Active filaments dynamics in motility assays for motor proteins: Pure and anomalous diffusion

In vitro motility assays are commonly used to study the mechanisms regulating the activity of motor proteins. Transport properties of active biofilaments in these systems are examined. A dynamics depending on surface concentration of biological motors is proposed in order to model gliding of individual filaments. Statistical analysis leads to purely diffusive dynamic laws. The presence of polymerization processes altering the length of fibres induces a breakdown of the central-limit theorem and leads to anomalous diffusion.