Scaling laws in simple and complex proteins: size scaling effects associated with domain number and folding class

The native states of the most compact globular proteins have been described as being in the so-called “collapsed-polymer regime,” characterized by the scaling law R _g ~ n ^ν, where R _g is radius of gyration, n is the number of residues, and ν ≈ 1/3. However, the diversity of folds and the plasticity of native states suggest that this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size scaling is influenced by the number of domains. For the set of domains belonging to the all-α, all-β, α/β, and α?+?β folding classes, we find that size-scaling exponents vary between 0.3?≤?ν?≤?0.4. Interestingly, even domains in the same folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by monomer density, decreases when domains originate from increasingly complex proteins.