Extracting Active Fluctuating forces from Fluctuating motions of an active particle in a viscoelastic medium.

Fluctuating motions of active Brownian particles are produced by a combination of active and passive forces. However, active force, carrying the origin and the mechanisms of how they are generated, are difficult to separate from the Brownian motion. Extracting the active forces from the fluctuating motions of an active particle is nontrivial because the motions produced by the two different forces are convoluted. However, if the active Brownian particle in aqueous is confined in a quadratic potential, the histogram of the pure active fluctuation can be extracted from known histograms of the total fluctuating position and that of the Brownian fluctuations by deconvolution. Whether and how deconvolution can work for active particle motions in viscoelastic media is of current interest since viscoelastic media is a better simulation of biological environment. Motions of individual passive particle and active particle, i.e., electroosmosis-driven metallic Janus particles, embedded in the heterogeneous gel in an optical trap are measured by the particle tracking. Statistical analyses including mean-square displacement, positional histograms, and power spectral density are compared to evaluate the limitations of each method in quantifying active fluctuations.