Principles of Protein Structure - G. Schultz 1982

Protein Evolution
Detection of Distant Evolutionary Relationships
Comparison of Layer Topologies

Comparisons of layer topologies highlight the critical importance of ß-pleated sheets for protein structures. Given the difficulties in translating average C_a-distances into standard significance levels, It is worth mentioning a less stringent approach to comparing chain folding. This method is based on ß-Structure topology and, naturally, applies only to Proteins containing ß-pleated sheets. Such topology is defined as The pathway of the chain within the ß-structure (a substructure considered rigid) without regard to precise coordinates [255] (Fig. 7.7). For example, different arrangements of sheets along the chain or varying connections between parallel sheets on opposite sides of the ß-structure describe distinct ß-structure topologies.

The topology of ß-structures can be quantified using combinatorial Methods. The number of distinct topologies for a parallel ß-structure consisting of six ß-sheets is 6! ∙ 2^6-2 = 11,520 [255]. Thus, the a priori probability of finding identical ß-structure topologies in two different proteins is 1/11,520, yielding an a priori significance of 11,520. This comparison is restricted solely to proteins comprising parallel six-sheet structures. Accounting for all other proteins increases this significance by a factor of roughly 10. An example of identical ß-structure topology is found in the NAD-binding domain of dehydrogenases [91]. In this case, the NAD-binding sites are also identical with respect to the ß-structure (positioned above the C-terminal ends of the ß-sheets, Fig. 7.7), which increases the a priori significance [255] by approximately 10-fold, bringing the total significance value to 1,152,000.

In two instances, approximate standard significance values for relatedness have been determined based on β-structure topologies. The a priori significance can be reduced to an approximate standard significance of 3,500 by accounting for the observed preference for ßaß-units (Sec. 5.2) and the observed correlation between neighboring residues in ß-structures (Fig. 5.15, a); both of these conditions reflect steric constraints that reduce the number of possible ß-structure topologies. A significance of 3,500 provides clear Evidence of the evolutionary relationship among dehydrogenases.

Standard significance has also been determined for the ß-structure topologies of IMMUNOGLOBULINS and superoxide dismutase [548]. Its value of 30,000 (calculated by the authors as 3,000, multiplied by 10 to account for the restricted set of compared proteins, as in the case of dehydrogenases) strongly indicates evolutionary relatedness. Although comparisons of ß-structure topologies are feasible for only a limited number of structures, they nevertheless demonstrate how chain folding can be compared and used to quantify the distant evolutionary relationships of proteins.