Gel Electrophoresis of Soft Nano-Spheres

We present a theoretical model---and accompanying experimental data---quantifying the electrophoretic mobility of soft nano-spheres in charged (polyelectrolyte) hydrogels. The theory accounts for electrical, hydrodynamic, and frictional coupling forces. By drawing on several reasonable, simplifying assumptions, we derive an analytical, closed-form solution of a more general electrokinetic model that captures several notable characteristics of experimental data; in particular, the previously unexplained possibility of negatively charged gold nano-particles migrating as if they bear a positive charge. By fitting the model to data from a series of experiments conducted with PEG-functionalized gold nano-particles in agarose hydrogels, we ascertain several fundamental parameters that characterize the hydrogel micro-structure, ultimately furnishing a remarkably robust and predictive model for the design and interpretation of functional nano-particle gel electrophoresis technologies.