Experimental Estimates Research Articles

Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations

Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 511 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely {}^{3}A_2 < {}^{1}E < {}^{1}A_1 < {}^{3}E3A2<1E<1A1<3E. Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.

Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning

The turnover number kcat, a measure of enzyme efficiency, is central to understanding cellular physiology and resource allocation. As experimental kcat estimates are unavailable for the vast majority of enzymatic reactions, the development of accurate computational prediction methods is highly desirable. However, existing machine learning models are limited to a single, well-studied organism, or they provide inaccurate predictions except for enzymes that are highly similar to proteins in the training set. Here, we present TurNuP, a general and organism-independent model that successfully predicts turnover numbers for natural reactions of wild-type enzymes. We constructed model inputs by representing complete chemical reactions through differential reaction fingerprints and by representing enzymes through a modified and re-trained Transformer Network model for protein sequences. TurNuP outperforms previous models and generalizes well even to enzymes that are not similar to proteins in the training set. Parameterizing metabolic models with TurNuP-predicted kcat values leads to improved proteome allocation predictions. To provide a powerful and convenient tool for the study of molecular biochemistry and physiology, we implemented a TurNuP web server.

Experimental and Theoretical Estimations of Atrazine's Adsorption in Mangosteen-Peel-Derived Nanoporous Carbons.

Nanoporous carbons were prepared via chemical and physical activation from mangosteen-peel-derived chars. The removal of atrazine was studied due to the bifunctionality of the N groups. Pseudo-first-order, pseudo-second-order, and intraparticle pore diffusion kinetic models were analyzed. Adsorption isotherms were also analyzed according to the Langmuir and Freundlich models. The obtained results were compared against two commercially activated carbons with comparable surface chemistry and porosimetry. The highest uptake was found for carbons with higher content of basic surface groups. The role of the oxygen-containing groups in the removal of atrazine was estimated experimentally using the surface density. The results were compared with the adsorption energy of atrazine theoretically estimated on pristine and functionalized graphene with different oxygen groups using periodic DFT methods. The energy of adsorption followed the same trend observed experimentally, namely the more basic the pH, the more favored the adsorption of atrazine. Micropores played an important role in the uptake of atrazine at low concentrations, but the presence of mesoporous was also required to inhibit the pore mass diffusion limitations. The present work contributes to the understanding of the interactions between triazine-based pollutants and the surface functional groups on nanoporous carbons in the liquid-solid interface.

Quantum computations in heavy noble-gas hydride cations: Reference energies and new spectroscopic data

Computational quantum chemistry has become a powerful tool with a wide range of possibilities to solve chemical-physical problems. As a result of this, the interest in the applications of computational quantum chemistry has expanded considerably, and has opened up novel research opportunities. In particular, those related to the characterization of heavy-atoms complexes, as most electronic structure calculations for such systems struggle with the problem posed by the large number of electrons present in them, and consequently, the introduction of relativistic effects. The present study performed an exhaustive assess to characterized the uncommon NgH+ (Ng = Kr, Xe, and Rn) hydride cations in order to provide accurate rovibrational data of their isotopes to assist in the laboratory characterization or even their astronomical detection. Scalar relativistic effects were included, and the ground and first electronically exited states potential curves were obtained from benchmark ab initio CCSD(T)/CBS and MRCI+Q electronic structure calculations. Next, such interaction potentials, correctly extended to long-range asymptotic regions, were employed in quantum bound state calculations and molecular spectroscopic constants were determined for the most abundance 84Kr, 132Xe, and 222Rn isotopes. Our results were discussed in comparison with available experimental and previous theoretical estimates, aiming to treat accuracy issues. The new sets provide reference data that could serve for spectroscopic characterization of such low abundance and high radioactive species.

Reconstructing the transport cycle in the sugar porter superfamily using coevolution-powered machine learning.

Sugar porters (SPs) represent the largest group of secondary-active transporters. Some members, such as the glucose transporters (GLUTs), are well known for their role in maintaining blood glucose homeostasis in mammals, with their expression upregulated in many types of cancers. Because only a few sugar porter structures have been determined, mechanistic models have been constructed by piecing together structural states of distantly related proteins. Current GLUT transport models are predominantly descriptive and oversimplified. Here, we have combined coevolution analysis and comparative modeling, to predict structures of the entire sugar porter superfamily in each state of the transport cycle. We have analyzed the state-specific contacts inferred from coevolving residue pairs and shown how this information can be used to rapidly generate free-energy landscapes consistent with experimental estimates, as illustrated here for the mammalian fructose transporter GLUT5. By comparing many different sugar porter models and scrutinizing their sequence, we have been able to define the molecular determinants of the transport cycle, which are conserved throughout the sugar porter superfamily. We have also been able to highlight differences leading to the emergence of proton-coupling, validating, and extending the previously proposed latch mechanism. Our computational approach is transferable to any transporter, and to other protein families in general.

Wagner interaction coefficients of nitrogen with chromium and molibdenum in liquid nickel-based alloys

The authors propose a simple theory of thermodynamic properties of liquid nitrogen solutions in alloys of the Fe – Ni – Cr and Fe – Ni – Mo systems. This theory is analogous to the theory for liquid nitrogen solutions in binary alloys of the Fe – Cr and Fe – Ni systems proposed previously by the authors in 2019 and 2021. The theory is based on lattice model of ternary liquid solutions of the Fe – Ni – Cr and Fe – Ni – Mo systems. The model assumes a FCC lattice. Atoms of Fe, Ni, Cr and Mo are deposed in the sites of the lattice. Nitrogen atoms are located in octahedral interstices. The nitrogen atom interacts only with the metal atoms located in the lattice sites neighboring to it. This interaction is pairwise. It is assumed that the energy of this interaction depends neither on composition nor on temperature. It is supposed that the liquid solutions in the Fe – Ni – Cr and Fe – Ni – Mo systems are perfect. Within the framework of the proposed theory, the relation is obtained that expresses the Wagner interaction coefficient between nitrogen and chromium in liquid nickel-based alloys \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Ni). The right-hand part of the appropriate formula is a function of the Wagner interaction coefficients between nitrogen and chromium \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Fe) and between nitrogen and nickel \(\varepsilon _{\rm{N}}^{{\rm{Ni}}}\)(Fe) in liquid iron-based alloys. A similar relation is obtained for the Wagner interaction coefficient between nitrogen and molybdenum in liquid nickel-based alloys \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni). According to the first of these formulas, the value \(\varepsilon _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –21,9 at a temperature of 1873 K is calculated. This corresponds to the value of the Langenberg interaction coefficient \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,108, which coincides with experimental estimate. According to the second formula, the value \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni) = –14,3 is calculated at a temperature 1873 K. This corresponds to the value of the Langenberg interaction coefficient \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,036, which is in satisfactory agreement with the experimental estimate \(\varepsilon _{\rm{N}}^{{\rm{Mo}}}\)(Ni) = –15,1; \(e _{\rm{N}}^{{\rm{Cr}}}\)(Ni) = –0,038.

Saturation vapor pressure characterization of selected low-volatility organic compounds using a residence time chamber

Abstract. Saturation vapor pressure (psat) is an important thermodynamic property regulating the gas-to-particle partitioning of organic compounds in the atmosphere. Low-volatility organic compounds (LVOCs), with sufficiently low psat values, primarily stay in the particle phase and contribute to aerosol formation. Obtaining accurate information on the psat of LVOCs requires volatility measurements performed at temperatures relevant to atmospheric aerosol formation. Here, we present an isothermal evaporation method using a residence time chamber to measure psat for dry single-compound nanoparticles at 295 K. Our method is able to characterize organic compounds with psat spanning from 10−8 to 10−4 Pa at 295 K. The compounds included four polyethylene glycols (PEGs: PEG6, PEG7, PEG8, and PEG9), two monocarboxylic acids (palmitic acid and stearic acid), two dicarboxylic acids (azelaic acid and sebacic acid), two alcohols (meso-erythritol and xylitol), and one ester (di-2-ethylhexyl sebacate). There was a good agreement between our measured psat values and those reported by previous volatility studies using different measurement techniques, mostly within 1 order of magnitude. Additionally, quantum-chemistry-based COSMOtherm calculations were performed to estimate the psat values of the studied compounds. COSMOtherm predicted the psat values for most of the studied compounds within 1 order of magnitude difference between the experimental and computational estimates.

Advancing carrier transport models for InAs/GaSb type-II superlattice mid-wavelength infrared photodetectors

To provide the best possible performance, modern infrared photodetector designs necessitate extremely precise modeling of the superlattice absorber region. We advance the Rode's method for the Boltzmann transport equation in conjunction with the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ band structure and the envelope function approximation for a detailed computation of the carrier mobility and conductivity of layered type-II superlattice structures, using which we unravel two crucial insights. First, the significance of both elastic- and inelastic-scattering mechanisms, particularly the influence of the interface roughness and polar optical phonon scattering mechanisms in technologically relevant superlattice structures. Second, that the structure-specific Hall mobility and Hall scattering factor reveal that temperature and carrier concentrations significantly affect the Hall scattering factor, which deviates significantly from unity even for small magnetic fields. This reinforces the caution that should be exercised when employing the Hall scattering factor in experimental estimations of drift mobilities and carrier concentrations. Our research hence offers a comprehensive microscopic understanding of carrier dynamics in such technologically relevant superlattices. Our models also provide highly accurate and precise transport parameters beyond the relaxation-time approximation and thereby paving the way to develop physics-based device modules for mid-wavelength infrared photodetectors.

Experimental estimates of germline mutation rate in eukaryotes: a phylogenetic meta-analysis.

Mutation is the ultimate source of all genetic variation, and over the last 10 years the ready availability of whole-genome sequencing has permitted direct estimation of mutation rate for many non-model species across the tree of life. In this meta-analysis, we make a comprehensive search of the literature for mutation rate estimates in eukaryotes, identifying 140 mutation accumulation (MA) and parent-offspring (PO) sequencing studies covering 134 species. Based on these data, we revisit differences in the single-nucleotide mutation (SNM) rate between different phylogenetic lineages and update the known relationships between mutation rate and generation time, genome size, and nucleotide diversity-while accounting for phylogenetic nonindependence. We do not find a significant difference between MA and PO in estimated mutation rates, but we confirm that mammal and plant lineages have higher mutation rates than arthropods and that unicellular eukaryotes have the lowest mutation rates. We find that mutation rates are higher in species with longer generation times and larger genome sizes, even when accounting for phylogenetic relationships. Moreover, although nucleotide diversity is positively correlated with mutation rate, the gradient of the relationship is significantly less than one (on a logarithmic scale), consistent with higher mutation rates in populations with smaller effective size. For the 29 species for which data are available, we find that indel mutation rates are positively correlated with nucleotide mutation rates and that short deletions are generally more common than short insertions. Nevertheless, despite recent progress, no estimates of either SNM or indel mutation rates are available for the majority of deeply branching eukaryotic lineages-or even for most animal phyla. Even among charismatic megafauna, experimental mutation rate estimates remain unknown for amphibia and scarce for reptiles and fish.

Algoritm podvizhnogo okna dlya parametricheskoy identifikatsii dinamicheskikh sistem s pryamougol'nymi i ellipsoidnymi oblastyami neopredelennosti parametrov

The parametric identification problem for dynamical systems with rectangular and ellipsoid parameter uncertainty domains is solved for the case in which the experimental data are given in the form of intervals. The state of the considered dynamical systems at each moment of time is a parametric set. An objective function that characterizes the degree of deviation of the parametric sets of states from experimental interval estimates is constructed in the space of parameter uncertainty domains. To minimize the objective function, a sliding window algorithm has been developed, which is related to gradient methods. It is based on an adaptive interpolation algorithm that allows one to explicitly obtain parametric sets of states of a dynamical system within a given parameter uncertainty domain (window). The efficiency and performance of the proposed algorithm are demonstrated.

Postures anomaly tracking and prediction learning model over crowd data analytics.

Innovative technology and improvements in intelligent machinery, transportation facilities, emergency systems, and educational services define the modern era. It is difficult to comprehend the scenario, do crowd analysis, and observe persons. For e-learning-based multiobject tracking and predication framework for crowd data via multilayer perceptron, this article recommends an organized method that takes e-learning crowd-based type data as input, based on usual and abnormal actions and activities. After that, super pixel and fuzzy c mean, for features extraction, we used fused dense optical flow and gradient patches, and for multiobject tracking, we applied a compressive tracking algorithm and Taylor series predictive tracking approach. The next step is to find the mean, variance, speed, and frame occupancy utilized for trajectory extraction. To reduce data complexity and optimization, we applied T-distributed stochastic neighbor embedding (t-SNE). For predicting normal and abnormal action in e-learning-based crowd data, we used multilayer perceptron (MLP) to classify numerous classes. We used the three-crowd activity University of California San Diego, Department of Pediatrics (USCD-Ped), Shanghai tech, and Indian Institute of Technology Bombay (IITB) corridor datasets for experimental estimation based on human and nonhuman-based videos. We achieve a mean accuracy of 87.00%, USCD-Ped, Shanghai tech for 85.75%, and IITB corridor of 88.00% datasets.

Experimental estimation of equivalent loads on upward two-phase crossflow in tube bundles via Kalman filtering

Tube bundles of heat exchangers are permanently exposed to flow-induced forces, which may lead to high amplitude vibrations compromising the lifetime. In this context, Flow-induced vibration (FIV) is the most crucial dynamic issue to deal with in the design and operation of shell-and-tube heat exchangers. The experimental investigation of FIV requires determining the nature of flow-induced forces and their consequences, which are given by the characteristics of tube vibration. However, the measurement of flow-induced forces is challenging due to space restrictions within a tube bundle and their intrinsic spatially-distributed nature, often represented by equivalent point forces. The present work aims to estimate the equivalent flow-induced forces in tube bundles due to two-phase crossflow using Virtual Sensing principles. In order to do that, a device is designed and constructed to replace a tube within a normal triangular (transversal pitch to diameter ratio of 1.26) tube bundle, which is subjected to two-phase flow with void fractions ranging from 30% to 95% and a wide range of mass velocities. The device is instrumented with two couples of accelerometers and strain sensors, aligned with drag and transverse directions. The measured dynamic responses are discussed in terms of void fraction, mass velocities, and flow patterns. The results confirm the severity of FIV under Intermittent-type flow patterns. Further, the equivalent force estimation is performed via the Augmented Kalman Filter (AKF), which requires a model approximation (based on EMA techniques) and the system’s outputs. The values of the input covariance matrix are determined through the L-curve regularization method. Finally, the quality of the estimated equivalent force is tested by simulating system accelerations, whose RMS values are compared with measured data. The results suggest better acceleration predictions in the transverse direction than in the main flow direction for relatively low mass velocities and Bubbles flow pattern.

Activation Energy of Ion Diffusion in an Electrode Material: Theoretical Calculation and Experimental Estimation with LiCoVO4 as an Example

The development of electrode materials for metal-ion batteries is a complex and resource-demanding process. The optimization of this development process requires a combination of theoretical and experimental methods. The former is used to predict the properties of materials and the latter to confirm them. Thus, it is very important to understand how the results of the modeling and experiment are related. In this study, we compare the results of determining the activation energies of lithium ion diffusion in cobalt(II)-lithium vanadate(V), which we obtained by calculations from first principles within the framework of density functional theory (DFT), with the experimental results, which we achieved by applying electrochemical methods such as cyclic voltammetry and galvanostatic and potentiostatic pulses. Based on the experimental and theoretical data obtained for LiCoVO4, we hypothesize that the limitation of the practically realizable capacity of the material at about 1/3 of the theoretical one is due to its structural limitations that lead to the impossibility of involving all lithium ions in the current-forming process. This reason is fixed by the simulation results, but is not detected by the experimental results.

Toward an Improved Method for Determining the Hamaker Constant of Solid Materials Using Atomic Force Microscopy. III: Experimental Validation of a New Approach-to-Contact Method

A robust experimental validation of an existing approach-to-contact atomic force microscopy (AFM) method for determining the self-Hamaker constant, A11, of a solid, nondeformable material is presented. By explicitly accounting for the underlying surface roughness of a given substrate, this method allows for an estimate of A11 to be obtained from the resulting distribution of AFM cantilever deflections at first contact with the surface, dc. Using this method, the self-Hamaker constants of amorphous silica, stainless steel, and sapphire were determined. Moreover, several plates comprised of the same material, but with different topographies (or values of their root-mean squared surface roughness), were also considered. The values of A11 obtained for these same material plates were found to be in excellent agreement, verifying that this approach-to-contact method properly accounts for the underlying roughness of a given surface. Furthermore, the average value of A11 across all plates for a particular material was in very good agreement with those results previously derived from Lifshitz theory. Finally, the uncertainties in these experimental estimates of A11 were found to be significantly reduced, compared to the uncertainties that arose in some previous approach-to-contact methods.

Preparation and experimental estimation of radiation shielding properties of novel epoxy reinforced with Sb2O3 and PbO

Abstract The present work aims to fabricate new inexpensive epoxy-based composites with a concentration described by the formula (90 − x)epoxy + 10Sb2O3 + xPbO, where x = 5, 10, 15, and 20 wt%. The impacts of the substitution of epoxy by PbO on the composite density and radiation shielding properties of the fabricated composites were studied. The density of the fabricated composites varied between 1.30 and 1.49 g·cm−3, enriching the PbO concentration. Utilizing the narrow beam transmission method, the linear attenuation coefficient (LAC) of the fabricated composites was measured using the NaI (Tl) detector as well as radioactive sources Am-241 and Cs-137. The LAC increased by 84% and 18% at gamma-ray energy of 0.059 and 0.662 MeV, when the PbO concentration raised between 5 and 20 wt%, respectively. Then the transmission rate and half-value layer of the fabricated composites were reduced by raising the PbO concentration. Therefore, the fabricated composite has good shielding properties in the low gamma-ray energy interval to be suitable for medical applications and low radioactive waste container constructions.

Golgi α-mannosidase: opposing structures of Drosophila melanogaster and novel human model using molecular dynamics simulations and docking at different pHs

The search for Golgi α-mannosidase II (GMII) potent and specific inhibitors has been a focus of many studies for the past three decades since this enzyme is a key target for cancer treatment. α-Mannosidases, such as those from Drosophila melanogaster or Jack bean, have been used as functional models of the human Golgi α-mannosidase II (hGMII) because mammalian mannosidases are difficult to purify and characterize experimentally. Meanwhile, computational studies have been seen as privileged tools able to explore assertive solutions to specific enzymes, providing molecular details of these macromolecules, their protonation states and their interactions. Thus, modelling techniques can successfully predict hGMII 3D structure with high confidence, speeding up the development of new hits. In this study, Drosophila melanogaster Golgi mannosidase II (dGMII) and a novel human model, developed in silico and equilibrated via molecular dynamics simulations, were both opposed for docking. Our findings highlight that the design of novel inhibitors should be carried out considering the human model’s characteristics and the enzyme operating pH. A reliable model is evidenced, showing a good correlation between K i /IC50 experimental data and theoretical ΔG binding estimations in GMII, opening the possibility of optimizing the rational drug design of new derivatives. Communicated by Ramaswamy H. Sarma

Partitioning of Precipitation Into Terrestrial Water Balance Components Under a Drying Climate

AbstractTo accurately project future water availability under a drying climate, it is important to understand how precipitation is partitioned into other terrestrial water balance components, such as fluxes (evaporation, transpiration, runoff) and changes in storage (soil moisture, groundwater). Many studies have reported unexpected large runoff reductions during drought, particularly for multi‐year events, and some studies report a persistent change in partitioning even after the meteorological drought has ended. This study focused on understanding how actual evapotranspiration (AET) and change in subsurface storage (ΔS) respond to climate variability and change, examining Australia's Millennium Drought (MD, 1997–2009). The study initially conducted a catchment‐scale water balance analysis to investigate interactions between ΔS and AET. Then the water balance analysis was extended to regional scale to investigate ΔS using interpolated rainfall and discharge with remotely sensed AET. Lastly, we evaluated conceptual rainfall‐runoff model performance of two commonly used models against these water balance estimates. The evaluation of water‐balance‐derived ΔS against Gravity Recovery and Climate Experiment (GRACE) estimates shows a significant multiyear storage decline; however, with different rates. In contrast, AET rates (annualized) remained approximately constant before and during the MD, contrasting with some reports of evapotranspiration enhancement elsewhere. Overall, given AET remained approximately constant, drought‐induced precipitation reductions were partitioned into ΔS and streamflow. The employed conceptual rainfall‐runoff models failed to realistically represent AET during the MD, suggesting the need for improved conceptualization of processes. This study provides useful implications for explaining future hydrological changes if similar AET behavior is observed under a drying climate.

Cross-modality image translation: CT image synthesis of MR brain images using multi generative network with perceptual supervision

Background: Computed tomography (CT) and magnetic resonance imaging (MRI) are the mainstream imaging technologies for clinical practice. CT imaging can reveal high-quality anatomical and physiopathological structures, especially bone tissue, for clinical diagnosis. MRI provides high resolution in soft tissue and is sensitive to lesions. CT combined with MRI diagnosis has become a regular image-guided radiation treatment plan.Methods: In this paper, to reduce the dose of radiation exposure in CT examinations and ameliorate the limitations of traditional virtual imaging technologies, we propose a Generative MRI-to-CT transformation method with structural perceptual supervision. Even though structural reconstruction is structurally misaligned in the MRI-CT dataset registration, our proposed method can better align structural information of synthetic CT (sCT) images to input MRI images while simulating the modality of CT in the MRI-to-CT cross-modality transformation.Results: We retrieved a total of 3416 brain MRI-CT paired images as the train/test dataset, including 1366 train images of 10 patients and 2050 test images of 15 patients. Several methods (the baseline methods and the proposed method) were evaluated by the HU difference map, HU distribution, and various similarity metrics, including the mean absolute error (MAE), structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and normalized cross-correlation (NCC). In our quantitative experimental results, the proposed method achieves the lowest MAE mean of 0.147, highest PSNR mean of 19.27, and NCC mean of 0.431 in the overall CT test dataset.Conclusions: In conclusion, both qualitative and quantitative results of synthetic CT validate that the proposed method can preserve higher similarity of structural information of the bone tissue of target CT than the baseline methods. Furthermore, the proposed method provides better HU intensity reconstruction for simulating the distribution of the CT modality. The experimental estimation indicates that the proposed method is worth further investigation.

The variational method of moments

Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by flexible function classes such as neural nets and kernel methods, while provably maintaining statistical efficiency unlike existing related minimax estimators. We also develop inference algorithms and demonstrate the empirical strengths of VMM estimation and inference in experiments.

Domain- and state-specific shape of the electric field tunes voltage sensing in voltage-gated sodium channels

The ability to sense transmembrane voltage underlies most physiological roles of voltage-gated sodium (Nav) channels. Whereas the key role of their voltage-sensing domains (VSDs) in channel activation is well established, the molecular underpinnings of voltage coupling remain incompletely understood. Voltage-dependent energetics of the activation process can be described in terms of the gating charge that is defined by coupling of charged residues to the external electric field. The shape of the electric field within VSDs is therefore crucial for the activation of voltage-gated ion channels. Here, we employed molecular dynamics simulations of cardiac Nav1.5 and bacterial NavAb, together with our recently developed tool g_elpot, to gain insights into the voltage-sensing mechanisms of Nav channels via high-resolution quantification of VSD electrostatics. In contrast to earlier low-resolution studies, we found that the electric field within VSDs of Nav channels has a complex isoform- and domain-specific shape, which prominently depends on the activation state of a VSD. Different VSDs vary not only in the length of the region where the electric field is focused but also differ in their overall electrostatics, with possible implications in the diverse ion selectivity of their gating pores. Due to state-dependent field reshaping, not only translocated basic but also relatively immobile acidic residues contribute significantly to the gating charge. In the case of NavAb, we found that the transition between structurally resolved activated and resting states results in a gating charge of 8e, which is noticeably lower than experimental estimates. Based on the analysis of VSD electrostatics in the two activation states, we propose that the VSD likely adopts a deeper resting state upon hyperpolarization. In conclusion, our results provide an atomic-level description of the gating charge, demonstrate diversity in VSD electrostatics, and reveal the importance of electric-field reshaping for voltage sensing in Nav channels.