Energetics of Multi-Ion Conduction Pathways in Potassium Ion Channels

Structural Insights and Influence of Terahertz Waves in Midinfrared Region on Kv1.2 Channel Selectivity Filter

Potassium ion channels are the structural basis for excitation transmission, heartbeat, and other biological processes. The selectivity filter is a critical structural component of potassium ion channels, whose structure is crucial to realizing their function. As biomolecules vibrate and rotate at frequencies in the terahertz band, potassium ion channels are sensitive to terahertz waves. Therefore, it is worthwhile to investigate how the terahertz wave influences the selectivity filter of the potassium channels. In this study, we investigate the structure of the selectivity filter of Kv1.2 potassium ion channels using molecular dynamics simulations. The effect of an electric field on the channel has been examined at four different resonant frequencies of the carbonyl group in SF: 36.75 37.06, 37.68, and 38.2 THz. As indicated by the results, 376GLY appears to be the critical residue in the selectivity filter of the Kv1.2 channel. Its dihedral angle torsion is detrimental to the channel structural stability and the transmembrane movement of potassium ions. 36.75 THz is the resonance frequency of the carbonyl group of 376GLY. Among all four frequencies explored, the applied terahertz electric field of this frequency has the most significant impact on the channel structure, negatively impacting the channel stability and reducing the ion permeability by 20.2% compared to the absence of fields. In this study, we simulate that terahertz waves in the mid-infrared frequency region can significantly alter the structure and function of potassium ion channels and that the effects of terahertz waves differ greatly based on frequency.

Probing Ion Configurations in the KcsA Selectivity Filter with Single-Isotope Labels and 2D IR Spectroscopy

The potassium ion (K+) configurations of the selectivity filter of the KcsA ion channel protein are investigated with two-dimensional infrared (2D IR) spectroscopy of amide I vibrations. Single 13C-18O isotope labels are used, for the first time, to selectively probe the S1/S2 or S2/S3 binding sites in the selectivity filter. These binding sites have the largest differences in ion occupancy in two competing K+ transport mechanisms: soft-knock and hard-knock. According to the former, water molecules alternate between K+ ions in the selectivity filter while the latter assumes that K+ ions occupy the adjacent sites. Molecular dynamics simulations and computational spectroscopy are employed to interpret experimental 2D IR spectra. We find that in the closed conductive state of the KcsA channel, K+ ions do not occupy adjacent binding sites. The experimental data is consistent with simulated 2D IR spectra of soft-knock ion configurations. In contrast, the simulated spectra for the hard-knock ion configurations do not reproduce the experimental results. 2D IR spectra of the hard-knock mechanism have lower frequencies, homogeneous 2D lineshapes, and multiple peaks. In contrast, ion configurations of the soft-knock model produce 2D IR spectra with a single peak at a higher frequency and inhomogeneous lineshape. We conclude that under equilibrium conditions, in the absence of transmembrane voltage, both water and K+ ions occupy the selectivity filter of the KcsA channel in the closed conductive state. The ion configuration is central to the mechanism of ion transport through potassium channels.

Ion channel selectivity through ion-modulated changes of selectivity filter pKa values

In bacterial voltage-gated sodium channels, the passage of ions through the pore is controlled by a selectivity filter (SF) composed of four glutamate residues. The mechanism of selectivity has been the subject of intense research, with suggested mechanisms based on steric effects, and ion-triggered conformational change. Here, we propose an alternative mechanism based on ion-triggered shifts in pKa values of SF glutamates. We study the NavMs channel for which the open channel structure is available. Our free-energy calculations based on molecular dynamics simulations suggest that pKa values of the four glutamates are higher in solution of K+ ions than in solution of Na+ ions. Higher pKa in the presence of K+ stems primarily from the higher population of dunked conformations of the protonated Glu sidechain, which exhibit a higher pKa shift. Since pKa values are close to the physiological pH, this results in predominant population of the fully deprotonated state of glutamates in Na+ solution, while protonated states are predominantly populated in K+ solution. Through molecular dynamics simulations we calculate that the deprotonated state is the most conductive, the singly protonated state is less conductive, and the doubly protonated state has significantly reduced conductance. Thus, we propose that a significant component of selectivity is achieved through ion-triggered shifts in the protonation state, which favors more conductive states for Na+ ions and less conductive states for K+ ions. This mechanism also suggests a strong pH dependence of selectivity, which has been experimentally observed in structurally similar NaChBac channels.

The Optimized Conformation Dynamics of the KcsA Filter as a Probe for Lateral Membrane Effects: A First Principle Based Femto-Sec Resolution MD Study

We provide a high resolution, all-atom, femto-second molecular dynamics (MD) simulation of the passage of K⁺ ions and H₂O molecules through the selectivity filter of the KcsA potassium ion channel, based on first principle physical methods. Our results show that a change in the length of the selectivity filter of as little as 3%, regardless of whether the filter is made longer or shorter, will reduce the K⁺ ion current by around 50%. In addition, further squeezing or stretching by about 9% can effectively stop the current. Our results demonstrate optimized conformational dynamics that associate an increased mobility of parts in the filter linings with a standard configuration, leading to maximized conduction rates that are highly sensitive to geometrical distortions. We discuss this latter aspect in relation to lateral membrane effects on the filter region of ion channels and the 'force from lipids' hypothesis.

Weak Cation Selectivity in HCN Channels Results From K+-Mediated Release of Na+ From Selectivity Filter Binding Sites

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels generate the pacemaker current which plays an important role in the timing of various biological processes like the heart beat. We used umbrella sampling to explore the potential of mean force for the conduction of potassium and sodium through the open HCN4 pore. Our data explain distinct functional features like low unitary conductance and weak selectivity as a result of high energetic barriers inside the selectivity filter of this channel. They exceed the 3-5 kJ/mol threshold which is presumed as maximal barrier for diffusion-limited conductance. Furthermore, simulations provide a thermodynamic explanation for the weak cation selectivity of HCN channels that contain only two ion binding sites in the selectivity filter (SF). We find that sodium ions bind more strongly to the SF than potassium and are easier released by binding of potassium than of another sodium. Hence ion transport and selectivity in HCN channels is not determined by the same mechanism as in potassium-selective channels; it rather relies on sodium as a weak blocker that can only be released by potassium.

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Ion Selectivity and Permeation Mechanism in a Cyclodextrin-Based Channel

Synthetic ion channels are a promising technology in the medical and materials sciences because of their ability to conduct ions. Channels based on cyclodextrin, a cyclic oligomer of glucose, are of particular interest because of their nontoxicity and biocompatibility. Using molecular dynamics-based free energy calculations, this study identifies cyclodextrin channel types that are best suited to serve as synthetic ion channels. Free energy profiles show that the connectivity in the channel determines whether the channel is cation-selective or anion-selective. Furthermore, the energy barrier for ion transport is governed by the number of glucose molecules making up the cyclodextrin units of the channel. A detailed mechanism is proposed for ion transport through these channels. Findings from this study will aid in designing cyclodextrin-based channels that could be either cation-selective or anion-selective, by modifying the linkages of the channel or the number of glucose molecules in the cyclodextrin rings.

Unraveling of a Strongly Correlated Dynamical Network of Residues Controlling the Permeation of Potassium in KcsA Ion Channel

The complicated patterns of the single-channel currents in potassium ion channel KcsA are governed by the structural variability of the selectivity filter. A comparative analysis of the dynamics of the wild type KcsA channel and several of its mutants showing different conducting patterns was performed. A strongly correlated dynamical network of interacting residues is found to play a key role in regulating the state of the wild type channel. The network is centered on the aspartate D80 which plays the role of a hub by strong interacting via hydrogen bonds with residues E71, R64, R89, and W67. Residue D80 also affects the selectivity filter via its backbones. This network further compromises ions and water molecules located inside the channel that results in the mutual influence: the permeation depends on the configuration of residues in the network, and the dynamics of network's residues depends on locations of ions and water molecules inside the selectivity filter. Some features of the network provide a further understanding of experimental results describing the KcsA activity. In particular, the necessity of anionic lipids to be present for functioning the channel is explained by the interaction between the lipids and the arginine residues R64 and R89 that prevents destabilizing the structure of the selectivity filter.

Quantum Mechanical Coherence of K+ Ion Wave Packets Increases Conduction in the KcsA Ion Channel

We simulate the transmission of K+ ions through the KcsA potassium ion channel filter region at physiological temperatures, employing classical molecular dynamics (MD) at the atomic scale together with a quantum mechanical version of MD simulation (QMD), treating single ions as quantum wave packets. We provide a direct comparison between both concepts, embedding the simulations into identical force fields and thermal fluctuations. The quantum simulations permit the estimation of coherence times and wave packet dispersions of a K+ ion over a range of 0.5 nm (a range that covers almost 50% of the filter domains longitudinal extension). We find that this observed extension of particle delocalization changes the mean orientation of the coordinating carbonyl oxygen atoms significantly, transiently suppressing their ‘caging action’ responsible for selective ion coordination. Compared to classical MD simulations, this particular quantum effect allows the K+ ions to ‘escape’ more easily from temporary binding sites provided by the surrounding filter atoms. To further elucidate the role of this observation for ion conduction rates, we compare the temporal pattern of single conduction events between classical MD and quantum QMD simulations at a femto-sec time scale. A finding from both approaches is that ion permeation follows a very irregular time pattern, involving flushes of permeation interrupted by non-conductive time intervals. However, as compared with classical behavior, the QMD simulation shortens non-conductive time by more than a half. As a consequence, and given the same force-fields, the QMD-simulated ion current appears to be considerably stronger as compared with the classical current. To bring this result in line with experimentally observed ion currents and the predictions based on Nernst–Planck theories, the conclusion is that a transient short time quantum behavior of permeating ions can successfully compromise high conduction rates with ion selectivity in the filter of channel proteins.

IR Spectroscopy Can Reveal the Mechanism of K+ Transport in Ion Channels

Ion channels like KcsA enable ions to move across cell membranes at near diffusion-limited rates and with very high selectivity. Various mechanisms have been proposed to explain this phenomenon. Broadly, there is disagreement among the proposed mechanisms about whether ions occupy adjacent sites in the channel during the transport process. Here, using a mixed quantum-classical approach to calculate theoretical infrared spectra, we propose a set of infrared spectroscopy experiments that can discriminate between mechanisms with and without adjacent ions. These experiments differ from previous ones in that they independently probe specific ion binding sites within the selectivity filter. When ions occupy adjacent sites in the selectivity filter, the predicted spectra are significantly redshifted relative to when ions do not occupy adjacent sites. Comparisons between theoretical and experimental peak frequencies will therefore discriminate the mechanisms.

Queueing arrival and release mechanism for K+ permeation through a potassium channel

The mechanism underlying ion permeation through potassium channels still remains controversial. K+ ions permeate across a narrow selectivity filter (SF) in a single file. Conventional scenarios assume that K+ ions are tightly bound in the SF, and, thus, they are displaced from their energy well by ion-ion repulsion with an incoming ion. This tight coupling between entering and exiting ions has been called the "knock-on" mechanism. However, this paradigm is contradicted by experimental data measuring the water-ion flux coupling ratio, demonstrating fewer ion occupancies. Here, the results of molecular dynamics simulations of permeation through the KcsA potassium channel revealed an alternative mechanism. In the aligned ions in the SF (an ion queue), the outermost K+ was readily and spontaneously released toward the extracellular space, and the affinity of the relevant ion was ~ 50 mM. Based on this low-affinity regime, a simple queueing mechanism described by loose coupling of entering and exiting ions is proposed.

Conduction through a narrow inward-rectifier K+ channel pore

G-protein–gated inwardly rectifying potassium channels are important mediators of inhibitory neurotransmission. Based on microsecond-scale molecular dynamics simulations, Bernsteiner et al. propose novel gating details that may enable K⁺ flux via a direct knock-on mechanism.

Inwardly rectifying potassium (Kir) channels play a key role in controlling membrane potentials in excitable and unexcitable cells, thereby regulating a plethora of physiological processes. G-protein–gated Kir channels control heart rate and neuronal excitability via small hyperpolarizing outward K⁺ currents near the resting membrane potential. Despite recent breakthroughs in x-ray crystallography and cryo-EM, the gating and conduction mechanisms of these channels are poorly understood. MD simulations have provided unprecedented details concerning the gating and conduction mechanisms of voltage-gated K⁺ and Na⁺ channels. Here, we use multi-microsecond–timescale MD simulations based on the crystal structures of GIRK2 (Kir3.2) bound to phosphatidylinositol-4,5-bisphosphate to provide detailed insights into the channel’s gating dynamics, including insights into the behavior of the G-loop gate. The simulations also elucidate the elementary steps that underlie the movement of K⁺ ions through an inward-rectifier K⁺ channel under an applied electric field. Our simulations suggest that K⁺ permeation might occur via direct knock-on, similar to the mechanism recently shown for K_v channels.

The conduction pathway of potassium channels is water free under physiological conditions

Ion conduction through potassium channels is a fundamental process of life. On the basis of crystallographic data, it was originally proposed that potassium ions and water molecules are transported through the selectivity filter in an alternating arrangement, suggesting a "water-mediated" knock-on mechanism. Later on, this view was challenged by results from molecular dynamics simulations that revealed a "direct" knock-on mechanism where ions are in direct contact. Using solid-state nuclear magnetic resonance techniques tailored to characterize the interaction between water molecules and the ion channel, we show here that the selectivity filter of a potassium channel is free of water under physiological conditions. Our results are fully consistent with the direct knock-on mechanism of ion conduction but contradict the previously proposed water-mediated knock-on mechanism.

Challenges and advances in atomistic simulations of potassium and sodium ion channel gating and permeation

Ion channels are implicated in many essential physiological events such as electrical signal propagation and cellular communication. The advent of K⁺ and Na⁺ ion channel structure determination has facilitated numerous investigations of molecular determinants of their behaviour. At the same time, rapid development of computer hardware and molecular simulation methodologies has made computational studies of large biological molecules in all-atom representation tractable. The concurrent evolution of experimental structural biology with biomolecular computer modelling has yielded mechanistic details of fundamental processes unavailable through experiments alone, such as ion conduction and ion channel gating. This review is a short survey of the atomistic computational investigations of K⁺ and Na⁺ ion channels, focusing on KcsA and several voltage-gated channels from the K_V and Na_V families, which have garnered many successes and engendered several long-standing controversies regarding the nature of their structure-function relationship. We review the latest advancements and challenges facing the field of molecular modelling and simulation regarding the structural and energetic determinants of ion channel function and their agreement with experimental observations.

Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins

We present a comparison of a classical and a quantum mechanical calculation of the motion of K⁺ ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions is not much smaller than the periodic structure of Coulomb potentials in the nano-pore model of the selectivity filter. This implies that an ion may no longer be viewed to be at one exact position at a given time but can better be described by a quantum mechanical wave function. Based on first principle methods, we demonstrate solutions of a non-linear Schrödinger model that provide insight into the role of short-lived (~1 ps) coherent ion transition states and attribute an important role to subsequent decoherence and the associated quantum to classical transition for permeating ions. It is found that short coherences are not just beneficial but also necessary to explain the fast-directed permeation of ions through the potential barriers of the filter. Certain aspects of quantum dynamics and non-local effects appear to be indispensable to resolve the discrepancy between potential barrier height, as reported from classical thermodynamics, and experimentally observed transition rates of ions through channel proteins.

Coulomb interaction rules timescales in potassium ion channel tunneling

Assuming the selectivity filter of KcsA potassium ion channel may exhibit quantum coherence, we extend a previous model by Vaziri and Plenio (2010 New J. Phys. 12 085001) to take into account Coulomb repulsion between potassium ions. We show that typical ion transit timescales are determined by this interaction, which imposes optimal input/output parameter ranges. Also, as observed in other examples of quantum tunneling in biological systems, the addition of moderate noise helps coherent ion transport.

A single NaK channel conformation is not enough for non-selective ion conduction

NaK and other non-selective channels are able to conduct both sodium (Na⁺) and potassium (K⁺) with equally high efficiency. In contrast to previous crystallographic results, we show that the selectivity filter (SF) of NaK in native-like lipid membranes adopts two distinct conformations that are stabilized by either Na⁺ or K⁺ ions. The atomic differences of these conformations are resolved by solid-state NMR (ssNMR) spectroscopy and molecular dynamics (MD) simulations. Besides the canonical K⁺ permeation pathway, we identify a side entry ion-conduction pathway for Na⁺ permeation unique to NaK. Moreover, under otherwise identical conditions ssNMR spectra of the K⁺ selective NaK mutant (NaK2K) reveal only a single conformational state. Therefore, we propose that structural plasticity within the SF and the selection of these conformations by different ions are key molecular determinants for highly efficient conduction of different ions in non-selective cation channels.

H. R, Thamleena A. H, Joseph A, Ben A, V. U. K. Roles of different amino-acid residues towards binding and selective transport of K+ through KcsA K+-ion channel

Each amino acid in the selectivity filter plays a distinct role towards binding and transport of K⁺ ion through KcsA.

The Roles of Water in the Protein Matrix: A Largely Untapped Resource for Drug Discovery

The value of thoroughly understanding the thermodynamics specific to a drug discovery/design study is well known. Over the past decade, the crucial roles of water molecules in protein structure, function, and dynamics have also become increasingly appreciated. This Perspective explores water in the biological environment by adopting its point of view in such phenomena. The prevailing thermodynamic models of the past, where water was seen largely in terms of an entropic gain after its displacement by a ligand, are now known to be much too simplistic. We adopt a set of terminology that describes water molecules as being "hot" and "cold", which we have defined as being easy and difficult to displace, respectively. The basis of these designations, which involve both enthalpic and entropic water contributions, are explored in several classes of biomolecules and structural motifs. The hallmarks for characterizing water molecules are examined, and computational tools for evaluating water-centric thermodynamics are reviewed. This Perspective's summary features guidelines for exploiting water molecules in drug discovery.

Simulating Current-Voltage Relationships for a Narrow Ion Channel Using the Weighted Ensemble Method

Ion channels are responsible for a myriad of fundamental biological processes via their role in controlling the flow of ions through water-filled membrane-spanning pores in response to environmental cues. Molecular simulation has played an important role in elucidating the mechanism of ion conduction, but connecting atomistically detailed structural models of the protein to electrophysiological measurements remains a broad challenge due to the computational cost of reaching the necessary time scales. Here, we introduce an enhanced sampling method for simulating the conduction properties of narrow ion channels using the Weighted ensemble (WE) sampling approach. We demonstrate the application of this method to calculate the current–voltage relationship as well as the nonequilibrium ion distribution at steady-state of a simple model ion channel. By direct comparisons with long brute force simulations, we show that the WE simulations rigorously reproduce the correct long-time scale kinetics of the system and are capable of determining these quantities using significantly less aggregate simulation time under conditions where permeation events are rare.

Bias-Exchange Metadynamics Simulations: An Efficient Strategy for the Analysis of Conduction and Selectivity in Ion Channels

Conduction through ion channels possesses two interesting features: (i) different ionic species are selected with high-selectivity and (ii) ions travel across the channel with rates approaching free-diffusion. Molecular dynamics simulations have the potential to reveal how these processes take place at the atomic level. However, analysis of conduction and selectivity at atomistic detail is still hampered by the short time scales accessible by computer simulations. Several algorithms have been developed to "accelerate" sampling along the slow degrees of freedom of the process under study and thus to probe longer time scales. In these algorithms, the slow degrees of freedom need to be defined in advance, which is a well-known shortcoming. In the particular case of ion conduction, preliminary assumptions about the number and type of ions participating in the permeation process need to be made. In this study, a novel approach for the analysis of conduction and selectivity based on bias-exchange metadynamics simulations was tested. This approach was compared with umbrella sampling simulations, using a model of a Na(+)-selective channel. Analogous conclusions resulted from both techniques, but the computational cost of bias-exchange simulations was lower. In addition, with bias-exchange metadynamics it was possible to calculate free energy profiles in the presence of a variable number and type of permeating ions. This approach might facilitate the definition of the set of collective variables required to analyze conduction and selectivity in ion channels.

Instantaneous ion configurations in the K+ ion channel selectivity filter revealed by 2D IR spectroscopy

Potassium channels are responsible for the selective permeation of K+ ions across cell membranes. K+ ions permeate in single file through the selectivity filter, a narrow pore lined by backbone carbonyls that compose four K+ binding sites. Here, we report on the two-dimensional infrared (2D IR) spectra of a semisynthetic KcsA channel with site-specific heavy (13C18O) isotope labels in the selectivity filter. The ultrafast time resolution of 2D IR spectroscopy provides an instantaneous snapshot of the multi-ion configurations and structural distributions that occur spontaneously in the filter. Two elongated features are resolved, revealing the statistical weighting of two structural conformations. The spectra are reproduced by molecular dynamics simulations of structures with water separating two K+ ions in the binding sites, ruling out configurations with ions occupying adjacent sites.

Atomistic detailed mechanism and weak cation-conducting activity of HIV-1 Vpu revealed by free energy calculations

The viral protein U (Vpu) encoded by HIV-1 has been shown to assist in the detachment of virion particles from infected cells. Vpu forms cation-specific ion channels in host cells, and has been proposed as a potential drug target. An understanding of the mechanism of ion transport through Vpu is desirable, but remains limited because of the unavailability of an experimental structure of the channel. Using a structure of the pentameric form of Vpu – modeled and validated based on available experimental data – umbrella sampling molecular dynamics simulations (cumulative simulation time of more than 0.4 µs) were employed to elucidate the energetics and the molecular mechanism of ion transport in Vpu. Free energy profiles corresponding to the permeation of Na⁺ and K⁺ were found to be similar to each other indicating lack of ion selection, consistent with previous experimental studies. The Ser23 residue is shown to enhance ion transport via two mechanisms: creating a weak binding site, and increasing the effective hydrophilic length of the channel, both of which have previously been hypothesized in experiments. A two-dimensional free energy landscape has been computed to model multiple ion permeation, based on which a mechanism for ion conduction is proposed. It is shown that only one ion can pass through the channel at a time. This, along with a stretch of hydrophobic residues in the transmembrane domain of Vpu, explains the slow kinetics of ion conduction. The results are consistent with previous conductance studies that showed Vpu to be a weakly conducting ion channel.

Ion permeation in K⁺ channels occurs by direct Coulomb knock-on

Potassium channels selectively conduct K(+) ions across cellular membranes with extraordinary efficiency. Their selectivity filter exhibits four binding sites with approximately equal electron density in crystal structures with high K(+) concentrations, previously thought to reflect a superposition of alternating ion- and water-occupied states. Consequently, cotranslocation of ions with water has become a widely accepted ion conduction mechanism for potassium channels. By analyzing more than 1300 permeation events from molecular dynamics simulations at physiological voltages, we observed instead that permeation occurs via ion-ion contacts between neighboring K(+) ions. Coulomb repulsion between adjacent ions is found to be the key to high-efficiency K(+) conduction. Crystallographic data are consistent with directly neighboring K(+) ions in the selectivity filter, and our model offers an intuitive explanation for the high throughput rates of K(+) channels.

Detailed Examination of a Single Conduction Event in a Potassium Channel

Although extensively studied, it has proved difficult to describe in detail how potassium ion channels conduct cations and water. We present a computational study that, by using stratified umbrella sampling, examines nearly an entire conduction event of the Kv1.2/2.1 paddle chimera and thereby identifies the expected stable configurations of ions and waters in the selectivity filter of the channel. We describe in detail the motions of the ions and waters during a conduction event, focusing on how waters and ions enter the filter, the rotation of water molecules inside the filter, and how potassium ions are coordinated as they move from a water to a protein environment. Finally, we analyze the small conformational changes undergone by the protein, showing that the stable configurations are most similar to the experimental crystal structure.