Brownian particles in a soft matter potential: A model for directional drug transport and release in polymer network

Improvement of efficiency in drug release is of profound importance in biomedical engineering. The drift and diffusion of Brownian particles in a flexible and porous medium is a typical model for describing the directional drug release system. The tilted periodic potential, usually referred to as the washboard potential (WBP), is a well-known model for describing the motion of Brownian particles in a complex medium. Considering that the drug cargo, such as hydrogel, is flexible and thermally fluctuating, a soft matter potential (SMP), which allows Brownian particles to actively modify the structure of the soft medium, is proposed to describe the polymer networks. The giant acceleration of diffusion (GAD) and the thermodynamic uncertainty relation (TUR) of Brownian particles are investigated in the SMP and WBP, and it is found that the SMP leads to lower GAD and energy cost < q > for a given precision A of drug directional transport. Furthermore, the results indicate that a more deformable drug cargo can achieve a higher directional transport efficiency, that is, a lower Q = < q > / A. This is potentially applicable to improve the efficiency of controlled directional drug release.