The cation conductance activated upon hyperpolarization of the membrane beyond the resting value appears to represent an ubiquitous type of membrane channel. Our understanding of the respective membrane current, termed Ih, in neurons has matured from that of a "queer" current toward that of a highly regulated mechanism that is particularly important in determining integrative behavior near rest and providing the pacemaker depolarization during rhythmic-oscillatory activity.

QUEER CURRENT AND PACEMAKER: The Hyperpolarization- Activated Cation Current in Neurons

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels comprise a small subfamily of proteins within the superfamily of pore-loop cation channels. In mammals, the HCN channel family com...

Hyperpolarization-activated cation channels: from genes to function.

Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neuron's onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current.

/pdf/a-universal-model-for-spike-frequency-adaptation-648bruaq52.pdf

A universal model for spike-frequency adaptation

▪ Abstract Ionic currents activated by hyperpolarization and regulated by cyclic nucleotides were first discovered more than 20 years ago. Recently the molecular identity of the underlying channels has been unveiled. The structural features of the protein sequences are discussed and related to the mechanisms of activation, selectivity for cyclic nucleotides, and ion permeation. Coverage includes a comparison of the biophysical properties of recombinant and native channels and their significance for the physiological functions of these channels.

Molecular diversity of pacemaker ion channels.

1. The contribution of a slow, mixed Na(+)-K+, inward rectifying current (Ih) and the T-type Ca2+ current (IT) (that underlies low-threshold Ca2+ potentials) to the low-frequency oscillations observed in rat and cat thalamocortical (TC) cells in vitro was studied using current clamp and single-electrode voltage clamp recordings. 2. From a holding potential of -50 mV, voltage steps negative to -60 mV showed the presence of a slow, non-inactivating inward current, Ih. This current was unaffected by Ba2+ (1-4 mM), tetrodotoxin (0.5-1 microM) and TEA (20 mM, n = 6), reversibly blocked by Cs+ (1-3 mM), and its reversal potential (-33.0 +/- 1.2 mV) followed changes in the extracellular Na+ and K+, but not Cl-, concentration. 3. Application of Cs+ (1-3 mM) abolished the pacemaker oscillations (n = 9), while in six cells that did not show any oscillatory activity Cs+ first evoked the spindle-like oscillations that, in the continuous presence of these ions, were then transformed into the pacemaker oscillations before all activities were finally blocked: all these effects were accompanied by a hyperpolarization and a progressive decrease and final blockade of Ih. Cs+ had no effect on the 'N-methyl-D-aspartate' (NMDA) oscillations (n = 5) and Ba2+ (2 mM, n = 8) did not block the pacemaker, the spindle-like and the 'NMDA' oscillations. 4. In ten cells that showed the pacemaker oscillations selective activation of beta-adrenoceptors by 10-50 microM-noradrenaline (in the presence of alpha-noradrenergic antagonists) or by 20 microM-isoprenaline first transformed the pacemaker oscillations into the spindle-like oscillations that, in the continuous activation of beta-receptors, were finally abolished: all these effects were accompanied by a depolarization and a progressive increase of Ih. 5. In TC cells that showed the pacemaker oscillations application of 1-octanol (50-100 microM), an antagonist of T-type Ca2+ currents, reversibly blocked this activity but concomitantly decreased (50%) the cell input resistance (n = 5). Application of Ni2+ (0.2-0.5 mM, n = 13), another antagonist of IT reversibly blocked the pacemaker, the spindle-like and the 'NMDA' oscillations. 7. In cells showing the pacemaker oscillations it was found that the current developing from the most hyperpolarized potential of an oscillation cycle was an inward relaxation whose time course differed from that of Ih evoked at the same potential.(ABSTRACT TRUNCATED AT 400 WORDS)

Two inward currents and the transformation of low-frequency oscillations of rat and cat thalamocortical cells.

1. A polarization-induced membrane current, IQ, was investigated in the slowly adapting lobster stretch receptor neurone using conventional electrophysiological techniques including intracellular ion measurements. 2. The current was readily blocked by Cs+ in a voltage-dependent manner, but proved to be unaffected by tetrodotoxin, tetraethylammonium and 4-aminopyridine. 3. From an analysis of the ionic basis of IQ, it appeared that the current is carried by both Na+ and K+ through a membrane channel whose permeability for K+ is about six times larger than that for Na+ in a normal ionic environment. In the presence of reduced external Na+ concentration the Q-channel increases its permeability for both Na+ and K+, but more so for Na+ than for K+. 4. Kinetically, IQ was found to be characterized by a steep sigmoidal relationship between membrane voltage and steady-state current activation, and by a bell-shaped relationship between membrane voltage and the time constant of the exponential phase of current activation or deactivation. A significant feature of the latter relationship is a tendency to level off at finite time-constant values in both strongly hyperpolarizing and strongly depolarizing voltage regions. 5. From the experiments a mathematical IQ model was inferred. This model was based on constant-field and channel-gating kinetics involving a voltage-dependent reaction step in series with a voltage-independent reaction step. The model was found to successfully reproduce IQ behaviour in the living preparation. 6. Functionally, the activation of IQ was found to play a role in setting the cell's resting polarization and membrane excitability. This function was inferred from experiments on unimpaled cells in which it was possible to demonstrate some overlap between the voltage ranges of IQ activation and impulse initiation. In addition, in impaled cells the activation of IQ was found to cause some shortening of post-tetanic membrane hyperpolarization and to accelerate, thereby, the post-tetanic restoration of membrane excitability to control levels.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1987.sp016476

Current activation by membrane hyperpolarization in the slowly adapting lobster stretch receptor neurone.

1. The gated membrane currents (a tetrodotoxin-sensitive Na+ current and a tetraethylammonium- and 4-aminopyridine-sensitive K+ current) of the rapidly adapting stretch receptor neurone of lobster were investigated with respect to their kinetic properties using electrophysiological, pharmacological, and mathematical techniques. 2. The currents were found to be controlled by slow inactivations as well as by fast Hodgkin-Huxley (1952) gating processes. They could be described by kinetic expressions which differed from those inferred for the slowly adapting receptor (Gestrelius & Grampp, 1983a; Gestrelius, Grampp & Sjolin, 1983) only with respect to some of the parameter values. 3. With these expressions, and additional equations for the cell's pump and leak current components (Edman, Gestrelius & Grampp, 1986), a mathematical receptor model was formulated which accurately predicts the impulse activity of the living preparation in different functional circumstances and which, therefore, was adopted as an appropriate theory of firing regulation. 4. From a model analysis it appeared (a) that the 'rapid' adaptation of the receptor's impulse activity is mainly an effect of slow Na+ current inactivation starting a regenerative process of accommodation which, basically, is due to a small ratio of subthreshold Na+ to K+ currents; (b) that, because of the transmembrane Na+ influx being limited by accommodation, impulse firing is only little affected by a Na+-dependent pump current activation; and (c) that the phenomenon of increased firing frequency initially during prolonged stimulation ('negative adaptation') is an effect of the slow K+ current inactivation being faster than the slow Na+ current inactivation at comparable degrees of membrane polarization. 5. From further model studies it also appeared that, during depolarizations between successive action potentials evoked by constant stimulation, the membrane behaves like a high-resistance constant-current generator feeding into a short-circuiting capacitor. In consequence, the cell's stimulus sensitivity (change in firing frequency with stimulation strength) is, at functionally relevant stimulation intensities, mainly determined by the membrane capacitance and by the amplitude of the interspike membrane depolarization while, at higher stimulation intensities and firing frequencies, it becomes more and more a function of the spike duration itself.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1987.sp016475

Analysis of gated membrane currents and mechanisms of firing control in the rapidly adapting lobster stretch receptor neurone.

1. The ion currents in the slowly and rapidly adapting stretch receptor neurone of lobster were investigated with respect to their nature and stationary kinetics in sub- and near-threshold voltage regions using electrophysiological and pharmacological techniques. 2. In both neurones the following currents were identified: (a) a tetrodotoxin-sensitive Na current, (b) a tetraethylammonium and 4-aminopyridine-sensitive K current, (c) a Co (or Mn)-sensitive Ca-dependent K current, (d) an ouabain-sensitive pump current and (e) a remaining leak current carried mainly by Na, K and Cl. 3. In suprathreshold voltage regions the balance between the individual membrane currents leads to the formation of a stationary negative conductance (negative slope in the voltage dependence of the ionic current) in the slowly, but not in the rapidly adapting cell. 4. These observations are compatible with the fact that during prolonged suprathreshold stimulation a stationary low frequency impulse during is possible in the slowly adapting cell, whereas in the rapidly adapting cell it is not.

Subthreshold and near-threshold membrane currents in lobster stretch receptor neurones.

The transmembrane exchange of Na+, K+, and Cl- in slowly and rapidly adapting lobster stretch receptor neurones was studied using ion-sensitive microelectrodes in combination with conventional electrophysiological techniques. The investigation was founded on the assumption that the transmembrane ion exchange is accomplished by active and passive transports which add up to zero in steady state for each ion involved. The active transports are assumed to include Na+ and K+ transports driven by an electrogenic Na-K pump. To these transports are also added equimolar fluxes of K+ and Cl- leaking from the impaling micro-electrode. The passive transports are assumed to pass through membrane channels in accordance with constant field kinetics. For a quantitative evaluation of the transmembrane ion exchange in resting conditions measurements were made of the resting concentrations of Na+, K+ and Cl-; the voltage dependence of the ungated leak current; and ouabain-induced changes in resting membrane current and intracellular ion concentrations. From the results it follows that both the resting pump current and the leak permeabilities for the ions investigated have values which do not seem to differ between slowly and rapidly adapting receptor neurones. For a quantitative evaluation of the relation between internal Na+ and pump current production, measurements were made of the outward membrane current as a function of internal Na+ and K+ following a shift of these ions by means of prolonged repetitive impulse activation. It was found that the investigated relation is compatible with Garay-Garrahan kinetics (Garay & Garrahan, 1973) in both receptor neurones, but the results imply a larger maximum Na+-extrusion capacity in slowly than in rapidly adapting cells. From recordings of the time course of post-tetanic normalization of both the membrane current and intracellular Na+ concentration, cell volume values could be deduced which were closely similar in slowly and rapidly adapting receptors. A corresponding similarity was also found for the cell area which was derived from membrane capacitance measurements.

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1986.sp016180

Transmembrane ion balance in slowly and rapidly adapting lobster stretch receptor neurones.

The kinetics of the TEA and 4-AP sensitive K+ current (IK) in the slowly adapting lobster stretch receptor neurone were investigated in sub- and near-threshold voltage regions using electrophysiological and pharmacological techniques. In dynamic conditions IK was found to display both fast and slow reactions. These were attributed to a Hodgkin-Huxley type of K activation, and a slow type of K inactivation, respectively. The slow K inactivation could be shown to be unrelated to K+ flux dependent changes in intra- and pericellular K+ concentrations. Its stationary voltage dependence was however shifted in a depolarizing direction by increasing, and in hyperpolarizing direction by decreasing the extracellular Ca++ concentration. In view of these findings, and of its kinetic properties, the slow K inactivation was classified as a genuine channel gating process. The process of K activation was too fast for a dynamic analysis with the recording technique available. An estimate of its stationary voltage dependence could however be obtained in a voltage range from about -100 to about -40 mV. The experimental observations were utilized in the formulation of a mathematical model describing the kinetic behaviour of IK in the present preparation based on constant field and state transition theories.

Kinetics of the TEA and 4-Ap sensitive K^+ current in the slowly adapting lobster stretch receptor neurone

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