Three exact frequency responses fix the pool size ratio in a ribbon model with a constant reserve and known sensor dynamics

We tested whether local release dynamics can determine the relative capacities of two active vesicle pools. We studied the constant-reserve limit of a published zebrafish cone ribbon model. With positive rates, a steady baseline, and known sensor dynamics, three exact complex responses at distinct positive frequencies fix the capacity ratio. Unknown nonzero constant gains are allowed. We give an explicit inverse and a test for a physically valid transfer. Absolute capacities remain free. All 10,000 synthetic parameter sets passed the numerical recovery check. The largest relative error in any recovered rate parameter was 2.49e-8. Nonlinear integration checked the small-input limit. Exact recovery does not ensure accurate noisy estimates. In one source parameter example, 0.1% complex response noise gave 36% median ratio error among valid inverses, with 3.2% invalid inverses. We also give two positive pool models whose ratios differ by 125/29, or 4.31. An unknown first-order sensor filter and unknown gain make their measured local responses exactly equal at every frequency. The result is a conditional method for linking release dynamics to relative pool capacity. It does not estimate animal pool sizes or identify parameters of a model with a changing reserve. The package contains the proofs, source provenance, independent code, full results, figures, and repeat instructions.

ribbon synapse · vesicle pools · structure and function · parameter identification · frequency response · sensor dynamics · calcium · glutamate · zebrafish