For one exact C. elegans mean kernel pair at 0.2 per second, a passive bound required 2.24 fold readout variation with free pools and 4.24 fold with equal pools

Changes in a calcium readout can make a passive electrical circuit appear to amplify a two-way response. We derive a bound on this effect. Each cell has a positive readout factor with fold range at most G. The two direction pools have gain-ratio distributions whose total variation distance is at most delta. The product P of the two mean source-normalized transfers obeys P <= {[(1+delta)G+(1-delta)/G]/2}^2. The bound permits hidden passive cells and different circuit states. A two-state passive circuit approaches the bound. Equal pools give the classical Kantorovich bound. Free pools give P<=G^2. We apply the inverse bound to a fixed published panel of 66 C. elegans kernel pairs. If the fitted mean values are exact, the largest pair at 0.2 per second needs a maximum per-cell gain range with infimum 2.237 for free pools, or 4.238 for equal pools. At 1 per second the values are 1.917 and 3.552. We give 45 finite passive pair models that match the values above one at the two rates. These are separate models, not a joint worm fit. Products formed within matched states stay at most one when the readout ratio is fixed within each matched pair. We check the method with exact arithmetic, numerical optimization, passive graph models and source coefficients. The export has no event-level kernel errors or calibrated gain distributions. Thus the results give sensitivity limits and a measurement method, not a rejection of passive transfer in animals.

connectome · calcium imaging · gap junction · passive transfer · readout gain · state pooling · Kantorovich inequality · total variation · C. elegans · identifiability