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Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus

dp{at}math.bu.edu Department of Mathematics and Statistics and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.

Theoden I. Netoff

tnetoff{at}bu.edu Department of Biomedical Engineering and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.

Horacio G. Rotstein

horacio{at}bu.edu Department of Mathematics and Statistics and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.

John A. White

jwhite{at}bu.edu Department of Biomedical Engineering and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.

Mark O. Cunningham

M.Cunningham{at}leeds.ac.uk School of Neurology, Neurobiology and Psychiatry, University of Newcastle, Newcastle upon Tyne, NE2 4HH, U.K.

Miles A. Whittington

M.A.Whittington{at}newcastle.ac.uk School of Neurology, Neurobiology and Psychiatry, University of Newcastle, Newcastle upon Tyne, NE2 4HH, U.K.

Nancy J. Kopell

nk{at}math.bu.edu Department of Mathematics and Statistics and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.

Cells that produce intrinsic theta oscillations often contain the hyperpolarization-activated current I_h. In this article, we use models and dynamic clamp experiments to investigate the synchronization properties of two such cells (stellate cells of the entorhinal cortex and O-LM cells of the hippocampus) in networks with fast-spiking (FS) interneurons. The model we use for stellate cells and O-LM cells is the same, but the stellate cells are excitatory and the O-LM cells are inhibitory, with inhibitory postsynaptic potential considerably longer than those from FS interneurons. We use spike time response curve methods (STRC), expanding that technique to three-cell networks and giving two different ways in which the analysis of the three-cell network reduces to that of a two-cell network. We show that adding FS cells to a network of stellate cells can desynchronize the stellate cells, while adding them to a network of O-LM cells can synchronize the O-LM cells. These synchronization and desynchronization properties critically depend on I_h. The analysis of the deterministic system allows us to understand some effects of noise on the phase relationships in the stellate networks. The dynamic clamp experiments use biophysical stellate cells and in silico FS cells, with connections that mimic excitation or inhibition, the latter with decay times associated with FS cells or O-LM cells. The results obtained in the dynamic clamp experiments are in a good agreement with the analytical framework.