  We present a theoretical model for the description of the adsorption kinetics
of globular proteins onto charged core-shell microgel particles based on
Dynamic Density Functional Theory (DDFT). This model builds on a previous
description of protein adsorption thermodynamics [Yigit \textit{et al},
Langmuir 28 (2012)], shown to well interpret the available calorimetric
experimental data of binding isotherms. In practice, a spatially-dependent
free-energy functional including the same physical interactions is built, and
used to study the kinetics via a generalised diffusion equation. To test this
model, we apply it to the case study of Lysozyme adsorption on PNIPAM coated
nanoparticles, and show that the dynamics obtained within DDFT is consistent
with that extrapolated from experiments. We also perform a systematic study of
the effect of various parameters in our model, and investigate the loading
dynamics as a function of proteins' valence and hydrophobic adsorption energy,
as well as their concentration and that of the nanoparticles. Although we
concentrated here on the case of adsorption for a single protein type, the
model's generality allows to study multi-component system, providing a reliable
instrument for future studies of competitive and cooperative adsorption effects
often encountered in protein adsorption experiments.
