The mechanism of addition of a soluble unstructured monomer to a preformed ordered amyloid fibril is a complex process. On the basis of the kinetics of monomer disassociation of A beta(1-40) from the amyloid fibril, it has been suggested that deposition is a multistep process involving a rapid reversible association of the unstructured monomer to the fibril surface (docking) followed by a slower conformational rearrangement leading to the incorporation onto the underlying fibril lattice (locking). By exploiting the vast time scale separation between the dock and lock processes and using molecular dynamics simulation of deposition of the disordered peptide fragment (35)MVGGVV(40) from the A beta peptide onto the fibril with known crystal structure, we provide a thermodynamic basis for the dock-lock mechanism of fibril growth. Free energy profiles, computed using implicit solvent model and enhanced sampling methods with the distance (delta(C)) between the center of mass of the peptide and the fibril surface as the order parameter, show three distinct basins of attraction. When delta(C) is large, the monomer is compact and unstructured and the favorable interactions with the fibril results in stretching of the peptide at delta(C) approximate to 13 angstrom. As delta(C) is further decreased, the peptide docks onto the fibril surface with a structure that is determined by a balance between intrapeptide and peptide fibril interactions. At delta(C) approximate to 4 angstrom, a value that is commensurate with the spacing between beta-strands in the fibril, the monomer expands and locks onto the fibril. Using simulations with implicit solvent model and all atom molecular dynamics in explicit water, we show that the locked monomer, which interacts with the underlying fibril, undergoes substantial conformational fluctuations and is not stable. The cosolutes urea and TMAO destabilize the unbound phase and stabilize the docked phase. Interestingly, small crowding particles enhance the stability of the fibril-bound monomer only marginally. We predict that the experimentally measurable critical monomer concentration, C-R, at which the soluble unbound monomer is in equilibrium with the ordered fibril, increases sharply as temperature is increased under all solution conditions.