Conductive Substrate Modulation of Spacing-Dependent Transcriptional Amplification: A Biophysical and Dynamical Systems Model

This study presents a mechanistic computational framework linking substrate conductivity to spacing-dependent transcriptional amplification through membrane-potential modulation and phosphatase kinetics. A biophysically derived substrate factor (φ) is incorporated into nonlinear ERK–CREB signaling models and transcriptional-delay systems to predict attenuation of spacing effects on conductive substrates such as ITO and PEDOT:PSS. The work combines membrane-clamping derivations, fitted ODE signaling models, transcriptional-delay extensions, and analysis of publicly available Drosophila RNA-seq datasets (GSE113344). Results predict monotonic collapse of the spacing amplification ratio (SAR) with increasing substrate conductivity. Included materials:- manuscript PDF- modeling scripts- generated figures- RNA-seq analysis- synthetic phosphoproteomic demonstration- supporting CSV outputs The framework is presented as a falsifiable and experimentally testable systems-level hypothesis connecting substrate electrical properties to temporal learning dynamics.