while the reverse circumstance, x >> y , gives y = ( k$_{0}$ ( N − 1) k$_{1}$ ) 1 / ( N − 1) + ... (6) v = N N − 1 k$_{0}$x + ... There is therefore a crossover from small x behavior, where the aggregation process, Ny ⇄ c$_{N}$ , dominates with velocity v = k$_{0}$x to the large x behavior where the x + ( N − 1) y ⇄ c$_{N}$ process dominates with velocity v = N N − $_{1}$k$_{0}$ x . Since this transition occurs in the normal growth regime - below the usual roughening transition - the growth rates are, in these limits, linear functions of the concentration, as expected. Small and medium sized clusters are those contributing the most in the switching, since for large N the growth velocities of the two regimes become practically indistinguishable. As we will discuss elsewhere, to get a more detailed sense of the interplay between these mechanisms, a simple model can be formulated for which numerically-exact results can be obtained using the theory of finite Markov processes[32]. In the simplified model, all dissolution processes were neglected. Experimental investigations[33, 34] have shown, however, that this is not valid for protein crystals growing at low driving forces. Here, we therefore incorporate desorption and dissolution processes in the full model. Including the desorption of surface molecules, k ′ 0 = 0, does not change the picture dramatically: the small x behavior is no longer linear but there is still a crossover between one well-defined growth mode at small x to another, faster mode at large x as in the simple model. Including all of the evaporation processes, k ′ 1 , 2 = 0, however, does change the picture significantly. First, detailed balance defines an equilibrium state at some finite value of x$_{0}$ . For bulk concentrations above this value, growth occurs but it will eventually end when a steady (equilibrium) state is reached. In between, a quasi-steady growth regime occurs during which a growth velocity can be defined. Detailed numerical solutions of the model again show a crossover in the growth velocity as the bulk concentration increases. The requirement of detailed balance at equilibrium, i.e. that the forward rates and backward B. Full model 6