We investigate the origin of high-energy emission in blazars within the context of the leptohadronic one-zone model. We find that γ-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 γ-ray regime. Thus, the temporal behaviour 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 this work, we apply these ideas to the non-thermal emission of Mrk 421, which is one of the best monitored TeV blazars. We focus on the observations of 2001 March, since during that period Mrk 421 showed multiple flares that have been observed in detail both in X-rays and γ-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 γ-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 γ-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 γ-rays. On the other hand, models based on pion decay can reproduce this behaviour in a much more natural way.