  Catalytically active macromolecules are envisioned as key building blocks in
development of artificial nanomotors. However, theory and experiments report
conflicting findings regarding their dynamics. The lack of consensus is mostly
caused by a limited understanding of specifics of self-propulsion mechanisms at
the nanoscale. Here, we study a generic model of a self-propelled nanoparticle
that does not rely on a particular mechanism. Instead, its main assumption is
the fundamental symmetry of microscopic dynamics of chemical reactions: the
principle of microscopic reversibility. Significant consequences of this
assumption arise if we subject the particle to an action of an external
time-periodic force. The particle diffusion coefficient is then enhanced
compared to the unbiased dynamics. The enhancement can be controlled by the
force amplitude and frequency. We also derive the power spectrum of particle
trajectories. Among new effects stemming from the microscopic reversibility are
the enhancement of the spectrum at all frequencies and sigmoid-shaped
transitions and a peak at characteristic frequencies of rotational diffusion
and external forcing. The microscopic reversibility is a generic property of a
broad class of chemical reactions, therefore we expect that the presented
results will motivate new experimental studies aimed at testing of our
predictions. This could provide new insights into dynamics of catalytic
macromolecules.
