Before revision:  It was found that the crowding effect is taken into account as the effective internal entropy ; and the crowding effect reduces the effective internal entropyof disordered states . Based on Monte Carlo simulation, we provide scenarios of crowding-induced fibril formation.
After revision:  Thanks to the simplicity of the model, we can exactly calculate the number of conformations of crowding agents, and this enables us to prove that the original grand canonical ensemble with a crowding agent reservoir is mathematically equivalent to a canonical ensemble without crowding agents. In this expression, the effect of macromolecular crowding is absorbed in the internal entropy of disordered states; it is clearly shown that the crowding effect reduces the effective internal entropyof disordered states . Based on Monte Carlo simulation, we provide scenarios of crowding-induced fibril formation.