Continuous Time Recurrent Neural Network Model of Recurrent Collaterals in the Hippocampus CA3 Region.

Recurrent collaterals in the brain represent the recollection and execution of various monotonous activities such as breathing, brushing our teeth, chewing, walking, etc. These recurrent collaterals are found throughout the brain, each pertaining to a specific activity. Any deviation from regular activity falls back to the original cycle of activities, thus exhibiting a limit cycle or attractor dynamics. Upon analysis of some of these recurrent collaterals from different regions of the brain, it is observed that rhythmic theta oscillations play a vital role coordinating the functionalities of different regions of the brain. The neuromodulator acetylcholine, is found to be present in almost all of the regions where recurrent collaterals are present. This notable observation points to an underlying link between the generation and functioning of theta oscillations present in these recurrent collaterals, with the neuromodulator acetylcholine. Further, we show that these recurrent collaterals can be mathematically modeled using continuous time recurrent neural networks to account for the frequency of action potentials which follow the excitatory-inhibitory-excitatory (E-I-E) and inhibitory-excitatory-inhibitory (I-E-I) model. As a first case study, we present a detailed preliminary analysis of the CA3 region of the hippocampus, which is one of the most widely studied recurrent collaterals network in the brain, known to be responsible for storing and recalling episodic memories and also learning tasks. The recurrent collaterals present in this region are shown to follow an E-I-E pattern, which is analyzed using a mathematical model derived from continuous time recurrent neural networks, using inputs from a leaky integrate-and-fire neuronal model.