  We perform joint fits using measurements of the proton structure functions
$F_2(x,Q^2)$ and $F_L(x,Q^2)$, of the photon structure function
$F_2^\gamma(x,Q^2)$ and of the total cross-sections $\sigma\left( \gamma p
\rightarrow X\right)$ and $\sigma \left( \gamma \gamma \rightarrow X\right)$.
The data is gathered from several sources including HERA and LEP. The
kinematical range considered is wide with a photon virtuality $Q^2 \leq400 \,
{\rm GeV}^2$, Bjorken variable $x<0.01$ and $\sqrt{s} > 4 \, {\rm GeV}$. This
is done by considering a $U\left(1\right)$ vector gauge field minimally coupled
to the graviton Regge trajectory in improved holographic QCD. We find good
agreement with the data for a joint fit of $F_2^\gamma$ and $\sigma\left(\gamma
\gamma \rightarrow X\right)$ with a $\chi_{d.o.f.}^2 = 1.07$. For a joint fit
of $F_2$, $F_L$ and $\sigma\left( \gamma p \rightarrow X\right)$ we find
$\chi_{d.o.f.}^2 = 1.40$. A joint fit of all observables for both processes
$\gamma^* \gamma$ and $\gamma^* p$ gives a $\chi_{d.o.f.}^2 = 1.38$. The
gravitational couplings of the $U\left(1\right)$ vector gauge field and of the
proton with the Reggeons of the graviton Regge trajectory are given as an
output of the fitting procedure. An approximate relation between the structure
functions, valid at NLO QCD, is used to estimate the parton distribution
function of the gluon inside the proton.
