The role of additive neurogenesis and synaptic plasticity in a hippocampal memory model with grid-cell like input

Abstract

Recently, we presented a study of adult neurogenesis in a simplified hippocampal memory model. The network was required to encode and decode memory patterns despite changing input statistics. We showed that additive neurogenesis was a more effective adaptation strategy compared to neuronal turnover and conventional synaptic plasticity as it allowed the network to respond to changes in the input statistics while preserving representations of earlier environments. Here we extend our model to include realistic, spatially driven input firing patterns in the form of grid cells in the entorhinal cortex. We compare network performance across a sequence of spatial environments using three distinct adaptation strategies: conventional synaptic plasticity, where the network is of fixed size but the connectivity is plastic; neuronal turnover, where the network is of fixed size but units in the network may die and be replaced; and additive neurogenesis, where the network starts out with fewer initial units but grows over time. We confirm that additive neurogenesis is a superior adaptation strategy when using realistic, spatially structured input patterns. We then show that a more biologically plausible neurogenesis rule that incorporates cell death and enhanced plasticity of new granule cells has an overall performance significantly better than any one of the three individual strategies operating alone. This adaptation rule can be tailored to maximise performance of the network when operating as either a short- or long-term memory store. We also examine the time course of adult neurogenesis over the lifetime of an animal raised under different hypothetical rearing conditions. These growth profiles have several distinct features that form a theoretical prediction that could be tested experimentally. Finally, we show that place cells can emerge and refine in a realistic manner in our model as a direct result of the sparsification performed by the dentate gyrus layer.

Figure 1. Our simplified hippocampal model.

Left panel: We focus on the role of the EC and DG, while the remaining areas are modeled only implicitly and are shown as grey in the figure. Connectivity that does not play a role in our model is indicated by grey arrows. Right panel: the autoencoding network we abstract from our simplified model. A continuous -dimensional EC input pattern, , is generated from a phenomenological model of grid cell firing and encoded into a binary -dimensional DG representation, . The encoded pattern is stored and later retrieved, then inverted to reproduce a continuous approximation to the original pattern, . The networks we simulate in the results section have units in the input layer and up to units in the hidden layer.

Figure 2. Topographic firing patterns in the EC.

Top left panel: Formation of a grid governing the firing of a particular EC cell. A single vertex is placed at the specified grid origin (solid circle) which we choose for this example to be at the centre of the environment, then surrounded by six further vertices at the specified grid spacing (grey-filled circles). These vertices in turn are surround by twelve further vertices (white-filled circles) which begins to cover the spatial environment with a grid of equilateral triangles. Bottom left panel: Completed grid covering the entire spatial environment. In our simulations, the grid is extended to 1 m beyond the boundary wall to minimise edge effects. Middle panels: Two example grids in environment . Firing rates range from zero Hertz (white) to twelve Hertz (black). The dashed lines indicate the “centre line” of each grid which passes through the grid origin. The grids have different origins as well as vertex spacings and field sizes, but similar orientations. Right panels: The same two grids after entry to environment . The grids have undergone a coherent rotation of grid orientation and independent random shifts in grid origin. The dashed lines show the new grid centre lines in environment superimposed on the (unrotated) centre line from the previous environment , shown as a dotted line.

Figure 3. Evolution of the recoding and retrieval errors over environments for the fixed, reinitialising and plastic networks.

Left panel: The recoding error (lower solid line) and retrieval error after adaptation to the final environment (dashed line) of the reinitialising network are a measure of how well a completely specialised network deals with the same kind of statistics. This is the best possible average recoding performance, and correspondingly the worst possible retrieval performance we can expect for a network with DG units. The recoding error of the fixed network (upper solid line) is a measure of how well a completely generic network deals with the statistics of the spatially driven input we have used. We expect that any adaptation strategy would produce at least this level of recoding accuracy. Right panel: Evolution of the recoding error (solid line) and the retrieval error (dashed line) as a function of environment number for a network that uses a neural gas-like plasticity algorithm with a recoding error threshold of . In all subsequent plots we conform to the convention of plotting recoding errors with a solid line and retrieval errors with a dashed line. The errors lie in the range to which we also adopt as our standard vertical scale. Conventional plasticity successfully reduces the recoding error in each environment to the target value but only at the expense of increasing the retrieval error for previously stored memory patterns.

Figure 4. Performance of a network using the random neuronal turnover adaptation strategy across environments.

Left panel: Random neuronal turnover successfully reduces the recoding error in each environment to the target level of but only at the expense of increasing the retrieval error for previously stored memory patterns. Right panel: Adding conventional plasticity improves network performance but does not qualitatively change this result.

Figure 5. Performance of a network using the targeted neuronal turnover adaptation strategy across environments.

Left panel: Targeted turnover is more successful than random turnover at preserving memory patterns, especially for those stored very recently, but still suffers from a disruption of more temporally distant patterns. Right panel: Adding conventional plasticity improves network performance but does not qualitatively change this result.

Figure 6. Performance of the neurogenesis network across environments.

Left panel: For the first five environments the neurogenesis algorithm reduces the recoding error in each environment to the target level of but from the sixth environment onwards the network starts to run out of units to add and the network can no longer achieve this level of performance. The retrieval error for previously stored memory patterns is identical to the recoding error when those patterns were stored, as the internal structure of those parts of the network used to originally encode those patterns does not change over time. Inset: A plot of a single simulation shows how this breakdown of adaptation occurs in a step-like manner when the network runs out of units to add. The gradual degradation in performance shown in the main plot is a result of averaging simulations, each of which breaks down at a different point in time. Right panel: Plasticity allows the network to make better use of the units it grows with the result that the network can, on average, deal fairly well with all twelve environments.

Figure 7. Performance of a network using a combination of neurogenesis and random turnover across environments.

Left panel: The more sophisticated algorithm successfully achieves a recoding accuracy of for all twelve environments but once again suffers from an increased retrieval error. Right panel: Adding plasticity improves network performance considerably resulting in a network that can deal with all twelve environments while producing a retrieval error that is consistently lower than either conventional plasticity or neuronal turnover algorithms operating alone.

Figure 8. Performance of a network using a combination of neurogenesis and targeted turnover across environments.

Left panel: The algorithm achieves a recoding accuracy of for all twelve environments. The retrieval error is the same as the recoding error for the three most recent environments then increases sharply for temporally more distant environments. Right panel: Adding plasticity improves network performance considerably. The result is a network that can deal with all twelve environments while at the same time having a retrieval error that is lower than either conventional plasticity or neuronal turnover algorithms operating alone.

Figure 9. Time course of neurogenesis in the dentate gyrus.

Left panel: Neurogenesis profile across twelve environments. On entry to each new environment there is an approximately exponentially decaying growth period. Later environments need fewer new units to achieve the same level of recoding error, indicated by the progressively lower peaks. This reflects an increasing level of generalisation in the network that permits the re-use of existing units. Right panel: Neurogenesis profile across four environments. The same trends of an exponentially decaying growth pattern and a reduction in the number of units added in the later environments compared to the earlier environments can be seen. However, the mean overall level of growth for four environments ( units) is lower compared to the mean overall level of growth for twelve environments ( units).

Figure 10. Development of spatial dependence of activity in the dentate gyrus layer of our network upon entry into a novel environment.

We show four cells (from top to bottom) at four different time points (, , and days, from left to right). Left column: After day in the new environment each DG cell us activated by a large area of the spatial environment. Middle left column: After days a degree of refinement has occurred and the place fields have become more restricted. Middle right column: After days further refinement leads to activation patterns that resemble place cells in the DG. Right column: After days the final response of the cells are very similar to experimentally observed place cells with one main place field and occasionally some scattered areas of secondary activation. The network uses an additive neurogenesis with plasticity algorithm, but results are qualitatively the same for any of the four variations of neurogenesis we explored in the results section.