Bursts and hyperexcitability in non-myelinated axons of the rat hippocampus.

Strict control over the initiation of action potentials is the primary task of a neuron. One way to lose proper spike control is to create several spikes, a burst, when only one should be initiated. We describe a new site for burst initiation in rat hippocampal CA3 neurons: the Schaffer collateral axons. These axons lack myelin, are long, extremely thin, and form synapses along their entire paths, features typical for many, if not most cortical axons in the mammalian brain. We used hippocampal slices and recorded from individual Schaffer collateral axons. We found that single action potentials were converted into bursts of two to six action potentials after blocking 4-aminopyridine (4-AP) sensitive K(+) channels. The CA3 somata and initial part of their axons were surgically removed in these experiments, leading to the conclusion that the bursts were initiated far out in the axons. This conclusion was supported by two additional kinds of experiments. First, local application of 4-AP to one out of two stimulated axonal branches of the same neuron showed bursting only at the 4-AP exposed branch. Second, intracellular recordings from CA3 somata showed that some spontaneously occurring bursts were resistant to somatic hyperpolarization. We then investigated a hyperexcitable period that follows individual spikes in the Schaffer collaterals. With extracellular excitability testing, we showed that the time course of this hyperexcitability was compatible with that of the bursts, so this hyperexcitability could be the underlying cause of the bursts. Furthermore, the hyperexcitability was enhanced by low doses of 4-AP (20 microM), alpha-dendrotoxin (alpha-DTX) or margatoxin (MgTX). Kv1.2 containing channels may therefore dampen the hyperexcitability, but because bursting was observed only at high 4-AP concentration (1 mM), other channels may be needed to prevent axonal bursting.

Activity-dependent excitability changes in hippocampal CA3 cell Schaffer axons.

The membrane potential changes following action potentials in thin unmyelinated cortical axons with en passant boutons may be important for synaptic release and conduction abilities of such axons. In the lack of intra-axonal recording techniques we have used extracellular excitability testing as an indirect measure of the after-potentials. We recorded from individual CA3 soma in hippocampal slices and activated the axon with a range of stimulus intensities. When conditioning and test stimuli were given to the same site the excitability changes were partly masked by local effects of the stimulating electrode at intervals < 5 ms. Therefore, we elicited the conditioning action potential from one axonal branch and tested the excitability of another branch. We found that a single action potential reduced the axonal excitability for 15 ms followed by an increased excitability for approximately 200 ms at 24 degrees C. Using field recordings of axonal action potentials we show that raising the temperature to 34 degrees C reduced the magnitude and duration of the initial depression. However, the duration of the increased excitability was very similar (time constant 135 +/- 20 ms) at 24 and 34 degrees C, and with 2.0 and 0.5 mM Ca2+ in the bath. At stimulus rates > 1 Hz, a condition that activates a hyperpolarization-activated current (Ih) in these axons, the decay was faster than at lower stimulation rates. This effect was reduced by the Ih blocker ZD7288. These data suggest that the decay time course of the action potential-induced hyperexcitability is determined by the membrane time constant.

[Motor learning with the minimal involvement of visual afferentation]. / Dvigatel'noe obuchenie pri minimal'nom uchastii zritel'noi afferentatsii.

Amongst motor control and learning models, "A Cerebellar Model of Timing and Prediction" of A. Barto and J. Houk is the most interesting and physiologically well-grounded. Developing D. Marr's "The Theory of Cerebellar Cortex", this model proposed the important role in motor learning of the ability of Purkinje cells to change their activity level by the dendritic bistability mechanism. The aim of this investigation was to verify this idea in experiments with human learning of precise elbow flexion. The unsupervisual method of learning was used in order to guarantee the principal role of proprioception in training. The experiments were carried out in darkness to exclude the vision control. Subjects were asked to perform a precise horizontal elbow flexion as fast as possible and repeat this action from 30 to 50 times up to the point of complete movement acquisition (stable movement with the error in the range of 5% of a given flexion amplitude). The target point (a given angle of the horizontal elbow flexion) was not presented to the subjects in advance. Reaching the target point was indicated by a short light flash. During training, subjects learned to hit target point with the given precision. Kinematic characteristics of the movement (time change of elbow flexion angle, velocity, and acceleration) together with EMG of the flexor and extensor were recorded. The obtained results were in good agreement with J. Houk and A. Barto's hypothesis. Analysis of changes in the kinematic characteristics in the course of training revealed an asymmetric velocity profile and a fragmentary shape of acceleration profile at the beginning of learning. In the course of training, the acceleration profile transformed into biphasic curve with a single change in polarity. Thus, it acquired a characteristic shape of a plateau. Correspondingly, to the end of training, the character of the asymmetry of the velocity profile changed. No correlation was observed between the velocity parameters and movement precision. These features essentially distinguish the motor reactions under study from the common visuomotor coordinations. It is suggested that the amplitude and duration of the acceleration plateau reflect the intensity and time of inhibition of the descending activity of Purkinje cells as a result of bistability (in accordance with Houk and Barto's hypothesis).

[Criteria of bistability of the cylindrical dendrite with the variable negative slope of the N-shaped current-voltage membrane characteristic]. / Uslovie bistabil'nosti tsilindricheskogo dendrita s peremennoi krutiznoi otritsatel'nogo naklona N-obraznoi vol't-ampernoi kharakteristiki membrany.

The criteria for hystheresis in the input current-voltage relation of a cylindrical dendrite, i.e. cable bistability, were studied earlier in case of the constant negative slope of the N-shaped membrane current-voltage characteristic. For a membrane with a variable negative slope of the current-voltage characteristic, only sufficient conditions of dendritic bistability were formulated: [equation: see text], where df/dV/h is the negative slope of the membrane current-voltage characteristic at zero current point, h; X is the electrotonic length of the dendrite. We propose to use as the necessary condition of bistability the above equation but with the maximal value of the negative slope df/dV/max instead of df/dV/h. Calculations illustrate that this necessary condition, with acceptable accuracy, can be used as the necessary and sufficient condition of the cable bistability when the N-shaped current-voltage characteristic of the membrane is arbitrary.

[The branching structure of the bistable dendrite]. / Vetviashchaiasia struktura bistabil'nogo dendrita.

A branching structure consisting of three bistable cylindrical branches was considered. Both stable and unstable solutions for the voltage distribution in such a structure, were obtained using the method developed in our laboratory. This made it possible to calculate the input current-voltage characteristic of the bistable branching structure, including unstable segments of this characteristic. Possible stable states of the structure when its proximal end is loaded by a resistance were determined. It is shown that the binary exclusive-OR could be accomplished by the elementary branching structure of a bistable dendrite. A model with overexcitation carried out by Ca-dependent K channels was developed. It is shown that the model parameters do not fall outside the physiological range of values.

[Adiabatic solution of the Ohmic cable equation. General theory, homogeneous cylindrical fiber]. / Adiabaticheskoe reshenie uravneniia omicheskogo kabelia. Obshchaia teoriia, odnorodnoe tsilindricheskoe volokno.

An adiabatic solution of the Ohmic cable equation is suggested, which reduces the non-stationary equation to a stationary form. The adiabatic length constant of the stationary equation is time-dependent. The adiabatic solutions for the boundary conditions that change in time linearly and exponentially were studied. In the latter case, the adiabatic length constant does not depend on time though it differs from the usual length constant. The cable input characteristics of exact and adiabatic solutions were compared in the cases of the voltage- and current-clamp, and electric field stimulation. The adiabatic and exact solutions are identical for the rising exponential stimuli. For the falling exponential stimuli, the adiabatic solution determines the exact asymptotic solution if the stimulus decays slower than the relaxation of initial conditions. It is propose to use linear and exponential ramp stimulation in electrotonic measurements.

[Adiabatic solution for the Ohmic cable equation. An homogeneous cell, prospects for electronic measurements]. / Adiabaticheskoe reshenie uravneniia omicheskogo kabelia. Odnorodnaia kletka, vozmozhnosti dlia élektronicheskikh izmerenii.

Exact and adiabatic electrotonic solutions [1] were calculated for reconstructed motoneurone and hippocampal interneurone in case of linear and exponential ramp stimulation by the fixed current, potential or homogenous electric field. For the rising exponential ramp the solutions are identical. In case of the decaying exponent the adiabatic solution becomes an asymptote for the exact one if the stimulus decays slower than relaxation of the initial conditions in the cell. If the stimulus decays faster, the asymptote is the current or potential axis, depending on the stimulation mode. For electrotonically short cell, the exact solution approaches the asymptote faster. The solution for the exponentially rising field does not depend on the dendritic tree configuration and depends only on the effective electrotonic length of the neurone. It could be useful to apply ramp stimulation, especially exponential ramp of the electric field, to estimate electrotonic parameters of cells.

Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation.

We present a theory for estimation of the dendritic electrotonic length constant and the membrane time constant from the transmembrane potential (TMP) induced by an applied electric field. The theory is adapted to morphologically defined neurons with homogeneous passive electric properties. Frequency characteristics and transients at the onset and offset of the DC field are considered. Two relations are useful for estimating the electrotonic parameters: 1) steady-state polarization versus the dendritic electrotonic length constant; 2) membrane time constant versus length constant. These relations are monotonic and may provide a unique estimate of the electrotonic parameters for 3D-reconstructed neurons. Equivalent tip-to-tip electrotonic length of the dendritic tree was estimated by measuring the equalization time of the field-induced TMP. For 11 turtle spinal motoneurons, the electrotonic length from tip to tip of the dendrites was in the range of 1-2.5 lambda, whereas classical estimation using injection of current pulses gave an average dendrite length of 0.9-1.1 lambda. For seven ventral horn interneurons, the estimates were 0.7-2.6 lambda and 0.6-0.9 lambda, respectively. The measurements of the field-induced polarization promise to be a useful addition to the conventional methods using microelectrode stimulation.

Bi-stable dendrite in constant electric field: a model analysis.

Some neurons possess dendritic persistent inward current, which is activated during depolarization. Dendrites can be stably depolarized, i.e. they are bi-stable if the net current is inward. A proper method to show the existence of dendritic bi-stability is putting the neuron into the electric field to induce transmembrane potential changes along the dendrites. Here we present analytical and computer simulation of the bi-stable dendrite in the d.c. field. A prominent jump to a depolarization plateau can be seen in the soma upon initial hyperpolarization of its membrane. If a considerable portion of dendrites are parallel to the field it is impossible to switch off the depolarization plateau by changing the direction and the strength of the electric field. There is nothing similar in neurons with ohmic dendrites. The results of the simulation conform to the experimental observations in turtle motoneurons [Hounsgaard J. and Kiehn O. (1993) J. Physiol., Lond. (in press)]; comparison of the theoretical and the experimental results makes semi-quantitative estimation of some electrical parameters of dendrites possible. We propose modifications of the experiment which enable one to measure dendritic length constants and other parameters of stained neurons.

[Relation between the excitatory synaptic currents and clamped somatic potential in the model of neuron with nonlinear dendrites]. / Zavisimost' vozbuzhdaiushchikh sinapticheskikh tokov ot fiksirovannogo potentsiala somy na modeli neirona s nelineinymi dendritami.

The influence of the clamped somatic potential on the excitatory synaptic current (EPSC) was studied in the model of the dendrite with N-shaped instantaneous stationary current--voltage curve. Proximal EPSC diminish and become narrower with decreasing hyperpolarization or modest depolarization, distal EPSC increase and become wider, intermediately distant EPSC change insignificantly. Under increasing depolarization all the EPSC become significantly wider and larger. EPSC facilitate stable depolarization of the dendrites. When the dendrite is stable depolarized EPSC becomes very small and narrow, but it becomes larger and wider as the soma is hyperpolarized. EPSC becomes especially large and wide when the soma is hyperpolarized just to terminate the stable depolarization of the dendrite branch where the active synapses are located. The model explains certain phenomena which are difficult to understand by the theory of ohmic dendrites. New phenomena are predicted.

[Shape and amplitude of stimulating postsynaptic potentials in a neuronal model with an N-shaped volt-ampere characteristic of the dendritic membrane]. / Forma i amplituda vozbuzhdaiushchikh postsinapticheskikh potentsialov na modeli neirona s N-obraznoi vol't-ampernoi kharakteristikoi dendritnoi membrany.

We developed a model of a neuron with N-shaped current--voltage characteristic of dendritic membrane and studied the change of shape and amplitude of excitatory postsynaptic potentials (EPSP) when changing the place of synapses on dendrites. Local EPSP can activate slow inward current. Consequently, the EPSP amplitude does not always diminish when the rise- and decay-time increases. In some cases the rise- and decay-time of a more distant synapse may become shorter than that of the more approximate one. The common method of judging about the location of synapses by means of the shape of EPSPs may be wrong.