br Discussion Before comparing our results with structural s
Discussion Before comparing our results with structural studies, we can turn to the Wiki on transition state theory (1935), which explains the reaction rates of elementary chemical reactions in terms of two parameters in one dimension. Structural studies contain information on the ground state, a minimum in configuration space, whereas rates are determined by the properties of transition states, technically also saddle points in configuration space. Both minima and saddle points are also thermodynamic critical points, where long-range attractive and short-range repulsive interactions are equal at the critical temperature, close to body temperature. Our conjecture here is that studying extrema, both the hydrophobic pivots and the hydrophilic hinges , provides one-dimensional insights into extremal sets of two parameters describing transition state properties, which can be compared to structural studies ,  of ground state properties. Because Uba1 is so large, the free chloroquine phosphate differences between these two states are very small, and the static and dynamic structural differences are expected to involve interdomain conformational motion. According to , Uba1-E1 consists of four building blocks: first, the adenylation domains composed of two motifs (labeled IAD (1–169) and AAD (404–594), for “inactive” and “active” adenylation domain, respectively), the latter of which binds ATP and Ub; second, the catalytic cysteine half-domains, which contain the E1 active site cysteine (CC (169–268) and CCD (594–860)) inserted into each of the adenylation domains; third, a four-helix bundle 4HB (268–356) that represents a second insertion in the IAD; and fourth, the C-terminal ubiquitin-fold domain (UFD (926–1024)), which recruits specific E2s. How do these structural and functional domains compare with our one-dimensional hydropathic profiles? Fig. 5 shows an excellent match, with the domain boundaries associated either with pivots or one amphiphilic side of a hinge. One could argue here that the separation of 4HB is unnecessary, but this secondary structure includes the deep and wide hydrophilic minimum 330–370, with a sharp edge at 320 of . The differences between ground and transition state properties are exemplified by a comparison of our human–yeast results with those of a structural study of possible differences in ubiquitin-Uba-1 binding in yeast (known structure) with human (simulated in ). Their discussion focuses on Ubiquitin contacts with Tyr 571 (618 in our site numbering) in the CCD domain. According to Fig. 3 and its caption, there are substantial differences between yeast and human profiles here, and they are related to differences in tilts of the hydrophobic pivots. These are consistent with the modeling results, and also show the importance of allometric interactions between folded CC and CCD domains (Fig. 5). Human AAD adenylation (ATP) sites are 478, 504, 515, and 528. The overall BLAST identities and positives for yeast and human Uba1 are 52% and 71%, and these increase in the 400–600 ADD range to 63% and 80%. This range is shown in Fig. 6, and we see strong similarities in the two profiles. Their correlation is 86%, which means that is more effective in the 400–600 ADD range than even BLAST positives (80%) because it uses the MZ scale and because W* has been chosen to display level set hydrophobic adenylation domain pivots. From Fig. 6 we see that the four sites are concentrated in the center of the ADD structural domain. They line the amphiphilic range from the hydrophobic pivot at 478 to close to the hydrophilic hinge at 535. The profile not only displays a stronger yeast–human ADD correlation than BLAST, but it also has revealed a hydropathic cascade of ATP binding sites. Among mammals the similarities are of course greater. The overall correlation of the mouse and human profiles is 97.2%, which increases in the 400–600 ADD range to 98.6 %.