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Electrophysiology of the Cerebellar Networks

Rodolfo R. Llinás

10.1002/cphy.cp010217

Source: Supplement 2: Handbook of Physiology, The Nervous System, Motor Control

Originally published: 1981

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Comparative Aspects of Cerebellar Circuits
2 Field Potentials
2.1 Local Stimulation of Cerebellar Cortex
2.2 Field Potentials Generated by White Matter Stimulation of Cerebellar Cortex
2.3 Summary
3 Unitary Cell Recording from Cerebellar Cortex
3.1 Electrophysiology of Purkinje Cells
3.2 Activation of Climbing Fiber Afferents
3.3 Mossy Fiber Afferents
3.4 Inhibitory Systems in Cerebellar Cortex
3.5 Summary
4 Purkinje Cell Target Neurons, Cerebellar Nuclei, and Deiters' Nucleus
4.1 Summary
5 Inferior Olive
5.1 Intracellular Recording From Inferior Olivary Cells In Vivo and In Vitro
5.2 Ionic Mechanisms in Spike Generation
5.3 Inferior Olivary Cell as Single‐Cell Oscillator
5.4 Long‐Term Changes in Inferior Olive Neuronal Excitability
5.5 Electrotonic Coupling
5.6 Summary
6 Overall Function of Cerebellum
6.1 Braitenberg's Timing Model
6.2 Marr's Learning Model
6.3 Pellionisz‐Llinás Tensor Model
6.4 Boylls' Synergic Parameterization Theory
6.5 Summary
Figure 1. Figure 1.

Upper left: diagram of basic cerebellar circuit comprising mossy and climbing fiber inputs to Purkinje cells. Activity in mossy fiber (MF) is relayed through granule cells (GC) via parallel fibers (PF) to the Purkinje cell (PC). Axons of these cells are the only output system from cerebellar cortex. Second afferent is a climbing fiber (CF), which establishes a monosynaptic input to Purkinje cell dendrites. Upper right: diagram of the 2 basic inhibitory systems of cerebellar cortex. On left, basket cell axon contacts the somata of Purkinje cells. These axons also contact dendrites of these cells. Stellate cell (not shown) establishes direct contact with Purkinje cell dendrites. Both basket (BC) and stellate cells receive input via parallel fibers (PF) and constitute the inhibitory systems of the molecular layer. Golgi cell (GC to right) receives input from parallel fibers, mossy fibers (MF), and climbing fibers (not shown) and relays inhibition onto dendrites of granule cells (GrC) in granular layer. Bottom: detail of geometric organization of neuronal elements of cerebellar cortex. Drawing demonstrates different sections through a cerebellar folium. A: transverse plane. B: saggital plane. C: tangential plane. Cellular elements are displayed in drawings A, B, and C, as though the cerebellum were transparent. Orthogonal organization of parallel fibers, with respect to isoplanar characteristics of dendrites of Purkinje cells and basket and stellate cells (SC), is self‐explanatory. Note that axons of basket and stellate cells run at right angles with respect to parallel fibers and that dendritic tree of Golgi cells is close to cylindrical rather than isoplanar.

Upper left and upper right adapted from Ramón y Cajal 215; bottom from Llinás 138
Figure 2. Figure 2.

Field potentials and corresponding current densities generated by Loc stimulation of cat cerebellar cortex. A: potentials recorded at 4 parallel tracks are arranged in columns. Records were obtained at indicated depths. Lowest trace in each column is surface response. First column is accurately on beam of excited parallel fibers (0 μm). Other columns are recorded at lateralities of 200, 400, and 600 μm from the beam, respectively. Perpendicular broken lines indicate point of measurement of field‐potential amplitudes displayed in B. B: depth and transverse measurements of amplitudes of field potentials shown in A. The 7 tracks indicate potential measurements in arbitrary units at 5.3 ms latency for series in A and also for the 3 other tracks at 100, 300, and 500 μm. Approximately isopotential contour lines are drawn for values indicated by arrows. Note large lateral and deep spread of positive potential field in track 400 μm lateral to center of beam of excited parallel fibers (0 μm). C: field potentials obtained at depth indicated to left. D: corresponding current source‐density analysis, demonstrating localization of current. Note that positivity below 200 μm in C is not accompanied by large current flow at that level in D. E: surface recording of field potential generated by parallel fiber activation. F: superimposed current‐source densities in similar location before and after application of synaptic blocking agent manganese. This enables the pre‐ and postsynaptic components to be verified. Time scales are the same, recording position is just below cerebellar surface.

A and B adapted from Eccles, Llinás, and Sasaki 54; C and D from Nicholson and Llinás 189; E and F from Nicholson et al. 186
Figure 3. Figure 3.

Cerebellar field potentials recorded at different depths and evoked by local stimulation of surface of cerebellum in different vertebrates. A: frog field potentials evoked by parallel fiber activation at surface of cerebellum and recorded at different depths from cerebellar surface as indicated in microns at left of records. Depth is same for all records in a given horizontal plane. Note that in frog the late negativity is clearly reversed at 200 μm. B: similar type of records obtained from an alligator cerebellum at indicated depths. Note large negative potential that follows the parallel fiber compound action current (first negativity) from surface up to 300‐μm depth. C: records obtained from pigeon cerebellum as in A and B. Note that as for alligator, late negativity recorded at surface is present up to 300‐μm depth. D: field potential generated in cat cerebellum by parallel fiber volley. Late negativity recorded at surface of cortex (0 μm) reversed at 100 μm, reached maximum at 200 μm, and decreased progressively with depth. Time and voltage calibrations as indicated.

From Llinás et al. 147
Figure 4. Figure 4.

Laminar field potentials evoked by antidromic activation of Purkinje cells in frog, alligator, and cat. Records illustrated were generated by JF stimulation and recorded at depth indicated in microns to left of each series of traces. In all records, early negative response diminishes in amplitude, increases in latency, and quickly reverses as microelectrode is withdrawn. Difference in time courses between frog and alligator and that of cat probably reflect temperature differences.

Data for frog from Llinás et al. 144; data for alligator from Nicholson and Llinás 188; data for cats from Eccles, Llinás, and Sasaki 52
Figure 5. Figure 5.

Field potentials and current densities evoked by mossy fiber activation at different depths in cerebellar cortex. A: field potentials evoked by transfolial stimulation. A superficial negativity, the N3 wave, is first potential to be seen in depth. It corresponds to action potential in parallel fibers via mossy fiber‐granule cell relay. At 300‐ to 500‐μm depths an earlier negativity, the N2 wave, is split by a sharp positivity (marked by arrow in trace at 500 μm) attributed to activation of ascending axons of granule cells. B: current‐density analysis of mossy fiber response. Current densities were computed from laminar field potentials. Flows toward pial surface are indicated as positive. Principal excitatory components of current densities at time t1 are indicated by vertically hatched areas and peak current by vertical bar. Calibrations: 50 g·wt for tension; 0.95 μA/mm2 for molecular layer and 0.50 μm2/mm2 for granular layer current densities.

A adapted from Eccles, Llinás, and Sasaki 55; B adapted from Kwan and Murphy 130
Figure 6. Figure 6.

Field potentials produced in cat cerebellar cortex by contralateral stimulation of inferior olive. Field potential is characterized by initial negativity followed by positivity at granular and molecular layers and by superficial negativity at levels above 200 μm. Small difference in latency of early negativity at different depths reflects conduction time of climbing fiber action potentials in molecular layer.

Adapted from Eccles, Llinás, and Sasaki 51
Figure 7. Figure 7.

Ionic mechanisms for Purkinje cell firing. A–F: recordings from mammalian Purkinje cell somata in vitro. A–C: repetitive firing obtained with prolonged current pulses. In A, threshold current stimulus produces repetitive activation of Purkinje cell after initial local response (arrow). In B and C., increases in current injection amplitude produce high‐frequency firing and an oscillatory behavior marked with arrows in B. D–E: tetrodotoxin (TTX) sensitivity of Purkinje cell spikes. In D, control response to square pulse depolarization. In E, similar pulse after addition of TTX to bath. Note that fast spikes are blocked, whereas slower oscillations and afterdepolarization (arrow) remain. F: addition of cobalt chloride (Co) to TTX saline removes all electroresponsiveness.

Adapted from Llinás and Sugimori 154
Figure 8. Figure 8.

Dendritic recording from mammalian Purkinje cells in vitro. A: composite picture showing relationship between somatic and dendritic action potentials following D. C: depolarization through recording electrode. A clear shift in amplitude of fast action potentials and dendritic calcium‐dependent spikes is seen when comparing the more superficial recording in B with the somatic recording in E. Note that at increasing distances from the soma, fast spikes are reduced in amplitude and are barely noticeable in more peripheral recordings. Prolonged and slow‐rising burst spikes are more prominent at dendritic level, however. F: calcium‐dependent plateau and burst spikes. These plateau potentials seen intradendritically with short depolarizations are recorded in presence of tetrodotoxin (TTX). As stimulus is increased, prolonged local responses are observed which ultimately result in full dendritic spike bursts. G: addition of cadmium chloride (Cd) to TTX solution produces complete blockage of plateau and burst response recorded intradendritically.

Adapted from Llinás and Sugimori 155
Figure 9. Figure 9.

Direct stimulation of an in vitro guinea pig Purkinje cell after blockage of calcium conductance with cobalt chloride (Co). Arrows indicate onset of slow voltage‐dependent sodium conductance, which generates repetitive firing. Note that plateau level seems independent at level of current injection (lower traces).

Adapted from Llinás and Sugimori 154
Figure 10. Figure 10.

Climbing fiber activation of mammalian Purkinje cell in vitro. A: all‐or‐none Purkinje cell activation after JF stimulation. B: reversal of climbing fiber‐evoked synaptic potential. Properties of reversal are particularly clear at 18, 22, and 28 nA, where biphasic nature of reversal is clearly observed. C: voltage‐current relationship for synaptic potential. Bottom: computer display of somatic potentials after synaptic activation of the 3 different compartments in cable model. The 1st set of records to left illustrates EPSP at normal resting potential and its reversal as membrane is depolarized to +50 mV. The EPSP is generated by superposition of synaptic inputs to compartments 1, 2, and 3. Next set of records (labeled 1) is produced by synaptic input restricted to 1st compartment, whereas 2 and 3 are restricted to 2nd and 3rd compartments, respectively. Note that when synaptic input is restricted to compartment 1, EPSP reversal (at approximately −15 mV) is a mirror image of its depolarized counterpart. Potential generated by an input to compartment 2 reverses at approximately +40 mV. Input to compartment 3 does not reverse at all for same current level. When 1, 2, and 3 are activated (with progressive delay of 0.2 ms between compartments to allow for climbing fiber propagation time), reversal is biphasic as in experimental data. Current‐injection levels increase from zero at lowest level to 40 nA at uppermost level, in 5‐nA steps.

From Llinás and Nicholson 151
Figure 11. Figure 11.

Climbing fiber activation of Purkinje cells recorded extra‐ and intracellularly. A–D: climbing fiber responses in frog Purkinje cells. In A, extracellular recording from Purkinje cell identified by its all‐or‐none antidromic activation from underlying white matter. As stimulus is increased, an all‐or‐none burst of 6 spikes is recorded (B), which has a very regular amplitude and time course (3 superimposed traces). In C and D, intracellular records from another frog Purkinje cell showing climbing fiber EPSP after stimulus to white matter. In C, all‐or‐none nature of EPSP is shown by electrical stimulation at threshold level. In D, 2 EPSPs are superimposed to show their regularity in latency and time course. Time and voltage calibration as indicated. E–F: extracellular recordings from alligator Purkinje cell. As in frog, alligator Purkinje cells are activated antidromically from white matter (E). All‐or‐none climbing fiber burst of spikes is shown in E, generating a large action potential followed by 3 small spikes. The regularity of this response is illustrated in F, where 2 sweeps have been superimposed. G–H: intracellular records from another Purkinje cell show all‐or‐none climbing fiber EPSP (G) and 2 superimposed with stimuli at suprathreshold level. Time and voltage calibrations as indicated. I–J: extracellular potentials from pigeon Purkinje cell after JF stimulation. In I, antidromic invasion of Purkinje cell. In J, all‐or‐none climbing fiber bursts of spikes. In K, intracellular record from same cell. After antidromic action potential, the climbing fiber activation generates a long‐lasting burst of spikes. Time and voltage calibration as indicated. L–O: extracellular potentials from cat Purkinje cells. L shows all‐or‐none antidromic Purkinje cell spike. In O, all‐or‐none climbing fiber spike burst. Intracellular record from another Purkinje cell after activation of underlying white matter (N) shows antidromic action potential followed by large climbing fiber depolarization. In O, all‐or‐none climbing fiber EPSP generated by stimulation of contralateral olive. Time and voltage calibration as indicated.

From Llinás and Hillman 146
Figure 12. Figure 12.

Intracellular recordings from Purkinje cells illustrate synaptic potentials evoked by climbing fiber activation. In 1st column, climbing fiber EPSP is reversed by currect injection in an in vitro frog preparation. In 2nd column (alligator), climbing fiber EPSP is evoked by white matter stimulation. All‐or‐none nature of EPSP is illustrated in upper trace. Reversal of EPSP is observed with depolarizing (Dep) current pulses. Arrows on left indicate onset of pulse. Arrows on right indicate stimulus artifact. In 3rd column are superimposed records of climbing fiber EPSPs evoked in a cat Purkinje cell by JF stimulation with depolarizing and hyperpolarizing (Hyp) current pulses. Note that reflexly activated repetitive climbing fiber response of this cell (marked by arrows) was altered by applied current in same way as directly evoked EPSP.

Data for frog from Hackett 83; data for alligator from Llinás and Nicholson 149; data for cat from Eccles, Llinás, and Sasaki 51
Figure 13. Figure 13.

Patches of tactile projections to left paramedian lobe (PML) portrayed by both figurine (A) and patch mosiac (B) methods. A: figurine map collated from data gathered in 2 rats. Black patch on each figurine shows receptive field (RF) location, which, when stimulated, activates multiple units in granule cell layer at site shown by black dots in C. Note that projections to PML derive from entire body, but primarily from upper and lower lips. However, RFs from these mouth parts are smaller than those from forelimb, hindlimb, and trunk. Contralateral RFs are shown by black patches on right side of body. B: schematic outlines shown here illustrate patchlike character of projections from specific body structures or regions. This mosaic of patch projections was prepared by drawing a line around all adjacent figures shown in A with similar RF projections. For example, most lateral hand patch (h) is similar in shape and size with region in A occupied by the 11 hand figurines. Boundaries between adjacent patch projections seem to be discrete rather than continuous, revealing a fractured (or disjunctive) somatotopic organization. Specific body regions may project to more than 1 patch, showing multiple representation. For example, there are several lower lip patches. Most contralateral patch projections (encircled by dots in B) are found medially. Bilateral fields (encircled by solid lines) are more lateral. A tiny contralateral projection from upper lip was found just lateral to all ipsilateral projections. fl, Forelimb; h, hand; hl, hindlimb (includes trunk and hindlimb); li, lower incisor, ll, lower lip; ui, upper incisor; ul, upper lip; V, mystacial vibrissae. C: drawing of cerebellum indicating location of electrode punctures (black dots).

From Shambes et al. 224
Figure 14. Figure 14.

Proposed radial organization of ascending axon of granule cells. Granule cells (in circle) are assumed to contact Purkinje cells (hatched) not only via parallel fibers but also via ascending portion of their axons. Granule cell to left indicates possibility of a number of contacts 4 between 1 ascending granule cell axon and 1 Purkinje cell.

From Llinás 141
Figure 15. Figure 15.

Inhibitory postsynaptic potentials in cat Purkinje cells. A: intracellular recording obtained at depth of 360 μm with graded Loc stimulation at indicated strengths; a corresponding just‐extracellular recording is below each trace. Time and voltage calibrations as indicated. B: inhibitory synaptic potential inverted by intracellular chloride injection. IPSPs recorded in Purkinje cell at 300‐μm depth was inverted by chloride diffusion out of electrode. First trace shows inhibitory synaptic noise in a series of 3 superimposed traces. In 6 subsequent traces, stimulation was progressively increased, as shown by strengths on arbitrary scale. Note difference in time course between normal and reversed IPSPs.

Adapted from Eccles, Llinás, and Sasaki 56
Figure 16. Figure 16.

Extracellular recording of responses of presumed inhibitory interneurons. A: volley of impulses recorded at 350‐μm depth was generated in parallel fibers by a stimulus of progressively increasing strength (given in arbitrary units to left) applied through a surface stimulating electrode. B: 2 parallel fiber volleys at 180‐μm depth. Conditioning and testing local stimuli were kept constant and stimulus interval was varied. Control testing response (CON) had 4 spikes. LOC, parallel fiber.

From Eccles, Llinás, and Sasaki 53
Figure 17. Figure 17.

Golgi cell inhibition. A–B: diagrams illustrating position of glomerulus in neuronal network of cerebellar cortex and an idealized version of its ultrastructure. A gives a quasi‐stereoscopic view of a small part of cerebellar folium into which mossy afferents (Mo) enter; their synaptic expansions are rosettes. Rosettes are connected mainly by short, claw‐shaped dendrites of granule cells (Gr) and by the descending dendrites of large Golgi neurons (black). Ascending axons of granule cells give rise to parallel fibers (Pf), which while running in longitudinal axis of folium, pierce flattened dendritic trees of Purkinje neurons (Pu, represented here as spade‐shaped boxes). Axon branches of Golgi neurons (Go ax) enter glomeruli and give rise to a plexus of small beaded terminals. B shows synaptic relations of these elements within glomerulus as seen with electron microscope. Mo, mossy afferent; GrD, granule dendrites entering through glial capsule (Gl) of glomerulus and terminating in characteristic bulbous terminals or digits; Dd, desmosomoid dendrodendritic contacts; GoD, descending dendrite of Golgi cell neuron with characteristic small spines, which makes broad contact with mossy rosette. Golgi axon terminals situated in periphery of glomerulus (hatched) establish synaptic contacts exclusively with granule cell dendrites. C illustrates electrode placement. D–G: inhibition of repetitive firing of impulses by granule cells in response to Loc stimulation. In D, single granule cell was fired repetitively by single stimulus to superficial radial nerve (SR). In E, this response was inhibited by a reconditioning Loc stimulus that preceded SR stimulus at increasing intervals. In F, spontaneous activity of several granule cells recorded at 600‐μm depth, inhibited by local stimulation in G. H–K: effects of a preceding Loc stimulation on EPSPs in Purkinje cell evoked by transfolial (TF) and local stimulation. The EPSP evoked by TF stimulation (H) was depressed by a preceding Loc stimulation of increasing strengths (I). The EPSP evoked in the same cell by an Loc stimulus (J) was not depressed by a conditioning Loc stimulus but enhanced (K).

A and B from Szentágothai 238; D–K from Eccles, Llinás, and Sasaki 55
Figure 18. Figure 18.

Stellate and basket cell inhibition of Purkinje cells in different vertebrates. In elasmobranch, intracellularly recorded EPSP‐IPSP sequence following local stimuli of increasing strength. Note ripples, indicated by dots, which appear to be unitary IPSPs. In frog, intracellular recordings from Purkinje cells after surface stimulation. Graded EPSP‐IPSP sequence is illustrated for increasing amplitudes of Loc stimulation. In alligator, 1st trace represents a threshold activation of parallel fibers. Stimulus strength is then increased from this level to 2.5 times threshold in the 5th trace. Last trace shows field potential recorded extracellularly in immediate vicinity of Purkinje cell. Arrow in upper trace indicates presence of spontaneous IPSP. In cat, similar set of records obtained by local stimulation in cerebellum. Recordings obtained immediately below beam of activated parallel fibers.

Data for elasmobranch from Nicholson, Llinás, and Precht 190; data for frog from Freeman and Lubozynski 70; data for alligator from Llinás and Nicholson 149; data for cat from Eccles, Llinás, and Sasaki 56
Figure 19. Figure 19.

Diagrammatic illustration of monosynaptic connections between cerebellar cortex and Deiters' neurons. In A, Deiters' nucleus (Deit), which generates vestibulospinal tract (VST), receives excitatory inputs from both mossy and climbing fiber collaterals. In addition it receives excitatory input from fastigial nucleus (F). Purkinje cells produce direct inhibition on Deiters' neurons. B–E: intracellular recordings obtained from Deiters' nucleus after stimulation of cerebellar cortex (S) and recorded with a microelectrode (M). The IPSP in Deiters' neurons is produced by stimulation of ipsilateral anterior lobe of cerebellum. Stimulation was increased from 1.9 to 30 V to vermal cortex at lobule IV. Dotted lines in E indicate time course of potential changes if similar to that shown in D. F: IPSP shown at slower sweep speed after activation of lobule III. G–H: suppression and rebound facilitation of spontaneous discharge induced by stimulation of lobule III. In H, there is absence of spontaneous firing.

Adapted from Ito and Yoshida 108
Figure 20. Figure 20.

Inhibitory action on Deiters' neurons via activation of Purkinje cell after spinal cord stimulation. A: extracellular and intracellular recording from Deiters' neurons to indicate (upper trace) antidromic invasion followed by 2 periods of excitation (arrows) and 2 silent periods in between. Lower trace, intracellular correlation of these excitability changes, consisting of an early and a late EPSP‐IPSP sequence. B: synaptic potential pattern evoked in Deiters' neurons by spinal cord stimulation at 2nd cervical vertebra. The 1st response is antidromic spike, which is followed by early excitation and inhibition. This response is followed (dot) by an excitatory potential and a fast inhibition produced by mossy fiber collateral activation of the nucleus and the inhibition via mossy fiber activation of Purkinje cells. The 2nd excitatory potential with a latency of 12 ms and the large inhibition and rebound excitation that ensues is due to activation of olivocerebellar pathway. C: early IPSP generated via mossy fiber Purkinje cell activation is quite stable, and late fast IPSP generated via climbing fiber activation of Purkinje cells shows discrete components. Its activation is very dependent on frequency. In D, discrete nature of this inhibition shows a clear latency shift for both early excitatory (dot) and fast inhibitory potential. E–F: disappearance of late IPSP after lesion of inferior olive. E: control inhibition, showing early and late (dot) IPSP at 2 different sweep speeds. In F, same situation as E, but after transection of olivocerebellar tract by midline section. Note lack of postinhibitory rebound in slow sweep speed record in F. Calibrations: voltage 5 mV except for top portion of A, which is 0.2 mV; time 10 ms except for right portion of E, which is 50 ms.

A and B from Bruggencate et al. 31; C–F from Bruggencate et al. 32
Figure 21. Figure 21.

Electrical excitability of mammalian inferior olivary cells tested in vitro. A–C: normal electroresponsiveness. D–F: electrophysiology after calcium blockage by extracellular cobalt (Co). G–I: electrophysiological properties after blockage of sodium conductance by extracellular tetrodotoxin (TTX), indicating 2 different sets of calcium‐dependent action potentials. In B, subthreshold current pulse is given at resting membrane potential. In A, subthreshold stimulus is superimposed on a small DC depolarization (dotted line, with respect to solid line), generating a fast action potential followed by an afterdepolarization and a prolonged afterhyperpolarization. In C, hyperpolarization about 8 mV from rest (dotted line) also produces an increase in excitability as seen by action potential generated by otherwise subthreshold stimulus. Records A–C have been separated for clarity. In D–F, there is a similar sequence as in A–C but after blockage of calcium conductance by extracellular cobalt. Notice that in D, action potential lacks afterdepolarization and prolonged afterhyperpolarization seen in A. In F, subthreshold stimulus riding on hyperpolarization is now incapable of generating an action potential. In G–I, sodium spike has been blocked by TTX. Again in H, subthreshold stimulus can generate an action potential by either depolarizing (G) or hyperpolarizing (I) membrane potential change. Although fast action potentials in A, C, and D are generated by sodium‐dependent conductances, the afterdepolarizations in A and C and in G and I are generated by calcium conductances. Those of A and G are generated by high‐threshold calcium‐dependent action potentials from dendrites. Those in C and I are generated by inactivating calcium conductances at somatic level.

From Llinás and Yarom 160
Figure 22. Figure 22.

Rhythmic firing of inferior olivary neurons. A: rebound calcium spike in presence of tetrodotoxin. Direct stimulation of inferior olivary neuron produces a dendritic calcium spike, followed by an afterhyperpolarization and a rebound spike (arrow). Small changes in DC hyperpolarizations (note current record) facilitate rebound spike, which becomes larger and moves to left. B: diagram illustrating sequence of events that generates inferior olivary cell rebound leading to oscillation. Antidromic or direct stimulation generates a somatic sodium spike having a fast rise and about 1‐ms duration (broken line). At appropriate membrane potential, this action potential generates a dendritic calcium spike that produces a plateau afterdepolarization followed by a sizable potassium conductance that generates prolonged afterhyperpolarization. This membrane hyperpolarization removes inactivation from somatic calcium conductance, which can then produce a rebound depolarization and can start the sequence once again.

Adapted from Llinás and Yarom 159
Figure 23. Figure 23.

Electrotonic coupling between inferior olivary (IO) neurons. A: 2 simultaneously recorded IO cells fired by antidromic stimulus. B: In a 2nd pair, hyperpolarization of lower cells through recording electrode hyperpolarizes 2nd cell (upper trace). To right: diagram of inferior olivary glomerulus. Top: general organization of IO glomerulus. In central core, dendritic branches are seen coupled by means of gap junctions (arrowheads). Central core is surrounded by synaptic terminals (ST), which establish contact with core elements. Bottom: on left, path of coupling current between 2 IO neurons and, on right, hypothetical function for synaptic junction at glomerulus. When synapses are activated, conductance change produced by synaptic transmitter action on postsynaptic membrane produces a shunt at glomerular level that reduces coupling coefficient between cells, since current tends to be lost across shunt.

A and B from Llinás and Yarom 159; diagrams on right from Llinás 139
Figure 24. Figure 24.

Limb movement as tensorial entity. A: on left, an upward displacement vector is a physical entity that can be expressed in different reference frames: e.g., by x,y coordinate system, or by α,β,γ‐ordered set of 3 quantities. On right, 2 reference frames shown are of fundamentally different kinds: applies to CNS‐independent external space; α,β,γ applies to space inherently connected to CNS. Limb‐displacement vector occurs in both spaces. Different expressions of the vector are related by limb‐displacement tensor, . B–D: covariant analysis and contravariant synthesis via a metric tensor. B: given a 2‐dimensional intended vector and 3 α,β,γ‐axes of an overcomplete reference frame, the decomposition could be performed by a 2‐step operation. First, covariant components of can be established (C), using geometry of 2‐space, to any number of directions independently. (Perpendicular projections, i.e., the inner products, provide “features” of desired vector in any coordinate direction.) Physical sum of covariant components, however, is not equal to displacement. Second, provided that metric tensor is available (in contravariant expression) for the α,β,γ‐space, corresponding set of contravariant components can be established (D). Physical sum of contravariant components physically generates displacement vector .

Adapted from Pellionisz and Llinás 209
Figure 25. Figure 25.

Circuit exemplifying certain mechanisms characteristic of Boylls' synergic parameterization theory. This circuit represents only 1 of a number of alternative realizations consistent with existing physiological knowledge. PF, parallel fibers; MF, mossy fibers; CF, climbing fibers; g, granule cells.


Figure 1.

Upper left: diagram of basic cerebellar circuit comprising mossy and climbing fiber inputs to Purkinje cells. Activity in mossy fiber (MF) is relayed through granule cells (GC) via parallel fibers (PF) to the Purkinje cell (PC). Axons of these cells are the only output system from cerebellar cortex. Second afferent is a climbing fiber (CF), which establishes a monosynaptic input to Purkinje cell dendrites. Upper right: diagram of the 2 basic inhibitory systems of cerebellar cortex. On left, basket cell axon contacts the somata of Purkinje cells. These axons also contact dendrites of these cells. Stellate cell (not shown) establishes direct contact with Purkinje cell dendrites. Both basket (BC) and stellate cells receive input via parallel fibers (PF) and constitute the inhibitory systems of the molecular layer. Golgi cell (GC to right) receives input from parallel fibers, mossy fibers (MF), and climbing fibers (not shown) and relays inhibition onto dendrites of granule cells (GrC) in granular layer. Bottom: detail of geometric organization of neuronal elements of cerebellar cortex. Drawing demonstrates different sections through a cerebellar folium. A: transverse plane. B: saggital plane. C: tangential plane. Cellular elements are displayed in drawings A, B, and C, as though the cerebellum were transparent. Orthogonal organization of parallel fibers, with respect to isoplanar characteristics of dendrites of Purkinje cells and basket and stellate cells (SC), is self‐explanatory. Note that axons of basket and stellate cells run at right angles with respect to parallel fibers and that dendritic tree of Golgi cells is close to cylindrical rather than isoplanar.

Upper left and upper right adapted from Ramón y Cajal 215; bottom from Llinás 138


Figure 2.

Field potentials and corresponding current densities generated by Loc stimulation of cat cerebellar cortex. A: potentials recorded at 4 parallel tracks are arranged in columns. Records were obtained at indicated depths. Lowest trace in each column is surface response. First column is accurately on beam of excited parallel fibers (0 μm). Other columns are recorded at lateralities of 200, 400, and 600 μm from the beam, respectively. Perpendicular broken lines indicate point of measurement of field‐potential amplitudes displayed in B. B: depth and transverse measurements of amplitudes of field potentials shown in A. The 7 tracks indicate potential measurements in arbitrary units at 5.3 ms latency for series in A and also for the 3 other tracks at 100, 300, and 500 μm. Approximately isopotential contour lines are drawn for values indicated by arrows. Note large lateral and deep spread of positive potential field in track 400 μm lateral to center of beam of excited parallel fibers (0 μm). C: field potentials obtained at depth indicated to left. D: corresponding current source‐density analysis, demonstrating localization of current. Note that positivity below 200 μm in C is not accompanied by large current flow at that level in D. E: surface recording of field potential generated by parallel fiber activation. F: superimposed current‐source densities in similar location before and after application of synaptic blocking agent manganese. This enables the pre‐ and postsynaptic components to be verified. Time scales are the same, recording position is just below cerebellar surface.

A and B adapted from Eccles, Llinás, and Sasaki 54; C and D from Nicholson and Llinás 189; E and F from Nicholson et al. 186


Figure 3.

Cerebellar field potentials recorded at different depths and evoked by local stimulation of surface of cerebellum in different vertebrates. A: frog field potentials evoked by parallel fiber activation at surface of cerebellum and recorded at different depths from cerebellar surface as indicated in microns at left of records. Depth is same for all records in a given horizontal plane. Note that in frog the late negativity is clearly reversed at 200 μm. B: similar type of records obtained from an alligator cerebellum at indicated depths. Note large negative potential that follows the parallel fiber compound action current (first negativity) from surface up to 300‐μm depth. C: records obtained from pigeon cerebellum as in A and B. Note that as for alligator, late negativity recorded at surface is present up to 300‐μm depth. D: field potential generated in cat cerebellum by parallel fiber volley. Late negativity recorded at surface of cortex (0 μm) reversed at 100 μm, reached maximum at 200 μm, and decreased progressively with depth. Time and voltage calibrations as indicated.

From Llinás et al. 147


Figure 4.

Laminar field potentials evoked by antidromic activation of Purkinje cells in frog, alligator, and cat. Records illustrated were generated by JF stimulation and recorded at depth indicated in microns to left of each series of traces. In all records, early negative response diminishes in amplitude, increases in latency, and quickly reverses as microelectrode is withdrawn. Difference in time courses between frog and alligator and that of cat probably reflect temperature differences.

Data for frog from Llinás et al. 144; data for alligator from Nicholson and Llinás 188; data for cats from Eccles, Llinás, and Sasaki 52


Figure 5.

Field potentials and current densities evoked by mossy fiber activation at different depths in cerebellar cortex. A: field potentials evoked by transfolial stimulation. A superficial negativity, the N3 wave, is first potential to be seen in depth. It corresponds to action potential in parallel fibers via mossy fiber‐granule cell relay. At 300‐ to 500‐μm depths an earlier negativity, the N2 wave, is split by a sharp positivity (marked by arrow in trace at 500 μm) attributed to activation of ascending axons of granule cells. B: current‐density analysis of mossy fiber response. Current densities were computed from laminar field potentials. Flows toward pial surface are indicated as positive. Principal excitatory components of current densities at time t1 are indicated by vertically hatched areas and peak current by vertical bar. Calibrations: 50 g·wt for tension; 0.95 μA/mm2 for molecular layer and 0.50 μm2/mm2 for granular layer current densities.

A adapted from Eccles, Llinás, and Sasaki 55; B adapted from Kwan and Murphy 130


Figure 6.

Field potentials produced in cat cerebellar cortex by contralateral stimulation of inferior olive. Field potential is characterized by initial negativity followed by positivity at granular and molecular layers and by superficial negativity at levels above 200 μm. Small difference in latency of early negativity at different depths reflects conduction time of climbing fiber action potentials in molecular layer.

Adapted from Eccles, Llinás, and Sasaki 51


Figure 7.

Ionic mechanisms for Purkinje cell firing. A–F: recordings from mammalian Purkinje cell somata in vitro. A–C: repetitive firing obtained with prolonged current pulses. In A, threshold current stimulus produces repetitive activation of Purkinje cell after initial local response (arrow). In B and C., increases in current injection amplitude produce high‐frequency firing and an oscillatory behavior marked with arrows in B. D–E: tetrodotoxin (TTX) sensitivity of Purkinje cell spikes. In D, control response to square pulse depolarization. In E, similar pulse after addition of TTX to bath. Note that fast spikes are blocked, whereas slower oscillations and afterdepolarization (arrow) remain. F: addition of cobalt chloride (Co) to TTX saline removes all electroresponsiveness.

Adapted from Llinás and Sugimori 154


Figure 8.

Dendritic recording from mammalian Purkinje cells in vitro. A: composite picture showing relationship between somatic and dendritic action potentials following D. C: depolarization through recording electrode. A clear shift in amplitude of fast action potentials and dendritic calcium‐dependent spikes is seen when comparing the more superficial recording in B with the somatic recording in E. Note that at increasing distances from the soma, fast spikes are reduced in amplitude and are barely noticeable in more peripheral recordings. Prolonged and slow‐rising burst spikes are more prominent at dendritic level, however. F: calcium‐dependent plateau and burst spikes. These plateau potentials seen intradendritically with short depolarizations are recorded in presence of tetrodotoxin (TTX). As stimulus is increased, prolonged local responses are observed which ultimately result in full dendritic spike bursts. G: addition of cadmium chloride (Cd) to TTX solution produces complete blockage of plateau and burst response recorded intradendritically.

Adapted from Llinás and Sugimori 155


Figure 9.

Direct stimulation of an in vitro guinea pig Purkinje cell after blockage of calcium conductance with cobalt chloride (Co). Arrows indicate onset of slow voltage‐dependent sodium conductance, which generates repetitive firing. Note that plateau level seems independent at level of current injection (lower traces).

Adapted from Llinás and Sugimori 154


Figure 10.

Climbing fiber activation of mammalian Purkinje cell in vitro. A: all‐or‐none Purkinje cell activation after JF stimulation. B: reversal of climbing fiber‐evoked synaptic potential. Properties of reversal are particularly clear at 18, 22, and 28 nA, where biphasic nature of reversal is clearly observed. C: voltage‐current relationship for synaptic potential. Bottom: computer display of somatic potentials after synaptic activation of the 3 different compartments in cable model. The 1st set of records to left illustrates EPSP at normal resting potential and its reversal as membrane is depolarized to +50 mV. The EPSP is generated by superposition of synaptic inputs to compartments 1, 2, and 3. Next set of records (labeled 1) is produced by synaptic input restricted to 1st compartment, whereas 2 and 3 are restricted to 2nd and 3rd compartments, respectively. Note that when synaptic input is restricted to compartment 1, EPSP reversal (at approximately −15 mV) is a mirror image of its depolarized counterpart. Potential generated by an input to compartment 2 reverses at approximately +40 mV. Input to compartment 3 does not reverse at all for same current level. When 1, 2, and 3 are activated (with progressive delay of 0.2 ms between compartments to allow for climbing fiber propagation time), reversal is biphasic as in experimental data. Current‐injection levels increase from zero at lowest level to 40 nA at uppermost level, in 5‐nA steps.

From Llinás and Nicholson 151


Figure 11.

Climbing fiber activation of Purkinje cells recorded extra‐ and intracellularly. A–D: climbing fiber responses in frog Purkinje cells. In A, extracellular recording from Purkinje cell identified by its all‐or‐none antidromic activation from underlying white matter. As stimulus is increased, an all‐or‐none burst of 6 spikes is recorded (B), which has a very regular amplitude and time course (3 superimposed traces). In C and D, intracellular records from another frog Purkinje cell showing climbing fiber EPSP after stimulus to white matter. In C, all‐or‐none nature of EPSP is shown by electrical stimulation at threshold level. In D, 2 EPSPs are superimposed to show their regularity in latency and time course. Time and voltage calibration as indicated. E–F: extracellular recordings from alligator Purkinje cell. As in frog, alligator Purkinje cells are activated antidromically from white matter (E). All‐or‐none climbing fiber burst of spikes is shown in E, generating a large action potential followed by 3 small spikes. The regularity of this response is illustrated in F, where 2 sweeps have been superimposed. G–H: intracellular records from another Purkinje cell show all‐or‐none climbing fiber EPSP (G) and 2 superimposed with stimuli at suprathreshold level. Time and voltage calibrations as indicated. I–J: extracellular potentials from pigeon Purkinje cell after JF stimulation. In I, antidromic invasion of Purkinje cell. In J, all‐or‐none climbing fiber bursts of spikes. In K, intracellular record from same cell. After antidromic action potential, the climbing fiber activation generates a long‐lasting burst of spikes. Time and voltage calibration as indicated. L–O: extracellular potentials from cat Purkinje cells. L shows all‐or‐none antidromic Purkinje cell spike. In O, all‐or‐none climbing fiber spike burst. Intracellular record from another Purkinje cell after activation of underlying white matter (N) shows antidromic action potential followed by large climbing fiber depolarization. In O, all‐or‐none climbing fiber EPSP generated by stimulation of contralateral olive. Time and voltage calibration as indicated.

From Llinás and Hillman 146


Figure 12.

Intracellular recordings from Purkinje cells illustrate synaptic potentials evoked by climbing fiber activation. In 1st column, climbing fiber EPSP is reversed by currect injection in an in vitro frog preparation. In 2nd column (alligator), climbing fiber EPSP is evoked by white matter stimulation. All‐or‐none nature of EPSP is illustrated in upper trace. Reversal of EPSP is observed with depolarizing (Dep) current pulses. Arrows on left indicate onset of pulse. Arrows on right indicate stimulus artifact. In 3rd column are superimposed records of climbing fiber EPSPs evoked in a cat Purkinje cell by JF stimulation with depolarizing and hyperpolarizing (Hyp) current pulses. Note that reflexly activated repetitive climbing fiber response of this cell (marked by arrows) was altered by applied current in same way as directly evoked EPSP.

Data for frog from Hackett 83; data for alligator from Llinás and Nicholson 149; data for cat from Eccles, Llinás, and Sasaki 51


Figure 13.

Patches of tactile projections to left paramedian lobe (PML) portrayed by both figurine (A) and patch mosiac (B) methods. A: figurine map collated from data gathered in 2 rats. Black patch on each figurine shows receptive field (RF) location, which, when stimulated, activates multiple units in granule cell layer at site shown by black dots in C. Note that projections to PML derive from entire body, but primarily from upper and lower lips. However, RFs from these mouth parts are smaller than those from forelimb, hindlimb, and trunk. Contralateral RFs are shown by black patches on right side of body. B: schematic outlines shown here illustrate patchlike character of projections from specific body structures or regions. This mosaic of patch projections was prepared by drawing a line around all adjacent figures shown in A with similar RF projections. For example, most lateral hand patch (h) is similar in shape and size with region in A occupied by the 11 hand figurines. Boundaries between adjacent patch projections seem to be discrete rather than continuous, revealing a fractured (or disjunctive) somatotopic organization. Specific body regions may project to more than 1 patch, showing multiple representation. For example, there are several lower lip patches. Most contralateral patch projections (encircled by dots in B) are found medially. Bilateral fields (encircled by solid lines) are more lateral. A tiny contralateral projection from upper lip was found just lateral to all ipsilateral projections. fl, Forelimb; h, hand; hl, hindlimb (includes trunk and hindlimb); li, lower incisor, ll, lower lip; ui, upper incisor; ul, upper lip; V, mystacial vibrissae. C: drawing of cerebellum indicating location of electrode punctures (black dots).

From Shambes et al. 224


Figure 14.

Proposed radial organization of ascending axon of granule cells. Granule cells (in circle) are assumed to contact Purkinje cells (hatched) not only via parallel fibers but also via ascending portion of their axons. Granule cell to left indicates possibility of a number of contacts 4 between 1 ascending granule cell axon and 1 Purkinje cell.

From Llinás 141


Figure 15.

Inhibitory postsynaptic potentials in cat Purkinje cells. A: intracellular recording obtained at depth of 360 μm with graded Loc stimulation at indicated strengths; a corresponding just‐extracellular recording is below each trace. Time and voltage calibrations as indicated. B: inhibitory synaptic potential inverted by intracellular chloride injection. IPSPs recorded in Purkinje cell at 300‐μm depth was inverted by chloride diffusion out of electrode. First trace shows inhibitory synaptic noise in a series of 3 superimposed traces. In 6 subsequent traces, stimulation was progressively increased, as shown by strengths on arbitrary scale. Note difference in time course between normal and reversed IPSPs.

Adapted from Eccles, Llinás, and Sasaki 56


Figure 16.

Extracellular recording of responses of presumed inhibitory interneurons. A: volley of impulses recorded at 350‐μm depth was generated in parallel fibers by a stimulus of progressively increasing strength (given in arbitrary units to left) applied through a surface stimulating electrode. B: 2 parallel fiber volleys at 180‐μm depth. Conditioning and testing local stimuli were kept constant and stimulus interval was varied. Control testing response (CON) had 4 spikes. LOC, parallel fiber.

From Eccles, Llinás, and Sasaki 53


Figure 17.

Golgi cell inhibition. A–B: diagrams illustrating position of glomerulus in neuronal network of cerebellar cortex and an idealized version of its ultrastructure. A gives a quasi‐stereoscopic view of a small part of cerebellar folium into which mossy afferents (Mo) enter; their synaptic expansions are rosettes. Rosettes are connected mainly by short, claw‐shaped dendrites of granule cells (Gr) and by the descending dendrites of large Golgi neurons (black). Ascending axons of granule cells give rise to parallel fibers (Pf), which while running in longitudinal axis of folium, pierce flattened dendritic trees of Purkinje neurons (Pu, represented here as spade‐shaped boxes). Axon branches of Golgi neurons (Go ax) enter glomeruli and give rise to a plexus of small beaded terminals. B shows synaptic relations of these elements within glomerulus as seen with electron microscope. Mo, mossy afferent; GrD, granule dendrites entering through glial capsule (Gl) of glomerulus and terminating in characteristic bulbous terminals or digits; Dd, desmosomoid dendrodendritic contacts; GoD, descending dendrite of Golgi cell neuron with characteristic small spines, which makes broad contact with mossy rosette. Golgi axon terminals situated in periphery of glomerulus (hatched) establish synaptic contacts exclusively with granule cell dendrites. C illustrates electrode placement. D–G: inhibition of repetitive firing of impulses by granule cells in response to Loc stimulation. In D, single granule cell was fired repetitively by single stimulus to superficial radial nerve (SR). In E, this response was inhibited by a reconditioning Loc stimulus that preceded SR stimulus at increasing intervals. In F, spontaneous activity of several granule cells recorded at 600‐μm depth, inhibited by local stimulation in G. H–K: effects of a preceding Loc stimulation on EPSPs in Purkinje cell evoked by transfolial (TF) and local stimulation. The EPSP evoked by TF stimulation (H) was depressed by a preceding Loc stimulation of increasing strengths (I). The EPSP evoked in the same cell by an Loc stimulus (J) was not depressed by a conditioning Loc stimulus but enhanced (K).

A and B from Szentágothai 238; D–K from Eccles, Llinás, and Sasaki 55


Figure 18.

Stellate and basket cell inhibition of Purkinje cells in different vertebrates. In elasmobranch, intracellularly recorded EPSP‐IPSP sequence following local stimuli of increasing strength. Note ripples, indicated by dots, which appear to be unitary IPSPs. In frog, intracellular recordings from Purkinje cells after surface stimulation. Graded EPSP‐IPSP sequence is illustrated for increasing amplitudes of Loc stimulation. In alligator, 1st trace represents a threshold activation of parallel fibers. Stimulus strength is then increased from this level to 2.5 times threshold in the 5th trace. Last trace shows field potential recorded extracellularly in immediate vicinity of Purkinje cell. Arrow in upper trace indicates presence of spontaneous IPSP. In cat, similar set of records obtained by local stimulation in cerebellum. Recordings obtained immediately below beam of activated parallel fibers.

Data for elasmobranch from Nicholson, Llinás, and Precht 190; data for frog from Freeman and Lubozynski 70; data for alligator from Llinás and Nicholson 149; data for cat from Eccles, Llinás, and Sasaki 56


Figure 19.

Diagrammatic illustration of monosynaptic connections between cerebellar cortex and Deiters' neurons. In A, Deiters' nucleus (Deit), which generates vestibulospinal tract (VST), receives excitatory inputs from both mossy and climbing fiber collaterals. In addition it receives excitatory input from fastigial nucleus (F). Purkinje cells produce direct inhibition on Deiters' neurons. B–E: intracellular recordings obtained from Deiters' nucleus after stimulation of cerebellar cortex (S) and recorded with a microelectrode (M). The IPSP in Deiters' neurons is produced by stimulation of ipsilateral anterior lobe of cerebellum. Stimulation was increased from 1.9 to 30 V to vermal cortex at lobule IV. Dotted lines in E indicate time course of potential changes if similar to that shown in D. F: IPSP shown at slower sweep speed after activation of lobule III. G–H: suppression and rebound facilitation of spontaneous discharge induced by stimulation of lobule III. In H, there is absence of spontaneous firing.

Adapted from Ito and Yoshida 108


Figure 20.

Inhibitory action on Deiters' neurons via activation of Purkinje cell after spinal cord stimulation. A: extracellular and intracellular recording from Deiters' neurons to indicate (upper trace) antidromic invasion followed by 2 periods of excitation (arrows) and 2 silent periods in between. Lower trace, intracellular correlation of these excitability changes, consisting of an early and a late EPSP‐IPSP sequence. B: synaptic potential pattern evoked in Deiters' neurons by spinal cord stimulation at 2nd cervical vertebra. The 1st response is antidromic spike, which is followed by early excitation and inhibition. This response is followed (dot) by an excitatory potential and a fast inhibition produced by mossy fiber collateral activation of the nucleus and the inhibition via mossy fiber activation of Purkinje cells. The 2nd excitatory potential with a latency of 12 ms and the large inhibition and rebound excitation that ensues is due to activation of olivocerebellar pathway. C: early IPSP generated via mossy fiber Purkinje cell activation is quite stable, and late fast IPSP generated via climbing fiber activation of Purkinje cells shows discrete components. Its activation is very dependent on frequency. In D, discrete nature of this inhibition shows a clear latency shift for both early excitatory (dot) and fast inhibitory potential. E–F: disappearance of late IPSP after lesion of inferior olive. E: control inhibition, showing early and late (dot) IPSP at 2 different sweep speeds. In F, same situation as E, but after transection of olivocerebellar tract by midline section. Note lack of postinhibitory rebound in slow sweep speed record in F. Calibrations: voltage 5 mV except for top portion of A, which is 0.2 mV; time 10 ms except for right portion of E, which is 50 ms.

A and B from Bruggencate et al. 31; C–F from Bruggencate et al. 32


Figure 21.

Electrical excitability of mammalian inferior olivary cells tested in vitro. A–C: normal electroresponsiveness. D–F: electrophysiology after calcium blockage by extracellular cobalt (Co). G–I: electrophysiological properties after blockage of sodium conductance by extracellular tetrodotoxin (TTX), indicating 2 different sets of calcium‐dependent action potentials. In B, subthreshold current pulse is given at resting membrane potential. In A, subthreshold stimulus is superimposed on a small DC depolarization (dotted line, with respect to solid line), generating a fast action potential followed by an afterdepolarization and a prolonged afterhyperpolarization. In C, hyperpolarization about 8 mV from rest (dotted line) also produces an increase in excitability as seen by action potential generated by otherwise subthreshold stimulus. Records A–C have been separated for clarity. In D–F, there is a similar sequence as in A–C but after blockage of calcium conductance by extracellular cobalt. Notice that in D, action potential lacks afterdepolarization and prolonged afterhyperpolarization seen in A. In F, subthreshold stimulus riding on hyperpolarization is now incapable of generating an action potential. In G–I, sodium spike has been blocked by TTX. Again in H, subthreshold stimulus can generate an action potential by either depolarizing (G) or hyperpolarizing (I) membrane potential change. Although fast action potentials in A, C, and D are generated by sodium‐dependent conductances, the afterdepolarizations in A and C and in G and I are generated by calcium conductances. Those of A and G are generated by high‐threshold calcium‐dependent action potentials from dendrites. Those in C and I are generated by inactivating calcium conductances at somatic level.

From Llinás and Yarom 160


Figure 22.

Rhythmic firing of inferior olivary neurons. A: rebound calcium spike in presence of tetrodotoxin. Direct stimulation of inferior olivary neuron produces a dendritic calcium spike, followed by an afterhyperpolarization and a rebound spike (arrow). Small changes in DC hyperpolarizations (note current record) facilitate rebound spike, which becomes larger and moves to left. B: diagram illustrating sequence of events that generates inferior olivary cell rebound leading to oscillation. Antidromic or direct stimulation generates a somatic sodium spike having a fast rise and about 1‐ms duration (broken line). At appropriate membrane potential, this action potential generates a dendritic calcium spike that produces a plateau afterdepolarization followed by a sizable potassium conductance that generates prolonged afterhyperpolarization. This membrane hyperpolarization removes inactivation from somatic calcium conductance, which can then produce a rebound depolarization and can start the sequence once again.

Adapted from Llinás and Yarom 159


Figure 23.

Electrotonic coupling between inferior olivary (IO) neurons. A: 2 simultaneously recorded IO cells fired by antidromic stimulus. B: In a 2nd pair, hyperpolarization of lower cells through recording electrode hyperpolarizes 2nd cell (upper trace). To right: diagram of inferior olivary glomerulus. Top: general organization of IO glomerulus. In central core, dendritic branches are seen coupled by means of gap junctions (arrowheads). Central core is surrounded by synaptic terminals (ST), which establish contact with core elements. Bottom: on left, path of coupling current between 2 IO neurons and, on right, hypothetical function for synaptic junction at glomerulus. When synapses are activated, conductance change produced by synaptic transmitter action on postsynaptic membrane produces a shunt at glomerular level that reduces coupling coefficient between cells, since current tends to be lost across shunt.

A and B from Llinás and Yarom 159; diagrams on right from Llinás 139


Figure 24.

Limb movement as tensorial entity. A: on left, an upward displacement vector is a physical entity that can be expressed in different reference frames: e.g., by x,y coordinate system, or by α,β,γ‐ordered set of 3 quantities. On right, 2 reference frames shown are of fundamentally different kinds: applies to CNS‐independent external space; α,β,γ applies to space inherently connected to CNS. Limb‐displacement vector occurs in both spaces. Different expressions of the vector are related by limb‐displacement tensor, . B–D: covariant analysis and contravariant synthesis via a metric tensor. B: given a 2‐dimensional intended vector and 3 α,β,γ‐axes of an overcomplete reference frame, the decomposition could be performed by a 2‐step operation. First, covariant components of can be established (C), using geometry of 2‐space, to any number of directions independently. (Perpendicular projections, i.e., the inner products, provide “features” of desired vector in any coordinate direction.) Physical sum of covariant components, however, is not equal to displacement. Second, provided that metric tensor is available (in contravariant expression) for the α,β,γ‐space, corresponding set of contravariant components can be established (D). Physical sum of contravariant components physically generates displacement vector .

Adapted from Pellionisz and Llinás 209


Figure 25.

Circuit exemplifying certain mechanisms characteristic of Boylls' synergic parameterization theory. This circuit represents only 1 of a number of alternative realizations consistent with existing physiological knowledge. PF, parallel fibers; MF, mossy fibers; CF, climbing fibers; g, granule cells.

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Article Title: Electrophysiology of the Cerebellar Networks
 

How to Cite

Rodolfo R. Llinás. Electrophysiology of the Cerebellar Networks. Compr Physiol 2011, Supplement 2: Handbook of Physiology, The Nervous System, Motor Control: 831-876. First published in print 1981. doi: 10.1002/cphy.cp010217