Differential Geometry and Polymer Conformation. 3. Single-Site and Nearest-Neighbor Distributions, and Nucleation of Protein Folding

S. Rackovsky, H. A. Scheraga

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


A differential geometric representation of polymer chains is used to study protein backbone structure on the four- and five-C” length scales. The analysis of the distribution of four-Cα units in the curvature-torsion (k, τ) plane reveals that there are islands of structure which occur with greater-than-random probability. These correspond to the well-known types of backbone structure-extended (E), right-handed -helical (Ar), and flat-bend (Ao) structure. It is shown that there are three distinct types of extended four-Cα structure-left-handed twisted (EL), right-handed twisted (Er), and nearly flat (E0). The Eo and EL structures form a structural continuum, but the Er region is separated from this continuum by a region of low occupation. The Ar and Aq regions also form a continuum. These high-frequency islands are distributed throughout the occupied region of the (k, τ) plane and include structures of all types except that in the AL (left-handed a-helical) region. The high frequency of occurrence of these structures suggests that they are of low energy and therefore likely to occur in nucleation structures in the folding of the denatured molecule. It follows from the fact that these high-frequency structures occur throughout the occupied region, however, that there is relatively low selectivity in nucleation on the four-Ca scale, with structures representative of the entire occupied region being potential nuclei on the four-Cα scale. Extension of the analysis to the five-Cα scale shows that the high-frequency structures on this scale are made up of combinations of the high-frequency four-Cα structures and that a higher degree of selectivity in nucleation appears on the five-C length scale than on the four-Cα scale. Substantial differences are noted in the frequency of occurrence of the various combinations. Within the extended region, for example, the most frequently occurring structures are EqE0, with ErEr being the least frequent. A study of the correlation between nearest-neighbor four-Cα structures reveals that certain pairs of four-Cα structures have a low probability of occurring. AoAr and ArAo have a low positive correlation, while ExAr and AhEx (where X is R, L, or 0) have a negative correlation, indicating that these structures tend to aVold pairing. Five-Cα components of nucleating structures are likely to be those which both occur with high frequency and show positive correlation between their four-Cα components. Of these, the most frequently occurring are EXEX and ARAR, which are repeating (regular) structures. The Ao four-Cα structure plays an important role in nucleation, despite its relative numerical infrequency, because it is the principal four-Cα structure which forms potential five-Cα nucleating structures which are nonregular. Larger nuclei, which are not considered explicitly in this paper, presumably arise as additional four-Cα units associated with five-Cα nuclei already present in the folding chain.

Original languageEnglish
Pages (from-to)1259-1269
Number of pages11
Issue number5
StatePublished - Sep 1981
Externally publishedYes


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