  We investigate the origin of high-energy emission in blazars within the
context of the leptohadronic one-zone model. We find that $\gamma$-ray emission
can be attributed to synchrotron radiation either from protons or from
secondary leptons produced via photohadronic processes. These possibilities
imply differences not only in the spectral energy distribution (SED) but also
in the variability signatures, especially in the X- and $\gamma$-ray regime.
Thus, the temporal behavior of each leptohadronic scenario can be used to probe
the particle population responsible for the high-energy emission as it can give
extra information not available by spectral fits. In the present work we apply
these ideas to the non-thermal emission of Mrk 421. We focus on the
observations of March 2001, since during that period Mrk 421 showed multiple
flares that have been observed in detail both in X-rays and $\gamma$-rays.
First, we obtain pre-flaring fits to the SED using the different types of
leptohadronic scenarios. Then, we introduce random-walk type, small-amplitude
variations on the injection compactness or on the maximum energy of radiating
particles and follow the subsequent response of the radiated photon spectrum.
For each leptohadronic scenario, we calculate the X-ray and $\gamma$-ray fluxes
and investigate their possible correlation. Whenever the `input' variations
lead, apart from flux variability, also to spectral variability, we present the
resulting relations between the spectral index and the flux, both in X-rays and
$\gamma$-rays. We find that proton synchrotron models are favoured
energetically but require fine tuning between electron and proton parameters to
reproduce the observed quadratic behaviour between X-rays and TeV
$\gamma-$rays. On the other hand, models based on pion-decay can reproduce this
behaviour in a much more natural way.
