rates, covering differences of two orders of magnitude in unitary conductance. The pore domains of large- and small-conductance K⁺ channels share a general architectural design comprising a conserved narrow selectivity filter, which forms intimate interactions with permeant ions, flanked by two wider vestibules toward the internal and external openings. In large-conductance K⁺ channels, the inner vestibule is wide, whereas in small-conductance channels it is narrow. Here we raise the idea that the physical dimensions of the hydrophobic internal vestibule limit ion transport in K⁺ channels, accounting for their diversity in unitary conductance.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Calculation of Lipid-Bilayer Permeabilities Using an Average Force

Calculations of lipid bilayer permeabilities from first principles, using molecular simulations, would be valuable to rapidly assess the bioavailability of drug candidates, as well as to decipher, at the atomic level, the mechanisms that underlie the translocation of permeants. The most common theoretical approach, the solubility-diffusion model, requires determination of the free energy and the diffusivity as functions of the position of the permeant. Quantitative predictions of permeability have, however, been stymied by acute difficulties in calculating the diffusivity, inadequate sampling, and, most insidiously, systematic biases due to imperfections in the force field, simulation parameters, and the inherent limitations of the diffusive model. In the present work, we combine importance-sampling simulations employing an adaptive biasing force with a Bayesian-inference algorithm to determine the free energy and diffusivity with noteworthy precision and spatial resolution. In multimicrosecond simulations, we probe the sensitivity of the permeability estimates to different aspects of the methodology, including the truncation of short-range interactions, the thermostat, the force-field parameters of the permeant, the time scale over which the diffusivity is estimated, and the size of the simulated system. The force-field parameters and time scale dependence of the diffusivities impose the greatest uncertainties on the permeability estimates. Our simulations highlight the importance of membrane distortion due to the presence of the permeant, which may be partially suppressed if the bilayer patch is not large enough. We suggest that improvements to force fields and more robust kinetic models may be needed to reduce systematic errors below a factor of two.

Towards co-evolution of membrane proteins and metabolism

Primordial metabolism co-evolved with the earliest membrane peptides to produce more environmentally fit progeny. Here, we map a continuous, evolutionary path that connects nascent biochemistry with simple, membrane-bound oligopeptides, ion channels and, further, membrane proteins capable of energy transduction and utilization of energy for active transport.

Flip-flop of oleic acid in a phospholipid membrane: rate and mechanism

Flip-flop of protonated oleic acid molecules dissolved at two different concentrations in membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine is studied with the aid of molecular dynamics simulations at a time scale of several microseconds. Direct, single-molecule flip-flop events are observed at this time scale, and the flip-flop rate is estimated at 0.2-0.3 μs(-1). As oleic acid molecules move toward the center of the bilayer during flip-flop, they undergo gradual, correlated translational, and rotational motion. Rare, double-flipping events of two hydrogen-bonded oleic acid molecules are also observed. A two-dimensional free energy surface is obtained for the translational and rotational degree of freedom of the oleic acid molecule, and the minimum energy path on this surface is determined. A barrier to flip-flop of ~4.2 kcal/mol is found at the center of the bilayer. A two-dimensional diffusion model is found to provide a good description of the flip-flop process. The fast flip-flop rate lends support to the proposal that fatty acids permeate membranes without assistance of transport proteins. It also suggests that desorption rather than flip-flop is the rate-limiting step in fatty acid transport through membranes. The relation of flip-flop rates to the evolution of ancestral cellular systems is discussed.

The adaptive biasing force method: everything you always wanted to know but were afraid to ask

In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates. Much of the appeal of the algorithm to the practitioner is in its physically intuitive underlying ideas and the absence of any requirements for prior knowledge about free-energy landscapes. Since its inception in 2001, the adaptive biasing force scheme has been the subject of considerable attention, from in-depth mathematical analysis of convergence properties to novel developments and extensions. The method has also been successfully applied to many challenging problems in chemistry and biology. In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions. Through free-energy calculations of prototypical molecular systems, many methodological aspects are examined, from stratification strategies to overcoming the so-called hidden barriers in orthogonal space, relevant not only to the adaptive biasing force algorithm but also to other importance-sampling schemes. On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

Conductance simulation of the purinergic P2X2, P2X4, and P2X7 ionic channels using a combined Brownian dynamics and molecular dynamics approach

This paper investigates the application of an original combined approach of molecular and Brownian dynamic methods with quantum chemistry calculations for modeling the process of conductance of ion channels using purinergic P2X family receptors P2X2, P2X4, and P2X7 as a case study. A simplified model of the ionic channel in the lipid bilayer has been developed. A high level of conductance (30 pS) of P2X2 ionic channel together with the key role of Asp349 in forming the selectivity filter of P2X2 has been shown by using this approach. Calculated P2X2 permeability to monovalent cations Li(+), Na(+), and K(+) conforms to the free diffusion coefficient of these ions, which shows the low selectivity of P2X2 ionic channel.

The crystal structure of samarosporin I at atomic resolution

The atomic resolution structures of samarosporin I have been determined at 100 and 293 K. This is the first crystal structure of a natural 15-residue peptaibol. The amino acid sequence in samarosporin I is identical to emerimicin IV and stilbellin I. Samarosporin is a peptide antibiotic produced by the ascomycetous fungus Samarospora rostrup and belongs to peptaibol subfamily 2. The structures at both temperatures are very similar to each other adopting mainly a 3₁₀-helical and a minor fraction of α-helical conformation. The helices are significantly bent and packed in an antiparallel fashion in the centered monoclinic lattice leaving among them an approximately 10-Å channel extending along the crystallographic twofold axis. Only two ordered water molecules per peptide molecule were located in the channel. Comparisons have been carried out with crystal structures of subfamily 2 16-residue peptaibols antiamoebin and cephaibols. The repercussion of the structural analysis of samarosporin on membrane function is discussed.

Theory and simulation of ion conduction in the pentameric GLIC channel

GLIC is a bacterial member of the large family of pentameric ligand-gated ion channels. To study ion conduction through GLIC and other membrane channels, we combine the one-dimensional potential of mean force for ion passage with a Smoluchowski diffusion model, making it possible to calculate single-channel conductance in the regime of low ion concentrations from all-atom molecular dynamics (MD) simulations. We then perform MD simulations to examine sodium ion conduction through the GLIC transmembrane pore in two systems with different bulk ion concentrations. The ion potentials of mean force, calculated from umbrella sampling simulations with Hamiltonian replica exchange, reveal a major barrier at the hydrophobic constriction of the pore. The relevance of this barrier for ion transport is confirmed by a committor function that rises sharply in the barrier region. From the free evolution of Na(+) ions starting at the barrier top, we estimate the effective diffusion coefficient in the barrier region, and subsequently calculate the conductance of the pore. The resulting diffusivity compares well with the position-dependent ion diffusion coefficient obtained from restrained simulations. The ion conductance obtained from the diffusion model agrees with the value determined via a reactive-flux rate calculation. Our results show that the conformation in the GLIC crystal structure, with an estimated conductance of ~1 picosiemens at 140 mM ion concentration, is consistent with a physiologically open state of the channel.

Diffusion models of protein folding

In theory and in the analysis of experiments, protein folding is often described as diffusion along a single coordinate. We explore here the application of a one-dimensional diffusion model to interpret simulations of protein folding, where the parameters of a model that "best" describes the simulation trajectories are determined using a Bayesian analysis. We discuss the requirements for such a model to be a good approximation to the global dynamics, and several methods for testing its accuracy. For example, one test considers the effect of an added bias potential on the fitted free energies and diffusion coefficients. Such a bias may also be used to extend our approach to determining parameters for the model to systems that would not normally explore the full coordinate range on accessible time scales. Alternatively, the propagators predicted from the model at different "lag" times may be compared with observations from simulation. We then present some applications of the model to protein folding, including Kramers-like turnover in folding rates of coarse-grained models, the effect of non-native interactions on folding, and the effect of the chosen coordinate on the observed position-dependence of the diffusion coefficients. Lastly, we consider how our results are useful for the interpretation of experiments, and how this type of Bayesian analysis may eventually be applied directly to analyse experimental data.