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Catalytically active macromolecules are envisioned as key building blocks indevelopment of artificial nanomotors. However, theory and experiments reportconflicting findings regarding their dynamics. The lack of consensus is mostlycaused by a limited understanding of specifics of self-propulsion mechanisms atthe nanoscale. Here, we study a generic model of a self-propelled nanoparticlethat does not rely on a particular mechanism. Instead, its main assumption isthe fundamental symmetry of microscopic dynamics of chemical reactions: theprinciple of microscopic reversibility. Significant consequences of thisassumption arise if we subject the particle to an action of an externaltime-periodic force. The particle diffusion coefficient is then enhancedcompared to the unbiased dynamics. The enhancement can be controlled by theforce amplitude and frequency. We also derive the power spectrum of particletrajectories. Among new effects stemming from the microscopic reversibility arethe enhancement of the spectrum at all frequencies and sigmoid-shapedtransitions and a peak at characteristic frequencies of rotational diffusionand external forcing. The microscopic reversibility is a generic property of abroad class of chemical reactions, therefore we expect that the presentedresults will motivate new experimental studies aimed at testing of ourpredictions. This could provide new insights into dynamics of catalyticmacromolecules.

Diffusion coefficient and power spectrum of active particles with a microscopically reversible mechanism of self-propelling