Mathematical Structure of Exceptionally Compact Globular Proteins Containing a Large Internal Functional Cavity
Authors: Vladimir N. Uversky
Type: Short Note
Issue: Volume 1, Issue 1
Publication date: 2026-11-05
Received: 2026-11-02
Accepted: 2026-11-04
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Abstract
The observation that some globular proteins exhibit hydrodynamic dimensions below the standard mass-dependent scaling law is recast as a scaling problem. We show that the total volume of a protein with a functional cavity is governed by the additive decomposition V'_tot(M) = V_prot(M) + V'_void(M) + V_cavity(M), and that the six structural scenarios previously described in qualitative terms correspond to explicit constraints on the scaling exponents of each term. Around this decomposition we identify three mathematical objects: an effective scaling exponent ν', a fractal dimension D_f = 1/ν', and a packing-density functional φ(M). Their composition yields a predictive map Ψ that converts measurable hydrodynamic data into a classification of compactness. The note argues that this mathematical profile, rather than the qualitative taxonomy, is what makes the phenomenon of exceptionally compact proteins operational and testable.