  Calibration of optically trapped particles in-vivo has been complicated given
the frequency dependence and spatial inhomogeneity of the cytoplasmic
viscosity, and the requirement of accurate knowledge of the medium refractive
index. Further, it has been demonstrated that the medium viscosity is dependent
upon the measurement probe leading to reliability issues for measurements with
even micrometer sized particles. Here, we employ a recent extension of
Jeffery's model of viscoelasticity in the microscopic domain to fit the passive
motional power spectra of micrometer-sized optically trapped particles embedded
in a viscoelastic medium. We find excellent agreement between the 0 Hz
viscosity in MCF7 cells and the typical values of viscosity in literature,
between 2 to 16 mPa sec expected for the typical concentration of proteins
inside the cytoplasmic solvent. This bypasses the dependence on probe size by
relying upon small thermal displacements. Our measurements of the relaxation
time also match values reported with magnetic tweezers, at about 0.1 sec.
Finally, we calibrate the optical tweezers and demonstrate the efficacy of the
technique to the study of in-vivo translational motion.
