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.

Fast bilayer-micelle fusion mediated by hydrophobic dipeptides.

To understand the transition from inanimate matter to life, we studied a process that directly couples simple metabolism to evolution via natural selection, demonstrated experimentally by Adamala and Szostak. In this process, dipeptides synthesized inside precursors of cells promote absorption of fatty acid micelles to vesicles, inducing their preferential growth and division at the expense of other vesicles. The process is explained on the basis of coarse-grained molecular dynamics simulations, each extending for tens of microseconds, carried out to model fusion between a micelle and a membrane, both made of fatty acids in the absence and presence of hydrophobic dipeptides. In all systems with dipeptides, but not in their absence, fusion events were observed. They involve the formation of a stalk made by hydrophobic chains from the micelle and the membrane, similar to that postulated for vesicle-vesicle fusion. The emergence of a stalk is facilitated by transient clusters of dipeptides, side chains of which form hydrophobic patches at the membrane surface. Committor probability calculations indicate that the size of a patch is a suitable reaction coordinate and allows for identifying the transition state for fusion. Free-energy barrier to fusion is greatly reduced in the presence of dipeptides to only 4-5 kcal/mol, depending on the hydrophobicity of side chains. The mechanism of mediated fusion, which is expected to apply to other small peptides and hydrophobic molecules, provides a robust means by which a nascent metabolism can confer evolutionary advantage to precursors of cells.

Computational Electrophysiology from a Single Molecular Dynamics Simulation and the Electrodiffusion Model.

The availability of high-resolution structures of ion channels opens the doors to reliable computations of electrophysiological properties, such as the dependence of ionic currents and selectivities on applied voltage. We develop two theoretical approaches for calculating these properties from molecular dynamics simulations at a single voltage, or even in the absence of voltage, combined with the electrodiffusion model in which ion motion in the channel is represented as one-dimensional diffusion in the potential of mean force exerted by other components of the system and the applied electric field. No knowledge of diffusivity or ion densities at other voltages is needed. Instead, in one approach, one-sided ion fluxes and density profiles are used to determine the free energy profile. In the other approach, committor probabilities for ions transported at the selected voltage are used for this purpose. Both approaches have been validated in an example of a simple ion channel formed by trichotoxin. The potentials of mean force calculated by way of the proposed approaches and obtained from traditional methods are in excellent agreement. Furthermore, the current-voltage dependence agrees very well with results obtained by way of computationally more demanding methods. We also have readily calculated the reversal potential, a computationally challenging electrophysiological property. The key assumptions of the electrodiffusion model, such as the independence of crossing events or the insensitivity of the potential of mean force to applied voltage, have been found to be satisfied. We also show that the voltage changes linearly in the hydrophobic core of the membrane and is constant elsewhere.

In vitro selections with RNAs of variable length converge on a robust catalytic core.

In vitro selection is a powerful tool that can be used to understand basic principles of molecular evolution. We used in vitro selection to understand how changes in length and the accumulation of point mutations enable the evolution of functional RNAs. Using RNA populations of various lengths, we performed a series of in vitro experiments to select for ribozymes with RNA ligase activity. We identified a core ribozyme structure that was robust to changes in RNA length, high levels of mutagenesis, and increased selection pressure. Elaboration on this core structure resulted in improved activity which we show is consistent with a larger trend among functional RNAs in which increasing motif size can lead to an exponential improvement in fitness. We conclude that elaboration on conserved core structures is a preferred mechanism in RNA evolution. This conclusion, drawn from selections of RNAs from random sequences, is consistent with proposed evolutionary histories of specific biological RNAs. More generally, our results indicate that modern RNA structures can be used to infer ancestral structures. Our observations also suggest a mechanism by which structural outcomes of early RNA evolution would be largely reproducible even though RNA fitness landscapes consist of disconnected clusters of functional sequences.

Evaluating Biosignatures for Life Detection.

Conceptual frameworks are developed for evaluating the ability of different biosignatures to provide evidence for the presence of life in planned missions or observational studies. The focus is on intrinsic characteristics of biosignatures in space environments rather than on their detection, which depends on technology. Evaluation procedures are drawn from extensive studies in decision theory on related problems in business, engineering, medical fields, and the social arena. Three approaches are particularly useful. Two of them, Signal Detection Theory and Bayesian hypothesis testing, are based on probabilities. The third approach is based on utility theory. In all the frameworks, knowledge about a subject matter has to be translated into probabilities and/or utilities in a multistep process called elicitation. We present the first attempt to cover all steps, from acquiring knowledge about biosignatures to assigning probabilities or utilities to global quantities, such as false positives and false negatives. Since elicitation involves human judgment that is always prone to perceptual and cognitive biases, the relevant biases are discussed and illustrated in examples. We further discuss at which stage of elicitation human judgment should be involved to ensure the most reliable outcomes. An example, how evaluating biosignatures might be implemented, is given in the Supplementary Information.

Big on Change, Small on Innovation: Evolutionary Consequences of RNA Sequence Duplication.

The potential for biopolymers to evolve new structures has important consequences for their ability to optimize function and our attempts to reconstruct their evolutionary histories. Prior work with in vitro systems suggests that structural remodeling of RNA is difficult to achieve through the accumulation of point mutations or through recombination events. Sequence duplication may represent an alternative mechanism that can more readily lead to the evolution of new structures. Structural and sequence elements in many RNAs and proteins appear to be the products of duplication events, indicating that this mechanism plays a major role in molecular evolution. Despite the potential significance of this mechanism, little experimental data is available concerning the structural and evolutionary consequences of duplicating biopolymer sequences. To assess the structural consequences of sequence duplication on the evolution of RNA, we mutagenized an RNA sequence containing two copies of an ATP aptamer and subjected the resulting population to multiple in vitro evolution experiments. We identified multiple routes by which duplication, followed by the accumulation of functional point mutations, allowed our populations to sample two entirely different secondary structures. The two structures have no base pairs in common, but both structures contain two copies of the same ATP-binding motif. We do not observe the emergence of any other functional secondary structures beyond these two. Although this result suggests a limited capacity for duplication to support short-term functional innovation, major changes in secondary structure, like the one observed here, should be given careful consideration as they are likely to frustrate attempts to infer deep evolutionary histories of functional RNAs.

Gene Expression Measurement Module (GEMM) for space application: Design and validation.

In order to facilitate studies on the impact of the space environment on biological systems, we have developed a prototype of GEMM (Gene Expression Measurement Module) - an automated, miniaturized, integrated fluidic system for in-situ measurements of gene expression in microbial samples. The GEMM instrument is capable of (1) lysing bacterial cell walls, (2) extracting and purifying RNA released from cells, (3) hybridizing the RNA to probes attached to a microarray and (4) providing electrochemical readout, all in a microfluidics cartridge. To function on small, uncrewed spacecraft, the conventional, laboratory protocols for both sample preparation and hybridization required significant modifications. Biological validation of the instrument was carried out on Synechococcus elongatus, a photosynthetic cyanobacterium known for its metabolic diversity and resilience to adverse conditions. It was demonstrated that GEMM yielded reliable, reproducible gene expression profiles. GEMM is the only high throughput instrument that can be deployed in near future on space platforms other than the ISS to advance biological research in space. It can also prove useful for numerous terrestrial applications in the field.

Sequence-Dependent Interfacial Adsorption and Permeation of Dipeptides across Phospholipid Membranes.

We investigate permeation of three blocked dipeptides with different side chain polarity across a phospholipid membrane and their behavior at the water-membrane interface by way of molecular dynamics simulations. Hydrophilic serine-serine dipeptide is found to desorb from the interface to aqueous phase, whereas hydrophobic phenylalanine-leucine and amphiphilic serine-leucine tend to accumulate at the interface with a free energy minimum of -3 kcal/mol. All three dipeptides exhibit free energy barriers to permeation across the membrane located at the center of the bilayer. The height of the barrier is strongly sequence dependent and increases with the dipeptide polarity. It is equal to 3.5, 6.4, and 10.0 kcal/mol for phenylalanine-leucine, serine-leucine, and serine-serine, respectively. The corresponding permeability coefficients are equal to 4.6 × 10-3, 4.5 × 10-5, and 8.7 × 10-8 cm/s. The apparent insensitivity of membrane permeability to hydrophobicity of dipeptides, found in some experiments, is attributed to neglecting corrections for unstirred water layers near membrane surface, which are significant for hydrophobic species. Different hydrophobicity of the dipeptides also influences their conformations and orientations, both at the interface and inside the membrane. In particular, penetration of hydrophilic serine-serine dipeptide causes the formation of water-filled defects in the bilayer. These results are relevant to the delivery of peptide-based therapeutic agents.

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.

Toward biotechnology in space: High-throughput instruments for in situ biological research beyond Earth.

Space biotechnology is a nascent field aimed at applying tools of modern biology to advance our goals in space exploration. These advances rely on our ability to exploit in situ high throughput techniques for amplification and sequencing DNA, and measuring levels of RNA transcripts, proteins and metabolites in a cell. These techniques, collectively known as "omics" techniques have already revolutionized terrestrial biology. A number of on-going efforts are aimed at developing instruments to carry out "omics" research in space, in particular on board the International Space Station and small satellites. For space applications these instruments require substantial and creative reengineering that includes automation, miniaturization and ensuring that the device is resistant to conditions in space and works independently of the direction of the gravity vector. Different paths taken to meet these requirements for different "omics" instruments are the subjects of this review. The advantages and disadvantages of these instruments and technological solutions and their level of readiness for deployment in space are discussed. Considering that effects of space environments on terrestrial organisms appear to be global, it is argued that high throughput instruments are essential to advance (1) biomedical and physiological studies to control and reduce space-related stressors on living systems, (2) application of biology to life support and in situ resource utilization, (3) planetary protection, and (4) basic research about the limits on life in space. It is also argued that carrying out measurements in situ provides considerable advantages over the traditional space biology paradigm that relies on post-flight data analysis.

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.

M2 proton channel: toward a model of a primitive proton pump.

Transmembrane proton transfer was essential to early cellular systems in order to transduce energy for metabolic functions. The reliable, efficient and controlled generation of proton gradients became possible only with the emergence of active proton pumps. On the basis of features shared by most modern proton pumps we identify the essential mechanistic steps in active proton transport. Further, we discuss the mechanism of action of a small, transmembrane M2 proton channel from influenza A virus as a model for proton transport in protocells. The M2 channel is a 94-residue long, α-helical tetramer that is activated at low pH and exhibits high selectivity and directionality. A shorter construct, built of transmembrane fragments that are only 24 amino acids in length, exhibits very similar proton transport properties. Molecular dynamics simulations on the microsecond time-scale carried out for the M2 channel provided atomic level details on the activation of the channel in response to protonation of the histidine residue, His37. The pathway of proton conduction is mediated by His37, which accepts and donates protons at different interconverting conformation states when pH is lower than 6.5. The Val27 and Trp41 gates and the salt bridge between Asp44 and Arg45 further enhance the directionality of proton transport. It is argued that the architecture and the mechanism of action similar to that found in the M2 channel might have been the perfect starting point for evolution towards the earliest proton pumps, indicating that active proton transport could have readily emerged from simple, passive proton channels.

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.

Combining molecular dynamics and an electrodiffusion model to calculate ion channel conductance.

Establishing the relation between the structures and functions of protein ion channels, which are protein assemblies that facilitate transmembrane ion transport through water-filled pores, is at the forefront of biological and medical sciences. A reliable way to determine whether our understanding of this relation is satisfactory is to reproduce the measured ionic conductance over a broad range of applied voltages. This can be done in molecular dynamics simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. Since this approach is computationally very expensive we develop a markedly more efficient alternative in which molecular dynamics is combined with an electrodiffusion equation. This alternative approach applies if steady-state ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. The theory refers only to line densities of ions in the channel and, therefore, avoids ambiguities related to determining the surface area of the channel near its endpoints or other procedures connecting the line and bulk ion densities. We apply the theory to a simple, model system based on the trichotoxin channel. We test the assumptions of the electrodiffusion equation, and determine the precision and consistency of the calculated conductance. We demonstrate that it is possible to calculate current/voltage dependence and accurately reconstruct the underlying (equilibrium) free energy profile, all from molecular dynamics simulations at a single voltage. The approach developed here applies to other channels that satisfy the conditions of the electrodiffusion equation.

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.

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.

Molecular crowding and early evolution.

The environment of protocells might have been crowded with small molecules and functional and non-specific polymers. In addition to altering conformational equilibria, affecting reaction rates and changing the structure and activity of water, crowding might have enhanced the capabilities of protocells for evolutionary innovation through the creation of extended neutral networks in the fitness landscape.

Activation and proton transport mechanism in influenza A M2 channel.

Molecular dynamics trajectories 2 µs in length have been generated for the pH-activated, tetrameric M2 proton channel of the influenza A virus in all protonation states of the pH sensor located at the His(37) tetrad. All simulated structures are in very good agreement with high-resolution structures. Changes in the channel caused by progressive protonation of His(37) provide insight into the mechanism of proton transport. The channel is closed at both His(37) and Trp(41) sites in the singly and doubly protonated states, but it opens at Trp(41) upon further protonation. Anions access the charged His(37) and by doing so stabilize the protonated states of the channel. The narrow opening at the His(37) site, further blocked by anions, is inconsistent with the water-wire mechanism of proton transport. Instead, conformational interconversions of His(37) correlated with hydrogen bonding to water molecules indicate that these residues shuttle protons in high-protonation states. Hydrogen bonds between charged and uncharged histidines are rare. The valve at Val(27) remains on average quite narrow in all protonation states but fluctuates sufficiently to support water and proton transport. A proton transport mechanism in which the channel, depending on pH, opens at either the histidine or valine gate is only partially supported by the simulations.