Through synapses to spatial memory maps via a topological model

Yuri Dabaghian

doi:10.1038/s41598-018-36807-0

Abstract

Various neurophysiological and cognitive functions are based on transferring information between spiking neurons via a complex system of synaptic connections. In particular, the capacity of presynaptic inputs to influence the postsynaptic outputs–the efficacy of the synapses–plays a principal role in all aspects of hippocampal neurophysiology. However, a direct link between the information processed at the level of individual synapses and the animal’s ability to form memories at the organismal level has not yet been fully understood. Here, we investigate the effect of synaptic transmission probabilities on the ability of the hippocampal place cell ensembles to produce a cognitive map of the environment. Using methods from algebraic topology, we find that weakening synaptic connections increase spatial learning times, produce topological defects in the large-scale representation of the ambient space and restrict the range of parameters for which place cell ensembles are capable of producing a map with correct topological structure. On the other hand, the results indicate a possibility of compensatory phenomena, namely that spatial learning deficiencies may be mitigated through enhancement of neuronal activity.

Highlights

The location-specific spiking activity of the hippocampal neurons, known as place cells[1], gives rise to an internalized representation of space–a cognitive map
If the spike transmission probability is high, the small variations of pdo not inflict a strong impact on Tmin, i.e., the time required to learn the spatial map in a network with strong synaptic connections is ttnohepeaorllelyoagruninciaanflgfsehtcitamepdeesboybf eothccoecmaesneiovhinriaoglnhommaneindsst,iiaonsnfspinodiftrseopptiiskmebsee..lOFoownrtpthchreiet,oitnthhteeerrcmhoaaencdtdiia,vtaietsyvpacllouomewspe, rlteshxetoflaeaialcrsentriotnapginrtoicmdruietciicenactlhrveeaalcsuoeesrrpacetrcitat, power rate, Tmin ∝ (p − pcrit )−κ, (2)
The dependencies (2) and (3) define the changes of the learning time induced by small variations in the transmission probability, δpTmin

Summary

Introduction

The location-specific spiking activity of the hippocampal neurons, known as place cells[1], gives rise to an internalized representation of space–a cognitive map. It was demonstrated that if the shape of the environment gradually changes, the place field map deforms in a way that preserves mutual overlaps, adjacencies, containments, etc., between the place fields[4,5,6,7,8] This observation implies that the sequence in which the place cells fire during animal’s navigation remains invariant throughout the reshaping of the arena and suggests that the place cells do not represent precise geometric information, but a set of qualitative connections between portions of the environment–a topological map[8,9,10,11]. A specific link is suggested by the classical Alexandrov-Čech’s theorem of Algebraic Topology asserts that the pattern of overlaps between regions that cover a space X does, capture its topological structure[17,18] The implementation of this theorem is based on constructing the so-called “nerve simplicial complex” , whose vertexes correspond to the Department of Neurology, The University of Texas McGovern Medical School, 6431 Fannin St, Houston, TX, 77030, www.nature.com/scientificreports/

Methods

Results

Conclusion