Voltage gating by molecular subunits of Na+ and K+ ion channels: higher-dimensional cubic kinetics, rate constants, and temperature

The structural similarity between the primary molecules of voltage-gated Na and K channels (alpha subunits) and activation gating in the Hodgkin-Huxley model is brought into full agreement by increasing the model's sodium kinetics to fourth order (m3 → m4). Both structures then virtually imply activation gating by four independent subprocesses acting in parallel. The kinetics coalesce in four-dimensional (4D) cubic diagrams (16 states, 32 reversible transitions) that show the structure to be highly failure resistant against significant partial loss of gating function. Rate constants, as fitted in phase plot data of retinal ganglion cell excitation, reflect the molecular nature of the gating transitions. Additional dimensions (6D cubic diagrams) accommodate kinetically coupled sodium inactivation and gating processes associated with beta subunits. The gating transitions of coupled sodium inactivation appear to be thermodynamically irreversible; response to dielectric surface charges (capacitive displacement) provides a potential energy source for those transitions and yields highly energy-efficient excitation. A comparison of temperature responses of the squid giant axon (apparently Arrhenius) and mammalian channel gating yields kinetic Q10 = 2.2 for alpha unit gating, whose transitions are rate-limiting at mammalian temperatures; beta unit kinetic Q10 = 14 reproduces the observed non-Arrhenius deviation of mammalian gating at low temperatures; the Q10 of sodium inactivation gating matches the rate-limiting component of activation gating at all temperatures. The model kinetics reproduce the physiologically large frequency range for repetitive firing in ganglion cells and the physiologically observed strong temperature dependence of recovery from inactivation.

How Hyperpolarization and the Recovery of Excitability Affect Propagation through a Virtual Anode in the Heart

Researchers have suggested that the fate of a shock-induced wave front at the edge of a “virtual anode” (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

Sequential Memory: A Putative Neural and Synaptic Dynamical Mechanism

A key issue in the neurophysiology of cognition is the problem of sequential learning. Sequential learning refers to the ability to encode and represent the temporal order of discrete elements occurring in a sequence. We show that the short-term memory for a sequence of items can be implemented in an autoassociation neural network. Each item is one of the attractor states of the network. The autoassociation network is implemented at the level of integrate-and-fire neurons so that the contributions of different biophysical mechanisms to sequence learning can be investigated. It is shown that if it is a property of the synapses or neurons that support each attractor state that they adapt, then everytime the network is made quiescent (e.g., by inhibition), then the attractor state that emerges next is the next item in the sequence. We show with numerical simulations implementations of the mechanisms using (1) a sodium inactivation-based spike-frequency-adaptation mechanism, (2) a Ca2+-activated K+ current, and (3) short-term synaptic depression, with sequences of up to three items. The network does not need repeated training on a particular sequence and will repeat the items in the order that they were last presented. The time between the items in a sequence is not fixed, allowing the items to be read out as required over a period of up to many seconds. The network thus uses adaptation rather than associative synaptic modification to recall the order of the items in a recently presented sequence.

Simulation of Different Firing Patterns in Paired Spider Mechanoreceptor Neurons: The Role of Na+ Channel Inactivation

The spider VS-3 slit-sense organ contains two types of primary mechanoreceptor neurons that are morphologically similar but have different electrical behavior. Type A neurons fire only one or two action potentials in response to a mechanical or electrical step of any amplitude above the threshold, whereas type B neurons fire prolonged bursts of action potentials in response to similar stimuli. Voltage-clamp studies have shown that two voltage-activated ion currents, a noninactivating potassium current and an inactivating sodium current, dominate the firing behavior. We simulated the electrical behavior of the two neuron types, using a simplified form of Hodgkin-Huxley model based on published voltage-clamp and current-clamp recordings. Changing only two parameters of sodium inactivation, the slope of the h ∞ curve and the time constant of recovery from inactivation, allowed a complete switch between the two firing patterns. Our simulations support previous evidence that sodium inactivation controls the firing properties of these neurons and indicate that two parameter changes are needed to achieve complete transformation between the two neuron types.