Biophysical mechanism of spike threshold dependence on the rate of rise of the membrane potential by sodium channel inactivation or subthreshold axonal potassium current

Spike threshold filters incoming inputs and thus gates activity flow through neuronal networks. Threshold is variable, and in many types of neurons there is a relationship between the threshold voltage and the rate of rise of the membrane potential (dVm/dt) leading to the spike. In primary sensory cortex this relationship enhances the sensitivity of neurons to a particular stimulus feature. While Na⁺ channel inactivation may contribute to this relationship, recent evidence indicates that K⁺ currents located in the spike initiation zone are crucial. Here we used a simple Hodgkin-Huxley biophysical model to systematically investigate the role of K⁺ and Na⁺ current parameters (activation voltages and kinetics) in regulating spike threshold as a function of dVm/dt. Threshold was determined empirically and not estimated from the shape of the Vm prior to a spike. This allowed us to investigate intrinsic currents and values of gating variables at the precise voltage threshold. We found that Na⁺ inactivation is sufficient to produce the relationship provided it occurs at hyperpolarized voltages combined with slow kinetics. Alternatively, hyperpolarization of the K⁺ current activation voltage, even in the absence of Na⁺ inactivation, is also sufficient to produce the relationship. This hyperpolarized shift of K⁺ activation allows an outward current prior to spike initiation to antagonize the Na⁺ inward current such that it becomes self-sustaining at a more depolarized voltage. Our simulations demonstrate parameter constraints on Na⁺ inactivation and the biophysical mechanism by which an outward current regulates spike threshold as a function of dVm/dt.     

Role of maximum rate of depolarization in predicting action potential duration during ventricular fibrillation

During ventricular fibrillation (VF) only 39% of the variation in action potential duration (APD) is accounted for by the previous diastolic interval [DI((n-1))], i.e., restitution, and the previous APD [APD((n-1))], i.e., memory. We tested the hypothesis that a characteristic of the AP upstroke, the maximum rate of depolarization (V(max)), also helps account for its APD. A floating microelectrode was used to make transmembrane recordings at 16,000 samples/s from the anterior left ventricular wall during four 20-s episodes of VF in each of six pigs. V(max), time from V(max) to 60% repolarization (APD(60)), and DI were calculated throughout all episodes. Stepwise linear regression was used to determine how well each APD(60) (APD(60n)) was predicted by V(max) of that AP, the four previous DIs (n-1, n - 2, n - 3, n - 4), and the three previous APD(60)s (n-1, n - 2, n - 3). V(max) entered in the regression equation significantly more often (86% of VF episodes) than either APD((n-1)) (47% of episodes) or DI((n-1)) (58% of episodes). When these three variables entered first or second, their coefficients were almost always positive, consistent with a longer APD associated with 1) a larger V(max), 2) a longer APD((n-1)), and 3) a longer DI((n-1)). R(2) of the regression for all entered variables was 0.51 +/- 0.01 (mean +/- SD). During the first 20 s of VF in swine, V(max) is a more important determinant of APD than the previous DI (restitution) or the previous APD (memory). All variables together account for only one-half of APD variation during VF.     

The dependence of calcium-activated potassium currents on membrane potential.

Previous experiments on cholinergic synapses in chick cochlear hair cells have shown that calcium entering through acetylcholine-activated synaptic channels in turn activates calcium-dependent potassium currents, resulting in synaptic inhibition. In voltage-clamp experiments such currents would be expected to increase with depolarization (as the driving force for potassium entry is increased) and then decrease towards zero as the membrane approaches the calcium equilibrium potential (when calcium entry is suppressed). In the hair cells, however, such currents approached zero at about +20 mV, more than 170 mV negative to the calcium equilibrium potential. Another feature of the synapse is its post-junctional morphology: a uniform 20 nm cleft is formed between the postsynaptic membrane and the outermost membrane of an underlying cisterna. Here we present a model in which synaptic activation results in calcium influx into the subsynaptic cleft and thence into the bulk of the cytoplasm. The model suggests that the voltage dependence of the calcium-activated potassium current can be accounted for by only two basic assumptions: (i) entry of calcium through the activated synaptic channels by simple diffusion; and (ii) activation of the potassium channels by the cooperative action of four calcium ions. In addition, the model suggests that during activation the calcium concentration in the restricted subsynaptic space can reach levels adequate to activate the potassium channels, without requiring additional, more complicated, considerations (for example, secondary calcium release from the cisterna).     

The action of sinusoidally modulated light on the membrane potential of Acetabularia

Cells of the alga Acetabularia crenulata were illuminated withlight of sinusoidally modulated intensity of different frequenciesand changes in membrane potential were measured with microelectrodes.The frequency response, investigated in the range of frequenciesof 8 to 1/40 cycles/min, displayed the following features: 1.The slope of the frequency response is, according to our results,6 db/octave or steeper. Experiments should be extended to higherfrequencies to gain more information concerning the slope ofthe frequency response and, thus, of the number of reactionsin the series. 2. The time course of changes in membrane potentialcaused by light reveals non-linearities in time-scale and amplitude,indicating that not only first-order reactions are involved.3. Time constants are slightly influenced by the intensity oflight. 4. Further evidence is given that the characteristicof the action of light is logarithmic. 5. A phenomenon similarto resonance is observed, which corresponds to the overshootsgenerated by square-wave illumination. Models show that thisis not necessarily explained by feedback systems, but also bycounteracting parallel pathways (Received October 8, 1970; )     

Fast frequency-dependent block of action potential upstroke in rabbit atrium by small local anesthetics.

Local anesthetics depress the rapid depolarizing phase of atrial action potentials in a frequency-dependent manner. Several local anesthetics were tested in this study at doses that only slightly depressed atrial action potential upstrokes at the spontaneous rate near 2 Hz, but that produced marked reductions in atrial fiber upstrokes when the drive rate was increased to 5 Hz. This frequency-dependent blocking action, especially the rate of development of the block during the 5-Hz stimulus train, is compared for several local anesthetics that have a wide range of lipid solubilities. Although the rate of block development does not correlate well with lipid solubility, it does correlate with molecular weight or size of the local anesthetic molecule. Smaller local anesthetics give faster frequency-dependent blocking. The beta-blocker propranolol also induces a frequency-dependent block of action potential upstroke, with the speed of such block development being predictable on the basis of the molecular weight of propranolol. The design of fast frequency-dependent blockers by using the criterion of smaller molecular size represents an important new structure-activity relation that may very well help in the design of better antifibrillatory drugs.     

Re-evaluation of the action potential upstroke velocity as a measure of the Na+ current in cardiac myocytes at physiological conditions

Background

The SCN5A encoded sodium current (I_Na) generates the action potential (AP) upstroke and is a major determinant of AP characteristics and AP propagation in cardiac myocytes. Unfortunately, in cardiac myocytes, investigation of kinetic properties of I_Na with near-physiological ion concentrations and temperature is technically challenging due to the large amplitude and rapidly activating nature of I_Na, which may seriously hamper the quality of voltage control over the membrane. We hypothesized that the alternating voltage clamp-current clamp (VC/CC) technique might provide an alternative to traditional voltage clamp (VC) technique for the determination of I_Na properties under physiological conditions.

Principal Findings

We studied I_Na under close-to-physiological conditions by VC technique in SCN5A cDNA-transfected HEK cells or by alternating VC/CC technique in both SCN5A cDNA-transfected HEK cells and rabbit left ventricular myocytes. In these experiments, peak I_Na during a depolarizing VC step or maximal upstroke velocity, dV/dt_max, during VC/CC served as an indicator of available I_Na. In HEK cells, biophysical properties of I_Na, including current density, voltage dependent (in)activation, development of inactivation, and recovery from inactivation, were highly similar in VC and VC/CC experiments. As an application of the VC/CC technique we studied I_Na in left ventricular myocytes isolated from control or failing rabbit hearts.

Conclusions

Our results demonstrate that the alternating VC/CC technique is a valuable experimental tool for I_Na measurements under close-to-physiological conditions in cardiac myocytes.     

The mechanistic nature of the membrane potential dependence of sodium-sugar cotransport in small intestine

Summary Methods are described which demonstrate the use of unidirectional influx of¹⁴C-tetraphenylphosphonium (¹⁴C-TPP⁺) into isolated intestinal epithelial cells as a quantitative sensor of the magnitude of membrane potentials created by experimentally imposed ion gradients. Using this technique the quantitative relationship between membrane potential () and Na⁺-dependent sugar influx was determined for these cells at various Na⁺ and -methylglucoside (-MG) concentrations. The results show a high degree of dependence for the transport Michaelis constant but a maximum velocity for transport which is independent of . No transinhibition by intracellular sugar (40mm) can be detected. Sugar influx in the absence of Na⁺ is insensitive to 1.3mm phlorizin and independent of . The mechanistic implications of these results were evaluated using the quality of fit between calculated and experimentally observed kinetic constants for rate equations derived from several transport models. The analysis shows that for models in which translocation is the potential-dependent step the free carrier cannot be neutral. If it is anionic, the transporter must be functionally asymmetric. A model in which Na⁺ binding is the potential-dependent step (Na⁺ well concept) also provides an appropriate kinetic fit to the experimental data, and must be considered as a possible mechanistic basis for function of the system.     

Macromolecular rate theory explains the temperature dependence of membrane conductance kinetics

The factor Q₁₀ is used in neuroscience to adjust reaction rates of voltage-activated membrane conductances to different temperatures and is widely assumed to be constant. By performing an analysis of published data of the reaction rates of sodium, potassium, and calcium membrane conductances, we demonstrate that 1) Q₁₀ is temperature dependent, 2) this relationship is similar across conductances, and 3) there is a strong effect at low temperatures (<15°C). We show that macromolecular rate theory (MMRT) explains this temperature dependency. MMRT predicts the existence of optimal temperatures at which reaction rates decrease as temperature increases, a phenomenon that we also found in the published data sets. We tested the consequences of using MMRT-adjusted reaction rates in the Hodgkin-Huxley model of the squid’s giant axon. The MMRT-adjusted model reproduces the temperature dependence of the rising and falling times of the action potential. Furthermore, the model also reproduces these properties for different squid species that live in different climates. In a second example, we compare spiking patterns of biophysical models based on human pyramidal neurons from the Allen Cell Types database at room and physiological temperatures. The original models, calibrated at 34°C, failed to generate realistic spikes at room temperature in more than half of the tested models, while the MMRT produces realistic spiking in all conditions. In another example, we show that using the MMRT correction in hippocampal pyramidal cell models results in 100% differences in voltage responses. Finally, we show that the shape of the Q₁₀ function results in systematic errors in predicting reaction rates. We propose that the optimal temperature could be a thermodynamical barrier to avoid over excitation in neurons. While this study is centered on membrane conductances, our results have important consequences for all biochemical reactions involved in cell signaling.