Protonisation fluctuations in addition instigate dipole moment fluctuations, which in turn lead to a correction of the dielectric constant of the protein ε p through a variant of the Kirkwood formula , derived by considering protonation-induced dipole fluctuation of a spherical cavity of radius R with an isotropic dielectric response ε ∞ . The relation between dipole fluctuations and the excess polarizability response function α is then