pone.0358239.t009 - <p> </p>

An analytical competition model captures this transition in a compact form (<i>R</i>² = 0.550), with effective microstates marking a numerical balance point between electrostatic and steric contributions. Cross-dataset validation on 652 multi-material nanoparticles supports transferability of the descriptor framework (). We emphasize that is a constructed information-theoretic descriptor rather than a thermodynamic entropy, and that all findings are derived from retrospective analysis of in vitro datasets and not from controlled experimental manipulation.

The identified threshold therefore represents a reproducible statistical pattern and a testable hypothesis for how ligand flexibility modulates interaction regimes. This framework provides a computable basis for organizing nanocarrier design hypotheses and motivates prospective validation in more complex carrier systems.</p></div>