Modeling hippocampal theta-coupled gamma oscillations in learning and memory

Abstract

Two of the most researched domains in the hippocampus are the oscillatory activity and encoding and retrieval of patterns in the hippocampal CA1 and CA3 regions. They are, how- ever, not studied together; and hence, the objective of our work is to study the cross-frequency coupling of theta-coupled gamma oscillations in CA1 and CA3 regions of the hippocampus while encoding and retrieving information. We have studied the cross-frequency coupling of theta-coupled gamma oscillations both individually and in our newly-proposed integrated model of CA1-CA3 to analyze the effects of Schaffer collaterals and CA1 back-projection cells on CA1 and CA3 regions of the hippocampus. Due to lack of literary evidence, we have also contributed our hypotheses about the effects of CA1 back-projection cells on CA1 and CA3 cell-types. Moreover, we have developed a deterministic rule-based cellular automata library to study cross-frequency coupling in single-neuron level and population neuronal net- works at the same time. The discrete model is theta-oscillations-aware and hence encoding and retrieving of patterns takes place during the half-cycles of theta oscillations. We have extended the septo-hippocampal population firing rate model proposed by Den- ham and Borisyuk (2000) to study (i) the influence of inhibitory interneurons, specifically PV-containing basket cells (BCs) and bistratified cells (BSCs) on theta and theta-coupled gamma oscillations in both CA1 and CA3 hippocampal networks; (ii) to study Schaffer col- laterals from CA3 to CA1 and the influence of back-projection cells in CA1 on CA3; (iii) to analyze and compare the phases of cross-frequency coupling of theta-coupled gamma oscil- lations among the different cell types in CA1 and CA3 regions; (iv) to study the influence of external inputs on CA1 and CA3. In our simulations, with constant external inputs, we identify the parameter regions that generate theta oscillations and that BCs and BSCs in CA1 are in anti-phase, as seen experi- mentally by Klausberger et. al (2008). Slow-gamma oscillations are generated due to the ac- tivity of BSCs and BCs in CA1 and CA3, and they are propagated from CA3 to CA1 through the Schaffer collaterals, as seen in Klausberger et. al (2008) where BSCs were observed to synchronize PC activity during theta-coupled gamma oscillations in CA1. In CA3, increas- ing excitation of CA3 pyramidal cells results in theta oscillations without the slow-gamma coupling. Increasing excitatory input to CA1 pyramidal cells results in steady state and de- creasing the excitatory input, results in reduced oscillatory activity in both CA1 and CA3 due to Schaffer collaterals and the feedback projections from CA1 to CA3. This demonstrates that changes in input excitation can move the networks from oscillatory to non-oscillatory states, comparable to the differences seen in animals between exploratory and resting state. Further, Mizuseki et. al (2009) observed experimentally that CA1, CA3 and EC are out- of-theta-phase with each other and that the phase observed in CA1 pyramidal cells are not a result of a simple integration of phases from CA3, EC or the medial septum. We have thus, simulated theta-frequency sine-wave inputs from CA3 and EC of relative phases in the model and observed the same results in our CA1 individual and CA1-CA3 integrated model. To study encoding and retrieval of patterns in an oscillating model, we took an engineer- ing approach by developing a discrete modeling system using cellular automata (CA) derived from the models of Pytte et. al (1991) and Claverol et. al (2002). The aim of this model is to (i) replicate the oscillatory and phasic results obtained using the continuous modeling ap- proach and (ii) extend the same model to study storage and recall of patterns in CA1 taking a theta-oscillations-aware approach. Encoding and retrieval happen at different half-cycles of theta where information pro- cessing takes places in the sub-cycles of the slow-gamma oscillations in each half-cycle of theta oscillation (Cutsuridis et. al, 2010, Hasselmo et. al, 1996). A set of rules is developed to replicate this for the CA model of CA1. The encoding and retrieval half-cycles are identi- fied using the basket cell activity, and hence synaptic learning is enabled during the encoding half-cycle of theta, and is disabled during the recall half-cycle of theta oscillations. This is also a biologically realistic enhancement for studying learning and recall in theta-coupled gamma oscillations using a discrete cellular automata approach.