creator Nicholson, Stanley Anselm 2023 Spring 2023 Thesis Illinois Institute of Technology MATH / Applied Mathematics advisor Minh, David advisor Liu, Chun Biophysics Molecular biology Physical chemistry Coherence Function Community Detection Hydrogen Bonds Linear Systems Analysis Molecular Dynamics Protein Mechanics en Most proteins reduce the complexity of atomic motion to stable and coherent structures. Molecular dynamics (MD) has provided swaths of trajectory data of proteins. We analyze these trajectories using classical stochastic signal analysis, well established and utilized by engineers. Linear systems analysis operates to uncover linearities given an input and output signal. The coherence function says an input and output are linearly related if and only if the coherence equals one. Analyzing protein motion in the frequency domain allows us to extract a frequency function relating the modes of motion as determined by atomic power spectra. Motivated by biochemistry, we analyze classical interactions like hydrogen bonds and salt bridges and find they act like a linear system, or effective spring. We test our analysis on two protein systems: crambin and the Mu Opioid Receptor (MOR). We extend our results to all pairwise interaction and determine coherent communities of atoms within the MOR. We present various community detection algorithms and demonstrate their validity using common metrics in MD. Identifying rigid and tightly correlated regions of the protein offers great potential in coarse graining protein structure and understanding protein motion. born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access http://hdl.handle.net/10560/islandora:1024334