Through synapses to spatial memory maps via a topological model

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.

From Topological Analyses to Functional Modeling: The Case of Hippocampus

“…In plain words, this result shows that accumulation of the topological information can start at any point (e.g., at the onset of the navigation or after an exploratory delay) and produce the desired stable map after about the same period of learning. In effect, this observation justifies using perennial coactivity complexes for estimating T min in Dabaghian et al ( 2012 ), Arai et al ( 2014 ), Basso et al ( 2016 ), Hoffman et al ( 2016 ), and Dabaghian ( 2019 ).…”

“…On the other hand, as p ∗ decreases further, the changes accumulate and, as p ∗ approaches a certain critical value p crit , learning times diverge at a power rate, with κ ranging typically between 0.1 and 0.5 ( Figure 4B ). The effects produced by the diminishing probability of the post-synaptic neurons' responses, q ∗ , are qualitatively similar but weaker than the effects of lowering the spike transmission probability p ∗ (Dabaghian, 2019 ).…”

“…Moreover, weakening synapses reduce the learning region down to its compete disappearance at p ∗ = p crit , which suggests that spatial learning may fail not only because the parameters of neuronal firing are pushed beyond a certain fixed “working range,” but also because that range itself may shrink or cease to exist. In particular, the fact that the learning region disappears if the transmission probability drops below the critical value implies that deterioration of memory capacity produced by the synaptic failure cannot be compensated by increasing the place field's firing rates or by recruiting a larger population of active neurons—for more details see Dabaghian ( 2019 ).…”

“…Methods of the Persistent Homology theory allow describing the dynamics of the topological loops in , e.g., evaluating the minimal time T min after which the topological structure of matches the topology of the environment, (De Silva and Ghrist, 2007 ; Curto and Itskov, 2008 ; Dabaghian et al, 2012 ). Biologically, this value provides a low-bound theoretical estimate for the time required to learn a novel topological map from place cell outputs ( Figure 1A ) (Dabaghian et al, 2012 ; Arai et al, 2014 ; Babichev et al, 2016a , b , 2018 ; Basso et al, 2016 ; Hoffman et al, 2016 ; Dabaghian, 2019 ).…”

“…A computational framework developed in Dabaghian et al ( 2012 ), Arai et al ( 2014 ), Hoffman et al ( 2016 ), Basso et al ( 2016 ), Babichev et al ( 2016a , b ), Babichev and Dabaghian ( 2018 ), Dabaghian ( 2019 ), and Dabaghian ( 2016 ) helps to understand these phenomena by integrating the activity of the individual neurons into a large-scale map of the environment and to study the dynamics of its appearance, using algebraic topology techniques. Below we review some basic ideas and key concepts used in this framework, and discuss how they may apply to hippocampal physiology and cognitive realm.…”