Dynamics Of Gate Research Articles

Biochemical, structural, and computational analyses of two new clinically identified missense mutations of ALDH7A1

Aldehyde dehydrogenase 7A1 (ALDH7A1) catalyzes a step of lysine catabolism. Certain missense mutations in the ALDH7A1 gene cause pyridoxine dependent epilepsy (PDE), a rare autosomal neurometabolic disorder with recessive inheritance that affects almost 1:65,000 live births and is classically characterized by recurrent seizures from the neonatal period. We report a biochemical, structural, and computational study of two novel ALDH7A1 missense mutations that were identified in a child with rare recurrent seizures from the third month of life. The mutations affect two residues in the oligomer interfaces of ALDH7A1, Arg134 and Arg441 (Arg162 and Arg469 in the HGVS nomenclature). The corresponding enzyme variants R134S and R441C (p.Arg162Ser and p.Arg469Cys in the HGVS nomenclature) were expressed in Escherichia coli and purified. R134S and R441C have 10,000- and 50-fold lower catalytic efficiency than wild-type ALDH7A1, respectively. Sedimentation velocity analytical ultracentrifugation shows that R134S is defective in tetramerization, remaining locked in a dimeric state even in the presence of the tetramer-inducing coenzyme NAD+. Because the tetramer is the active form of ALDH7A1, the defect in oligomerization explains the very low catalytic activity of R134S. In contrast, R441C exhibits wild-type oligomerization behavior, and the 2.0 Å resolution crystal structure of R441C complexed with NAD+ revealed no obvious structural perturbations when compared to the wild-type enzyme structure. Molecular dynamics simulations suggest that the mutation of Arg441 to Cys may increase intersubunit ion pairs and alter the dynamics of the active site gate. Our biochemical, structural, and computational data on two novel clinical variants of ALDH7A1 add to the complexity of the molecular determinants underlying pyridoxine dependent epilepsy.

Oxidation effect on the ultrafast carrier dynamics of GaTe studied by terahertz spectroscopy

Effect of oxygen on the physical properties of GaTe is investigated by optical pump–terahertz probe spectroscopy. Oxygen erosion in GaTe leads to significant reductions in lifetime and transient conductivity. Terahertz emission is also evaluated. Terahertz radiation intensity gradually dies away with increasing air exposing time. Such phenomena are attributed to the trapping of photogenerated carriers by oxygen–introduced defects, which can result in the reduction of the carrier density, acceleration of the photocarrier relaxation, and impediment of the terahertz emission.

The solute carrier SPNS2 recruits PI(4,5)P2 to synergistically regulate transport of sphingosine-1-phosphate

Solute carrier spinster homolog 2 (SPNS2), one of only four known major facilitator superfamily (MFS) lysolipid transporters in humans, exports sphingosine-1-phosphate (S1P) across cell membranes. Here, we explore the synergistic effects of lipid binding and conformational dynamics on SPNS2's transport mechanism. Using mass spectrometry, we discovered that SPNS2 interacts preferentially with PI(4,5)P2. Together with functional studies and molecular dynamics (MD) simulations, we identified potential PI(4,5)P2 binding sites. Mutagenesis of proposed lipid binding sites and inhibition of PI(4,5)P2 synthesis reduce S1P transport, whereas the absence of the N terminus renders the transporter essentially inactive. Probing the conformational dynamics of SPNS2, we show how synergistic binding of PI(4,5)P2 and S1P facilitates transport, increases dynamics of the extracellular gate, and stabilizes the intracellular gate. Given that SPNS2 transports a key signaling lipid, our results have implications for therapeutic targeting and also illustrate a regulatory mechanism for MFS transporters.

The opening dynamics of the lateral gate regulates the activity of rhomboid proteases.

Rhomboid proteases hydrolyze substrate helices within the lipid bilayer to release soluble domains from the membrane. Here, we investigate the mechanism of activity regulation for this unique but wide-spread protein family. In the model rhomboid GlpG, a lateral gate formed by transmembrane helices TM2 and TM5 was previously proposed to allow access of the hydrophobic substrate to the shielded hydrophilic active site. In our study, we modified the gate region and either immobilized the gate by introducing a maleimide-maleimide (M2M) crosslink or weakened the TM2/TM5 interaction network through mutations. We used solid-state nuclear magnetic resonance (NMR), molecular dynamics (MD) simulations, and molecular docking to investigate the resulting effects on structure and dynamics on the atomic level. We find that variants with increased dynamics at TM5 also exhibit enhanced activity, whereas introduction of a crosslink close to the active site strongly reduces activity. Our study therefore establishes a strong link between the opening dynamics of the lateral gate in rhomboid proteases and their enzymatic activity.

Experimental and Bioinformatic Insights into the Effects of Epileptogenic Variants on the Function and Trafficking of the GABA Transporter GAT-1.

In this article, we identified a novel epileptogenic variant (G307R) of the gene SLC6A1, which encodes the GABA transporter GAT-1. Our main goal was to investigate the pathogenic mechanisms of this variant, located near the neurotransmitter permeation pathway, and compare it with other variants located either in the permeation pathway or close to the lipid bilayer. The mutants G307R and A334P, close to the gates of the transporter, could be glycosylated with variable efficiency and reached the membrane, albeit inactive. Mutants located in the center of the permeation pathway (G297R) or close to the lipid bilayer (A128V, G550R) were retained in the endoplasmic reticulum. Applying an Elastic Network Model, to these and to other previously characterized variants, we found that G307R and A334P significantly perturb the structure and dynamics of the intracellular gate, which can explain their reduced activity, while for A228V and G362R, the reduced translocation to the membrane quantitatively accounts for the reduced activity. The addition of a chemical chaperone (4-phenylbutyric acid, PBA), which improves protein folding, increased the activity of GAT-1WT, as well as most of the assayed variants, including G307R, suggesting that PBA might also assist the conformational changes occurring during the alternative access transport cycle.

Effect of Sec62 on the conformation of the Sec61 channel in yeast

Most eukaryotic secretory and membrane proteins are funneled by the Sec61 complex into the secretory pathway. Furthermore, some substrate peptides rely on two essential accessory proteins, Sec62 and Sec63, being present to assist with their translocation via the Sec61 channel in post-translational translocation. Cryo-electron microscopy (cryo-EM) recently succeeded in determining atomistic structures of unbound and signal sequence-engaged Sec complexes from Saccharomyces cerevisiae, involving the Sec61 channel and the proteins Sec62, Sec63, Sec71 and Sec72. In this study, we investigated the conformational effects of Sec62 on Sec61. Indeed, we observed in molecular dynamics simulations that the conformational dynamics of lateral gate, plug and pore region of Sec61 are altered by the presence/absence of Sec62. In molecular dynamics simulations that were started from the cryo-EM structures of Sec61 coordinated to Sec62 or of apo Sec61, we observed that the luminal side of the lateral gate gradually adopts a closed conformation similar to the apo state during unbound state simulations. In contrast, it adopts a wider conformation in the bound state. Furthermore, we demonstrate that the conformation of the active (substrate-bound) state of the Sec61 channel shifts toward an alternative conformation in the absence of the substrate. We suggest that the signal peptide holds/stabilizes the active state conformation of Sec61 during post-translational translocation. Thus, our study explains the effect of Sec62 on the conformation of the Sec61 channel and describes the conformational transitions of Sec61 channel.

Integrated AlphaFold2 and DEER investigation of the conformational dynamics of a pH-dependent APC antiporter

The Amino Acid-Polyamine-Organocation (APC) transporter GadC contributes to the survival of pathogenic bacteria under extreme acid stress by exchanging extracellular glutamate for intracellular γ-aminobutyric acid (GABA). Its structure, determined in an inward-facing conformation at alkaline pH, consists of the canonical LeuT-fold with a conserved five-helix inverted repeat, thereby resembling functionally divergent transporters such as the serotonin transporter SERT and the glucose-sodium symporter SGLT1. However, despite this structural similarity, it is unclear if the conformational dynamics of antiporters such as GadC follow the blueprint of these or other LeuT-fold transporters. Here, we used double electron-electron resonance (DEER) spectroscopy to monitor the conformational dynamics of GadC in lipid bilayers in response to acidification and substrate binding. To guide experimental design and facilitate the interpretation of the DEER data, we generated an ensemble of structural models in multiple conformations using a recently introduced modification of AlphaFold2 . Our experimental results reveal acid-induced conformational changes that dislodge the Cterminus from the permeation pathway coupled with rearrangement of helices that enables isomerization between inward- and outward-facing states. The substrate glutamate, but not GABA, modulates the dynamics of an extracellular thin gate without shifting the equilibrium between inward- and outward-facing conformations. In addition to introducing an integrated methodology for probing transporter conformational dynamics, the congruence of the DEER data with patterns of structural rearrangements deduced from ensembles of AlphaFold2 models illuminates the conformational cycle of GadC underpinning transport and exposes yet another example of the divergence between the dynamics of different families in the LeuT-fold.

Probing the Structural Dynamics of the Activation Gate of KcsA Using Homo-FRET Measurements.

The allosteric coupling between activation and inactivation processes is a common feature observed in K+ channels. Particularly, in the prokaryotic KcsA channel the K+ conduction process is controlled by the inner gate, which is activated by acidic pH, and by the selectivity filter (SF) or outer gate, which can adopt non-conductive or conductive states. In a previous study, a single tryptophan mutant channel (W67 KcsA) enabled us to investigate the SF dynamics using time-resolved homo-Förster Resonance Energy Transfer (homo-FRET) measurements. Here, the conformational changes of both gates were simultaneously monitored after labelling the G116C position with tetramethylrhodamine (TMR) within a W67 KcsA background. At a high degree of protein labeling, fluorescence anisotropy measurements showed that the pH-induced KcsA gating elicited a variation in the homo-FRET efficiency among the conjugated TMR dyes (TMR homo-FRET), while the conformation of the SF was simultaneously tracked (W67 homo-FRET). The dependence of the activation pKa of the inner gate with the ion occupancy of the SF unequivocally confirmed the allosteric communication between the two gates of KcsA. This simple TMR homo-FRET based ratiometric assay can be easily extended to study the conformational dynamics associated with the gating of other ion channels and their modulation.

Molecular Gating of an Engineered Enzyme Captured in Real Time.

Enzyme engineering tends to focus on the design of active sites for the chemical steps, while the physical steps of the catalytic cycle are often overlooked. Tight binding of a substrate in an active site is beneficial for the chemical steps, whereas good accessibility benefits substrate binding and product release. Many enzymes control the accessibility of their active sites by molecular gates. Here we analyzed the dynamics of a molecular gate artificially introduced into an access tunnel of the most efficient haloalkane dehalogenase using pre-steady-state kinetics, single-molecule fluorescence spectroscopy, and molecular dynamics. Photoinduced electron-transfer-fluorescence correlation spectroscopy (PET-FCS) has enabled real-time observation of molecular gating at the single-molecule level with rate constants ( kon = 1822 s-1, koff = 60 s-1) corresponding well with those from the pre-steady-state kinetics ( k-1 = 1100 s-1, k1 = 20 s-1). The PET-FCS technique is used here to study the conformational dynamics in a soluble enzyme, thus demonstrating an additional application for this method. Engineering dynamical molecular gates represents a widely applicable strategy for designing efficient biocatalysts.

C-terminal kink formation is required for lateral gating in BamA

In Gram-negative bacteria, the outer membrane contains primarily β-barrel transmembrane proteins and lipoproteins. The insertion and assembly of β-barrel outer-membrane proteins (OMPs) is mediated by the β-barrel assembly machinery (BAM) complex, the core component of which is the 16-stranded transmembrane β-barrel BamA. Recent studies have indicated a possible role played by the seam between the first and last β-barrel strands of BamA in the OMP insertion process through lateral gating and a destabilized membrane region. In this study, we have determined the stability and dynamics of the lateral gate through over 12.5 μs of equilibrium simulations and 4 μs of free-energy calculations. From the equilibrium simulations, we have identified a persistent kink in the C-terminal strand and observed spontaneous lateral-gate separation in a mimic of the native bacterial outer membrane. Free-energy calculations of lateral gate opening revealed a significantly lower barrier to opening in the C-terminal kinked conformation; mutagenesis experiments confirm the relevance of C-terminal kinking to BamA structure and function.

Active Site Gate Dynamics Modulate the Catalytic Activity of the Ubiquitination Enzyme E2-25K

The ubiquitin proteasome system (UPS) signals for degradation of proteins through attachment of K48-linked polyubiquitin chains, or alterations in protein-protein recognition through attachment of K63-linked chains. Target proteins are ubiquitinated in three sequential chemical steps by a three-component enzyme system. Ubiquitination, or E2 enzymes, catalyze the central step by facilitating reaction of a target protein lysine with the C-terminus of Ub that is attached to the active site cysteine of the E2 through a thioester bond. E2 reactivity is modulated by dynamics of an active site gate, whose central residue packs against the active site cysteine in a closed conformation. Interestingly, for the E2 Ubc13, which specifically catalyzes K63-linked ubiquitination, the central gate residue adopts an open conformation. We set out to determine if active site gate dynamics play a role in catalysis for E2-25K, which adopts the canonical, closed gate conformation, and which selectively synthesizes K48-linked ubiquitin chains. Gate dynamics were characterized using mutagenesis of key residues, combined with enzyme kinetics measurements, and main chain NMR relaxation. The experimental data were interpreted with all atom MD simulations. The data indicate that active site gate opening and closing rates for E2-25K are precisely balanced.

Molecular Dynamics Simulations of Orai Reveal How the Third Transmembrane Segment Contributes to Hydration and Ca2+ Selectivity in Calcium Release-Activated Calcium Channels.

Calcium release-activated calcium (CRAC) channels open upon depletion of Ca2+ from the endoplasmic reticulum, and when open, they are permeable to a selective flux of calcium ions. The atomic structure of Orai, the pore domain of CRAC channels, from Drosophila melanogaster has revealed many details about conduction and selectivity in this family of ion channels. However, it is still unclear how residues on the third transmembrane helix can affect the conduction properties of the channel. Here, molecular dynamics and Brownian dynamics simulations were employed to analyze how a conserved glutamate residue on the third transmembrane helix (E262) contributes to selectivity. The comparison between the wild-type and mutated channels revealed a severe impact of the mutation on the hydration pattern of the pore domain and on the dynamics of residues K270, and Brownian dynamics simulations proved that the altered configuration of residues K270 in the mutated channel impairs selectivity to Ca2+ over Na+. The crevices of water molecules, revealed by molecular dynamics simulations, are perfectly located to contribute to the dynamics of the hydrophobic gate and the basic gate, suggesting a possible role in channel opening and in selectivity function.

Mechanistic modelling of a recombinase‐based two‐input temporal logic gate

Site-specific recombinases (SSRs) mediate efficient manipulation of DNA sequences in vitro and in vivo. In particular, serine integrases have been identified as highly effective tools for facilitating DNA inversion, enabling the design of genetic switches that are capable of turning the expression of a gene of interest on or off in the presence of a SSR protein. The functional scope of such circuitry can be extended to biological Boolean logic operations by incorporating two or more distinct integrase inputs. To date, mathematical modelling investigations have captured the dynamical properties of integrase logic gate systems in a purely qualitative manner, and thus such models are of limited utility as tools in the design of novel circuitry. Here, the authors develop a detailed mechanistic model of a two-input temporal logic gate circuit that can detect and encode sequences of input events. Their model demonstrates quantitative agreement with time-course data on the dynamics of the temporal logic gate, and is shown to subsequently predict dynamical responses relating to a series of induction separation intervals. The model can also be used to infer functional variations between distinct integrase inputs, and to examine the effect of reversing the roles of each integrase on logic gate output.

Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers

To reach the video bandwidth requirements on the supply paths, power amplifiers with dynamic bias schemes are constrained to reduce the values of the low-frequency (LF) decoupling capacitors on their bias lines. This can entail a decrease of the LF stability margins, among other negative effects. In this work, a methodology is proposed to experimentally monitor and control the dominant poles that govern the LF dynamics of both gate and drain bias lines from dc to high compression power. A specific topology for the bias observation accesses allows a consistent characterization in large-signal regimes. An automatic procedure to trace root contours versus four control parameters is also developed. The complete approach can be used to optimize the design of the bias lines in terms of video bandwidth, relative stability margins, and bias voltage transfer function characteristics. Moreover, the design can account for the effect of the large-signal RF drive on these LF performances. The methodology is exemplified and validated in a demonstrator prototype specifically built for that purpose.

Structural features and dynamic investigations of the membrane-bound cytochrome P450 17A1

Cytochrome P450 (CYP) 17A1 is a dual-function monooxygenase with a critical role in the synthesis of many human steroid hormones. The enzyme is an important target for treatment of breast and prostate cancers that proliferate in response to estrogens and androgens. Despite the crystallographic structures available for CYP17A1, no membrane-bound structural features of this enzyme at atomic level are available. Accumulating evidence has indicated that the interactions between bounded CYPs and membrane could contribute to the recruitment of lipophilic substrates. To this end, we have investigated the effects on structural characteristics in the presence of the membrane for CYP17A1. The MD simulation results demonstrate a spontaneous insertion process of the enzyme to the lipid. Two predominant modes of CYP17A1 in the membrane are captured, characterized by the depths of insertion and orientations of the enzyme to the membrane surface. The measured heme tilt angles show good consistence with experimental data, thereby verifying the validity of the structural models. Moreover, conformational changes induced by the membrane might have impact on the accessibility of the active site to lipophilic substrates. The dynamics of internal aromatic gate formed by Trp220 and Phe224 are suggested to regulate tunnel opening motions. The knowledge of the membrane binding characteristics could guide future experimental and computational works on membrane-bound CYPs so that various investigations of CYPs in their natural, lipid environment rather than in artificially solubilized forms may be achieved.

Insights into the Distinctly Different Sensitivities of α7 and α7β2 nAChRs to the Volatile Anesthetic Isoflurane

Nicotinic acetylcholine receptors (nAChRs) mediate the fast synaptic transmission in the central and peripheral nervous systems. They are also targets of general anesthetics. Among the nAChR subtypes, α7 and α4β2 nAChRs are the most abundant subtypes found in the brain. Despite their high sequence homology, the α4β2 nAChR is hypersensitive but the α7 nAChR is insensitive to volatile general anesthetics. The underlying cause for the functional discrepancy between these homologous receptors presents an intriguing enigma. In this study, we have found that the α7β2 nAChR is hypersensitive to the volatile anesthetic isoflurane and that the β2 subunit is primarily responsible for conferring anesthetic sensitivity. Using high-resolution NMR, we identified intrasubunit isoflurane binding sites at the extracellular and intracellular ends of the β2 and α7 transmembrane domains, respectively. Cavity analyses revealed that β2, but not α7, has a pocket large enough to accommodate isoflurane binding to the extracellular end of the transmembrane domain. Variations in pocket size result from subtle structural differences between β2 and α7, where the angle between the TM2 and TM4 helices differs by ∼7° between β2 and α7. While isoflurane binding perturbed dynamics for both β2 and α7, only the binding to the extracellular end of the β2 transmembrane domain produced significant dynamics changes for the pore-lining residues. The study suggests that a subtle structural difference could affect drug binding. Furthermore, only the drug binding that affects the dynamics of the channel gate is able to generate the functional effect. Supported by NIH (R01GM66358, R01GM56257, and R37GM049202).

Rapamycin Allosterically Inhibits the Proteasome

Rapamycin is a canonical allosteric inhibitor of the mammalian tarpet of rapamycin (mTOR) kinase with immunosuppressive and proapoptotic activities. We found that in vitro rapamycin also regulates the proteasome, which is an essential intracellular protease of the ubiquitin-proteasome pathway. Rapamycin inhibits proteinase and selected peptidase activities of the catalytic core proteasome at low micromolar concentrations. Moreover, the drug interferes with binding of the 19S cap essential for processing of polyubiquitinylated substrates and with the PA200 proteasome activator to the 20S catalytic core proteasome. These protein complexes are known to bind to specific grooves on the α face region of the 20S core. Treatment with rapamycin affects the conformational dynamics of the proteasomal gate, which is centrally positioned within the α face and allosterically regulated element responsible for the intake of substrates. We showed that rapamycin shares all the proteasome targeting properties not only with other two-domain, closed-ring analogs (rapalogs) but also with its single domain mimics and seco-rapamycin, which is the first in vivo open-ring metabolite of rapamycin that does not affect mTOR. We hypothesize that rapamycin and related compounds bind to the α face and allosterically impact proteasome function. This article discusses the implications of our findings for the mechanism of in vivo actions of rapamycin and for the design of novel allosteric drugs targeting the proteasome.

Symmetry-Constrained Analysis of Pulsed Double Electron–Electron Resonance (DEER) Spectroscopy Reveals the Dynamic Nature of the KcsA Activation Gate

Distance determination from an echo intensity modulation obtained by pulsed double electron-electron resonance (DEER) experiment is a mathematically ill-posed problem. Tikhonov regularization yields distance distributions that can be difficult to interpret, especially in a system with multiple discrete distance distributions. Here, we show that by using geometric fit constraints in symmetric homo-oligomeric protein systems, we were able to increase the accuracy of a model-based fit solution based on a sum of Rice distributions. Our approach was validated on two different ion channels of known oligomeric states, KcsA (tetramer) and CorA (pentamer). Statistical analysis of the resulting fits was integrated within our method to help the experimenter evaluate the significance of a symmetry-constrained vs standard model distribution fit and to examine multidistance confidence regions. This approach was used to quantitatively evaluate the role of the C-terminal domain (CTD) on the flexibility and conformation of the activation gate of the K(+) channel KcsA. Our analysis reveals a significant increase in the dynamics of the inner bundle gate upon opening. Also, it explicitly demonstrates the degree to which the CTD restricts the motion of the lower gate at rest and during activation gating.

Magnetization dynamics, throughput and energy dissipation in a universal multiferroic nanomagnetic logic gate with fan-in and fan-out

The switching dynamics of a multiferroic nanomagnetic NAND gate with fan-in/fan-out is simulated by solving the Landau–Lifshitz–Gilbert (LLG) equation while neglecting thermal fluctuation effects. The gate and logic wires are implemented with dipole-coupled two-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of ∼50 mV applied to the piezoelectric layer generating 10.1 MPa stress in the magnetostrictive layers for switching. We show that a pipeline bit throughput rate of ∼0.5 GHz is achievable with proper magnet layout and sinusoidal four-phase clocking. The gate operation is completed in 2 ns with a latency of 4 ns. The total (internal + external) energy dissipated for a single gate operation at this throughput rate is found to be only ∼500 kT in the gate and ∼1250 kT in the 12-magnet array comprising two input and two output wires for fan-in and fan-out. This makes it respectively three and five orders of magnitude more energy-efficient than complementary-metal–oxide–semiconductor-transistor (CMOS)-based and spin-transfer-torque-driven nanomagnet-based NAND gates. Finally, we show that the dissipation in the external clocking circuit can always be reduced asymptotically to zero using increasingly slow adiabatic clocking, such as by designing the RC time constant to be three orders of magnitude smaller than the clocking period. However, the internal dissipation in the device must remain and cannot be eliminated if we want to perform fault-tolerant classical computing.

Dynamics and sensitivity analysis of high-frequency conduction block

The local delivery of extracellular high-frequency stimulation (HFS) has been shown to be a fast acting and quickly reversible method of blocking neural conduction and is currently being pursued for several clinical indications. However, the mechanism for this type of nerve block remains unclear. In this study, we investigate two hypotheses: (1) depolarizing currents promote conduction block via inactivation of sodium channels and (2) the gating dynamics of the fast sodium channel are the primary determinate of minimal blocking frequency. Hypothesis 1 was investigated using a combined modeling and experimental study to investigate the effect of depolarizing and hyperpolarizing currents on high-frequency block. The results of the modeling study show that both depolarizing and hyperpolarizing currents play an important role in conduction block and that the conductance to each of three ionic currents increases relative to resting values during HFS. However, depolarizing currents were found to promote the blocking effect, and hyperpolarizing currents were found to diminish the blocking effect. Inward sodium currents were larger than the sum of the outward currents, resulting in a net depolarization of the nodal membrane. Our experimental results support these findings and closely match results from the equivalent modeling scenario: intra-peritoneal administration of the persistent sodium channel blocker ranolazine resulted in an increase in the amplitude of HFS required to produce conduction block in rats, confirming that depolarizing currents promote the conduction block phenomenon. Hypothesis 2 was investigated using a spectral analysis of the channel gating variables in a single-fiber axon model. The results of this study suggested a relationship between the dynamical properties of specific ion channel gating elements and the contributions of corresponding conductances to block onset. Specifically, we show that the dynamics of the fast sodium inactivation gate are too slow to track the high-frequency changes in membrane potential during HFS, and that the behavior of the fast sodium current was dominated by the low-frequency depolarization of the membrane. As a result, in the blocked state, only 5.4% of nodal sodium channels were found to be in the activatable state in the node closest to the blocking electrode, resulting in conduction block. Moreover, we find that the corner frequency for the persistent sodium channel activation gate corresponds to the frequency below which high-frequency stimuli of arbitrary amplitude are incapable of inducing conduction block.