Inter-Postsynaptic Functional Links for Associative Memory: Feasibility in a Realistic Neuropil Model

To quantify neuronal input degeneracy and test computationally whether nanoscale (≤30 nm) spine appositions are structurally eligible sites for inter-postsynaptic functional links (IPLs) underlying associative learning, assuming plausible pathway convergence onto abutted spine pairs. Empirical Constraint: Neuronal firing exhibits extreme input degeneracy. Any subset of inputs arriving at ~100-200 out of ~10⁴ spines can trigger an action potential; ~140 inputs yield >10³⁰⁰ possible effective input combinations. This degeneracy introduces ambiguity regarding the specific input combinations that contribute to associative encoding. Testable Mechanism: The semblance hypothesis proposes a spine-level conjunction code between co-active spines forming inter-postsynaptic functional links (IPLs) that operate independently of postsynaptic neuronal firing, and are proposed to maintain the fidelity of original associations during retrieval. Computational Validation: During retrieval, cue-induced reactivation of IPLs is hypothesized to depolarize inter-linked spines and generate semblances. Taking the depolarization of an inter-linked spine in the absence of direct presynaptic input as an "operational semblance" constituting the elemental substrate of associative recall, a computational model was implemented within a biologically realistic 1000 μm³ neuropil volume containing 1600 dendritic spines (density 1.6/μm³; diameter 0.6-0.7 μm) as independent dendritic segments. Of 391 crossing dendritic sites, 151 have abutted spine pairs, using ≤30 nm inter-spine distance as a candidate eligibility criterion, motivated by reported nanoscale appositions. Spine density, diameter, and separation were parameterized from electron microscopy and confocal/super-resolution imaging literature; coupling strength (0.7) was fixed and exploratory. IPL formation was implemented probabilistically across 20 learning trials (formation probability = 0.30 per trial at each of the 49 designated sites; reversal probability = 0.04), producing a gradual acquisition curve and trial-to-trial variance emerging naturally from the two-state Markov dynamics. Across 100 independent simulations, 49 of the 151 abutted pairs were designated as structurally eligible Bell-Food convergence sites; of these, 44.7 ± 2.1 developed active IPLs after 20 trials, generating operational semblances per retrieval (recall accuracy 36.93% ± 1.71%; paired t-test, p < 0.001; Cohen's d = 30.54, illustrative not calibrated). This work demonstrates that given a plausible convergence of associative pathways onto existing abutted spine pairs, the structural relations between spines in the cortical neuropil are compatible with the formation of a spine-level conjunction code as a potential substrate for associative learning.