It is widely believed that learning involves synaptic modifications and that one important variable for this is the temporal relationship between different afferents onto a postsynaptic cell and between the pre- and post-synaptic activations (Collingridge and Bliss 1987). Recently, interest has developed in the relationship between the optimal parameters for synaptic enhancement and the firing patterns observed in freely moving animals (Larson and Lynch 1989; Otto et al. 1991). The pattern o f firing associated with the phase shift places interesting conditions on the temporal relations between synaptically coupled cells and thus on the possibility that synaptic connection between place cells will be strengthened (or reduced) in a given environment.
One possibility is that the timing of the pre-synaptic input relative to the 0 rhythm cycle is important. Pavlides et al. (1988) reported good long term potentiation if the electrically induced afferent barrages impinged on the cells during the positive phase o f the dentate EEG, and no change or a decrease in synaptic efficacy if the inputs occurred at the negative phase. It is possible that afferent inputs to the cell at some phases in the 0 cycle could be most effective in producing synaptic enhancement. This might mean that only spikes occurring at one part o f the place field (e.g. at the edge of the field) would be effective in strengthening the synapses onto the downstream cells.
An alternative is that the absolute phase of theta at which the burst occurs is less relevant than the relative timing of the spikes in the two cells. In this case the relative spatial location o f place cells could influence their synaptic coupling. M uller et al. (1991) have assumed that the synaptic coupling strength falls off as a monotonie function of the time between place cell activations, and therefore that cells with neighbouring fields will be more strongly coupled than those with distant ones. However, the phase shift phenomenon suggests that the relationship between synaptic coupling and place field location is more complex.
If it is assumed that the effective time window for synaptic modification is less than one 0 rhythm cycle, and further, that all of the cells in a region o f the hippocampus (e.g. the CA3 field) fire with a phase shifts that begins at the same phase of the 0
rhythm, as appears to be the case in the data shown in Figure 7.7. With this assumption it follows that the synaptic coupling function between connected cells o f similar field sizes will not be a monotonie function of distance. Cells with completely overlapping fields will experience the strongest coupling, because the spike trains will coincide throughout each run through the fields (ignoring the delays introduced by the conduction and EPSP rise times). As the place field centres are shifted relative to each other, the time separating the bursts in one train will shift relative to those in the second spike train. At the point where one field centre is shifted to lie on the periphery o f the second field (50% overlap o f the fields) the temporal spike patterns will occur 180° out o f phase with each other, and a maximum temporal disparity will be reached. As the fields separate even further, however, the spike bursts in one train will approach the bursts of the next 6 cycle in the second train, and the temporal disparity will begin to decrease. The next maximum would occur at the point at which the fields were completely separated and abutting, but this maximum would not reach the same strength as the complete overlap condition, since only the spike bursts at the beginning and end o f the trains would occur contemporaneously. The synaptic strengthening function, on this model, would have two peaks: a large one when complete overlap occurs, and a smaller one when fields are edge-abutting. If long term depression (LTD) exists, and can be shown to occur when two spike trains have a 180° phase relation, it would enhance the above effect.
This type o f synaptic change could provide a mechanism for the construction of maps that have a uniform representation of spatial locations. Consider, for example, that in a new environment place cells have a fixed radius, but the centres o f the place fields are randomly distributed. In this case many more place cells will be active in some random locations, as compared to others. However, as the animal explores the environment, only overlapping or abutting place fields will meet the conditions for synaptic change. Furthermore if interneurons suppress the activity o f completely overlapping place cells then the number of place cells active in each spatial location will gradually become more uniform. However if the time window for synaptic change is
longer than one 0 rhythm cycle, as some data suggest (Gustafsson and W igstrom 1990) than this model will not hold.
8.5 Hidden frequency models
In the discussion sections o f Chapters 6 and 7, second frequencies (other than the observed 0 rhythm) and the notion that each pyramidal cell acts as an oscillator were suggested as a method to model how the place cell firing could have a stable spatial pattern. This model raises many questions for future consideration. The first concerns the origin o f the two frequencies. One possibility is that they are both external to the hippocampus, and that the hippocampal cells are essentially passive devices whose sole function is to sum their inputs. The alternative view is that the hippocampal cells act as oscillators, perhaps as voltage controlled oscillators (Hoppensteadt 1986), whose dynamics translate input voltages to output frequencies. This leads to questions such as whether each cell has a fixed natural frequency, or alternatively whether the frequency varies with the environment. The phase shift vs. position curves for some cells are best approximated by straight lines, suggesting that the second input frequency in the field has a fixed difference from the EEG 0 rhythm. In others (e.g. Figure 7.1) the curves may have a more sigmoidal shape, which would be more in keeping with a second frequency that rises, peaks and then falls. In some curves there is evidence o f a lessening o f the phase precession as the animal exits the field, which is clear evidence o f a frequency reduction. There are several suggestions as to how the membrane and channel properties of single cells might enable them to oscillate either as individuals (Llinas
1988) or when imbedded in networks (Traub et al. 1989).
More work is required to fit these results within a single model. The speed correlation required a hidden frequency that was lower than the 0 frequency, but the wave packets proposed in the discussion of the phase shift required a missing frequency that was higher than the 0 rhythm frequency. It is not yet clear how this model can be extended to incorporate all o f the new results. In particular, there is a problem in the model if all of the hidden frequencies are outside o f the cell. In this case, each cell
might add the same two frequencies and it would be difficult to construct independent place fields for each o f the two cells. However, if one o f the hidden frequencies is internal to the cell then a place field that is constructed from a beat function can be shifted by changing the phase of the interal constant frequency oscillator.
Also the fact that, in some o f the data sets, the sequence of changes in the 0 rhythm frequency was found to predict the speed does not fit with the notion o f spatially stable place fields. The model in which the 0 rhythm frequency is combined with a hidden lower frequency to produce stable wave packets requires that the frequency changes at the same time that the speed changes. However, as suggested above, this may be explained by a difference in the way that the animal is moving through space. If it is using the cue-based navigation system then stable place fields occur, whereas if it is using an inertial navigation system the entire place field is predicted.
Suggestive new findings have resulted from this research, but many questions are left unanswered. There are hints o f a simple spatial coding for environments, which further developments of the present methods may help resolve. The approach o f looking at individual action potentials and cycles of the hippocampal 0 rhythm has provided some new insight. However, changes in these variables will be easier to interpret if better simultaneous measurements are made o f the animal's behaviour. The 0 frequency correlation with the animal's speed can be further investigated with a more controlled task in which the animal can be asked to switch between the hypothesised navigation systems. Also, further theoretical work is necessary to piece together these new data into a better model of how the hippocampus represents spatial locations.