Among the dipole models of deep inelastic scattering at small values of the Bjorken variable $x$, one has been recently proposed which relates the virtual photon-proton cross section to the dipole-proton forward scattering amplitude in momentum space
. The latter is parametrized by an expression which interpolates between its behavior at saturation and the travelling wave, ultraviolet, amplitudes predicted by perturbative QCD from the Balitsky-Kovchegov equation. Inspired by recent developments in coordinate space, we use this model to parametrize the proton structure function and confront it to HERA data on $ep$ deep inelastic scattering. Both event-by-event and the physical amplitudes are considered, the latter used to investigate the effect of gluon number fluctuations, beyond the mean-field approximation. We conclude that fluctuations are not present in DIS at HERA energies.
