Spikes as Perturbations of Resonant Neural Circuits: From Membrane Biophysics to a Cognitive Framework

Computational neuron models commonly reduce subthreshold membrane dynamics to a leaky RC integrator, confining computation to the spike and treating the inter-spike membrane trajectory as passive decay. Yet direct impedance measurements and modern channel-specific analyses show that many excitable membranes exhibit band-pass, inductance-like impedance profiles with a tuneable resonant peak—dynamics that a first-order RC model cannot represent. This paper develops a spike-as-perturbation framework in which spikes function as perturbative control events that launch regime-dependent transient trajectories in an equivalent parallel RLC membrane. We present a representational comparison showing that post-perturbation RLC ringdowns carry structured circuit-identity and perturbation-timing state variables absent from RC exponential decays, and demonstrate a concrete computational primitive—phase-based temporal discrimination—that is not present as an intrinsic membrane-level transient feature in matched first-order RC models (independent of what more elaborate network-level RC circuits might achieve through delays or recurrence). A simulation analysis—using representative parameters (Q = 2, τ_RC = 25 ms, f₀ = 10 Hz) and an analytic sensitivity metric—shows that temporal sensitivity persists 2.5× longer under these assumptions than in matched RC decays, with model-derived sensitivity ratios exceeding 17× at 100 ms readout latency for Q = 2 (ratios scale with Q; see Fig. 5c). We derive four falsifiable predictions spanning cellular, network, decoding, and cognitive levels, and discuss implications for neuromorphic architectures incorporating resonant elements and adaptive coupling. The argument is presented in three tiers of decreasing evidential support: a well-supported biophysical substrate, a plausible spike-as-perturbation interpretation, and candidate cognitive-level hypotheses offered for future investigation.