Metabotropic glutamate receptor activation in cerebellar Purkinje cells as substrate for adaptive timing of the classically conditioned eye-blink response

Abstract

To understand how the cerebellum adaptively times the classically conditioned nictitating membrane response (NMR), a model of the metabotropic glutamate receptor (mGluR) second messenger system in cerebellar Purkinje cells is constructed. In the model, slow responses, generated postsynaptically by mGluR-mediated phosphoinositide hydrolysis and calcium release from intracellular stores, bridge the interstimulus interval (ISI) between the onset of parallel fiber activity associated with the conditioned stimulus (CS) and climbing fiber activity associated with unconditioned stimulus (US) onset. Temporal correlation of metabotropic responses and climbing fiber signals produces persistent phosphorylation of both AMPA receptors and Ca(2+)-dependent K+ channels. This is responsible for long-term depression (LTD) of AMPA receptors. The phosphorylation of Ca(2+)-dependent K+ channels leads to a reduction in baseline membrane potential and a reduction of Purkinje cell population firing during the CS-US interval. The Purkinje cell firing decrease disinhibits cerebellar nuclear cells, which then produce an excitatory response corresponding to the learned movement. Purkinje cell learning times the response, whereas nuclear cell learning can calibrate it. The model reproduces key features of the conditioned rabbit NMR: Purkinje cell population response is timed properly; delay conditioning occurs for ISIs of up to 4 sec, whereas trace conditioning occurs only at shorter ISIs; mixed training at two different ISIs produces a double-peaked response; and ISIs of 200-400 msec produce maximal responding. Biochemical similarities between timed cerebellar learning and photoreceptor transduction, and circuit similarities between the timed cerebellar circuit and a timed dentate-CA3 hippocampal circuit, are noted.

Fig. 1.

Basic neuronal circuitry of the cerebellum that forms the basis for the present model of adaptive timing of eye blinks. Inhibitory neurons, dark; excitatory neurons,white. PC, Purkinje cell; BA, basket cell; ST, stellate cell; GR, granule cell;PF, parallel fiber; MF, mossy fiber;CF, climbing fiber; N, cerebellar nuclear cell;PN, precerebellar neuron that issues mossy fibers;IO, inferior olive; CS, conditioned stimulus;CR, conditioned response; US, unconditioned stimulus.

Fig. 2.

NMRs after mixed ISI delay conditioning. Group 200F received all 200 msec ISI trials. Group P n/8 received mixed trials in a ratio of n 200 msec to 8 − n700 msec ISI trials. Group 700F received all 700 msec ISI trials. As shown in the right-hand column, 700 msec CS test trials result in double-responding. (Reprinted with permission from Millenson et al., 1977.)

Fig. 3.

Components of the metabolic transmission pathway within a Purkinje cell dendrite. DAG, Diacylglycerol; G, guanine nucleotide-binding protein;glu, glutamate; mGluR1, metabotropic glutamate receptor subtype 1; PKC, protein kinase C; PLC, phospholipase C;PIP₂, phosphatidylinositol 4,5-bisphosphate; IP₃, inositol 1,4,5-trisphosphate.

Fig. 4.

Open probability of IP₃R in model (dashed line) and in experiments with IP₃R reconstituted into planar lipid bilayers (Bezprozvanny et al., 1991) in the presence of 2 μm IP₃. Normalized from maximum open probability of 15%. Model parameter values:R_max = 1, k₁₃/k₁₂ = 0.81, k₁₅/k₁₄ = 0.0556, n = 1.65.

Fig. 5.

A, Voltage and calcium dependencies of the mGluR-activated Ca²⁺-dependent K⁺ channels of cultured cerebellar granule cells. (Reprinted with permission from Fagni et al., 1991.) B, Equation 17 plotted as a function of voltage for various cytoplasmic calcium concentrations.

Fig. 6.

Processes mediating learning of a timed response in cerebellar Purkinje cells. AMPA, Amino-3-hydroxy-5-methyl-4-isoxazole propionic acid-sensitive glutamate receptor; cGMP, cyclic guanosine monophosphate;DAG, diacylglycerol; glu, glutamate;GC, guanylyl cyclase; g_K, Ca²⁺-dependent K⁺ channel protein; GTP, guanosine triphosphate;IP₃, inositol 1,4,5-trisphosphate;NO, nitric oxide; NOS, nitric oxide synthase;P, phosphate; PLC, phospholipase C;PKC, protein kinase C; PKG, cGMP-dependent protein kinase; PP-1, protein phosphatase-1. NOS is probably not localized in Purkinje cell, as discussed in text.

Fig. 7.

Model responses to mGluR activation. Parameters as described in text, with [glu] = 10 μm,B_max = 1.5. A, Rise in cytoplasmic calcium concentration after release from endoplasmic reticulum. B, The plasma membrane potential driven by the Na/Ca exchange current in the absence of Ca²⁺-dependent K⁺ current ($\overline{g}$ = 0). C, The plasma membrane potential change when both Na/Ca exchange current and Ca²⁺-dependent K⁺ current are present ($\overline{g}$ = 100).

Fig. 8.

Spectrum produced by variation inB_max in response to sustained [glu] concentration. B_max = {360, 21, 4.7, 1.73, 0.97, 0.625, 0.458, 0.368, 0.315, 0.283, 0.261, 0.245, 0.236, 0.23, 0.226}; these receptor concentration values were chosen to give approximately equally spaced responses spanning 4 sec. With a sustained [glu] input, [Ca²⁺] spike response can be observed out to ∼5 sec if the B_maxdistribution is allowed to range down to 0.

Fig. 9.

Spectrum produced by variation inB_max in response to a 50 msec [glu] application. B_max = {360, 18, 6.5, 3.9, 3.18, 2.93, 2.87, 2.859, 2.858, 2.8579}; values within the indicated range were chosen to give equally spaced responses. The value 2.585 is the smallest B_max for which the 50 msec [glu] stimulus was sufficient to induce a [Ca²⁺] spike in the mGluR pathway.

Fig. 10.

A, Metabotropic glutamate response in a slice population of Purkinje cells recorded using the three-chamber grease-gap method. (Reprinted with permission from Batchelor and Garthwaite, 1993.) B, Model population response produced by summation of spectral components in response to a 150 msec agonist application at the arrow, with α = 0.1, N = 60, B_max = {360, 170, 100, 65, 42, 29, 21, 15.7, 12, 9.2, 7.2, 5.8, 4.7, 3.8, 3.15, 2.65, 2.25, 1.96, 1.73, 1.55, 1.4, 1.27, 1.15, 1.06, 0.97, 0.89, 0.82, 0.763, 0.706, 0.66, 0.625, 0.59, 0.555, 0.525, 0.5, 0.478, 0.458, 0.44, 0.422, 0.407, 0.393, 0.38, 0.368, 0.357, 0.347, 0.338, 0.33, 0.322, 0.315, 0.309, 0.303, 0.298, 0.293, 0.288, 0.283, 0.279, 0.275, 0.271, 0.267, 0.264}; values within the indicated range were chosen to give a smooth population response. This distribution was used for all results except those reported in Figures 8 and 9.

Fig. 11.

Progress of model population response during 30 pairings of CS and US at an ISI of 500 msec. Initially, mGluR activation produces a depolarizing response, but as learning progresses, a timed hyperpolarization is realized. Spectral components are the same as for Figure 10B.

Fig. 12.

Average nictitating membrane movement (top) and peristimulus histogram of interpositus nucleus neural activity (bottom) during classical conditioning of a rabbit with a 25 msec pontine stimulation as the CS and an air-puff delivered 225 msec later as the US. (Reprinted with permission fromSteinmetz, 1990b.)

Fig. 13.

Comparison of CR strength–ISI dependency curves for the model and the behavioral data. Data of Steinmetz (1990a) is normalized to 86% CRs. Model data are the magnitude of the learned hyperpolarization below −50 mV, normalized to the amount of hyperpolarization obtained at asymptote during training with an ISI of 250 msec.

Fig. 14.

Progress of population response during first 10 extinction trials after 30 CS–US pairings with alternating ISIs of 350 and 1000 msec. After conditioning, the 1100 msec CS2 is used to elicit a double-peaked CR.