Determination of Condensate Material Properties from Droplet Deformation

I derive theoretical results that relate the effective spring constant, chi, of protein droplets to their material properties. chi, defined as the ratio between a uniaxial applied force and the extent of the corresponding deformation, can be measured by optical tweezers. When the deformation is static, where the applied force is balanced by the interfacial tension of the droplet, the spring constant allows for the determination of the surface tension (gamma). When a sinusoidal force is applied (at frequency omega), the dynamic spring constant chi(omega) is related to both gamma and the complex shear modulus, G*(omega), of the droplet. The results derived here enable accurate extraction of gamma and G*(omega) from chi(omega) data.