Thermodynamics of Loop Formation in the Denatured State of Rhodopseudomonas palustris Cytochrome c′: Scaling Exponents and the Reconciliation Problem

The observation that denatured proteins yield scaling exponents, ν, consistent with random-coil behavior and yet can also have pockets of residual or nonrandom structure has been termed the “reconciliation problem”. To provide greater insight into the denatured state of a foldable sequence, we have measured histidine–heme loop formation equilibria in the denatured state of a class II c-type cytochrome, cytochrome c′ from Rhodopseudomonas palustris. We have prepared a series of variants that provide His–heme loop stabilities, pKloop(His), for loop sizes ranging from 10 to 111 residues at intervals of 7 to 11 residues along the sequence of the protein. We observe a scaling exponent for loop formation, ν3, of 2.5 ± 0.3. Theoretical values for ν3 range from 1.8 to 2.4; thus, the observed ν3 is consistent with random-coil behavior. However, in contrast to data for loop formation as a function of loop size obtained with peptides of homogeneous sequence, we observe considerable scatter about the linear dependence of loop stability on loop size. Thus, foldable sequences behave very differently from homogeneous peptide sequences. The observed scatter suggests that there is considerable variation in the conformational properties along the backbone of a foldable sequence, consistent with alternating compact and extended regions. With regard to the reconciliation problem, it is evident that a scaling exponent consistent with a random coil is necessary but not sufficient to demonstrate random-coil behavior.