Resonant Spin-Selective Gating in Magnesium-Dependent ATPase: A 288-Dimensional Analysis of Magnetic Isotope Effect Robustness

This repository contains the numerical datasets and computational framework for simulating the Magnesium Magnetic Isotope Effect (MIE) in the catalytic site of F1-ATPase. The study focuses on the resonant spin-selective gating within a high-dimensional nuclear environment. Computational Implementation The provided Python script utilizes a stationary Liouville-Lindblad solver to determine the steady-state density matrix (\rho_{ss}) for a radical pair system. The solver addresses the D^2 \times D^2 Liouville space using the Generalized Minimal Residual (GMRES) algorithm with a diagonal preconditioner to ensure numerical stability and trace preservation (\text{Tr}(\rho) = 1.0).