  We exploit moderately resolved [OIII], [CII] and dust continuum ALMA
observations to derive the gas density ($n$), the gas-phase metallicity ($Z$)
and the deviation from the Kennicutt-Schmidt (KS) relation ($\kappa_s$) on
~sub-kpc scales in the interstellar medium (ISM) of five bright Lyman Break
Galaxies at the Epoch of Reionization ($z\approx 7$). To do so, we use GLAM, a
state-of-art, physically motivated Bayesian model that links the [CII] and
[OIII] surface brightness ($\Sigma_{\rm [CII]}$, $\Sigma_{\rm [OIII]}$) and the
SFR surface density ($\Sigma_{\rm SFR}$) to $n$, $\kappa_s$, and $Z$. All five
sources are characterized by a central starbursting region, where the
$\Sigma_{\rm gas}$ vs $\Sigma_{\rm SFR}$ align ~10x above the KS relation
($\kappa_s\approx10$). This translates into gas depletion times in the range
$t_{\rm dep}\approx 80-250$ Myr. The inner starbursting centers are
characterized by higher gas density ($\log (n/{\rm cm^{-3}}) \approx 2.5-3.0$)
and higher metallicity ($\log (Z/Z_{\odot}) \approx -0.5$) than the galaxy
outskirts. We derive marginally negative radial metallicity gradients ($\nabla
\log Z \approx -0.03 \pm 0.07$dex/kpc), and a dust temperature
($T_d\approx$32-38 K) that anticorrelates with the gas depletion time.
