Yosef Yarom

Resonance, oscillation and the intrinsic frequency preferences of neurons

The realization that different behavioural and perceptual states of the brain are associated with different brain rhythms has sparked growing interest in the oscillatory behaviours of neurons. Recent research has uncovered a close association between electrical oscillations and resonance in neurons. Resonance is an easily measurable property that describes the ability of neurons to respond selectively to inputs at preferred frequencies. A variety of ionic mechanisms support resonance and oscillation in neurons. Understanding the basic principles involved in the production of resonance allows for a simplified classification of these mechanisms. The characterization of resonance and frequency preference captures those essential properties of neurons that can serve as a substrate for coordinating network activity around a particular frequency in the brain.

GABA in the mammalian suprachiasmatic nucleus and its role in diurnal rhythmicity

Mammals manifest circadian behaviour timed by an endogenous clock in the hypothalamic suprachiasmatic nucleus (SCN). Considerable progress has been made in identifying the molecular basis of the circadian clock, but the mechanisms by which it is translated into cyclic firing activity, high during the day and low at night, are still poorly understood. GABA (γ-aminobutyric acid), a common inhibitory neurotransmitter in the central nervous system, is particularly densely distributed within the SCN, where it is located in the majority of neuronal somata and synaptic terminals. Using an in vitro brain-slice technique, we have now studied the effect of bath-applied GABA on adult SCN neurons at various times of the day. We find that GABA acts as an inhibitory neurotransmitter at night, decreasing the firing frequency; but during the day GABA acts as an excitatory neurotransmitter, increasing the firing frequency. We show that this dual effect, which is mediated by GABAA receptors, may be attributed to an oscillation in intracellular chloride concentration. A likely explanation is that the amplitude of the oscillation in firing rate, displayed by individual neurons, is amplified by the dual effect of GABA in the SCNs GABAergic network.

Subthreshold oscillations and resonant frequency in guinea‐pig cortical neurons: physiology and modelling.

1. Intracellular recordings were made from neurons in slices from guinea‐pig frontal cortex. In 50% of the cells, sustained subthreshold voltage oscillations were evoked by long (> 6 s) depolarizing pulses. The peak‐to‐peak amplitude of these oscillations was less than 5 mV and the frequency was voltage dependent, increasing with depolarization from 4 (near rest) to 20 Hz (at 30 mV depolarization). 2. The impedance‐frequency relationship of both oscillating and non‐oscillating cells was studied by intracellular injection of sinusoidal current with linearly changing frequency. In most cells, a peak in the impedance magnitude (resonant behaviour) was observed at depolarized levels. The frequency of the peak impedance (peak frequency) increased with depolarization from 3 (near rest) to 15 Hz (at 30 mV depolarization). 3. Application of TTX (10(‐6) M) significantly decreased the impedance magnitude near the peak frequency. The subthreshold oscillations, however, as well as the action potentials, were fully blocked by TTX. On the other hand, TEA (15 mM) and Cs+ (5 mM) abolished both the subthreshold oscillations and the resonant behaviour. Replacing Ca2+ with Co2+ (5 mM) or Ni2+ (1 mM) did not abolish the subthreshold oscillations. The peak in the frequency‐response curve was only slightly reduced. 4. An isopotential membrane model, consisting of a leak current, a fast persistent sodium current, a slow non‐inactivating potassium current (with the kinetics of the M‐current) and membrane capacitance, is sufficient to produce both voltage oscillations and resonant behaviour. The kinetics of the K+ current by itself is sufficient to produce resonance behaviour. The Na+ current amplifies the peak impedance magnitude and is essential for the generation of subthreshold oscillation. The model correctly predicted the behaviour of the frequency response before and after TTX and TEA application, as well as the relation between the expected passive impedance and the experimental impedance. 5. We speculate that the tendency of the neurons to generate voltage signals at a certain frequency (as a result of the subthreshold oscillations) and to preferentially respond to inputs arriving at the same frequency (the resonance behaviour) promotes population activity at that preferred frequency.

Bistability of cerebellar Purkinje cells modulated by sensory stimulation.

A persistent change in neuronal activity after brief stimuli is a common feature of many neuronal microcircuits. This persistent activity can be sustained by ongoing reverberant network activity or by the intrinsic biophysical properties of individual cells. Here we demonstrate that rat and guinea pig cerebellar Purkinje cells in vivo show bistability of membrane potential and spike output on the time scale of seconds. The transition between membrane potential states can be bidirectionally triggered by the same brief current pulses. We also show that sensory activation of the climbing fiber input can switch Purkinje cells between the two states. The intrinsic nature of Purkinje cell bistability and its control by sensory input can be explained by a simple biophysical model. Purkinje cell bistability may have a key role in the short-term processing and storage of sensory information in the cerebellar cortex.

Physiology, morphology and detailed passive models of guinea‐pig cerebellar Purkinje cells.

1. Purkinje cells (PCs) from guinea‐pig cerebellar slices were physiologically characterized using intracellular techniques. Extracellular caesium ions were used to linearize the membrane properties of PCs near the resting potential. Under these conditions the average input resistance, RN, was 29 M omega, the average system time constant, tau 0, was 82 ms and the average cable length, LN, was 0.59. 2. Three PCs were fully reconstructed following physiological measurements and staining with horseradish peroxidase. Assuming that each spine has an area of 1 micron 2 and that the spine density over the spiny dendrites is ten spines per micrometre length, the total membrane area of each PC is approximately 150,000 microns 2, of which approximately 100,000 microns 2 is in the spines. 3. Detailed passive cable and compartmental models were built for each of the three reconstructed PCs. Computational methods were devised to incorporate globally the huge number of spines into these models. In all three cells the models predict that the specific membrane resistivity, Rm, of the soma is much lower than the dendritic Rm (approximately 500 and approximately 100,000 omega cm2 respectively). The specific membrane capacitance, Cm, is estimated to be 1.5‐2 muF cm‐2 and the specific cytoplasm resistivity, Ri, is 250 omega cm. 4. The average cable length of the dendrites according to the model is 0.13 lambda, suggesting that under caesium conditions PCs are electrically very compact. Brief somatic spikes, however, are expected to attenuate 30‐fold when spreading passively into the dendritic terminals. A simulated 200 Hz train of fast, 90 mV somatic spikes produced a smooth 12 mV steady depolarization at the dendritic terminals. 5. A transient synaptic conductance increase, with a 1 nS peak at 0.5 ms and a driving force of 60 mV, is expected to produce approximately 20 mV peak depolarization at the spine head membrane. This EPSP then attenuates between 200‐ and 900‐fold into the soma. Approximately 800 randomly distributed and synchronously activated spiny inputs are required to fire the soma. 6. The passive model of the PC predicts a poor resolution of the spatio‐temporal pattern of the parallel fibre input. An equally sized, randomly distributed group of approximately 1% of the parallel fibres, activated within a time window of a few milliseconds, would result in approximately the same composite EPSP at the soma.

Ionic currents and firing patterns of mammalian vagal motoneurons in vitro.

The electrophysiological properties of guinea-pig dorsal vagal motoneurons were studied in an in vitro slice preparation. Antidromic, orthodromic and direct stimulation of the neurons demonstrated that the action potential is comprised of several distinct components: a fast initial spike followed by afterdepolarization and an early and a late afterhyperpolarizations. The fast initial spike and the early afterhyperpolarization were blocked by tetrodotoxin and tetraethylammonium ions, respectively. The afterdepolarization (present on the falling phase of the spike) and the late afterhyperpolarization were blocked by the addition of ions known to block calcium conductance (CdCl2, CoCl2 or MnCl2), indicating close association between these two potentials. Prolonged outward current injection through the recording electrode produced two different firing patterns, depending on the initial level of the membrane potential. From resting potential (usually -60 mV) the firing pattern was characterized by a short train of action potentials appearing shortly after the onset of the depolarization step. By contrast, when the depolarization was delivered from a hyperpolarized membrane potential level, a short train of repetitive firing appeared after an initial delay of 300-400 ms. The membrane current responsible for this initial reduction in excitability was studied by means of a single-electrode voltage-clamp technique. The magnitude, direction and kinetics of such current flow are consistent with the presence of early potassium current (IA), partly inactive at the resting potential. Synaptic activation of vagal motoneurons could be obtained by electrical stimulation of the tissue surrounding the vagal nucleus or by direct activation of the vagal nerve. Perivagal stimulation generated excitatory and inhibitory synaptic potentials which could be reversed by shifting the membrane potential. Vagal nerve stimulation, in addition to the antidromic activation of the cells, generated depolarizing responses which were unitary in nature and did not show much sensitivity to shifts in membrane potential. Perivagal and vagal nerve-evoked depolarizations could generate action potentials as well as partial dendritic spikes. We conclude that spike electroresponsiveness in vagal motoneurons is generated by voltage-dependent Na+ and Ca2+ conductances. In addition, the Ca2+-dependent current triggers a K+ conductance which is responsible for modulating the firing frequency obtained from the normal resting level.(ABSTRACT TRUNCATED AT 400 WORDS)

The impact of parallel fiber background activity on the cable properties of cerebellar Purkinje cells

Neurons in the mammalian CNS receive 104-105 synaptic inputs onto their dendritic tree. Each of these inputs may fire spontaneously at a rate of a few spikes per second. Consequently, the cell is bombarded by several hundred synapses in each and every millisecond. An extreme example is the cerebellar Purkinje cell (PC) receiving approximately 100,000 excitatory synapses from the parallel fibers (p.f.s) onto dendritic spines covering the thin dendritic branchlets. What is the effect of the p.f.s activity on the integrative capabilities of the PC? This question is explored theoretically using analytical cable models as well as compartmental models of a morphologically and physiologically characterized PC from the guinea pig cerebellum. The input of individual p.f.s was modeled as a transient conductance change, peaking at 0.4 nS with a rise time of 0.3 msec and a reversal potential of +60 mV relative to rest. We found that already at a firing frequency of a few spikes per second the membrane conductance is several times larger than the membrane conductance in the absence of synaptic activity. As a result, the cable properties of the PC significantly change; the most sensitive parameters are the system time constant (0) and the steady-state attenuation factor from dendritic terminal to soma. The implication is that the cable properties of central neurons in freely behaving animals are different from those measured in slice preparation or in anesthetized animals, where most of the synaptic inputs are inactive. We conclude that, because of the large conductance increase produced by the background activity of the p.f.s, the activity of the PC will be altered from this background level either when the p.f.s change their firing frequency for a period of several tens of milliseconds or when a large population of the p.f.s fires during a narrow time window.

Organization of Octopus Arm Movements: A Model System for Studying the Control of Flexible Arms

Octopus arm movements provide an extreme example of controlled movements of a flexible arm with virtually unlimited degrees of freedom. This study aims to identify general principles in the organization of these movements. Video records of the movements ofOctopus vulgaris performing the task of reaching toward a target were studied. The octopus extends its arm toward the target by a wave-like propagation of a bend that travels from the base of the arm toward the tip. Similar bend propagation is seen in other octopus arm movements, such as locomotion and searching. The kinematics (position and velocity) of the midpoint of the bend in three-dimensional space were extracted using the direct linear transformation algorithm. This showed that the bend tends to move within a single linear plane in a simple, slightly curved path connecting the center of the animal’s body with the target location. Approximately 70% of the reaching movements demonstrated a stereotyped tangential velocity profile. An invariant profile was observed when movements were normalized for velocity and distance. Two arms, extended together in the same behavioral context, demonstrated identical velocity profiles. The stereotyped features of the movements were also observed in spontaneous arm extensions (not toward an external target). The simple and stereotypic appearance of the bend trajectory suggests that the position of the bend in space and time is the controlled variable. We propose that this strategy reduces the immense redundancy of the octopus arm movements and hence simplifies motor control.

A model of the olivo-cerebellar system as a temporal pattern generator

The olivo-cerebellar system has been implicated in temporal coordination of task components. Here, we propose a novel model that enables the olivo-cerebellar system to function as a generator of temporal patterns. These patterns could be used for timing of motor, sensory and cognitive tasks. The proposed mechanism for the generation of these patterns is based on subthreshold oscillations in a network of inferior olivary neurons and their control by the cerebellar cortex and nuclei. Our model, which integrates a large body of anatomical and physiological observations, lends itself to simple, testable predictions and provides a new conceptual framework for olivo-cerebellar research.

Subthreshold voltage noise of rat neocortical pyramidal neurones

Neurones are noisy elements. Noise arises from both intrinsic and extrinsic sources, and manifests itself as fluctuations in the membrane potential. These fluctuations limit the accuracy of a neurones output but have also been suggested to play a computational role. We present a detailed study of the amplitude and spectrum of voltage noise recorded at the soma of layer IV–V pyramidal neurones in slices taken from rat neocortex. The dependence of the noise on holding potential, synaptic activity and Na+ conductance is systematically analysed. We demonstrate that voltage noise increases non‐linearly as the cell depolarizes (from a standard deviation (s.d.) of 0.19 mV at −75 mV to an s.d. of 0.54 mV at −55 mV). The increase in voltage noise is accompanied by an increase in the cell impedance, due to voltage dependence of Na+ conductance. The impedance increase accounts for the majority (70%) of the voltage noise increase. The increase in voltage noise and impedance is restricted to the low‐frequency range (0.2–2 Hz). At the high frequency range (5–100 Hz) the voltage noise is dominated by synaptic activity. In our slice preparation, synaptic noise has little effect on the cell impedance. A minimal model reproduces qualitatively these data. Our results imply that ion channel noise contributes significantly to membrane voltage fluctuations at the subthreshold voltage range, and that Na+ conductance plays a key role in determining the amplitude of this noise by acting as a voltage‐dependent amplifier of low‐frequency transients.