Abstract
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.
The authors declare no conflict of interest.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ermentrout, G.B., Chow, C.C.: Modeling neural oscillations. Physiol. Behav. 77, 629–633 (2002)
Buzsáki, G., Draguhn, A.: Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004)
Sander, R.: Slow brain waves play key role in coordinating complex activity. UC Berkeley News (2006)
Lisman, J.E., Jensen, O.: The theta-gamma neural code. Neuron 77, 1002–1016 (2013)
Bragin, A., Jandó, G., Nádasdy, Z., Hetke, J., Wise, K., Buzsáki, G.: Gamma (40–100 Hz) oscillation in the hippocampus of the behaving rat. J. Neurosci. 15, 47–60 (1995)
Osipova, D., Takashima, A., Oostenveld, R., Fernández, G., Maris, E., Jensen, O.: Theta and gamma oscillations predict encoding and retrieval of declarative memory. J. Neurosci. 26, 7523–7531 (2006)
Colgin, L.L.: Theta–gamma coupling in the entorhinal–hippocampal system. Curr. Opin. Neurobiol. 31, 45–50 (2015)
Taverna, S., Ilijic, E., Surmeier, D.J.: Recurrent collateral connections of striatal medium spiny neurons are disrupted in models of Parkinson’s disease. J. Neurosci. 28, 5504–5512 (2008)
Fischer, Y., Gähwiler, B.H., Thompson, S.M.: Activation of intrinsic hippocampal theta oscillations by acetylcholine in rat septo-hippocampal cocultures. J. Physiol. 519, 405–413 (1999)
Hasselmo, M.E.: The role of acetylcholine in learning and memory. Curr. Opin. Neurobiol. 16, 710–715 (2006)
Rennó-Costa, C., Lisman, J.E., Verschure, P.F.: A signature of attractor dynamics in the CA3 region of the hippocampus. PLoS Comput. Biol. 10, e1003641 (2014)
Gray, C.M.: Synchronous oscillations in neuronal systems: mechanisms and functions. J. Comput. Neurosci. 1, 11–38 (1994)
Papp, O.I., Karlócai, M.R., Tóth, I.E., Freund, T.F., Hájos, N.: Different input and output properties characterize parvalbumin-positive basket and Axo-axonic cells in the hippocampal CA3 subfield. Hippocampus 23, 903–918 (2013)
Kunec, S., Hasselmo, M.E., Kopell, N.: Encoding and retrieval in the CA3 region of the hippocampus: a model of theta-phase separation. J. Neurophysiol. 94, 70–82 (2005)
Káli, S., Dayan, P.: The involvement of recurrent connections in area CA3 in establishing the properties of place fields: a model. J. Neurosci. 20, 7463–7477 (2000)
Witter, M.P.: Intrinsic and extrinsic wiring of CA3: indications for connectional heterogeneity. Learn. Memory 14, 705–713 (2007)
Rolls, E.T.: Memory, Attention, and Decision-Making. OUP, Oxford (2008). Chapter 2
Sejnowski, T.J., Tesauro, G.: The Hebb rule for synaptic plasticity: algorithms and implementations. In: Neural Models of Plasticity: Experimental and Theoretical Approaches, pp. 94–103 (1989)
Grön, G., Bittner, D., Schmitz, B., Wunderlich, A.P., Tomczak, R., Riepe, M.W.: Hippocampal activations during repetitive learning and recall of geometric patterns. Learn. Memory 8, 336–345 (2001)
Vertes, R.P., Hoover, W.B., Di Prisco, G.V.: Theta rhythm of the hippocampus: subcortical control and functional significance. Behav. Cogn. Neurosci. Rev. 3, 173–200 (2004)
Lisman, J.E.: Bursts as a unit of neural information: making unreliable synapses reliable. Trends Neurosci. 20, 38–43 (1997)
Easton, A., Douchamps, V., Eacott, M., Lever, C.: A specific role for septohippocampal acetylcholine in memory? Neuropsychologia 50, 3156–3168 (2012)
Croxson, P.L., Browning, P.G., Gaffan, D., Baxter, M.G.: Acetylcholine facilitates recovery of episodic memory after brain damage. J. Neurosci. 32, 13787–13795 (2012)
Kesner, R.P.: A process analysis of the CA3 subregion of the hippocampus. Front Cell 409 (2015)
Burkitt, A.N.: A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern. 95, 1–19 (2006)
Fernandez, F.R., Engbers, J.D., Turner, R.W.: Firing dynamics of cerebellar purkinje cells. J. Neurophysiol. 98, 278–294 (2007)
Kuznetsov, Y.A.: Saddle-node bifurcation. Scholarpedia 1, 1859 (2006)
Tomkins, A., Vasilaki, E., Beste, C., Gurney, K., Humphries, M.D.: Transient and steady-state selection in the striatal microcircuit. In: Basal Ganglia: Physiological, Behavioral, and Computational Studies (2015)
Andersen, P.: The Hippocampus Book. Oxford University Press, Oxford (2007)
Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1 (1972)
Acknowledgements
This research is funded by the University of Stirling International Doctoral studentship. Professor A. Hussain is also supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant no. EP/M026981/1, and the Digital Health & Care Institute (DHI) funded Exploratory project: PD2A. The authors are grateful to Prof B. Graham at the University of Stirling, and the anonymous reviewers for their insightful comments and suggestions, which helped improve the quality of this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Shiva, A.S., Hussain, A. (2016). Continuous Time Recurrent Neural Network Model of Recurrent Collaterals in the Hippocampus CA3 Region. In: Liu, CL., Hussain, A., Luo, B., Tan, K., Zeng, Y., Zhang, Z. (eds) Advances in Brain Inspired Cognitive Systems. BICS 2016. Lecture Notes in Computer Science(), vol 10023. Springer, Cham. https://doi.org/10.1007/978-3-319-49685-6_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-49685-6_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49684-9
Online ISBN: 978-3-319-49685-6
eBook Packages: Computer ScienceComputer Science (R0)