Cylindrical Field Profiles Around Microtubules: From Visual Analogy to PDE-Based Model Selection

This theoretical framework develops a model-selection approach for radial measurements around cylindrical biological filaments, using microtubules as the motivating geometry. Gaussian, Lorentzian, modified-Bessel KO, ordinary-Bessel JO, sinc-like, and Hankel radial families are related to candidate diffusion, screening, wave, heavy-tail, and forced-field models. The work does not assume that microtubules generate any particular field. Instead, it derives experimentally distinguishable spatial, temporal, and frequency-dependent signatures and proposes falsification criteria for comparing candidate PDE models against future measurements.