also contribute to growth. In this Section, we will limit ourselves to the model of Eqs.(1), which will be used as a reference for sorting out the different growth regimes in a transparent manner and as a basis for comparison with the Monte Carlo simulations. This approximation is expected to be valid for high supersaturations where step growth is less important. Finally, we only consider the process in which one molecule is directly incorporated from the solution since, for the conditions considered here, we expect this to be dominant over processes involving two or more molecules coming from solution. To illustrate the basic mechanism leading to a change in growth regimes, we first ignore depletion of the protein in solution near the interface so that a = a ′ = 0 and x = x$_{0}$ and neglect all dissolution processes so that k ′ 0 = k ′ 1 = k ′ 2 = 0. This limit should describe to a good approximation crystals growing in the kinetically-limited regime. What remains is then the simplified dynamics, A. A simplified model Since there is no detailed balance, there is no equilibrium state. However, a steady state where dy dt = 0 exists, implying a constant growth velocity, N dc$_{N}$ dt = v . The concentration of adsorbed molecules is then determined by and the velocity is When the concentration of protein in solution is small compared to that adsorbed on the surface, x << y , one finds dy dt = k$_{0}$x − ( N − 1) k$_{1}$xy N − 1 − Nk$_{2}$y N (2) dc$_{N}$ dt = k$_{1}$xy N − 1 + k$_{2}$y N 0 = k$_{0}$x − ( N − 1) k$_{1}$xy N − 1 − Nk$_{2}$y N (3) v = Nk$_{1}$xy N − 1 + Nk$_{2}$y N (4) y = ( k$_{0}$x Nk$_{2}$ ) 1 /N + ..., (5) v = k$_{0}$x + ... 5