Mechanisms and models of cardiac sodium channel inactivation

ABSTRACT Shortly after cardiac Na+ channels activate and initiate the action potential, inactivation ensues within milliseconds, attenuating the peak Na+ current, INa, and allowing the cell membrane to repolarize. A very limited number of Na+ channels that do not inactivate carry a persistent INa, or late INa. While late INa is only a small fraction of peak magnitude, it significantly prolongs ventricular action potential duration, which predisposes patients to arrhythmia. Here, we review our current understanding of inactivation mechanisms, their regulation, and how they have been modeled computationally. Based on this body of work, we conclude that inactivation and its connection to late INa would be best modeled with a “feet-on-the-door” approach where multiple channel components participate in determining inactivation and late INa. This model reflects experimental findings showing that perturbation of many channel locations can destabilize inactivation and cause pathological late INa.


Introduction
In atrial and ventricular myocytes, the Na C current (I Na ) initiates the action potential (AP) by depolarizing the membrane potential (V m ) from approximately ¡60 mV to C40 mV. The peak I Na determines the maximum upstroke velocity (dV m /dt max ) and thus the conduction velocity. 1 Within milliseconds (ms), most Na C channels inactivate and allow outward K C current to repolarize the membrane. The extent of Na C channel inactivation and the time to begin recovery from inactivation determines the absolute or effective refractory period (ARP, ERP) where AP initiation is not possible (Fig. 1). 2 Na C channel inactivation, recovery from inactivation, and associated deactivation further dictate the relative refractory period (RRP). The RRP describes a time period when sufficient Na C channels are available for reactivation and the V m is further repolarized so that a stronger stimulus may initiate the next AP. 2 When Na C channels do not inactivate completely, a measurable current of less than 0.5% of the peak current persists in the myocyte, known as late or persistent I Na . This current is sustained because it travels through Na C channels that do not inactivate completely, so they do not need go through recovery from inactivation. In large mammals, such as dogs and humans, late I Na significantly modulates AP duration (APD) by providing a sustained influx of depolarizing Na C , which disrupts the "delicate balance" between the inward (primarily L-type Ca 2C current) and outward K C currents of the AP plateau (Fig. 2). 3,4 Due to the length of the AP plateau, this late component can contribute approximately twice the Na C "load" over time compared with the peak current. 5,6 Because the fraction of channels that carry late I Na is small, minute changes to inactivation kinetics at normal heart rate will result in substantial changes to its magnitude, which will affect APD and facilitate (or prevent) anti-arrhythmic activity. APD prolongation based on altered Na C channel inactivation and enhanced late I Na is linked to arrhythmia in patients with inherited mutations, 7 heart failure, 8 and myocardial infarction. 9 The purpose of this paper is to review recent and classical findings that shed light on the molecular mechanisms of inactivation and its regulation, how inactivation determines late I Na , and how computational models may capture these mechanisms to connect them to arrhythmia mechanisms.

Mechanisms of inactivation
Hodgkin and Huxley clearly recognized the concept of I Na inactivation in 1952 during the first recordings of the axon I Na and modeled it as a monoexponential time and voltage-dependent decay. 10 Work with NaF perfused axons first identified late I Na , which was especially pronounced during depolarizations to elevated potentials, suggesting two components of inactivation. 11,12 Subsequent work identified additional components of inactivation that span many time domains, indicative of multiple relaxations. The fast component became known as fast inactivation (< 10 ms), while intermediate (»100 ms), slow (1 s to 1 min), and ultra-slow (> 1 min) inactivation defined components of inactivation with longer time domains. 13 During an AP, fast inactivation reduces the current to »0.5% of the peak within millseconds. 6 Cardiac Na C channels display reduced slow or ultraslow inactivation compared with neuronal channels, consistent with their essential role in initiating the heartbeat. 14 Over the remainder of the AP, intermediate inactivation will continue to diminish late I Na until Na C channels begin to deactivate at negative potentials (below -60 mV). 13 Sustained effort has been applied to measuring inactivation in these different time domains and connecting it to its molecular determinants within the Na C channel.
Much of the work to elucidate effects on Na C inactivation kinetics was conducted using voltage clamp techniques on Na C channels in various expression systems. One must use caution when examining Na C kinetic inactivation data because the voltage clamp measurements require adjustments for artifacts, and leak during recording may affect measurement of the late I Na .
Measurement of tetrodotoxin (TTX) sensitive currents is commonly used to correct for membrane leak because it is particularly effective on the late I Na compared with the peak I Na . 15 These experiments work by subtracting currents with TTX added from the control current to isolate the sensitive components. However, the cardiac Na C channel (Na V 1.5) is not particularly sensitive to TTX, so there are two possibilities to explain this enhanced sensitivity. First, the late I Na may be carried by neuronal Na C channels, which are highly TTX sensitive. 16 Another possibility is that Na C channels with altered inactivation may inherently be more sensitive to TTX. Further work is needed to distinguish between these two scenarios to precisely Figure 1. A representative action potential (AP) depicting the corresponding extent of Na C channel inactivation (gray dashed line) with labeled absolute (ARP) and relative (RRP) refractory periods. Stimulation immediately after the initial AP results in shortened APs with reduced peak membrane potential (V m ) and peak Na C current (I Na ). Once the Na C channels have recovered sufficiently, they may be reactivated to elicit another full strength AP.
identify which channels are primarily carrying the late I Na .
Further confounding the measurement of Na C current, larger cells require a significant amount of time to charge the membrane to a certain potential. This slow charging is problematic when recording rapid Na C channel activation kinetics, which are tightly coupled to inactivation kinetics. The cut-open Vaseline gap voltage clamp addresses this difficulty by isolating a patch of large oocytes for recording. 17,18 In smaller cells, such as HEK cells, the patch clamp technique requires compensation for the resistance of the recording electrode and access to the cell, and even then, voltage artifacts are present when recording large currents, making peak current measurements unreliable. 19 Whatever the expression system, it is always difficult to clamp the V m when examining fast, large inward currents because during a depolarizing pulse the inward I Na is moving the potential in the same direction as the amplifier, creating unstable positive feedback. 20 These challenges in recording I Na are likely responsible for significant variability in published results, particularly regarding the magnitude of the late I Na , which relies on an accurate measure of the peak I Na .
Functional voltage-gated Na C channels (Na v ) include nine isoforms that are formed by an a-subunit that comprises four homologous domains (DI-DIV) each with six helical membrane-spanning segments (S1-S6) (Fig. 3). 21,22 In addition to Na v 1.5 in cardiac tissue and Na v 1.4 in the skeletal muscle, seven other isoforms are expressed in the nervous system. 22 Within each domain, S1-S4 form the voltage sensing domain (VSD), which senses changes in V m , and S5-S6 form the pore that allows for selective passage of Na C ions. In the VSD, S4 contains positive charges, usually arginines, that are thrust outward upon membrane depolarization. These voltage-dependent conformational changes are tightly coupled to the activation, inactivation, deactivation, and recovery from inactivation of the Na C channel. Intracellular linkers attach each domain to the next, connect the channel to the cytoskeleton and intracellular signaling pathways, and regulate channel gating. The C-terminus is composed of a structured proximal portion and unstructured distal portion. 23,24 The structured portion has six a-helices that form an EF hand-like structure (a helices 1-5) and an IQ motif which surprisingly has higher calcium binding affinity than the EF-hand (a helix 6). 24 Clever experiments with intracellularly applied pronase, a non-specific protease, demonstrated that the fast inactivation gate is located on the intracellular face of the Na C channel. 25 Intracellular pronase perfusion removed inactivation while preserving I Na activation and deactivation. After the Na C channel was cloned, further work showed that Figure 2. Major currents participating in the action potential (AP) plateau. Late I Na is very effective at modulating the action potential duration (APD) because the other participating currents are relatively small and balance each other out, increasing membrane resistance and reducing the magnitude of dV m /dt max. 142 Representations of the cardiac Na C current (I Na ), the L-type Ca 2C channel (I Ca,L ), the rapid and slow delayed rectifier K C channels (I Kr and I Ks ), the inward rectifier K C channel (I K1 ), and current generated by the Na C -Ca 2C exchanger are shown during the AP.
antibodies, 26 cleavage, 27 and additions 28 to the intracellular DIII-DIV linker were sufficient to inhibit inactivation, and a primarily hydrophobic motif identified through site-directed mutagenesis on the linker is crucial for successful fast inactivation (IFMT): I-1488, F-1489, M-1490, and T-1491. [29][30][31] Sulfhydryl accessibility studies showed that F1489 becomes inaccessible during fast inactivation, 32 and the interaction between the channel and the motif is hydrophobic. 30 Smaller residues containing glycine and proline provide the flexibility for a "hinged lid" or "chain" that allows IFMT to occlude the channel. 33 How and where the DIII-DIV linker and these primarily hydrophobic residues interact with the rest of the channel has remained a key topic of research for many years.
Gating current recordings have yielded critical insights into the DIII-DIV linker interactions with the VSDs. The gating current arises from the rapid movement of the S4 charges within membrane, which enables their detection. 34 Early gating current recordings showed that two-thirds of the gating charge, which is measured as the integral over time of the gating current, is immobilized when fast inactivation occurs, suggesting a connection between the VSDs and inactivation. 35 The application of voltage clamp fluorometry (VCF) to Na V channels has allowed monitoring of each VSD individually, rather than the summation of their movement reported by the gating current. 36,37 During VCF experiments, a fluorophore is attached to the S4 segment of a domain. When a potential is applied, S4 displacement results in a change of environment around the fluorophore, which is detected as a deflection in the fluorescence intensity with a high dynamic range amplifier. Using VCF, Cha et al. showed that the voltage-dependent kinetics of the DIII and DIV VSDs are modulated by inactivation. 37 Site-directed mutagenesis has provided additional insights, showing inactivation can also be modulated by the S4-S5 linkers of DIII and DIV. A conserved alanine on the Na v 1.2 DIII S4-S5 linker severely disrupted inactivation when it was mutated to glutamine and was proposed to serve as a hydrophobic "docking" site for the IFMT motif. 38 Further work showed that some patients with long QT type 3 syndrome, which increases late I Na , carry a mutation to a homologous conserved alanine within this linker in Na v 1.5. 39 The DIV S4-S5 has also been shown to significantly affect inactivation and suggested as a potential "docking" site for the inactivation gate. 40,41 Confoundingly, accessibility studies with Na v 1.4 showed that both the DIII S4-S5 and DIV S4-S5 linkers remain accessible when channels are inactivated. 40,42 Mutagenesis work also aided in demonstrating that the S6 segments of DI, DII, and DIV modulate fast inactivation. An alanine-mutagenesis study showed that mutations in the center 43 and in intracellular 44 end of DIV S6 segment in Na v 1.2 inhibited inactivation. Double mutations within the center and intracellular end of DIV S6 exhibit more inactivation inhibition, but the IFMT does not likely interact with the S6 segments as changing the hydrophobic characteristics of the mutations did not affect the phenotype. Mutations in the intracellular end of DIS6 and DIIS6 in Na v 1.2 also inhibit fast inactivation 45 while no mutations were found in DIIIS6. 46 Finally, work with tryptophan scanning mutations in Na v 1.4 in the DI and DIV S6 segments identified the "WCW" window located on the intracellular DI S6 segment that impairs fast inactivation. 47 The C-terminus also plays an important role in modulating Na C channel inactivation. 48 Generally, each Na C channel homolog has distinct fast inactivation kinetics. For example, Na v 1.5 fast inactivation is slower than Na v 1.4 due to differences in amino acid sequences in the C-terminal domains. 49 In addition, swapping C-terminal domains between Na v 1.5 and Na v 1.2 causes a shift in voltage-dependent steady-state inactivation toward the potential of the original isoform. 50 Mutations in the C-terminal domain have also been shown to disrupt fast inactivation and cause cardiac arrhythmias such as long QT syndrome. 51,52 Work with truncated C-terminal mutants identified the importance of the sixth helix and the distal portion in inactivation regulation. When just the distal, unstructured portion of the C-terminus was removed, inactivation was not affected; however, when the distal portion along with the sixth helix were removed, inactivation was inhibited. 23 Pull-down assays confirmed that the DIII-DIV linker interacts with the sixth helix and distal portion of the C-terminus, and mutagenesis showed that the interaction likely stabilizes the inactivated state. 53 Toward the goal of understanding how various channel domains regulate Na V channel gating, recent VCF experiments have shown that DIV-VSD translocation serves as a rate limiting step to initiate fast inactivation. 54 Later results also showed that the VSDs of DI-DIII are also likely involved with slower components of inactivation. 55,56 Work with inactivation deficient mutations shows that the DIII-VSD also participates in fast inactivation but only after pulses with durations of 100s of ms. 57,58 Together these results suggest a model where the hydrophobic IFM sequence of DIII-DIV linker quickly associates with DIV-VSD to initiate fast inactivation (Fig. 4). After about 100 ms, the DIII-DIV linker then associates with the DIII-VSD and supports its activated conformation. This late association will stabilize the inactivated state, causing a reduction in late I Na .
The above results show that Na v inactivation is a complex phenomenon that involves locations across the a-subunit. The various structures participating inactivation are highlighted in Fig. 3. The primary structure of fast inactivation is the DIII-DIV linker, which physically occludes the intracellular mouth of the channel. The linker's IFMT motif mediates successful occlusion through hydrophobic interactions between the linker and the channel. While the DIII-DIV linker occludes the pore, various structures across the a-subunit modulate the extent of inactivation and therefore late I Na : the DIII and DIV VSDs, the DI and DIV S6 segments, and the C-terminal domain.

Regulation of inactivation by accessory subunits
Na C channel inactivation is not only modulated by a-subunit structures, but also by external factors, such as accessory subunits and the external environment. These may regulate inactivation alone or in combination with the a-subunit. . Inactivation is significantly determined by the DIII and DIV VSDs. 57 After channel activation, IFM associates with the DIV-VSD to control inactivation onset. After »100 ms, the IFM also associates with the DIII-VSD, supporting its activated conformation. Only after the IFM dissociates from the DIII and DIV VSDs. © Hsu et al. Adapted by permission of the CC BY 4.0 license. Permission to reuse must be obtained from the rightsholder. 57 .
The most studied interacting partners of the Na v a-subunit are the b-subunits, which are found in complex with the Na V channel a-subunit after purification. There are five types of voltage-gated Na C channel b-subunits (b1-4 and b1b, a splice variant of b1). [59][60][61][62][63] All b-subunits, with the exception of b1b, are composed of an extracellular immunoglobulin domain, a transmembrane segment, and an intracellular C-terminus. 64 b1b is missing the transmembrane segment. 65 The b1 and b3 subunits interact noncovalently with a-subunit 62,66 while b2 and b4 covalently bind to a subunit through disulfide bonds. 64,67 The expression level for each b-subunit is tissue and cell-specific with varying patterns over the course of development. [68][69][70] While each b-subunit paralog causes an increase in channel expression, the regulation of biophysical properties including voltage-dependence of activation and inactivation, rate of inactivation, recovery from inactivation, and magnitude of persistent and resurgent I Na are unique. 63,64,[71][72][73][74] Very recent structures of the Na v 1.4-b1 complex in the electric eel show that the immunoglobulin domain of the b1 subunit interacts with the extracellular loops of the DI and DIV pore domain while the transmembrane domain interacts with the DIII-VSD. 75 This structure serves as a basis for determining how b1-subunit interactions with the a-subunit mediate biophysical property regulation. 75 However, the interactions revealed by this structure failed to elucidate how b1 regulates channel inactivation, suggesting that kinetic data are essential for fully understanding regulation of the channel by b subunits. Concurrently, we used the VCF technique to assess the modulation of Na C channel VSD conformations by b1 and b3 during gating. 76 The b1 subunit caused the DIV-VSD to activate at higher potentials. Because the DIV-VSD activation has been connected to fast inactivation onset, modulation of the DIV-VSD by b1 explains why it affects channel inactivation. Intriguingly, despite the sequence homology between the b1 and b3 subunit, the b3 subunit controls the DIII-VSD along with the DIV-VSD. This additional interaction with the DIII-VSD allows b3 to alter both current activation and inactivation kinetics.
The regulatory effects of b-subunits on Na C channel inactivation are system and cell type specific. As a result, there are many conflicting results regarding the magnitude and direction of the inactivation shifts by different b-subunits. 77 These discrepancies likely reflect the fact that a-subunits interact not only with b-subunits but also with many other modulating proteins that altogether form the macromolecular Na C channel complex. 78 Multiple Brugada syndrome-associated mutations have been identified in SCN1B (encoding for b1 subunit, E87Q, and b1b subunit H162P, W179X, R214Q), SCN2B (encoding for b2 subunit, D211G), and SCN3B (encoding for b3 subunit, L10P, V110I). 65 Patients with the Brugada syndrome often have reduced I Na , which can lead to arrhythmia through a variety of mechanisms. 79 These mutations can cause I Na reduction by lowering I Na density, due to a hyperpolarizing shift in steady-state inactivation or altering inactivation onset and recovery rates. 65 In contrast, mutations in b4 (L179F) and b1B (P213T) that are associated with long QT syndrome cause a depolarizing shift in steady-state inactivation. 80 These mutations lead to increased channel availability and elevated late I Na , which prolongs the ventricular AP and therefore the QT interval.
Work with various Na v b-subunit knockout mouse models have also revealed associated cardiac abnormalities. The Scn1b null mouse model exhibited increased APD and prolonged QT intervals with transient and persistent peak I Na . 81 Scn2b null mice showed reduced I Na density with slower conduction velocity and repolarization in the right ventricular outflow tract, leading to ventricular arrhythmia. 82 The Scn3b null mice also displayed cardiac abnormalities such as reduced peak I Na and altered sinoatrial node recovery. 83,84 Together, these findings demonstrate the physiologic relevance of b-subunits on the regulation of Na C channel biophysical properties including inactivation, reactivation, and recovery.
Other than Na V b-subunits, the Na V a-subunit is associated with plethora of auxiliary subunits for additional regulatory effects. One prominent auxiliary subunit well known to bind the Na V a-subunit C-terminal domain is calmodulin (CaM). 85 CaM is a bi-lobed, »17 kDa protein which functions as a ubiquitous Ca 2C sensing protein. 86 Therefore, CaM association to Na V channels may endow the channels with Ca 2C regulation. The leading hypothesis concerning the nature of Ca 2C regulation of Na V channels involves shifts in the steadystate inactivation, thus tuning Na C channel availability depending on levels of intracellular Ca 2C . 87 Despite extensive characterization, Ca 2C regulation of Na V channels appear to be idiosyncratic and isoform specific. [88][89][90][91] Elevated intracellular Ca 2C has been reported to induce a depolarizing shift in the steady-state inactivation of Na V 1.5, 89,92-94 but other studies reported no shift in the steady-state inactivation of Na V 1.5 in response to elevated intracellular Ca 2C . 88,91 Furthermore, elevated intracellular Ca 2C levels were reported to induce a hyperpolarizing shift in the steady-state inactivation in Na V 1.4. 88 Just as the functional effect of Ca 2C on Na V channel is controversial, the mechanism behind Ca 2C regulation of Na V channels is also debated. Ca 2C has been proposed to directly bind the C-terminal domain of Na V a-subunit to exert regulatory effect independent of CaM. 92 Other models proposed that upon Ca 2C binding, Ca 2C /CaM interacts with DIII-DIV linker to induce regulation of steady-state inactivation. 95 Overall, the question of whether Ca 2C itself, or the ion in complex with CaM, regulates Na C channel inactivation remains a controversial topic.
A group of four proteins, fibroblast growth factors (FGF [11][12][13][14], also referred to as fibroblast growth homologous factors (FHFs 1-4), interact with the C-terminal domain in the Ca 2C -CaM complex. 96,97 FHFs are differentially expressed in various tissues and lack the N-terminal signal sequence, causing them to remain in the cytoplasm and allowing them to regulate Na V and Ca 2C channels. 78,96,98 Work with FHF1B demonstrated that its interaction with the C-terminal domain of Na v 1.5 produces a hyperpolarizing shift in steady-state inactivation, and the mutation D1790G, which is already associated with the long QT type 3 syndrome, interrupts interaction between FHF1B and the C-terminus. 99 In addition, a mutation in Na v 1.5 that interrupts FHF binding to the Cterminal domain displayed slowed inactivation kinetics, resulting in increased late I Na and prolonged APD. 100 As can be appreciated from the results discussed above, many different accessory subunits can regulate Na V channel inactivation and disruption of this regulation leads to deadly arrhythmias. Fig. 5 presents a pictorial representation of accessory subunits involved in modulating inactivation. A precise understanding of how accessory subunits regulate inactivation will prove challenging because the channels are composed of subunits that interact with each other. However, this work will lead to an improved understanding of diseased states and potentially new therapeutic routes.

Environmental regulation of inactivation
Acidosis and febrile states are both environmental factors that alter cardiac electrical activity by shifting Na C channel inactivation properties. These effects are often exacerbated by underlying Na V 1.5 mutations, which can lead to life-threatening phenotypes. [101][102][103] In physiologic conditions, human arterial blood pH is maintained at approximately 7.4. 101 If pH drops just 0.05 units, protein function may be altered, 101 and pH below 6.95 results in deleterious effects on protein function in cardiomyocytes. 101 During cardiac ischemia, myocytes experience pH as low as 5.9. Reduced extracellular pH due to arterial blood acidosis has been shown to reversibly destabilize the fast-inactivated state in wild-type Na V 1.5 channels, leading to increased window current and increased late I Na , and to destabilize the slow inactivated state. 101,104 Specifically, proton block of wild-type channels accelerates the recovery from open state fast inactivation and delays its onset. 101,102 In silico studies have demonstrated that these effects on wild-type channels can be sufficient to prolong the AP and decrease its maximum upstroke Figure 5. Accessory subunits involved in modulating Na v 1.5 inactivation: b-subunit (green), 59 velocity, which affects conduction velocity. 1,103,105 Both AP effects predispose patients to arrhythmia. 103,106 The conclusions from these modeling studies have been strengthened by multiple reports of Brugada syndrome phenocopy induced by acidosis. 107,108 When the patient's blood pH returned to physiologic conditions and electrolytes were balanced, the Brugada syndrome characteristic ECG was no longer present. 108 Certain Na v 1.5 mutations that cause long QT or Brugada syndromes result in APs that are more sensitive to acidosis. 109,110 Studies have shown that a low pH environment in combination with these underlying mutations exacerbates the electrical abnormalities in individuals. 103 For example, decreased extracellular pH paired with E1784K, the most common SCN5A (encoding for Na v 1.5) mutant linked to both Brugada syndrome and LQT3, leads to significantly larger increases in late I Na due to more severe alterations to the channel inactivation. 109 Other groups have shown that certain long QT type 3 syndrome mutations are more sensitive to intracellular acidosis than others. 111 Another environmental factor modulating the Na C channel is body temperature. In healthy humans, without underlying mutations in Na v 1.5 or other conditions, temperature-dependent cardiac abnormalities may occur in extreme hyperthermia but seldom when they experience a mild fever. 112,113 In contrast, individuals with Na V channel mutations are more sensitive to core body temperature fluctuations with their susceptibility to arrhythmia being dependent on the mutation that they carry. 110,114,115 Several studies have shown that hyperthermia has detrimental effects on asymptomatic Brugada syndrome patients causing Brugada syndrome ECG patterns to be unmasked under febrile conditions and remain unmasked when core body temperature is restored. 116,117 Other clinical studies have presented in patients who only possessed a Brugada syndrome ECG pattern while in the febrile state. 118,119 While the mechanisms responsible for this phenomenon are still under investigation, it is known that elevated temperature increases the rate of fast inactivation recovery and onset for wild-type Na C channels, which leads to decreased late I Na . 114,116 The T1620M missense mutation found in SCN5A alters the temperature sensitivity of Na C channel fast inactivation in patients with Brugada syndrome. As temperatures increase toward the physiologic range, these mutant cardiac Na C channels demonstrate slower recovery from inactivation, leading to further loss of function of I Na . 115 Q10 extrapolation results suggest that febrile states would elicit worsening of this mutant's inactivation properties and become more arrhythmogenic.
However, studies of different SCN5A mutations suggest that febrile states do not worsen these mutation effects. 116 Keller et al. demonstrated patients who had fever-induced type 1 Brugada syndrome and fever-induced arrhythmias also possessed mutations, such as R535X and L325R, which result in severe to absolute loss of I Na at physiologic temperature. Thus, the study suggested that fever could not make the channel function any worse, and fever did not significantly worsen the biophysical changes to the channel. Therefore, the authors hypothesized that in heterozygous patients, possessing both wildtype and mutated Na C channels, the effect of temperature accelerating the inactivation of the wildtype channels, not the effect on mutant channels, is responsible for altering the delicate balance of depolarization and repolarization currents and thus may lead to fever-induced arrhythmias. This hypothesis is supported by Gima and Rudy's modeling study which demonstrated that accelerated inactivation, a consequence of fever, of the T1620M Na V 1.5 mutant channel causes a Brugada syndrome pseudo ECG phenotype through the resultant decrease in late I Na combined with the already reduced peak I Na from the mutant channel. 116,120 Regardless of whether a SCN5A mutant makes a channel more sensitive to temperature effects, it is evident that febrile temperatures in combination with mutations increase the risk of fever-induced arrhythmias, particularly from asymptomatic Brugada syndrome patients.
Temperature-dependent cardiac electrical abnormalities are not limited to mutations in SCN5A. A recent study identified FHF2, a member of the FHF protein family known to modulate voltage-gated Na C channel inactivation as previously discussed, as a key regulator of myocardial excitability that prevents conduction failure in mouse heart under hyperthermic conditions. 121,122 Loss of FHF2, accelerates the rate of both open state and closed state inactivation of the Na C channel. This change becomes functionally relevant under febrile temperatures when temperature dependence increases the inactivation rate, resulting in severely suppressed I Na and ultimately conduction failure.
Environmental factors, such as acidosis and temperature, have significant effects on Na C channel inactivation and are depicted in Fig. 5. Patients already harboring mutations for cardiac abnormalities, such as long QT or Brugada syndromes, often exhibit aggravated symptoms when subject to acidosis or hyperthermia. Understanding how environmental factors combine with channel structure to disrupt inactivation may lead to better clinical strategies for preventing these pathological situations.

Models of inactivation
Modeling of Na V channel inactivation began with Hodgkin and Huxley's work in 1952 with the squid giant axon. 10 When analyzing the Na C conductance curves, they inferred that Na C conductance could be represented by a product of probabilistic gates, which required residence in a permissive conformation for conduction to occur. These gates could regulate either activation, with initial and maximum values of zero and one, respectively, or inactivation with hyperpolarized and depolarized values of one and zero, respectively. Hodgkin and Huxley found that the product of 3 activation gates and one inactivation gate adequately described the conductance curves. Under this model, 3 of 4 domains had an activation gate that must open for conduction to occur, and one domain had a gate that would close to mimic inactivation. Because conductance was represented as product of activation and inactivation, the activation and inactivation processes were assumed to be independent. While we now know that activation and inactivation are instead coupled, this idea that three domains primarily control activation and one primarily controls inactivation is still useful. 123 Chandler and Meves' later work in 1970 suggested multiple components of Hodgkin and Huxley's inactivation gate. 11,12 Their work with NaF perfused squid axons demonstrated that large depolarizations resulted in less steady-state inactivation and thus maintained late I Na . They suggested amending Hodgkin and Huxley's single inactivation gate model to an inactivation gate with two components to account for transient peak in Na C channel conductance upon activation followed by sustained late conductance. Further, they suggested that the Na C channel may have two open states with a higher and lower probability of conductance.
As mentioned previously, the early pronase experiments, which localized inactivation to the intracellular part of the channel, suggested the use of a "inactivation particle" that would physically occlude the channel. 25 Several years later, a study on gating charge movement suggested that inactivation immobilizes two thirds of the gating charge, but the inactivation process itself is not associated with any gating current. 35,124 Because a voltage-dependent process produces an associated gating current, and inactivation lacks this associated gating current, Armstrong and Bezanilla concluded that inactivation must be a voltage-independent process, which is contrast to Hodgkin and Huxley's original theory. 35 Additionally, because the fast time component of activation moves more than half of the total gating charge, and inactivation immobilizes two thirds of the total gating charge, Armstrong and Bezanilla deduced that inactivation must immobilize gating charge that was moved by channel activation. Thus, the processes of activation and inactivation are coupled. Combining these results led to the "ball and chain model" of inactivation. This model proposes that a "ball," tethered to the intracellular channel by a polypeptide "chain," occludes the mouth of the channel to bring about fast inactivation only after activation. 35 The discovery of the IFMT motif on the DIII-DIV linker crucial for successful fast inactivation suggested that the "ball and chain" model of inactivation needed updating. First, the determination that a primarily hydrophobic IFM motif controls successful inactivation demonstrates that hydrophobic interactions occlude the pore rather than the proposed electrostatic attraction between the inactivation particle and channel. 29 Second, structural studies determined that the middle of the DIII-DIV linker has an a-helical structure containing the IFMT motif, which is flanked by glycines N-terminally and prolines C-terminally. 29,31 This structure and residue sequence suggests that the DIII-DIV linker functions as a "hinged lid" to occlude the pore instead of the "loosely tethered" blocking ball. In the "hinged lid" model of inactivation the DIII-DIV linker closes in on its "hinges," composed of glycine or proline, to block the intracellular mouth of the channel. 29 West further suggests that the IFM sequence serves as a hydrophobic "latch" to keep the lid closed.
Data collected from single-channel recordings in the giant squid axon in combination with the gating charge data required Markov type models that include statedependent transitions to simulate their results. 125,126 Experimental recordings kinetics confirm that transitions between hypothetical states can be made sufficiently fast for a valid state-dependent representation of Na C channel processes such as inactivation. 127 Markov models are also more generalizable and allow for activation and inactivation to be modeled as a coupled process and may be reduced to the Hodgkin-Huxley formalism if desired for simplicity. 128 The earliest models incorporating inactivation included 3 states: an open, closed, and inactivated state. 125,126 Vandenberg and Bezanilla in 1991 created a Markov-type model of I Na with data from single-channel recordings in the giant squid axon. 129 The recordings showed that channels not only inactivate from the open state but also from the closed state as well. In addition to adding transitions between inactivated, closed and open states, the models incorporated reversible inactivation along multiple closed states for better fits to recordings. Rate constants were obtained from the single-channel recordings using maximum likelihood analysis and scaled up to yield macroscopic gating and channel currents.
In the spirit of Chandler and Meves' observations of two types of Na C channel conductance in 1970, Keynes detailed a "mode switching hypothesis" to explain inactivation. 130 This hypothesis included two open states: one initial open state with a high probability of opening and a second open state with a lower probability of opening. He proposed that "modulation of energy wells" rather than movement of an inactivating particle to block the channel pore would theoretically explain the transition from the first open state to the second. Practically, he suggested that "voltage sensor S4d" drives the channel to a second open state through "lateral movement" or deionization of charge. This theory is in accordance with the finding that fluorescence signals near the DIV-VSD are associated with the slow component of gating and appear after signals associated with the faster component of gating (DI-DIII). 131 Keynes defended his "mode switching" hypothesis based on new evidence suggesting Na C channels maintain conductance even during inactivation. 132 He also cited single channel recordings from Vandenberg and Bezanilla 1991 to support his theory. 129 The recordings depict a channel with multiple openings initially after activation, but with time the number of openings would decrease. He thought this channel behavior would be best captured by a model with two open states. Later Keynes (1998) updated his model to include recent mutation studies suggesting that DIV S4 movement controls the onset of fast inactivation, or in other words, the initial transition from the first to the second open state. 133 He further proposed that the hydration of the Na C channel would control the transition from the second open state into an inactivated state. He finally suggested that the DIII-DIV linker controls the "hydration equilibrium" that eventually closes the channel.
Finally, the discovery of inherited long QT syndrome mutations that impair Na C channel inactivation informed a new generation of models. In 1999, Clancy and Rudy simulated the DKPQ channel using a Markov type model. 134 This mutation is in the DIII-DIV linker, and single channel recordings showed that the channel could enter a bursting state where inactivation fails to inactivate. To model this behavior, a six-state wild-type model was extended to include a "burst mode" that represents channel that fail to inactivate. Once a channel entered the "burst mode," the channel lost its access to inactivation until it exited, producing late I Na. . The model successfully recapitulated single channel data and reproduced the cell level behavior producing a prolonged APD, consistent with the long QT phenotype.

Toward molecularly detailed models of inactivation
While recent models are capable of recapitulating single channel behavior, they conflict with experimental evidence that shows that many different channel locales contribute to channel inactivation. Specifically, the models suggest that a specific, identifiable switch causes the channel to enter a mode where inactivation is impossible.
In contrast, the experimental findings detailed above suggest that several different channel domains contribute to inactivation during an AP. During the first few ms the DIV-VSD activates, enabling fast inactivation, which closes most of the channels. Subsequently, at least the DIII-VSD and C-terminal domain stabilize the inactivated conformation, causing more channels to occupy a non-conducting state. This mechanism is reminiscent of the "foot-on-the-door" mechanism used to explain Cd 2C ions promoting closure of the ultraslow inactivation gate in Na v 1.4. 135 However, instead of a single foot on the door, there are at least two feet, the C-terminal domain and the DIII-VSD that stabilize the inactivated state. Fig. 6 compares the traditional and the "feet-on-the-door" models of inactivation. The traditional model suggests that a switch induces the channel to enter a mode where inactivation is not possible while the "feeton-the-door" model suggests that increased late I Na is a consequence of one of the feet failing to stabilize the inactivated state. Because this model suggests that disruption of many different stabilizing events can cause increased late I Na , it explains why mutations in various channel locations can augment late I Na .
The creation of computational models that explicitly represent the molecular determinants of inactivation will not be trivial because each of these components cooperatively interact with each other, significantly increasing model complexity. Recent developments in channel optimization algorithms may be helpful in this effort. 136,137 One potential approach to create a Markov type model with a large training set is to use statemutating optimization routine. Instead of fixing the model topology which may overcomplicate the optimization, the routine identifies the optimal number of states along the corresponding rate parameters. 136 Using the matrix exponential to compute cost saves time compared with using standard ODE solvers during the optimization. 137 This expedited cost computation allows for larger sets of training data to be recapitulated in a reasonable amount of time.
While the challenge of creating molecularly based models of inactivation is not insignificant, there are many potential rewards. Because computational models of channels are readily incorporated into multiscale cell and tissue models, 136,138 this approach could be used to identify how inactivation should be targeted therapeutically to stabilize excitation at the tissue level to prevent arrhythmia. As additional structural data emerges, including the Cryo-EM structure of a mammalian Na V channel, 139 conformational data from fluorescence experiments, 140 and even NMR data showing channel dynamics, 141 these models will only improve, provided that the computational approaches needed to incorporate this type of information into the models continue to be developed in parallel.

Disclosure of potential conflicts of interest
No potential conflicts of interest were disclosed.