describing the amount of excitatory synaptic activation received by the whole cell) and h(t) (the amount of occult conductance at the starred synapse):

(4)

m(t)≈F(t) · h(t) ≈ F(1)S", K(t−t) f(t) dt.

0

The average calcium influx during the observation period T should determine the amount of strengthening of the synapse. This average, M, is then

(5)

M =

'm(1)dt ≈ —S′′ S, F(1) K(t−t) f(t)dt dt.

1
T 0 0

We consider only times t greater than the settling time of the function K(t) that describes the time course of the unitary occult conductance event, so that the starred spine has an average conductance that is constant (because f(t) is assumed to be a stationary random process). Changing variables and order of integration, we find that

That is, the average calcium influx depends on the integral of the cross correlation function between the firing function for the starred synapse, f(t), and that for all the other synapses in the cell, F(t):

If the cross correlation between f(t) and F(t) decays more rapidly than the characteristic time of K(t) (i.e., about half a second), then M is simply the integral of C(t). If, in the other limit, C(t) decays slowly on the scale set by this characteristic time, then only correlations out to about a half second contribute. The properties of the NMDA-class channels naturally give synaptic strengthening that depends on the extent to which the starred synapse has activity correlated with that in other inputs. Since each synapse will simultaneously be playing the role of the starred synapse, an entire circuit of such neurons will be constantly strengthening synapses in accordance with mutual correlations. Presumably, the strength of synapses negatively correlated with others will simultaneously be weakened to prevent the system from driving each synapse to maximal strength throughout the life of the animal.

Several points need to be stressed. First, F(t) reflects only the activity of QUIS channels, but it should include the effects of NMDA-class channels at all synapses. As we have, for this example, assumed stationarity, the NMDA component would contribute relatively little because of the filtering by the function K(t). That is, the voltage fluctuations produced by the NMDA receptor channels would be much smaller than those produced by the QUIS channels due to the smoothing effect of the 400-ms time constant for the NMDA component of the synaptic current. In general, however, synaptic

activity would not be stationary, and the effect would have to be considered; useful calculations about these more complex situations cannot be made without knowing more about the precise ways in which inputs might be nonstationary. Second, the above calculation included only effects of excitatory synapses. In general, F(t) should contain two components, one for excitatory synapses and the other for inhibitory synapses. Third, the effect of f(t) on itself should be included; that is, F(t) should contain f(t), also. Finally, the neuron has been treated as isopotential, and voltage drops through the dendritic tree and across the spine neck have been neglected. Although many neurons are electrically compact (Johnston and Brown 1983), doubtless nonisopotentiality would play an important role in others. One can imagine situations, for example, in which only correlations of synaptic activity within a single dendritic branch are of importance in determining synaptic strengthening.

Discussion

We have proposed here that the properties of the NMDA and QUIS channels, as revealed by single channel recordings, naturally give rise to two distinct modes of information processing in the brain. One implication of the special mode, the one mediated by the NMDA class channels, is that - according to the standard theory for LTP – synaptic strengthening would depend on the cross-correlation function between the activity at a particular synapse and that in all other synapses impinging on the neuron. The effect of these correlations extends over about half a second.

We have not considered the voltage-mediated processes generated by the NMDA channels, but these apparently are also used in neuronal computations (Wallen and Grillner 1987). One obvious way they can be used is in making temporal comparisons in which current activity reads out the average effect of inputs occurring over the past half second.

Without knowing more about how the second information processing mode is used, speculations about implications of failures in this mode are difficult. Nevertheless, specific pharmacological interventions can selectively block second mode operation, and presumably some of the effects of these interventions reveal the net effects produced by this mode. The psychotomimetic agent phencyclidine (PCP) quite effectively blocks NMDA channels (Honey et al. 1985; Contreras et al. 1987) so that the second computational mode would be selectively removed. The experimental drug MK-801 has the same effect (Huettner and Bean 1988) and is more specific for the NMDA receptors (some of the PCP effect presumably arises through the action of this agent on sigma receptors). It will be interesting to investigate the extent to which the psychological effects of PCP and MK-801 may reflect a disordered second computational mode.

REFERENCES

Andrews, S.B.; Leapman, R.D.; Landis, D.M.D.; and Reese, T.S. Activity-dependent accumulation of calcium in Purkinje cell dendritic spines. Proceedings of the National Academy of Sciences of the United States of America 85:1682-1685, 1988. Collingridge, G.L., and Bliss, T.V.P. NMDA receptors their role in long-term potentiation. TINS 10:288-293, 1987.

Contreras, P.C.; Monahan, J.B.; Lanthorn, T.H.; Pullan, L.M.; DiMaggio, D.A.; Handelmann, G.E.; Gray, N.M.; and O'Donohue, T.L. Phencyclidine: Physiological actions, interactions with excitatory amino acids and endogenous ligands. Molecular Neurobiology 1:191-211, 1987.

Cull-Candy, S.G., and Usowicz, M.M. Multiple-conductance channels activated by excitatory amino acids in cerebellar neurons. Nature 325:525-528, 1987.

Dale, N., and Grillner, S. Dual-component synaptic potentials in the lamprey mediated by excitatory amino acid receptors. Journal of Neuroscience 6:2653-2661, 1986. Dale, N., and Roberts, A. Dual-component amino-acid-mediated synaptic potentials: Excitatory drive for swimming in Xenopus embryos. Journal of Physiology 363:3559, 1985.

Davies, J.; Miller, A.J.; and Sheardown, M.J. Amino acid receptor mediated excitatory synaptic transmission in the cat red nucleus. Journal of Physiology 376:13-29, 1986. Forsythe, I.D., and Westbrook, G.L. Slow excitatory postsynaptic currents mediated by N-methyl-D-aspartate receptors on cultured mouse central neurones. Journal of Physiology 396:515-533, 1988.

Gustafsson, B., and Wigstrom, H. Physiological mechanisms underlying long-term potentiation. TINS 11:156-162, 1988.

Honey, C.R.; Miljkovic, Z.; and MacDonald, J.F. Ketamine and phencyclidine cause a voltage-dependent block of responses to L-aspartic acid. Neuroscience Letters 61:135-139, 1985.

Huettner, J.E., and Bean, B.P. Block of N-methyl-D-aspartate-activated current by the anticonvulsant MK-801: Selective binding to open channels. Proceedings of the National Academy of Sciences of the United States of America 85:1307-1311, 1988. Jahr, C.E., and Stevens, C.F. Glutamate activates multiple single channel conductances in hippocampal neurons. Nature 325:522-525, 1987. Johnston, D., and Brown, T.H. Interpretation of voltage-clamp measurements in hippocampal neurons. Journal of Neurophysiology 50(2):464-486, 1983. Klockgether, T. Excitatory amino acid receptor-mediated transmission of somatosensory evoked potentials in the rat thalamus. Journal of Physiology 394:445-461, 1987. MacDermott, A.B.; Mayer, M.L.; Westbrook, G.L.; Smith, S.J; and Barker, J.L. NMDA-receptor activation increases cytoplasmic calcium concentration in cultured spinal cord neurons. Nature 321:519-522, 1986.

MacDonald, J.F.; Porietis, A.V.; and Wojtowicz, J.M. L-aspartic acid induces a region of negative slope conductance in the current-voltage relationship of cultured spinal cord neurons. Brain Research 237:248-253, 1982.

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Mayer, M.L., and Westbrook, G.L. The physiology of excitatory amino acids in the vertebrate central nervous system. Progress in Neurobiology 28:197-276, 1987. Mayer, M.L.; Westbrook, G.L.; and Guthrie, P.B. Voltage-dependent block by Mg of NMDA responses in spinal cord neurones. Nature 309:261-263, 1984. Nowak, L.; Bregestovski, P.; Ascher, P.; Herbet, A.; and Prochiantz, A. Magnesium

gates glutamate-activated channels in mouse central neurones. Nature 307:462465, 1984.

Salt, T.E. Excitatory amino acid receptors and synaptic transmission in the rat ventrobasal thalamus. Journal of Physiology 391:499-510, 1987.

Salt, T.E. Mediation of thalamic sensory input by both NMDA receptors and nonNMDA receptors. Nature 322:263-268, 1986.

Thomson, A.M. A magnesium-sensitive post-synaptic potential in rat cerebral cortex resembles neuronal responses to N-methylaspartate. Journal of Physiology 370:531-549, 1986.

Vlachova, V.; Vyklicky, L.; Vyklicky, Jr., L.; and Vyskocil, F. The action of excitatory amino acids on chick spinal cord neurones in culture. Journal of Physiology 386:425438, 1987.

Wallen, P., and Grillner, P. N-Methyl-D-Aspartate receptor-induced, inherent oscillatory activity in neurons active during fictive locomotion in the lamprey. Journal of Neuroscience 7:2745-2755, 1987.

Watkins, J.C., and Evans, R.H. Excitatory amino acid transmitters. Annual Review of Pharmacology and Toxicology 21:165-204, 1981.

Signal Transduction and Plasticity

GTP-Binding Protein Specificity of Action in Activating the Cardiac Muscarinic Receptor

D.E. Clapham**, D.E. Logothetis*, D. Kim**, J. Northup,
+
and E. Neer

+

*Pharmacology Department, Mayo Foundation
*Cardiovascular Division, Brigham and Women's Hospital
# Physiology Department, Harvard Medical School
*Pharmacology Department, Yale University School of Medicine

The vagus nerve releases acetylcholine onto pacemaker and atrial cells of the heart and slows beating (Gaskell 1886; Loewi 1921). The slowing of heart rate is accomplished by the coupling of the muscarinic (M2) receptor of heart to at least three ion channels. Two inward depolarizing currents, Ica.L and If, are affected by the muscarinic inhibition of adenylyl cyclase through an inhibitory GTP-binding protein (G protein; G1). An outward, hyperpolarizing, potassium-selective current (IK-ACh) is increased directly. Previous experiments have shown that soluble second messengers do not couple the M2 receptor to IK.ACh (Soejima and Noma 1984; Nargeot et al. 1983) but that a pertussis toxin-sensitive G protein may more directly link the receptor and channel (Pfaffinger et al. 1985; Breitwieser and Szabo 1985; Kurachi et al. 1986; Logothetis et al. 1987; Yatani et al. 1987; Codina et al. 1987).

Using patch clamp techniques, small patches of membrane may be detached from atrial cells and the inside and outside surfaces then bathed with various ligands. In the inside-out patch clamp mode, the intracellular surface is exposed to the bath and perfused with GTP, nonhydrolyzable GTP analogs, or purified G protein subunits. In this paper, we examine the steps between receptor binding and the activation of the muscarinic-gated, inwardrectifying K channel. We conclude that both a and By subunits of G proteins may activate iK.ACh although in different concentration ranges. By from