MATLAB Analysis Pipeline for Procrustes-Aligned Orientational Consistency Index (O_ij).

Integrated MD Trajectory Analysis Pipeline for Orientational Consistency (Oij) and Positional Dynamics in CRBP Ensembles Overview This repository provides the master MATLAB analysis pipeline, helper utilities, and processed molecular dynamics (MD) trajectory datasets used to evaluate residue-level orientational consistency (Oij) alongside conventional dynamic cross-correlation (Cij, DCCM). The framework systematically deciphers internal dipole synchronizations across wild-type (WT Apo, WT Holo) and charge-perturbed (Q108R Holo) cellular retinol-binding protein (CRBP) ensembles across independent production replicas. Dataset Description & Directory Layout All trajectory vectors and coordinate frames have been rigorously pre-processed via periodic boundary condition correction (gmx trjconv -pbc nojump) and mapped into an internal reference frame via global rotational and translational alignment (fit rot+trans) to completely eliminate stochastic Brownian tumbling across the explicit solvent box. ├── fit_upload_intergrated.m # Master script generating Oij and Figures 1–5├── load_md_data_fit.m # Global environment and dataset path configuration├── apo/ # WT Apo simulation dataset (Replicas 1–3)│ ├── MD_fit_vectors_rep*_fit.mat # Pre-processed Cα-C=O backbone dipole trajectories (dipole_dir)│ ├── rmsd_rep*.xvg, gyrate_rep*.xvg, energy_rep*.xvg│ └── dccm_rep*.dat (matrix_cut*.dat)├── holo/ # WT Holo simulation dataset (Replicas 1–3)└── q108r_holo/ # Q108R Holo simulation dataset (Replicas 1–3) Key Features & Analysis Modules Macrostructural Stability & Convergence Profiling (Figure S1, Table S1): Parses GROMACS XVG output files to compute time series, 10 ns window block-averaged means, and twofold standard deviation envelopes forRMSD, radius of gyration, and thermodynamic energy components (potential, kinetic, total). Verifies structural convergence and defines the equilibrated production phase window (100–200 ns, 10,000 frames). Positional Displacement Correlations (Cij, DCCM) (Figures 1 & S2): Evaluates pairwise Cartesian displacement cross-correlations (Cij, scaled [-1, 1]) across individual trajectories and ensemble averages. Optimal Procrustes Orientational Consistency Pipeline (Oij) (Figures 2 & S3): Implements proper Procrustes rotational superimposition via Singular Value Decomposition (SVD) on zero-mean centered dipole unit vector trajectories. Determines dynamic in-phase vs. anti-phase rotational synchronization from the optimal rotation matrix trace. Decouples static secondary structural geometric offsets from genuine dynamic orientational fluctuations. Multi-Metric Comparative & Spatial Persistence Analysis (Figures 3, 4): Establishes system-specific data-adaptive significance thresholds derived from off-diagonal ensemble distributions. Quantifies sequence-distance decay P(d) to highlight that Oij operates as a contact-independent descriptor capable of detecting distal tertiary coupling transparent to coordinate-based metrics. Generates split-triangle dual-metric comparison maps (|Cij| vs. |Oij|). 2D Phase-Space Quadrant & Artifact Filtering Benchmark (Figures 5): Performs 2D phase-space quadrant analysis (|Oij^0| vs. |Oij|) to partition residue pairs into uncoupled baselines (LL), conserved anchors (HH), emergent orientational synchronizations (LH), and spurious geometric overlaps (HL). Requirements & Usage Software Environment: MATLAB (R2022b or later; R2023b/R2024a recommended) Required Toolboxes: Parallel Computing Toolbox (for parfor acceleration during pair-wise SVD operations), Statistics and Machine Learning Toolbox Execution: Ensure all pre-processed data directories (apo, holo, q108r_holo) and load_md_data_fit.m are located in the working path. Run fit_upload_intergrated.m. All manuscript figures (Figures 1–5) and quantitative tables (Table S1) will be generated and displayed automatically. Changelog Version 2.0.0 (Current): Trajectories and dipole vectors were fully upgraded to globally fitted coordinate frames (fit rot+trans) to eliminate Brownian solvent tumbling. Superseded unaligned trajectories and fixed empirical cutoff protocols (0.5 cutoff) were replaced with the rigorous, data-adaptive statistical threshold framework.