Confinement Reweights Protein Orientational Phase Space in Crystallization: A PDB-Anchored Hamiltonian Comparison of Hanging-Drop and Langmuir–Blodgett Nanotemplates

This study quantifies how confinement changes the orientational phase space of proteins by comparing hanging-drop (HD) with Langmuir–Blodgett (LB) conditions within a unified probabilistic framework grounded in structural data from the Protein Data Bank (PDB). For each protein, principal moments of inertia are computed from atomic coordinates, trace-normalized, and used to define a geometry-based benchmark for the probability of occupying a predefined productive-orientation set. In parallel, a Hamiltonian-weighted probability is obtained within a classical statistical–mechanical treatment by reconstructing the orientational distribution over the polar–azimuthal domain under a fixed global confinement protocol. The analysis is carried out on a ten-protein panel spanning diverse sizes and anisotropies, and the HD→LB contrast is characterized through probability gains, distributional distances, and an energy-basin decomposition that distinguishes basin depth from basin measure. Under identical parameterization, LB globally produces higher productive-orientation probabilities than HD across all proteins, establishing a uniform direction of the confinement effect while preserving protein-dependent magnitudes. The inertia-based benchmark exhibits broader dispersion in LB/HD amplification, whereas the Hamiltonian construction yields a more regular cross-protein gain, consistent with LB acting as a global reweighting of orientational phase space rather than a protein-specific re-tuning. By integrating PDB-derived structural descriptors with a statistical–mechanical operator, the framework provides a transparent bridge between molecular geometry and confinement-driven ordering and offers a compact basis for comparing crystallization-relevant confinement protocols across structurally heterogeneous proteins.