A model for cytoplasmic rheology consistent with magnetic twisting cytometry

Magnetic twisting cytometry is gaining wide applicability as a tool for the investigation of the rheological properties of cells and the mechanical pr operties of receptor-cytoskeletal interactions. Current technology involves the application and release of magnetically induced torques on small magne tic particles bound to or inside cells, with measurements of the resulting angular rotation of the particles. The properties of purely elastic or pure ly viscous materials can be determined by the angular strain and strain rat e, respectively. However, the cytoskeleton and its linkage to cell surface receptors display elastic, viscous, and even plastic deformation, and the s imultaneous characterization of these properties using only elastic or visc ous models is internally inconsistent. Data interpretation is complicated b y the fact that in current technology, the applied torques are not constant in time, but decrease as the particles rotate. This paper describes an int ernally consistent model consisting of a parallel viscoplastic element in s eries with a parallel viscoelastic element, and one approach to quantitativ e parameter evaluation. The unified model reproduces all essential features seen in data obtained from a wide variety of cell populations, and contain s the pure elastic, viscoelastic, and viscous cases as subsets.