A unified toeplitz framework for sequence-dependent molecular sensing: an analytical synthetic proof of concept

Sequence-dependent biosensors infer molecular identity from signals generated by finite local contexts, but highly parameterized decoders often obscure how context distinguishability, sensor calibration, and sensing width constrain reconstruction. We present an interpretable multichannel Toeplitz framework, evaluated exclusively on controlled synthetic data, that represents local sequence-to-signal coupling as a finite-support, translation-invariant operator supporting forward signal generation, least-squares kernel calibration, constrained dynamic-programming reconstruction, and residual-based localization of signal anomalies. Beyond the matched-condition results reported previously, we show algebraically that practical identifiability of the calibrated kernel depends on the zero-padded sequence boundary rather than being an intrinsic property of the local sensing window; quantify the degradation of calibration, reconstruction, and residual localization as the data-generating process departs from the additive assumption through an explicit pairwise-interaction term; benchmark the framework against a K-mer-lookup baseline, a posterior (forward-backward) decoder, ridge regression, and a nonlinear (multilayer-perceptron) regressor; and replace the original rank-only event detector with a null-distribution-calibrated, false-positive-rate-controlled threshold. Under matched conditions the calibrated kernel still attains mean sequence-reconstruction accuracies above 99% with as few as five calibration sequences, but detection of the manuscript's original illustrative perturbation amplitude recovers only 37-58% of true events once the detector's false-positive rate is properly controlled, rising to F₁ > 0.9 only above 1.5-3× that amplitude. The revised framework is presented explicitly as an analytical, synthetic proof of concept, and we discuss the specific respects in which its component algorithms are established versus newly combined.