Voltage sensors of a Na+ channel dissociate from the pore domain and form inter-channel dimers in the resting state.

Understanding voltage-gated sodium (Nav) channels is significant since they generate action potential. Nav channels consist of a pore domain (PD) and a voltage sensor domain (VSD). All resolved Nav structures in different gating states have VSDs that tightly interact with PDs; however, it is unclear whether VSDs attach to PDs during gating under physiological conditions. Here, we reconstituted three different voltage-dependent NavAb, which is cloned from Arcobacter butzleri, into a lipid membrane and observed their structural dynamics by high-speed atomic force microscopy on a sub-second timescale in the steady state. Surprisingly, VSDs dissociated from PDs in the mutant in the resting state and further dimerized to form cross-links between channels. This dimerization would occur at a realistic channel density, offering a potential explanation for the facilitation of positive cooperativity of channel activity in the rising phase of the action potential.

The structural basis of divalent cation block in a tetrameric prokaryotic sodium channel.

Divalent cation block is observed in various tetrameric ion channels. For blocking, a divalent cation is thought to bind in the ion pathway of the channel, but such block has not yet been directly observed. So, the behaviour of these blocking divalent cations remains still uncertain. Here, we elucidated the mechanism of the divalent cation block by reproducing the blocking effect into NavAb, a well-studied tetrameric sodium channel. Our crystal structures of NavAb mutants show that the mutations increasing the hydrophilicity of the inner vestibule of the pore domain enable a divalent cation to stack on the ion pathway. Furthermore, non-equilibrium molecular dynamics simulation showed that the stacking calcium ion repel sodium ion at the bottom of the selectivity filter. These results suggest the primary process of the divalent cation block mechanism in tetrameric cation channels.

Imaging single CaMKII holoenzymes at work by high-speed atomic force microscopy.

Ca2+/calmodulin-dependent protein kinase II (CaMKII) plays a pivotal role in synaptic plasticity. It is a dodecameric serine/threonine kinase that has been highly conserved across metazoans for over a million years. Despite the extensive knowledge of the mechanisms underlying CaMKII activation, its behavior at the molecular level has remained unobserved. In this study, we used high-speed atomic force microscopy to visualize the activity-dependent structural dynamics of rat/hydra/C. elegans CaMKII with nanometer resolution. Our imaging results revealed that the dynamic behavior is dependent on CaM binding and subsequent pT286 phosphorylation. Among the species studies, only rat CaMKIIα with pT286/pT305/pT306 exhibited kinase domain oligomerization. Furthermore, we revealed that the sensitivity of CaMKII to PP2A in the three species differs, with rat, C. elegans, and hydra being less dephosphorylated in that order. The evolutionarily acquired features of mammalian CaMKIIα-specific structural arrangement and phosphatase tolerance may differentiate neuronal function between mammals and other species.

Antithetic effects of agonists and antagonists on the structural fluctuations of TRPV1 channel.

Transient receptor potential vanilloid member 1 (TRPV1) is a heat and capsaicin receptor that allows cations to permeate and cause pain. As the molecular basis for temperature sensing, the heat capacity (ΔCp) model [D. E. Clapham, C. Miller, Proc. Natl. Acad. Sci. U.S.A. 108, 19492-19497 (2011).] has been proposed and experimentally supported. Theoretically, heat capacity is proportional to a variance in enthalpy, presumably related to structural fluctuation; however, the fluctuation of TRPV1 has not been directly visualized. In this study, we directly visualized single-molecule structural fluctuations of the TRPV1 channels in a lipid bilayer with the ligands resiniferatoxin (agonist, 1,000 times hotter than capsaicin) and capsazepine (antagonist) by high-speed atomic force microscopy. We observed the structural fluctuations of TRPV1 in an apo state and found that RTX binding enhances structural fluctuations, while CPZ binding suppresses fluctuations. These ligand-dependent differences in structural fluctuation would play a key role in the gating of TRPV1.

Biophysical Reviews Issue Focus call: Computational biophysics of atomic force microscopy.

This Commentary describes an open call for submissions to an Issue Focus of the IUPAB Biophysical Reviews journal on the topic of the, 'Computational biophysics of atomic force microscopy'. The Issue Focus will be published in Volume 15 Issue 6 of Biophysical Reviews in late December of 2023. The submission deadline is September 1st of 2023. Interested parties are requested to contact the Special Issue Editors prior to submission.

Computational biophysics of atomic force microscopy-an IUPAB-sponsored workshop.

Atomic Force Microscopy (AFM) is a structural determination technique that involves 'prodding' surfaces with a nanometer sized needle with concomitant measurement of the resisting force. Due to its ability to interrogate the nanometer-to-micrometer size range, AFM is especially suited to the structural analysis of everything from biopolymers to cells and, as such, has become an important biophysical method. As AFM was only invented in 1986 it is relatively less scientifically developed than other structural techniques, such as NMR, X-ray crystallography and electron microscopy, that have a longer history of usage. In September of 2022 the first workshop of its kind was held to examine modern computational methods useful for simulating and analysing bioAFM experiments. Sponsored by a small IUPAB workshop grant, the three day meeting was of the hybrid (joint online /in person) type and had presenting participants based in Australia, UK, Finland, Thailand, South Korea, Vietnam and Japan. Each invited speaker was asked to deliver a lecture composed of half educational material (pitched at the level of an advanced postgraduate student) and half cutting edge research material (gathered from their own studies). IUPAB funds were used to invite young researchers (postgraduate students and early career scientists) from both within Japan and countries in the near asian region who had an interest in learning about the theoretical and experimental basis of the AFM technique. This Editorial describes the workshop and introduces the written contributions from the invited lecturers.

Computation of topographic and three-dimensional atomic force microscopy images of biopolymers by calculating forces.

Atomic force microscopy (AFM) is widely utilized to visualize the molecular motions of biomolecules. Comparison of experimentally measured AFM images with simulated AFM images based on known structures of biomolecules is often necessary to elucidate what is actually resolved in the images. Experimental AFM images are generated by force measurements; however, conventional AFM simulation has been based on geometrical considerations rather than calculating forces using molecular dynamics simulations due to limited computation time. This letter summarizes recently developed methods to simulate topographic and three-dimensional AFM (3D-AFM) images of biopolymers such as chromosomes and cytoskeleton fibers. Scanning such biomolecules in AFM measurements usually results in nonequilibrium-type work being performed. As such, the Jarzynski equality was employed to relate the nonequilibrium work to the free energy profiles, and the forces were calculated by differentiating the free energy profiles. The biomolecules and probes were approximated using a supra-coarse-grained model, allowing the simulation of force-distance curves in feasible time. It was found that there is an optimum scanning velocity and that some of polymer structures are resolved in the simulated 3D-AFM images. The theoretical background adopted to rationalize the use of small probe radius in the conventional AFM simulation of biomolecules is clarified.

Computed Three-Dimensional Atomic Force Microscopy Images of Biopolymers Using the Jarzynski Equality.

Three-dimensional atomic force microscopy (3D-AFM) has resolved three-dimensional distributions of solvent molecules at solid-liquid interfaces at the subnanometer scale. This method is now being extended to the imaging of biopolymer assemblies such as chromosomes or proteins in cells, with the expectation of being able to resolve their three-dimensional structures. Here, we have developed a computational method to simulate 3D-AFM images of biopolymers by using the Jarzynski equality. It is found that some parts of the fiber structure of biopolymers are indeed resolved in the 3D-AFM image. The dependency of 3D-AFM images on the vertical scanning velocity is investigated, and optimum scanning velocities are found. It is also clarified that forces in nonequilibrium processes are measured in 3D-AFM measurements when the dynamics of polymers are slower than the scanning of the probe.

Vectorial insertion of a ß-helical peptide into membrane: a theoretical study on polytheonamide B.

Spontaneous unidirectional, or vectorial, insertion of transmembrane peptides is a fundamental biophysical process for toxin and viral actions. Polytheonamide B (pTB) is a potent cytotoxic peptide with a ß6.3-helical structure. Previous experimental studies revealed that the pTB inserts into the membrane in a vectorial fashion and forms a channel with its single molecular length long enough to span the membrane. Also, molecular dynamics simulation studies demonstrated that the pTB is prefolded in aqueous solution. These are unique features of pTB because most of the peptide toxins form channels through oligomerization of transmembrane helices. Here, we performed all-atom molecular dynamics simulations to examine the dynamic mechanism of the vectorial insertion of pTB, providing underlying elementary processes of the membrane insertion of a prefolded single transmembrane peptide. We find that the insertion of pTB proceeds with only the local lateral compression of the membrane in three successive phases: "landing," "penetration," and "equilibration" phases. The free energy calculations using the replica-exchange umbrella sampling simulations present an energy cost of 4.3 kcal/mol at the membrane surface for the membrane insertion of pTB from bulk water. The trajectories of membrane insertion revealed that the insertion process can occur in two possible pathways, namely "trapped" and "untrapped" insertions; in some cases, pTB is trapped in the upper leaflet during the penetration phase. Our simulations demonstrated the importance of membrane anchoring by the hydrophobic N-terminal blocking group in the landing phase, leading to subsequent vectorial insertion.

Conductance selectivity of Na+ across the K+ channel via Na+ trapped in a tortuous trajectory.

Ion selectivity of the potassium channel is crucial for regulating electrical activity in living cells; however, the mechanism underlying the potassium channel selectivity that favors large K+ over small Na+ remains unclear. Generally, Na+ is not completely excluded from permeation through potassium channels. Herein, the distinct nature of Na+ conduction through the prototypical KcsA potassium channel was examined. Single-channel current recordings revealed that, at a high Na+ concentration (200 mM), the channel was blocked by Na+, and this blocking was relieved at high membrane potentials, suggesting the passage of Na+ across the channel. At a 2,000 mM Na+ concentration, single-channel Na+ conductance was measured as one-eightieth of the K+ conductance, indicating that the selectivity filter allows substantial conduit of Na+ Molecular dynamics simulations revealed unprecedented atomic trajectories of Na+ permeation. In the selectivity filter having a series of carbonyl oxygen rings, a smaller Na+ was distributed off-center in eight carbonyl oxygen-coordinated sites as well as on-center in four carbonyl oxygen-coordinated sites. This amphipathic nature of Na+ coordination yielded a continuous but tortuous path along the filter. Trapping of Na+ in many deep free energy wells in the filter caused slow elution. Conversely, K+ is conducted via a straight path, and as the number of occupied K+ ions increased to three, the concerted conduction was accelerated dramatically, generating the conductance selectivity ratio of up to 80. The selectivity filter allows accommodation of different ion species, but the ion coordination and interactions between ions render contrast conduction rates, constituting the potassium channel conductance selectivity.

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.

Capturing the Freeze-Drying Dynamics of NaCl Nanoparticles Using THz Spectroscopy.

Sodium chloride (NaCl) aqueous solution becomes NaCl hydrate, NaCl·2H2O, at low temperature, which is different from potassium chloride and is a typical complex model for studying the freeze-drying process in foods and pharmaceuticals. Here, we detected unit-cell-sized NaCl particles in ice as precursor substances of NaCl·2H2O during freezing of NaCl solution by using terahertz (THz) spectroscopy. In the freezing process, Na+ and Cl- ions form two types of metastable unit-cell-sized NaCl particles on the pathway to the well-known NaCl·2H2O crystal production, which are not listed in the phase diagram of freezing of NaCl solution but have absorption peaks in THz spectra. This finding of single unit-cell-sized particles signifies the importance of studying the freeze-drying process in-depth and offers a new possibility for the development of freeze-drying technology for the manufacture of nanometer-sized particles such as ultrafine pharmaceutical powders, which more readily dissolve in water.

Structure and dynamics of solvent molecules inside the polytheonamide B channel in different environments: a molecular dynamics study.

The ß6.3-helical channel of the marine cytotoxic peptide, polytheonamide B (pTB), is examined in water, the POPC bilayer, and a 1 : 1 chloroform/methanol mixture using all-atom molecular dynamics simulations. The structures and fluctuations of the ß6.3-helix of pTB are investigated in the three environments. The average structure of pTB calculated in the mixed solvent is in good agreement with the NMR-resolved structure in the mixed solvent, indicating the validity of the parameters used for the non-standard groups in pTB. The configuration and dynamics of solvent molecules inside the pore are examined in detail. It is found that the motions of methanol molecules inside the pore are not correlated because of the absence of strong hydrogen bonds (HBs) between adjacent methanol molecules. On the other hand, the motions of water molecules inside the pore are highly correlated, both translationally and orientationally, due to the strong HBs between neighboring water molecules. It is suggested that the collective behavior of water molecules inside the pore in the membrane is crucial for the permeation of ions through the pTB channel.

Digitalized K(+) Occupancy in the Nanocavity Holds and Releases Queues of K(+) in a Channel.

The mechanisms of ion permeation through potassium channels have been extensively examined. Molecular dynamics (MD) simulations have demonstrated that rapidly permeating ions collide near the selectivity filter (SF) ("knock-on" mechanism), but this oversimplified mechanism is insufficient to account for the experimentally observed single-channel current amplitudes. Here, we analyzed the MD-simulated ion trajectories through a Kv1.2 potassium channel using an event-oriented analysis method, and surprisingly, we found that the nanocavity (NC) governs ion permeation in a digital fashion. The NC has a maximal diameter of 10 Å and stands between the intracellular bulk solution and the SF, which holds only up to one K(+) during permeation. Accordingly, the K(+) concentration in the intracellular solution is translated as a digitalized zero or one K(+) in the NC. When the ion number in the NC is zero, the multiple ions in the SF are mostly immobilized. By contrast, when the number of ions in the NC is one, the structured water in the NC mediates the ion-occupied status to the queueing ions in the SF, and the ions then initiate a collective outward motion. Accordingly, the one ion in the NC serves as a catalytic intermediate for permeation, which quantitatively accounts for the experimentally obtained conductance-concentration relationships. We conclude that the ion movements are coherent across the entire pore.

Origin of the Shape of Current-Voltage Curve through Nanopores: A Molecular Dynamics Study.

Ion transports through ion channels, biological nanopores, are essential for life: Living cells generate electrical signals by utilizing ion permeation through channels. The measured current-voltage (i-V) relations through most ion channels are sublinear, however, its physical meaning is still elusive. Here we calculated the i-V curves through anion-doped carbon nanotubes, a model of an ion channel, using molecular dynamics simulation. It was found the i-V curve reflects the physical origin of the rate-determining step: the i-V curve is sublinear when the permeation is entropy bottlenecked, while it is superlinear in the case of the energy bottlenecked permeation. Based on this finding, we discuss the relation between the molecular mechanism of ion permeation through the biological K(+) channels and the shape of the i-V curves through them. This work also provides a clue for a novel design of nanopores that show current rectification.

Mechanism of ion permeation through a model channel: roles of energetic and entropic contributions.

Mechanism of ion permeation through an anion-doped carbon nanotube (ANT), a model of ion channel, is investigated. Using this model system, many trajectory calculations are performed to obtain the potential energy profile, in addition to the free energy profile, that enables to separate the energy and the entropic contributions, along the ion permeation. It is found that the mechanism of the transport is governed by the interplay between the energetic and the entropic forces. The rate of the ion permeation can be controlled by changing the balance between these contributions with altering, for example, the charge and/or the length of ANT, which increases the rate of the ion permeation by nearly two orders of magnitude. The dominant free energy barrier at the entrance of ANT is found to be caused by the entropy bottleneck due to the narrow phase space for the exchange of a water molecule and an incoming ion.

The open gate structure of the membrane-embedded KcsA potassium channel viewed from the cytoplasmic side.

Crystallographic studies of channel proteins have provided insight into the molecular mechanisms of ion channels, even though these structures are obtained in the absence of the membrane and some structural portions have remained unsolved. Here we report the gating structure of the membrane-embedded KcsA potassium channel using atomic force microscopy (AFM). The activation gate of the KcsA channel is located on the intracellular side, and the cytoplasmic domain was truncated to clear the view of this location. Once opened, the individual subunits in the tetramer were resolved with the pore open at the center. Furthermore, AFM was able to capture the previously unsolved bulge helix at the entrance. A molecular dynamics simulation revealed that the bulge helices fluctuated dramatically at the open entryway. This dynamic behavior was observed as vigorous open-channel noise in the single-channel current recordings. The role of the bulge helices in the open gate structure is discussed.

Cycle flux algebra for ion and water flux through the KcsA channel single-file pore links microscopic trajectories and macroscopic observables.

In narrow pore ion channels, ions and water molecules diffuse in a single-file manner and cannot pass each other. Under such constraints, ion and water fluxes are coupled, leading to experimentally observable phenomena such as the streaming potential. Analysis of this coupled flux would provide unprecedented insights into the mechanism of permeation. In this study, ion and water permeation through the KcsA potassium channel was the focus, for which an eight-state discrete-state Markov model has been proposed based on the crystal structure, exhibiting four ion-binding sites. Random transitions on the model lead to the generation of the net flux. Here we introduced the concept of cycle flux to derive exact solutions of experimental observables from the permeation model. There are multiple cyclic paths on the model, and random transitions complete the cycles. The rate of cycle completion is called the cycle flux. The net flux is generated by a combination of cyclic paths with their own cycle flux. T.L. Hill developed a graphical method of exact solutions for the cycle flux. This method was extended to calculate one-way cycle fluxes of the KcsA channel. By assigning the stoichiometric numbers for ion and water transfer to each cycle, we established a method to calculate the water-ion coupling ratio (CR(w-i)) through cycle flux algebra. These calculations predicted that CR(w-i) would increase at low potassium concentrations. One envisions an intuitive picture of permeation as random transitions among cyclic paths, and the relative contributions of the cycle fluxes afford experimental observables.