Differential Hebbian learning [1] is a theoretical neuronal learning scheme which can account for classical conditioning. Recent physiological findings now show that this may be implemented in neocortex. Short-term synaptic depression [2,3] together with alteration in excitatory synaptic efficacy due to the precise timing of postsynaptic action potentials (APs) and excitatory post-synaptic potentials (EPSPs) [4,5] can provide a partial mechanism for the neurobiological implementation of differential Hebbian learning.
For differential Hebbian learning, Klopf defines the change in synaptic weight strength to be
where is the weight value at time t, is the change in activity of the post-synaptic unit, the are positive constants, is the change in the pre-synaptic input at time t-j, and rect(x) returns x if or 0 if x < 0. The determine the sensitivity of to changes in .
Tsodyks and Markram [3] now provide evidence that the excitatory post-synaptic current (and hence the EPSP) due to a presynaptic spike train at an excitatory synapse starts off large, then diminishes towards a steady state as the synaptic resources are depleted. Though this differs from the term above in the general case, it provides a similar result in the case of the onset of a presynaptic spike train, as is required for Klopf's delay conditioning and conditional inhibition.
Markram et al. [5] report an increase in excitatory synaptic efficacy when the EPSP precedes the AP by 10ms, and a decrease when the AP precedes the EPSP. The effect is larger when the APs occur at 40Hz than at 10Hz: since the experiments used blocks of 5 APs the synaptic efficacy increase could be proportional to either the postsynaptic activity, y(t) or to its increase, . The change is ascribed to the antidromic AP interacting with NMDA receptors possibly through Ca inflow: such inflow is likely to build up, then suffer from depression, making the changes it mediates depend on a lowpass filtered version of y(t), which is similar to for y(t) altering from inactive to active. Thus short-term synaptic depression together with the effect on activated excitatory synapses of APs provides a mechanism for increasing the efficacy of excitatory synapses in a way similar to that suggested by Klopf. This aspect of Klopf's learning rule provides delay conditioning.
To provide conditional inhibition, Klopf's rule requires negative values for : these could be implemented either as decreases in efficacy of excitatory synapses, or increases in efficacy of inhibitory synapses. To discover these would require an experimental protocol in which onset of presynaptic firing just preceded the offset of APs in the postsynaptic neuron: we would expect to find either a decrease in efficacy of an excitatory synapse, or an increase in efficacy of an inhibitory synapse.
Leslie S. Smith (March 1997)
Centre for Cognitive and Computational Neuroscience
Department of Computing Science, University of Stirling,
Stirling FK9 4LA, Scotland
1. Klopf A.H. Psychobiology, 16, 2, 85-125 (1988).
2. Koch C. Nature, 385, 207-210 (1997).
3. Tsodyks M.V. & Markram H. Proc. Natl. Acad. Sci. USA, 94, 719-723 (1997).
4. Stuart G.J. & Sakmann B. Nature, 367, 69-72 (1994).
5. Markram H., Luebke J., Frotscher M. & Sakmann B. Science, 275, 213-215 (1997).