8.6 Mathematical models of hippocampal spatial memory  (Page 13/13)

While metaplasticity suffices in providing a means of final weight stability, with our current set of parameters we are unable to achieve place field stability. As displayed by the matrix of firing degrees for cell 60 (shown above in [link] ), after continued potentiation of weights, the cell's place field will rapidly expand to span the entire track. This is a result of the high firing rate at which metaplasticity takes effect: the upper bound on firing rate is reached only once the synaptic weights have become strong enough to independently stimulate each other, resulting in continuous firing regardless of external input/position and place fields spread across the track. More tuning of metaplasticity will be needed in order to obtain the desired final place field stability. This will most likely be achieved by increasing the rate of NMDAR removal or decreasing the rate of NMDAR insertion, which should decrease the maximum firing rate and halt backward shift to effectively achieve place field stability.

After evaluating additive and multiplicative STDP alongside CaDP in explaining the phenomena associated with spatial memory in hippocampal place cells, we find that CaDP provides the most reasonable explanation for the mechanisms of synaptic plasticity. In CaDP, the mechanisms of potentiation and depression of weights are based upon biologically-supported pathways, whereas STDP does not explicitly draw connections between its weight changes and the biological mechanisms involved. In particular, the stabilization of synaptic weights is reasonably explained by coupling metaplasticity with CaDP, where STDP requires the use of an unrealistic upper weight limit to stabilize its place fields. The additional parameters involved with the model allow for more variations in the behavior of the system under different calcium LTD/LTP bounds, conductances, etc. One downside from a computational standpoint, especially when modeling a large network, lies in the additional parameters that are required to model the plasticity compared to STDP, which requires fewer parameters and yields similar results. However, if more biological accuracy and a wider range of tunability is desired, CaDP is the model of choice for synaptic plasticity.

Conclusions/future work

In this report we discussed the modeling of hippocampal place cells using two different plasticity models: Spike-time Dependent Plasticity and Calcium Dependent Plasticity. We have described the equations behind the plasticity models and their specific effects on the cell network interactions. We have discussed some of the differences between the two models, which include CaDP's rate-dependent plasticity as well as its inclusion of a second LTD window. We demonstrated that both models account for the backward shift of place fields observed experimentally. We also find that by coupling metaplasticity with CaDP, we can achieve final stability of synaptic weights; whereas STDP relies on weight bounds to achieve this effect.

While implementing metaplasticity successfully stabilizes synaptic weights, our simplified model does not exhibit final place field stability. Further work will be needed to tune the parameters involved with metaplasticity in order to obtain final place field stability. Once we are able to achieve the desired effects with metaplasticity, a possible area of interest would be to develop a means of coupling metaplasticity with STDP and comparing the results to that of CaDP with metaplasticity.

Other areas of interest include augmenting the 120-cell ring model to contain overlapping place fields at the beginning of the simulation and observing how this may affect the final weight distribution. Another modification to this model would be to implement a Gaussian distribution of place cell input firing rates instead of a uniform distribution with constant input rate. The original synaptic weight distribution could also be modified such that the 120 cell network contained connections to all other cells instead of using the simplified ring architecture. It can also be set to have randomized initial weights as well to make the initial state of the place cells more realistic. Once these modifications have been well studied, it could then be incorporated into a larger model of the hippocampal neural network, involving inhibitory connections as well as grid cell and head-direction cell inputs.

The backward shift and the stabilization of place fields have been closely associated with the development of spatial memory. Modeling and understanding the biochemical and biophysical processes behind synaptic plasticity and how they explain experimental results will aid us in better comprehending the mechanisms behind spatial memory. Further progress in this field may provide us with the knowledge to better understand not only how we develop a memory of our environment but also how plasticity mechanisms in the hippocampus are involved in diseases such as Alzheimer's or Epilepsy.

Acknowledgements

First and foremost, I would like to thank my mentor, Katie Ward, for all the help and guidance that she has given me this summer. I would also like to thank Dr. Cox for his support and encouragement. My thanks also goes out to Georgene Jalbuena for assisting me in learning LaTeX. Finally, I would like to thank Rice University's VIGRE program for sponsoring this research.