Modelling Permittivity in Proteins: A User-Friendly Approach

<jats:p>Protein-based biosensors exploit the extraordinary selectivity of proteins toward specific ligands—other proteins, ions, electromagnetic signals—often surpassing engineered recognition systems. Ligand binding induces structural rearrangements that alter a protein’s electrical and dielectric properties, and in electrical biosensors these changes, particularly in conductance, are what allow the target analyte to be quantified. Yet despite decades of effort, no unified strategy exists for defining and calculating protein permittivity (κ), a quantity central to interpreting such signals. Here we present a computationally inexpensive framework for evaluating protein permittivity, built on a network representation of the protein derived from its three-dimensional topology, in which each amino acid’s permittivity is assigned continuously between a dry, intrinsic value and the bulk solvent value according to its coordination number. Applied to 60 structurally diverse proteins, the model reveals a robust relationship between effective permittivity and a simple topological compactness index. As a proof of concept, we compute the electrical impedance of apo-azurin and of the protein NP_888769.1 under two electrode-contact configurations, finding a measurable, geometry-dependent response that vanishes under a uniform dielectric constant—an experimentally testable signature of internal dielectric structure that invites a re-examination of what protein permittivity experiments actually measure.</jats:p>