[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.

Electrotonic structure of motoneurons in the spinal cord of the turtle: inferences for the mechanisms of bistability.

Understanding how voltage-regulated channels and synaptic membrane conductances contribute to response properties of neurons requires reliable knowledge of the electrotonic structure of dendritic trees. A novel method based on weak DC field stimulation and the classical method based on current injection were used to obtain two independent estimates of the electrotonic structure of motoneurons in an in vitro preparation of the turtle spinal cord. DC field stimulation was also used to ensure that the passive membrane properties near the resting membrane potential were homogeneous. In two cells, the difference in electrotonic lengths estimated with the two methods in the same cell was 6 and 9%. The majority of dendritic branches terminated at a distance of 1 electrotonic unit from the recording site. The longest branches reached 2 lambda. In the third cell, the difference was 36%, demonstrating the need to use both methods, field stimulation and current injection, for reliable measurements of the electrotonical structure. Models of the reconstructed cells endowed with voltage-dependent conductances were used to explore generation mechanisms for the experimentally observed hysteresis in input current-voltage relation of bistable motoneurons. The results of modeling suggest that only some dendrites need to possess L-type calcium current to explain the hysteresis observed experimentally and that dendritic branches with different electrotonical lengths can be bistable. Independent bistable behavior in individual dendritic branches can make motoneurons complex processing units.

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons.

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.

Detection of inhomogeneities in membrane ohmic resistance in geometrically complex systems.

DC field-evoked transients in arbitrarily shaped neurons and syncytia were analyzed theoretically. In systems with homogeneous passive membrane properties, the transients develop much faster than the membrane discharges. Conductance of the proximal membrane could be larger due to the injury imposed by sharp electrode impalement. In this case, the transients have an overshoot and an undershoot when the field is switched on and off. The overshoot and undershoot decay with the time constant of the response to current injection. If the conductance of the distal membrane is larger, the fast transients develop only partially and have slow tails which decay according to the time constant of the response to current injection. We recorded DC field-evoked potentials in motoneurons in turtle spinal cord slices by sharp electrodes and in the whole-cell mode. All three theoretically predicted types of responses were observed. The sharp electrodes were found not to impose a shunt in 60% of recorded cells. Detection of various membrane inhomogeneities in 1D-syncytium is discussed. We also suggest that it is possible to detect the inhomogeneities in intercellular resistance of the syncytium and intracellular resistance of a neuron when the membrane passive properties are homogeneous.

[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.

[Theoretical analysis of the multistability of pyramidal neurons]. / Teoreticheskii analiz mul'tistabil'nosti piramidnykh neironov.

The two-step switch off the long duration Ca action potential was observed recently in neocortex pyramids [1]. The phenomenon was interpreted as an evidence of the N-type Ca-channel distribution in isolated loci [1]. We demonstrate here that the two-step switch off can be imitated in the model with even channel distribution in a reconstructed pyramidal neuron as well. The first high plateau of the action potential corresponds to steady polarization of the whole membrane. The first switch off of the high plateau to the second low plateau corresponds to the switch off of the steady depolarization of the short basal dendrites. The steady depolarization of the long apical dendrite is more stable thus the switch off of the low plateau is a consequence of the apical dendrite repolarization. The model includes N-channel inactivation and a somatic shunt. The shunt may be artifactual, due to implement, or natural, due to postspike hyperpolarization. Recent experiments [2] have proved that the Ca-channels are located everywhere in the pyramidal cell.

Transmitter regulation of plateau properties in turtle motoneurons.

In motoneurons, generation of plateau potentials is promoted by modulators that block potassium channels. In voltage-clamp experiments with triangular voltage ramp commands, we show that cis-(+/-)-1-aminocyclopentane-1, 3-dicarboxylic acid (cis-ACPD) and muscarine promote the generation of plateau potentials by increasing the dihydropyridine sensitive inward current, by increasing the input resistance, and by depolarizing the resting membrane potential. Type I metabotropic glutamate receptors (mGluR I) mediate the effects of cis-ACPD. Baclofen suppresses generation of plateau potentials by decreasing the dihydropyridine sensitive inward current, by decreasing the input resistance, and by hyperpolarizing the resting membrane potential. These results suggest that membrane properties of motoneurons are continuously modulated by synaptic activity in ways that may have profound effects on synaptic integration and pattern generation.

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.

Metabotropic synaptic regulation of intrinsic response properties of turtle spinal motoneurones.

1. The effect of a brief train of electric stimuli in the dorsolateral funiculus on the intrinsic response properties of turtle motoneurones was investigated in transverse sections of the spinal cord in vitro. 2. Even when glutamatergic, GABAergic and glycinergic ionotropic synaptic transmission was blocked by antagonists of AMPA, NMDA, glycine and GABA receptors, dorsolateral funiculus (DLF) stimulation induced a facilitation of plateau potentials during current clamp and the underlying inward current in voltage clamp. This facilitation lasted more than 10 s. 3. The plateau potential and the facilitation by DLF stimulation was absent in the presence of 10 microM nifedipine. The DLF-induced facilitation was reduced by antagonists of 5-HT1A, group 1 metabotropic glutamate receptors and muscarine receptors. 4. These findings suggest that the intrinsic properties of spinal motoneurones are dynamically regulated by afferent synaptic activity. These afferents can be of spinal and extraspinal origin. Continuous regulation of intrinsic response properties could be a mechanism for motor flexibility.

Depolarization-induced facilitation of a plateau-generating current in ventral horn neurons in the turtle spinal cord.

Plasticity at the neuronal level commonly involves use-dependent changes in strength of particular synaptic pathways or regulation of postsynaptic properties by modulatory transmitters. Here we analyze a novel form of short-term plasticity mediated by use-dependent facilitation of postsynaptic responsiveness. Using current- and voltage-clamp recordings, we found that all spinal ventral horn neurons able to generate plateau potentials showed depolarization-induced facilitation of the underlying inward current. Facilitation was noticeable when the neurons were depolarized to more than -50 mV at intervals <4 s. When stimulation with fast triangular voltage ramps was used, the inward current activated at a less depolarized potential during the second ramp. The inward current and facilitation was eliminated by nifedipine, a selective antagonist of L-type calcium channels. Depolarization-induced facilitation of low-voltage-activated L-type calcium channels is suggested to be the underlying mechanism. It is noted that facilitation occurs on a time scale compatible with a role in phasic motor activity.

Detection of a membrane shunt by DC field polarization during intracellular and whole cell recording.

Lower input resistance with intracellular recording, rather than with whole cell recording, usually has been ascribed to a shunt produced by penetration injury. An alternative explanation is a higher input resistance during whole cell recording due to wash-out of cytoplasmatic substances. We have used neuronal polarization at the onset and termination of an applied electric field for shunt detection. An analytical expression was derived for field-induced polarization in a shunted ohmic cable. When the shunt is negligible, the transient response to a step in DC field decays much faster than the response to current injected through the recording electrode. In the case of a significant shunt an over- and undershoot of the transmembrane potential appear at the shunted end when the field is switched on and off. Over- and undershoot decay with the same slowest time constant as the response to injected current. The results for the cable are generalized for nonuniform fields and arbitrary branching neurons with homogeneous membrane. The field effect was calculated for two reconstructed neurons with different branching pattern. The calculations confirmed the theoretical inferences. The field polarization can be used for shunt detection. The theory was checked experimentally in 18 ventral neurons in transverse slices of the turtle spinal cord. In seven neurons, field-induced under- and overshoots were observed when sharp electrodes were used. This indicates the presence of an injury shunt. In the remaining 11 neurons, however, there were no under- or overshoots, indicating that a shunt is not always induced. When patch electrodes were used, the seal quality was checked by inducing a spike with a strong field stimulus before and after the rupture of the membrane. When the threshold field strength for spike initiation was not changed by membrane rupture, under- and overshoots were not observed. This was taken to indicate a good seal. In such recordings under- and overshoots were observed when a shunt was induced by local application of glycine. The fast and monotonic response to weak field stimulation suggests homogeneous electric properties of the soma-dendritic membrane when active conductances are not recruited. We propose using polarization by weak DC fields to ensure the quality of recordings with sharp and whole cell electrodes and for checking the ohmic homogeneity of the membrane. These controls are particularly important for evaluation of electrotonic parameters.

[Theoretical analysis of direct current field-induced polarization of ohmic neurons]. / Teoreticheskii analiz poliarizatsii omicheskogo neirona, navedennoi polem postoiannogo toka.

A theory for the DC field-induced polarization of arbitrarily branching dendrites is being suggested. Contributions of the dendrites and the axon to polarisation of the soma are estimated for a quasi-reconstructed turtle motoneuron. The polarization depends on the length constant monotonously and dose not depend on other electronic parameters. The measurement of the DC field-induced potential may be used for unique determination of the electrotonic structure of reconstructed cells, provided that a whole-cell recording is employed and the axons are unmyelinated, or truncated, or oriented across the field. Polarization of the distal dendrites is also being analyzed to get into insight into the phenomenon of the field-induced steady depolarization of the dendrites.

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.