is the experimental diffusion coefficient, $\eta$ the viscosity of the medium, $k_{B}$ the Boltzmann constant, $T$ the absolute temperature. Next, we identify $R_A=R^{H}_A$, $R_I=R^{H}_I$, and $\delta_F=R^{H}_F$, while $R_F$ is set by imposing that the experimental surface concentration found for Fib corresponds to its close packing configuration in the “standing up” conformation [@Lu1994]. These conditions give $R_{A}=3.55$ nm, $R_I=5.51$ nm, $R_F=9.29$ nm and $\delta_F=11$ nm. Protein masses $M_{A}=67$ kDa, $M_{I}=150$ kDa, $M_{F}=340$ kDa, necessary to determine the time scales, are known from experiments [@Noh2007].

Because we include only repulsive protein-protein interaction, for sake of simplicity we set all the protein-protein $\epsilon_{i,j}=\epsilon_{A,S}$. Protein-surface attraction energy $\epsilon_{i,S}$ can be calculated from the adsorption rate constants [@Lu1994]. These rates are proportional to the probability for a protein $i$ to attach to the nearby surface $$P_{i}\propto \exp\left(\frac{\epsilon_{i,S}}{k_{B}T}\right).$$ However, the $\epsilon_{i,S}$ in physical units are not known [*a priori*]{}. Hence, we consider the relative probabilities for different proteins $\frac{P_{i}}{P_{j}}\propto
\exp\left(\frac{\epsilon_{i,S}-\epsilon_{j,S}}{k_{B}T}\right)$, from which is possible to determine the values of the different energies as $$\frac{\epsilon_{j,S}}{\epsilon_{A,S}}=1-
\frac{k_{B}T}{\epsilon_{A,S}}\ln\left(\frac{P_{A}}{P_{j}}\right)
\label{5}$$ adopting $\epsilon_{A,S}$ for Alb as the energy units. We set $\epsilon_{A,S}$, the only free parameter of our model, by comparing our simulations results with experiments at ambient temperature, and get 