Three self responses give sharp lower bounds after full block in passive gap networks with hidden cells, fixed leaks and gains, and known uniform block
We asked what three steady measurements from one cell can show about full gap block when other cells are hidden. We prove a sharp lower bound for a finite passive gap network. Cell leaks must be positive and fixed. Recording gains must stay fixed. The same known conductance factor must apply to all gaps. The formula uses three current-to-voltage self responses. A circuit with one hidden cell can attain the lower bound. We give a conservative tool for supplied response error limits. A four-cell family has the same three measurements and no finite upper full-block response. This obstruction extends to any finite number of states short of full block when the hidden network is free. We tested the method on 302 neural slots and 1,091 electrical pairs from the Cook worm contact map. We chose positive membrane parameters. We did not fit animal activity. At the main gap strength, we used readings with 75%, 50%, and 0% of gap conductance removed. Mean lower-bound shortfall fell from 3.29% with two states to 1.96% with three states. The largest cell shortfall was 69.7%. Supplied response error limits of plus or minus 1% removed most of the added benefit. Source audits, exact examples, independent matrix solves, and a clean numerical repeat passed. The package preserves proof, code, data provenance, parameters, results, figures, and repeat instructions. These are conditional model results. They do not establish block effects in living neurons or calibrate drug efficacy.
electrical synapse · gap junction · hidden neurons · input resistance · partial block · passive network · rational bound · connectome
References
9- usesKnown uniform partial gap block gives lower DC self response bounds with hidden cells in passive reciprocal models with fixed gains sci:sha256:414733cb1beca44d7b9eed7435b453b468b0397e5ab9ab4a8533a5b59d95987c
We reuse its verified Cook electrical graph facts, positive main parameter rule, and two-state scalar inverse secant comparator. We add a sharp three-self-response limit, interval tool, and a finite-state non-identifiability construction.
- usesA known uniform partial gap block fixed full-removal responses in linear models with exact maps, fixed properties and access to all changed endpoints sci:sha256:95ac12b3a874d66f0797316e12b93c843679c18a9574f98a391415ae4a094800
This is an earlier source of the attributed electrical graph tables, obtained through the verified hidden-cell partial block archive.
- usesWith known leaks and reciprocal gaps, full voltage responses leave 26 coupling changes unresolved in a Cook C. elegans model with instantaneous chemical transmission sci:sha256:0c1c93618d6713502f3eae4aefb7443ba21acd429acb804f7548932c222ef542
This is the original SCI factual extract of the Cook neural electrical pairs and labels, reused through the two later block studies and checked here against the original workbook.
- usesdoi:10.1038/s41586-019-1352-7
The corrected July 2020 hermaphrodite workbook supplies the neural electrical contact graph. Serial sections set model weights, not measured conductances.
- doi:10.1063/1.1666314
Multipoint rational approximation bounds for Stieltjes functions are prior mathematics. We do not claim a new general rational-approximation theorem.
- doi:10.1109/TCSI.2012.2215780
Kron reduction and the Schur complement are the established network reduction tools used in the proof.
- doi:10.1523/JNEUROSCI.22-10-04142.2002
Earlier neural models show how hidden electrical networks affect input conductance estimates.
- doi:10.1016/j.jtbi.2005.10.009
Earlier work estimates intrinsic and junctional conductances from dual-recorded cells embedded in a coupled network.
- doi:10.1073/pnas.0402044101
Experimental blocker work illustrates why calibrated efficacy and stable membrane properties need separate checks.
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