Effects of reactivity on mobility: insights from an exactly solvable two-state model

Recent experimental reports of activity-induced enhanced mobility by Wang et al (2020 Science 369 537) have renewed the debate about the reality of a phenomenon that, since its first observation in 2000, has been both reaffirmed and called into question. In an effort to find theoretical grounds for or against these observations, we apply a one-dimensional model of two-state Brownian dynamics to determine to what extent chemical reactivity, as represented in the equations of particle motion by source and sink terms that induce inter-state transitions, affects how much farther or nearer the particle travels on average in a time interval t in relation to the distance it would have traveled in the absence of a reaction. We find-based on exact calculations carried out in Laplace space-that depending on the strengths of the potentials that define the two states, as well as the locations of their minima and the speed of exchange between them, the particle's relative displacement can be indeed be enhanced by substantial amounts, but it can also be decreased. While these findings do not necessarily resolve the questions around the boosted mobility effect, they do provide further evidence of its potential observability.

Automated summary

Recent experimental reports have reignited the debate on the reality of activity-induced enhanced mobility. Using a one-dimensional model of two-state Brownian dynamics, researchers found that chemical reactivity can both increase and decrease the average displacement of particles.