Ion Channels From Structure to Electrophysiology and Back

A reliable way to establish whether our understanding of a channel is satisfactory is to reproduce its measured ionic conductance over a broad range of applied voltages in computer simulations. In molecular dynamics (MD), this can be done 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 have developed a markedly more efficient alternative in which MD is combined with the electrodiffusion (ED) equation. In this approach, the assumptions of the ED equation can be rigorously tested, and the precision and consistency of the calculated conductance can be determined. We have demonstrated that the full current/voltage dependence and the underlying free energy profile for a simple channel can be reliably calculated from equilibrium or non-equilibrium MD simulations at a single voltage. Free energy profiles can be obtained from non-equilibrium simulations without a loss of accuracy even without the knowledge of diffusion coefficient. To carry out MD simulations, a structural model of a channel has to be assumed, which is an important constraint, considering that high-resolution structures are available for only very few simple channels. If the comparison of calculated ionic conductance with electrophysiological data is satisfactory, it greatly increases our confidence that the structure and the function are described sufficiently accurately. We examined the validity of the ED for several channels embedded in phospholipid membranes - four naturally occurring channels: trichotoxin, alamethicin, p7 from hepatitis C virus (HCV) and Vpu from the HIV-1 virus, a synthetic, hexameric channel, formed by a 21-residue peptide that contains only leucine and serine and a bacterial pentameric ligand-gated ion channel, GLIC. All these channels mediate transport of potassium and chloride ions. It was found that the ED equation is satisfactory for these systems. In some of them, experimental and calculated electrophysiological properties are in good agreement, whereas in others there are strong indications that the structural models are incorrect

Thoughts Without Content are Empty, Intuitions Without Concepts are Blind - Determinism and Contingency Revisited

Was the emergence of life a predictable outcome of chemical evolution on earth? Could evolution produce life very different from ours? These are one of the oldest questions in the field of the origin of life that not only have broad philosophical implications but also impact how we approach the problem from the methodological standpoint. Framing the issue in terms of the dichotomy between contingency and determinism is not a fortunate because these two terms in their conventional meaning are neither mutually exclusive nor jointly exhaustive. Determinism, represented in natural sciences by Newtonian physics, relies on the assumption that every event is causally determined by a chain of previous events. In the context of the origin of life it means that once the initial conditions on the early earth have been specified further evolution follows inevitably. Considering uncertainties about conditions on the prebiotic earth, many plausible sets of initial conditions can be defined, each followed by a separate deterministic trajectory. This conventional understanding of determinism does not admit contingency. Further, it has no implications for evaluating how many sets of initial conditions lead to the emergence of life. It appears that a better framing of the problem is as follows: given plausible sets of initial conditions on the early earth how probable and broadly spread are evolutionary trajectories that lead to life? Instead of undertaking an impossible task of specifying microscopic initial conditions for all components of the system one uses a reduced representation of this system and specify only a small set of essential macroscopic parameters, values (or ranges of values) of which can be identified, inferred or estimated from experiment, theory or historical record. The following evolutionary trajectories are still governed by laws of physics and chemistry but become probabilistic and "contingency" is admitted as variations in other variables in the system. A similar reasoning is common in other fields of science, for example in statistical mechanics. Some trajectories lead to life, perhaps in different forms, whereas others do not. Of our true interest is the ratio of these two outcomes. The issue of determinism does not directly enter the picture. The debate about the likelihood of the emergence of life is quite old. One view holds that the origin of life is an event governed by chance, and the result of so many random events (contingencies) is unpredictable. This view was eloquently expressed by Monod. In his book "Chance or Necessity" he argued that life was a product of "nature's roulette." In an alternative view, expressed in particular by deDuve and Morowitz, the origin of life is considered a highly probable or even inevitable event (although its details need not be determined in every respect). Only in this sense the origin of life can be considered a "deterministic event"

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warrante

Proteins with Novel Structure, Function and Dynamics

Recently, a small enzyme that ligates two RNA fragments with the rate of 10(exp 6) above background was evolved in vitro (Seelig and Szostak, Nature 448:828831, 2007). This enzyme does not resemble any contemporary protein (Chao et al., Nature Chem. Biol. 9:8183, 2013). It consists of a dynamic, catalytic loop, a small, rigid core containing two zinc ions coordinated by neighboring amino acids, and two highly flexible tails that might be unimportant for protein function. In contrast to other proteins, this enzyme does not contain ordered secondary structure elements, such as alphahelix or betasheet. The loop is kept together by just two interactions of a charged residue and a histidine with a zinc ion, which they coordinate on the opposite side of the loop. Such structure appears to be very fragile. Surprisingly, computer simulations indicate otherwise. As the coordinating, charged residue is mutated to alanine, another, nearby charged residue takes its place, thus keeping the structure nearly intact. If this residue is also substituted by alanine a salt bridge involving two other, charged residues on the opposite sides of the loop keeps the loop in place. These adjustments are facilitated by high flexibility of the protein. Computational predictions have been confirmed experimentally, as both mutants retain full activity and overall structure. These results challenge our notions about what is required for protein activity and about the relationship between protein dynamics, stability and robustness. We hypothesize that small, highly dynamic proteins could be both active and fault tolerant in ways that many other proteins are not, i.e. they can adjust to retain their structure and activity even if subjected to mutations in structurally critical regions. This opens the doors for designing proteins with novel functions, structures and dynamics that have not been yet considered

Activation and Proton Transport Mechanism in Influenza A M2 Channel

AbstractMolecular 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 His37 tetrad. All simulated structures are in very good agreement with high-resolution structures. Changes in the channel caused by progressive protonation of His37 provide insight into the mechanism of proton transport. The channel is closed at both His37 and Trp41 sites in the singly and doubly protonated states, but it opens at Trp41 upon further protonation. Anions access the charged His37 and by doing so stabilize the protonated states of the channel. The narrow opening at the His37 site, further blocked by anions, is inconsistent with the water-wire mechanism of proton transport. Instead, conformational interconversions of His37 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 Val27 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

Calculating Conductance of Ion Channels

We have simulated two small ion channels in a water/membrane system, which consists of 71,000-72,000 atoms, and have estimated the conductance by way of counting ions crossing these channels in applied field. The calculated values of conductance have been compared with predictions of the electrodiffusion model. In a recently developed theoretical framework, all commonly used assumptions of the model can be tested. If they are satisfied, which is often the case, the approach provides a rigorous way to extrapolate conductance calculated at one voltage to other voltages. This, in turn, allows for efficient estimations of current-voltage dependence, examining rectifying behavior of channels and calculating the reversal potential. Furthermore, the consistency of the results can be precisely tested. Simulations at microsecond time scales are required to sufficiently reduce statistical errors and separate them from possible systematic errors. Only then the accuracy of the proposed approach can be properly tested. Linking simulations with electrophysiology provides a stringent, highly relevant test for the correctness of computer simulations of ion channels. Considering biological, medical and pharmaceutical importance of these proteins, results of the proposed study might motivate the development of improved hardware and software that would enable applying a similar strategy to more complex channels at longer times

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments

The Origins of Transmembrane Ion Channels

Even though membrane proteins that mediate transport of ions and small molecules across cell walls are among the largest and least understood biopolymers in contemporary cells, it is still possible to shed light on their origins and early evolution. The central observation is that transmembrane portions of most ion channels are simply bundles of -helices. By combining results of experimental and computer simulation studies on synthetic models and natural channels, mostly of non-genomic origin, we show that the emergence of -helical channels was protobiologically plausible, and did not require highly specific amino acid sequences. Despite their simple structure, such channels could possess properties that, at the first sight, appear to require markedly larger complexity. Specifically, we explain how the antiamoebin channels, which are made of identical helices, 16 amino acids in length, achieve efficiency comparable to that of highly evolved channels. We further show that antiamoebin channels are extremely flexible, compared to modern, genetically coded channels. On the basis of our results, we propose that channels evolved further towards high structural complexity because they needed to acquire stable rigid structures and mechanisms for precise regulation rather than improve efficiency. In general, even though architectures of membrane proteins are not nearly as diverse as those of water-soluble proteins, they are sufficiently flexible to adapt readily to the functional demands arising during evolution

Water as a Solvent for Life

"Follow the water" is our basic strategy in searching for life in the universe. The universality of water as the solvent for living systems is usually justified by arguing that water supports the rich organic chemistry that seeds life, but alternative chemistries are possible in other organic solvents. Here, other, essential criteria for life that have not been sufficiently considered so far, will be discussed