br Introduction The ubiquitin activating enzyme Uba

Introduction The ubiquitin-activating enzyme Uba1 (E1) constitutes the first step in the covalent cascade modification of target proteins with ubiquitin (Ub). Ubiquitin itself, discovered less than 50 years ago, tags thousands of diseased proteins for destruction  [1], [2]. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish and even worms. Because of its universality, Ub is a valuable proving ground for universal biophysical theories discussing protein amino Talabostat mesylate sequences, structure and function [3]. Indeed key features of Ub functionality (hydropathic waves) were identified using critical point thermodynamic scaling theory  [4]. The general biochemical logistics of Ub activation, conjugation and ligation are orchestrated sequentially by the Ub conjugation cascade of E1, E2 and E3 enzymes. Humans are known to harbor two E1, ∼30 E2 and ∼600 E3 enzymes in the Ub conjugation cascade  [5]. While Ub is “perfect”, Uba1 (E1) has evolved only modestly from slime mold to humans. The details of this evolution express several leading features of enzyme functionality. Uba1 (E1) is a large protein (>1000 amino acids), but it is readily treated by critical point thermodynamic scaling theory, with its firm foundations in statistical mechanics and its bioinformatically determined universal parameters  [3]. It turns out that hydropathic waves are also useful for Uba1 (E1), which is >14 times larger than Ub. As before  [3], [4], all calculations are based on thermodynamically first- and second-order hydropathic (amino acid) scales  [6], [7], linearly scaled to a common center and a common range for each of the 20 amino acids. These are then converted to a triangular matrix , where is the length of a sliding window centered on each amino acid site. We have studied the range , which is includes values of W much larger than the small value, fixed at , in most calculations using sliding windows  [8]. Just as one focuses a microscope to optimize its image, one scans W to optimize its recognition of allometric regularities of hydropathic hot spots (hydrophobic extrema of ) at special values of .
Results The hydrophobic extrema of neuroglobin form sophisticated patterns that are closely related to the evolution of specific species. For example, mouse and rabbit escape predators in different ways, and these differences are recognizable in their profiles  [9]. There are several other examples already of proteins whose hydrophobic extrema form level sets. In Fig. 1 we plot the profiles of Uba1 (E1) for humans and slime mold. The choice levels the human hydrophobic extrema, and simultaneously aligns the slime mold extrema linearly with a small tilt (about 15% of the overall range). Such excellent alignments (to within 1%) are unlikely and not accidental. For instance, the differences between the MZ and KD scales are small (85% correlation  [10]), yet as Fig. 2 shows, the successful pivotal alignment with the MZ scale is lost with the KD scale.