Microtubule Coherence Index: A Minimal Excitable Lattice Model of Conformational Propagation and Phase Boundary Collapse

This paper introduces the Microtubule Coherence Index (MCI), a minimal classical excitable-lattice model designed to investigate threshold-governed conformational propagation in microtubule protofilaments. Extending the previously published Tissue Coherence Index (TCI), Follicular Coherence Index (FCI), and Pecten Coherence Index (PCI) computational twins, the model tests whether microtubule-scale propagation collapse exhibits the same logistic phase-boundary behavior observed in tissue-level biological systems.A one-dimensional lattice of coupled αβ-tubulin dimers was constructed using classical dynamics only: nearest-neighbor dipole coupling, GTP-driven energy pumping, spontaneous hydrolysis, and thermal noise. The model demonstrates a sharp logistic transition between coherent and fragmented propagation states, confirming that threshold-governed collapse is a general dynamical phenomenon across scales. However, the dimensionless critical threshold diverges substantially from the tissue-level twins, revealing that actively pumped microtubule systems belong to a different dynamical regime than passively dissipative tissue networks.Importantly, the study reports several genuine negative results. Previously proposed dimensionless coupling groups (Π₄ and related formulations) fail to converge on the tissue-scale threshold, and the microtubule transition is significantly less sharp than the follicular coherence boundary. Rather than weakening the framework, these failures demonstrate that the model distinguishes between dynamical universality classes rather than forcing artificial convergence.The work does not claim proof of quantum coherence, Orch-OR, or universal biological laws. Instead, it provides a falsifiable computational framework for studying propagation collapse in actively pumped biological media and offers experimentally testable predictions for microtubule conformational signaling under varying coupling, noise, and energy conditions.