Background: It has been observed that single-domain proteins and domains in multidomain proteins favor a chain length in the range 100-150 amino acids. To understand the origin of the favored size, we construct an empirical function for the free energy of unfolding versus the chain length. The parameters in the function are derived by fitting to the energy of hydration, entropy and enthalpy of unfolding of nine proteins. Our energy function cannot be used to calculate the energetics accurately for individual proteins because the energetics also depend on other factors, such as the composition and the conformation of the protein. Nevertheless, the energy function statistically characterizes the general relationship between the free energy of unfolding and the size of the protein.
Results: The predicted optimal number of residues, which corresponds to the maximum free energy of unfolding, is 100. This is in agreement with a statistical analysis of protein domains derived from their experimental structures. When a chain is too short, our energy function indicates that the change in enthalpy of internal interactions is not favorable enough for folding because of the limited number of inter-residue contacts. A long chain is also unfavorable for a single domain because the cost of configurational entropy increases quadratically as a function of the chain length, whereas the favorable change in enthalpy of internal interactions increases linearly.
Conclusions: Our study shows that the energetic balance is the dominant factor governing protein sizes and it forces a large protein to break into several domains during folding.