Analysis code for "Emergent hydrodynamic synchronization between microbeads labeling bacterial flagellar motors"

Abstract

This repository contains Python scripts/Jupyter Notebooks for analyzing the rotational dynamics and hydrodynamic synchronization of microbeads attached to bacterial flagella. Based on time-series trajectory data of bead centroids (x, y), the provided code performs the following analyses: 3D Trajectory Reconstruction: Reconstruction of three-dimensional trajectories from 2D motion. Phase Dynamics: Calculation of instantaneous phase difference ($\Delta$) and phase velocity ($\dot{\Delta}$) between pairs of beads. Synchronization & Slip Analysis: Determination of in-phase synchronization and phase-slip durations, as well as their respective fractions. Population Phase Distributions: Analysis of phase difference distributions across multiple bead pairs, including surrogate data testing for statistical validation. Kinematic Parameters: Estimation of intrinsic rotational frequencies ($\omega_1, \omega_2$), trajectory center coordinates, and orbital radii ($R$). Effective Potential: Estimation of the normalized effective potential $\widetilde{V}(\Delta)$ from phase velocity dynamics. Hydrodynamic Coupling: Computation of the hydrodynamic coupling coefficient ($C$). Data Input Note: The scripts accept centroid time-series data obtained from standard particle-tracking software (such as ImageJ / Fiji). Users may need to adjust the file loading/parsing sections of the code depending on their specific input file formats.