Electromechanical Coupling Mechanism Research Articles

Analysis of the electromechanical coupling mechanism and torsional vibration characteristics of a high‐speed train drive system

The high-speed train transmission system is a complex electromechanical coupling system, which consists of a motor, a universal shaft, a gearbox, and a wheel set. In order to solve dynamic problems such as torsion vibration caused by a high-speed train transmission system, the simplified model and equivalent mechanics model of the system were established, the natural vibration frequency was solved, and the simulation results of the system under a fixed torque input were analysed. The results showed that the natural vibration frequency of the universal shaft was 4.19 Hz, the natural vibration frequency of the pinion was 7.54 Hz, the natural vibration frequency of the big gear was 35.6 Hz, and the natural vibration frequency of the wheel set was 107.45 Hz. The natural vibration frequency of each part of the system increased gradually during the transmission from the motor to the wheel set. A fixed torque was added to the input end of the simulation model. The simulation results showed that the change amplitude of the torsion angle displacement of the big gear and the wheel set decreases. It is known that the angular displacement caused by the torsional vibration is weakened by the larger torsion stiffness of the axle.

Comparison of flexoelectric and piezoelectric ring energy harvester

Flexoelectric/piezoelectric effect is an electromechanical coupling effect occurring in dielectrics. In this study, a flexoelectric/piezoelectric ring energy harvester is proposed based on the direct flexoelectric/piezoelectric effect. The flexoelectric/piezoelectric ring energy harvester is made of an elastic ring and a flexoelectric/piezoelectric patch laminated on its surface. The electromechanical coupling mechanism of the flexoelectric/piezoelectric ring energy harvester is explored. Then the voltage and power output across the load resistance are derived in the closed-circuit condition for the energy harvester. The distinctive characteristics between the flexoelectric and the piezoelectric energy harvesters are discussed and compared in detail. The output power/voltage is related to various parameters, such as flexoelectric/piezoelectric patch size, load resistance, and flexoelectric/piezoelectric patch thickness, which are discussed to improve the power output across the load resistance. The flexoelectric ring energy harvester is more effective than the piezoelectric ring energy harvester in the transverse oscillation-bending dominant vibration, since the flexoelectric effect is sensitive to the strain gradient (bending strain). This study, including theoretical derivations and simulation plots, provide design guidelines in engineering applications for flexoelectric/piezoelectric effect.

Review on Electromechanical Coupling Properties of Biomaterials.

Electromechanical coupling properties of biological materials, especially cellulose from plant cell walls and proteins from animals, are of great interest for applications in biocompatible sensors and actuators and ecofriendly energy harvesters. On the basis of their anisotropic nanostructures, cellulose and fibrous proteins such as collagen, silk, keratin, etc. are expected to be piezoelectric; however, this property does not necessarily translate to cellulose- or protein-containing bulk materials. In fact, the values of piezoelectric coefficients reported for cellulose and proteins in the literature vary over several orders of magnitude, which raises the question of whether these are truly intrinsic piezoelectric properties of biological materials or whether they are obscured with other electromechanical coupling processes such as electrostriction, flexoelectricity, electrochemical transport, or electrostatic deformation. This critical question about intrinsic and extrinsic electromechanical coupling mechanisms is reviewed in this article. The origin of piezoelectricity of cellulose and collagen (the most widely studied protein for piezoelectricity) is discussed based on their molecular structures. Key requirements to construct macroscopic piezoelectric biocomposites are addressed in terms of packing orders or arrangements of polar domains in composites. On the basis of this structural argument, truly piezoelectric responses of macroscopic materials fabricated with or containing cellulose and collagen are found to be extremely difficult to observe or quantify; most values reported in the literature as piezoelectric coefficients of such materials appear to originate from other electromechanical coupling mechanisms. Clarifying these mechanisms is important to properly design electromechanical devices using biobased materials.

Time-Resolved Neutron Interferometry and the Mechanism of Electromechanical Coupling in Voltage-Gated Ion Channels.

The mechanism of electromechanical coupling for voltage-gated ion channels (VGICs) involved in neurological signal transmission, primarily Nav- and Kv-channels, remains unresolved. Anesthetics have been shown to directly impact this mechanism, at least for Kv-channels. Molecular dynamics computer simulations can now predict the structures of VGICs embedded within a hydrated phospholipid bilayer membrane as a function of the applied transmembrane voltage, but significant assumptions are still necessary. Nevertheless, these simulations are providing new insights into the mechanism of electromechanical coupling at the atomic level in 3-D. We show that time-resolved neutron interferometry can be used to investigate directly the profile structure of a VGIC, vectorially oriented within a single hydrated phospholipid bilayer membrane at the solid-liquid interface, as a function of the applied transmembrane voltage in the absence of any assumptions or potentially perturbing modifications of the VGIC protein and/or the host membrane. The profile structure is a projection of the membrane's 3-D structure onto the membrane normal and, in the absence of site-directed deuterium labeling, is provided at substantially lower spatial resolution than the atomic level. Nevertheless, this novel approach can be used to directly test the validity of the predictions from molecular dynamics simulations. We describe the key elements of our novel experimental approach, including why each is necessary and important to providing the essential information required for this critical comparison of "simulation" vs "experiment." In principle, the approach could be extended to higher spatial resolution and to include the effects of anesthetics on the electromechanical coupling mechanism in VGICs.

A True Hybrid Solar Wind Turbine Electric Generator System for Smaller Hybrid Renewable Energy Power Plants

Contemporary Hybrid Solar-Wind farms are implemented using separate solar Photovoltaic (PV) cell arrays and wind turbines, where electricity generated from both devices are combined. However, this solution requires a large amount of space to cater for the PV arrays and wind turbines of the system. This paper proposes a new type of renewable energy electric generator with a small power production footprint (PPF) that allows reduction in land usage. The technology introduced in this True Hybrid Wind-Solar (THWS) generator allows for the solar panels to rotate along with a VAWT wind turbine it is attached to through a specially designed electromechanical coupling mechanism. The working principal behind the connections described in this paper. The design of a hybrid circuit module that serves to combine current generated via the solar cells and wind generator and also automatically disconnects inactive wind or solar generators is also described. This is important in order to eliminate unwanted loads generated from the inactive generators from within the THWS itself.

Analytical Framework of Gearbox Monitoring Based on the Electro-mechanical Coupling Mechanism

Abstract Along with the development of the Hybrid Electric Vehicles (HEVs), the permanent magnetic synchronous motor (PMSM) and the planetary gearbox is widely used because of its high power density. There is much significant electro-mechanical coupling phenomenon in the mechanical installations. The aim of this paper is the analytical study of a planetary gearbox by using the stator current signature analysis in the PMSM based on the electro-mechanical coupling mechanism. This paper proposes a mathematical framework based on the electro-mechanical coupling model of the PMSM-planetary gearbox system, considering the load torque oscillation and the time-varying mesh stiffness. The model simulation result shows that from the mathematical framework, the load torque oscillation frequency and the time-varying mesh stiffness frequency can be predicted through the current frequency. The proposed mathematical model is verified by the model simulation. And a test-bed based on a 60 kW three-phase PMSM connected to a planetary gearbox has been used. Fourier transform is applied to the demodulated torque signal and current signal for denoising and removing the intervening neighbouring features.

Mechanisms of electromechanical and electrochemical coupling in olfactory cilia of the frog (Rana temporaria)

The mechanisms of electromechanical and electrochemical coupling in olfactory cilia of the frog (Rana temporaria) have been investigated. High-resolution optical television microscopy of live tissue and pharmacological analysis have been used to reveal the regulation of the motility of olfactory cilia in the absence of odorants; the entry of Ca2+ ions mediated by three types of ion channels (mechanosensitive, cyclic nucleotide gated, and voltage-gated) was shown to determine the motility of cilia. Stimulation of the olfactory adenylate cyclase by movements of the cilia in the absence of odors has been demonstrated and the regulation of cilia motility by membrane potential has been revealed. Membrane potential can affect olfactory acuity and the ability to perceive weak olfactory stimuli in the absence of adequate stimulation.

The effect of inter-granular constraints on the response of polycrystalline piezoelectric ceramics at the surface and in the bulk

The electro-mechanical coupling mechanisms in polycrystalline ferroelectric materials, including a soft PbZrxTi1−xO3 (PZT) and lead-free 0.9375(Bi1/2Na1/2)TiO3-0.0625BaTiO3 (BNT-6.25BT), have been studied using a surface sensitive low-energy (12.4 keV) and bulk sensitive high-energy (73 keV) synchrotron X-ray diffraction with in situ electric fields. The results show that for tetragonal PZT at a maximum electric field of 2.8 kV/mm, the electric-field-induced lattice strain (ε111) is 20% higher at the surface than in the bulk, and non-180° ferroelectric domain texture (as indicated by the intensity ratio I002/I200) is 16% higher at the surface. In the case of BNT-6.25BT, which is pseudo-cubic up to fields of 2 kV/mm, lattice strains, ε111 and ε200, are 15% and 20% higher at the surface, while in the mixed tetragonal and rhombohedral phases at 5 kV/mm, the domain texture indicated by the intensity ratio, I111/I111¯ and I002/I200, are 12% and 10% higher at the surface than in the bulk, respectively. The observed difference in the strain contributions between the surface and bulk is suggested to result from the fact that surface grains are not constrained in three dimensions, and consequently, domain reorientation and lattice expansion in surface grains are promoted. It is suggested that the magnitude of property difference between the surface and bulk is higher for the PZT than for BNT-6.25BT due to the level of anisotropy in the strain mechanism. The comparison of the results from different methods demonstrates that the intergranular constraints have a significant influence on the electric-field-induced electro-mechanical responses in polycrystalline ferroelectrics. These results have implications for the design of higher performance polycrystalline piezoelectrics.

Modulation of mechanical resonance by chemical potential oscillation in graphene

The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of is a modulation in the static force due to variation in the internal chemical potential, the second and third are change in static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study a capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited the particular choice of material, geometry, or mechanism for variation in chemical potential, and can thus be extended to other low-dimensional systems.

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Flexoelectricity, representing the coupling between electrical polarizations and strain gradients, should be taken into account in the analysis of electromechanical responses of nanostructures where large strain gradients are expected. In this paper, we will explore the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported piezoelectric nanoplate by using the Kirchhoff plate theory. The governing equations and corresponding boundary conditions are deduced from Hamilton’s principle, and the analytical solutions are obtained for the deflection and natural frequency. The results indicate that the deflections predicted by the present model are smaller than those calculated by the classical one which only considers piezoelectricity, while the frequencies exhibit the opposite trend. In addition, the flexoelectric effect is more prominent for thinner plates; the differences of the deflections or frequencies between the two models are gradually diminishing with an increase in the plate thickness. The current work may contribute to the understanding of the higher-order electromechanical coupling mechanism. Moreover, the modified plate model can be utilized to accurately design novel piezoelectric nanoplate-based sensors in nanoelectromechanical systems.

Quantitative Mapping of Interactions in the Voltage-Sensor Pore Interface of the Shaker Potassium Channel

Changes in the membrane potential of an excitable cell induce movement of voltage-sensing units within voltage-gated ion channels (VGICs). The energy associated with this movement is transmitted to the channel gate, ultimately promoting its opening. Numerous proposals have been made as to how this signal is relayed from the voltage-sensors to the channel gate, such as side chain interactions and backbone movement; however, it has been difficult to ascertain the precise molecular mechanisms underlying energy transduction. Recently, it was shown that median voltage estimates from the charge-voltage relationship of VGICs can be used to derive the net free energy change (ΔGnet) associated with their voltage-dependent activation. By combining this approach with mutant cycle analysis, it is possible to identify residues that are energetically coupled and contribute to the activation process. Here, we have undertaken a systematic analysis of contact pairs at the interface between the voltage-sensor and pore domains of Shaker potassium channel in order to gain insight into how an initial signal can propagate from one region of the channel to another and trigger the opening of the channel gate. Our results will be discussed in the context of overall molecular mechanism of electromechanical coupling in voltage-gated ion channels.

Application of piezoelectric materials in a novel linear ultrasonic motor based on shear-induced vibration mode

A novel linear ultrasonic motor based on d15 effect of piezoelectric materials was presented. The design idea aimed at the direct utilization of the shear-induced vibration modes of piezoelectric material. Firstly, the inherent electromechanical coupling mechanism of piezoelectric material was investigated, and shear vibration modes of a piezoelectric shear block was specially designed. A driving point’s elliptical trajectory induced by shear vibration modes was discussed. Then a dynamic model for the piezoelectric shear stator was established with finite element (FE) method to conduct the parametric optimal design. Finally, a prototype based on d15 converse piezoelectric effect is manufactured, and the modal experiment of piezoelectric stator was conducted with laser doppler vibrometer. The experimental results show that the calculated shear-induced vibration modes can be excited completely, and the new linear ultrasonic motor reaches a speed 118 mm/s at noload, and maximal thrust 12.8 N.

Mechanisms of electromechanical coupling in strain based scanning probe microscopy

Electromechanical coupling is ubiquitous in nature and underpins the functionality of materials and systems as diverse as ferroelectric and multiferroic materials, electrochemical devices, and biological systems, and strain-based scanning probe microscopy (s-SPM) techniques have emerged as a powerful tool in characterizing and manipulating electromechanical coupling at the nanoscale. Uncovering underlying mechanisms of electromechanical coupling in these diverse materials and systems, however, is a difficult outstanding problem, and questions and confusions arise from recent experiment observations of electromechanical coupling and its apparent polarity switching in some unexpected materials. We propose a series of s-SPM experiments to identify different microscopic mechanisms underpinning electromechanical coupling and demonstrate their feasibility using three representative materials. By employing a combination of spectroscopic studies and different modes of s-SPM, we show that it is possible to distinguish electromechanical coupling arising from spontaneous polarization, induced dipole moment, and ionic Vegard strain, and this offers a clear guidance on using s-SPM to study a wide variety of functional materials and systems.

Soft Starting Behavior of a Motorized Spindle System Based on Electromechanical Coupling Dynamic Model

It is very important to achieve fast and stable starting for motorized spindles to shorten idle process, improve machining efficiency and reduce an impact on the system. The drawbacks of the existing methods are focused on. The dynamic changes in both starting current and starting torque can not be reflected using the traditional method. Furthermore, the method is easy to produce no convergence with reduced voltage and reduced frequency. The finite element method is not employed in engineering due to low efficiency. The motor itself is only considered in the dynamic analysis method based on motor model and Park transformation. The analysis method of the soft starting performance for a motorized spindle system is proposed based on electromechanical coupling dynamic model. The soft starting transient process of the system is studied by the proposed method. The effects of electromechanical parameters on starting current, starting torque, pulsation torque and so on are analyzed. The experiment is also performed on a prototype. The physical mechanism of electromechanical coupling is revealed. The method is presented to suppress vibration, improve stability and accelerate starting. The validity of the proposed analysis method is confirmed by simulation and experiment.

Structural Investigation of a Bacterial Voltage-Gated Sodium Channel NaVRh

Voltage-gated sodium (Nav) channels are essential for the rapid depolarization of nerve and muscle, and are important drug targets. Elucidation of the structures and functional mechanisms of Nav channels will shed light on fundamental ion channel mechanisms and facilitate potential clinical applications. A family of bacterial Nav channels, exemplified by NaChBac (Na+-selective Channel of Bacteria), provides a good model system for structure-function analysis. We determined the crystal structure of NavRh, a NaChBac orthologue from marine bacteria, Rickettsiales sp. HIMB114 (denoted Rh), at 3.05 A resolution. The channel comprises an asymmetric tetramer. The carbonyl oxygen atoms of Thr178 and Leu179 constitute an inner site within the selectivity filter (178TLSSWE183) where a hydrated Ca2+ can bind and resides in the crystal structure. The outer mouth of the Na+ selectivity filter, defined by Ser181 and Glu183, is closed, as is the activation gate at the intracellular side of the pore. The voltage sensors adopt a depolarized conformation with all the gating charges exposing to the extracellular side. We hypothesize that NavRh is captured in an inactivated conformation. Comparison of NavRh with NavAb reveals that the VSD segments undergo discordant conformational shifts concurrent with domain rotation that may underlie the electromechanical coupling mechanism of voltage-gated channels.

Electromechanical Coupling among Edge Dislocations, Domain Walls, and Nanodomains in BiFeO3 Revealed by Unit-Cell-Wise Strain and Polarization Maps

The performance of ferroelectric devices, for example, the ferroelectric field effect transistor, is reduced by the presence of crystal defects such as edge dislocations. For example, it is well-known that edge dislocations play a crucial role in the formation of ferroelectric dead-layers at interfaces and hence finite size effects in ferroelectric thin films. The detailed lattice structure including the relevant electromechanical coupling mechanisms in close vicinity of the edge dislocations is, however, not well-understood, which hampers device optimization. Here, we investigate edge dislocations in ferroelectric BiFeO3 by means of spherical aberration-corrected scanning transmission electron microscopy, a dedicated model-based structure analysis, and phase field simulations. Unit-cell-wise resolved strain and polarization profiles around edge dislocation reveal a wealth of material states including polymorph nanodomains and multiple domain walls characteristically pinned to the dislocation. We locally determine the piezoelectric tensor and identify piezoelectric coupling as the driving force for the observed phenomena, explaining, for example, the orientation of the domain wall with respect to the edge dislocation. Furthermore, an atomic model for the dislocation core is derived.

A Limited 4 Å Radial Displacement of the S4-S5 Linker Is Sufficient for Internal Gate Closing in Kv Channels

Voltage-gated ion channels are responsible for the generation of action potentials in our nervous system. Conformational rearrangements in their voltage sensor domains in response to changes of the membrane potential control pore opening and thus ion conduction. Crystal structures of the open channel in combination with a wealth of biophysical data and molecular dynamics simulations led to a consensus on the voltage sensor movement. However, the coupling between voltage sensor movement and pore opening, the electromechanical coupling, occurs at the cytosolic face of the channel, from where no structural information is available yet. In particular, the question how far the cytosolic pore gate has to close to prevent ion conduction remains controversial. In cells, spectroscopic methods are hindered because labeling of internal sites remains difficult, whereas liposomes or detergent solutions containing purified ion channels lack voltage control. Here, to overcome these problems, we controlled the state of the channel by varying the lipid environment. This way, we directly measured the position of the S4-S5 linker in both the open and the closed state of a prokaryotic Kv channel (KvAP) in a lipid environment using Lanthanide-based resonance energy transfer. We were able to reconstruct the movement of the covalent link between the voltage sensor and the pore domain and used this information as restraints for molecular dynamics simulations of the closed state structure. We found that a small decrease of the pore radius of about 3-4 Å is sufficient to prevent ion permeation through the pore.

Structural Characterization of the Voltage-Sensor Domain and Voltage-Gated K+-Channel Proteins Vectorially Oriented within a Single Bilayer Membrane at the Solid/Vapor and Solid/Liquid Interfaces via Neutron Interferometry

The voltage-sensor domain (VSD) is a modular four-helix bundle component that confers voltage sensitivity to voltage-gated cation channels in biological membranes. Despite extensive biophysical studies and the recent availability of X-ray crystal structures for a few voltage-gated potassium (Kv) channels and a voltage-gate sodium (Nav) channel, a complete understanding of the cooperative mechanism of electromechanical coupling, interconverting the closed-to-open states (i.e., nonconducting to cation conducting) remains undetermined. Moreover, the function of these domains is highly dependent on the physical-chemical properties of the surrounding lipid membrane environment. The basis for this work was provided by a recent structural study of the VSD from a prokaryotic Kv-channel vectorially oriented within a single phospholipid (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)) membrane investigated by X-ray interferometry at the solid/moist He (or solid/vapor) and solid/liquid interfaces, thus achieving partial to full hydration, respectively (Gupta et al. Phys. Rev. E2011, 84, 031911-1-15). Here, we utilize neutron interferometry to characterize this system in substantially greater structural detail at the submolecular level, due to its inherent advantages arising from solvent contrast variation coupled with the deuteration of selected submolecular membrane components, especially important for the membrane at the solid/liquid interface. We demonstrate the unique vectorial orientation of the VSD and the retention of its molecular conformation manifest in the asymmetric profile structure of the protein within the profile structure of this single bilayer membrane system. We definitively characterize the asymmetric phospholipid bilayer solvating the lateral surfaces of the VSD protein within the membrane. The profile structures of both the VSD protein and phospholipid bilayer depend upon the hydration state of the membrane. We also determine the distribution of water and exchangeable hydrogen throughout the profile structure of both the VSD itself and the VSD:POPC membrane. These two experimentally determined water and exchangeable hydrogen distribution profiles are in good agreement with molecular dynamics simulations of the VSD protein vectorially oriented within a fully hydrated POPC bilayer membrane, supporting the existence of the VSD's water pore. This approach was extended to the full-length Kv-channel (KvAP) at a solid/liquid interface, providing the separate profile structures of the KvAP protein and the POPC bilayer within the reconstituted KvAP:POPC membrane.

Crystal structure of an orthologue of the NaChBac voltage-gated sodium channel

Voltage-gated sodium (Na(v)) channels are essential for the rapid depolarization of nerve and muscle, and are important drug targets. Determination of the structures of Na(v) channels will shed light on ion channel mechanisms and facilitate potential clinical applications. A family of bacterial Na(v) channels, exemplified by the Na(+)-selective channel of bacteria (NaChBac), provides a useful model system for structure-function analysis. Here we report the crystal structure of Na(v)Rh, a NaChBac orthologue from the marine alphaproteobacterium HIMB114 (Rickettsiales sp. HIMB114; denoted Rh), at 3.05 Å resolution. The channel comprises an asymmetric tetramer. The carbonyl oxygen atoms of Thr 178 and Leu 179 constitute an inner site within the selectivity filter where a hydrated Ca(2+) resides in the crystal structure. The outer mouth of the Na(+) selectivity filter, defined by Ser 181 and Glu 183, is closed, as is the activation gate at the intracellular side of the pore. The voltage sensors adopt a depolarized conformation in which all the gating charges are exposed to the extracellular environment. We propose that Na(v)Rh is in an 'inactivated' conformation. Comparison of Na(v)Rh with Na(v)Ab reveals considerable conformational rearrangements that may underlie the electromechanical coupling mechanism of voltage-gated channels.

Mechanism of electromechanical coupling in voltage-gated potassium channels.

Voltage-gated ion channels play a central role in the generation of action potentials in the nervous system. They are selective for one type of ion – sodium, calcium, or potassium. Voltage-gated ion channels are composed of a central pore that allows ions to pass through the membrane and four peripheral voltage sensing domains that respond to changes in the membrane potential. Upon depolarization, voltage sensors in voltage-gated potassium channels (Kv) undergo conformational changes driven by positive charges in the S4 segment and aided by pairwise electrostatic interactions with the surrounding voltage sensor. Structure-function relations of Kv channels have been investigated in detail, and the resulting models on the movement of the voltage sensors now converge to a consensus; the S4 segment undergoes a combined movement of rotation, tilt, and vertical displacement in order to bring 3–4e+ each through the electric field focused in this region. Nevertheless, the mechanism by which the voltage sensor movement leads to pore opening, the electromechanical coupling, is still not fully understood. Thus, recently, electromechanical coupling in different Kv channels has been investigated with a multitude of techniques including electrophysiology, 3D crystal structures, fluorescence spectroscopy, and molecular dynamics simulations. Evidently, the S4–S5 linker, the covalent link between the voltage sensor and pore, plays a crucial role. The linker transfers the energy from the voltage sensor movement to the pore domain via an interaction with the S6 C-termini, which are pulled open during gating. In addition, other contact regions have been proposed. This review aims to provide (i) an in-depth comparison of the molecular mechanisms of electromechanical coupling in different Kv channels; (ii) insight as to how the voltage sensor and pore domain influence one another; and (iii) theoretical predictions on the movement of the cytosolic face of the Kv channels during gating.