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

Emergence of Complexity in Protein Functions and Metabolic Networks

In modern organisms proteins perform a majority of cellular functions, such as chemical catalysis, energy transduction and transport of material across cell walls. Although great strides have been made towards understanding protein evolution, a meaningful extrapolation from contemporary proteins to their earliest ancestors is virtually impossible. In an alternative approach, the origin of water-soluble proteins was probed through the synthesis of very large libraries of random amino acid sequences and subsequently subjecting them to in vitro evolution. In combination with computer modeling and simulations, these experiments allow us to address a number of fundamental questions about the origins of proteins. Can functionality emerge from random sequences of proteins? How did the initial repertoire of functional proteins diversify to facilitate new functions? Did this diversification proceed primarily through drawing novel functionalities from random sequences or through evolution of already existing proto-enzymes? Did protein evolution start from a pool of proteins defined by a frozen accident and other collections of proteins could start a different evolutionary pathway? Although we do not have definitive answers to these questions, important clues have been uncovered. Considerable progress has been also achieved in understanding the origins of membrane proteins. We will address this issue in the example of ion channels - proteins that mediate transport of ions across cell walls. Remarkably, despite overall complexity of these proteins in contemporary cells, their structural motifs are quite simple, with -helices being most common. By combining results of experimental and computer simulation studies on synthetic models and simple, natural channels, I will show that, 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

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"

Free-Energy Calculations. A Mathematical Perspective

Ion channels are pore-forming assemblies of transmembrane proteins that mediate and regulate ion transport through cell walls. They are ubiquitous to all life forms. In humans and other higher organisms they play the central role in conducting nerve impulses. They are also essential to cardiac processes, muscle contraction and epithelial transport. Ion channels from lower organisms can act as toxins or antimicrobial agents, and in a number of cases are involved in infectious diseases. Because of their important and diverse biological functions they are frequent targets of drug action. Also, simple natural or synthetic channels find numerous applications in biotechnology. For these reasons, studies of ion channels are at the forefront of biophysics, structural biology and cellular biology. In the last decade, the increased availability of X-ray structures has greatly advanced our understanding of ion channels. However, their mechanism of action remains elusive. This is because, in order to assist controlled ion transport, ion channels are dynamic by nature, but X-ray crystallography captures the channel in a single, sometimes non-native state. To explain how ion channels work, X-ray structures have to be supplemented with dynamic information. In principle, molecular dynamics (MD) simulations can aid in providing this information, as this is precisely what MD has been designed to do. However, MD simulations suffer from their own problems, such as inability to access sufficiently long time scales or limited accuracy of force fields. To assess the reliability of MD simulations it is only natural to turn to the main function of channels - conducting ions - and compare calculated ionic conductance with electrophysiological data, mainly single channel recordings, obtained under similar conditions. If this comparison is satisfactory it would greatly increase our confidence that both the structures and our computational methodologies are sufficiently accurate. Channel conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD 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. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if 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. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations

Is Water Necessary for Life?

The universality of water as the solvent for life is usually justified by its role in supporting the rich organic chemistry. It has been pointed out, however, that even richer synthetic chemistry is possible in other organic solvents. Does it mean that water is not necessary for life? Here, other, essential criteria for solvent for life that have not been sufficiently considered are discussed. In biological systems, complex molecules are not only constantly synthesized but also degraded. Solvent-mediated degradation is essential for regulating cell content, preventing overcrowding and allowing for recycling organic material. Achieving a balance between synthetic and degradative processes is facile in water, but not in many other organic liquids. Thus, the so-called water paradox according to which water is both necessary to life and toxic to biopolymer synthesis might not be paradoxical at all. The machinery of life is based on non-covalent interactions that do not involve making or breaking chemical bonds. Their strength needs to be properly tuned. If they are too weak, there might be undesired response to natural fluctuations of physical or chemical parameters. If they are too strong, the kinetics and energetics of cellular processes could adversely influenced. The solvent must allow for balancing these interactions, which provides strong, universal constraints on the medium for life. Water influences non-covalent interactions mainly by two mechanisms. First, it reduces strong, electrostatic interactions between molecules, chemical groups or atoms carrying electric charge or dipole. Second, it induces the hydrophobic effect, the tendency to remove non-polar (hydrophobic) molecules and groups from direct contact with aqueous solution and, instead, interact with each other. In living systems, the hydrophobic effect is largely responsible for self-organization of molecules to more complex structures, such as aggregation of lipid molecules to form biological membranes and protein folding. Water exists as stable liquid in a large temperature range, and the hydrophobic effects are a consequence of the temperature insensitivity of essential properties of its liquid state. In summary, water accomplishes an amazing feat it reduces strong interactions between dissolved species and simultaneously increases the strength of weak interactions, bringing all of them to the right range. Once we consider not only synthetic capabilities but also other required traits of the solvent for life, no viable alternative to water is currently known

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

Small Ion Channel Linking Molecular Simulations and Electrophysiology

Ion channels are pore-forming protein assemblies that mediate the transport of small ions across cell membranes. Otherwise, membrane bilayers would be almost impermeable to ions incapable to traverse the low dielectric constant, hydrophobic membrane core. Ion channels are ubiquitous to all life forms. In humans and other higher organisms they play the central role in conducting nerve impulses, cardiac functions, muscle contraction and apoptosis. On the other extreme of biological complexity, viral ion channels (viroporins) influence many stages of the virus infection cycle either through regulating virus replication, such as entry, assembly and release or modulating the electrochemical balance in the subcellular compartments of host cells. Ion channels were crucial components of protocells. Their emergence facilitated adaptation of nascent life to different environmental conditions. The earliest ion channels must have been much simpler than most of their modern ancestors. Viral channels are among only a few naturally occurring models to study the structure, function and evolution of primordial channels. Experimental studies of these properties are difficult and often unreliable. In principle, computational methods, and molecular dynamics (MD) simulations in particular, can aid in providing information about both the structure and the function of ion channels. However, MD suffers from its own problems, such as inability to access sufficiently long time scales or limited accuracy of force fields. It is, therefore, essential to determine the reliability of MD simulations. We propose to do so on the basis of two criteria. One is channel stability on time scales that extend for several microseconds or longer. The other is the ability to reproduce the measured ionic conductance as a function of applied voltage. If both the stability and the calculated ionic conductance are satisfactory it will greatly increase our confidence that the structure and the function of a channel are described sufficiently accurately. To our knowledge, long time scale stability (approx.10 micro-sec) and the correct electrophysiology have been shown so far for only one channel - the synthetic LS3 hexamer). In this presentation, this approach will be discussed in application to two viral channels - Vpu, encoded by the HIV-1 genome and p7 of hepatitis C

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