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Notes: Summary Structural transitions in oligomeric proteins due to ligand binding are important in biomolecular regulatory processes. The transitions may occur on the secondary, tertiary or quarternary structure levels. Detailed consideration of the time sequence of ligand binding to the oligomer shows that there is an intrinsic dynamic asymmetry in all oligomer transitions, even if the initial and the final state are completely symmetric. This asymmetry has important bearing on the evolution and the divergence of the primary structure (amino acid sequence) of oligomeric proteins. It may explain (at least in part) the occurence of oligomeric proteins with similar but not identical protomers. Certain specific groups of oligomers are shown to be under greater evolutionary pressure for protomer structure divergence. The dynamic asymmetry of oligomer transitions also results in higher complexity in reaction kinetics. Some implications on ribosome structural evolution are discussed.

Notes: Summary A binomially distributed statisticpχ i 2 is defined which in conjunction with a set of critical tables permits, for peptides or proteins of arbitrary lengths, a well-defined answer to the question: Does the proportion of a particular amino acidi present in that protein deviate significantly from random expectation? An analogous statistic is defined for nucleic acids. This statistic is simply related to the classical chi-squared test. The classical χ2 and thepχ i 2 are supplementary in that the former permits one to determine that a non-randomness in amino acid composition exists in a protein, while the latter permits one to localize that non-randomness to particular amino acids. Thepχ i 2 statistic takes into account explicitly the compositional fluctuations imposed by the finite length of proteins. The tables are more exact than any hitherto existing, and require no intermediate calculations for their use: from the direct experimental measurement of the number of residues of amino acidi, one immediately reads from the tables whether the number observed is within random expectation or not. These statistics are used to analyze eight proteins of diverse length, function, and origin in an accompanying paper.

Notes: Summary Eight proteins of diverse lengths, functions, and origin, are examined for compositional non-randomness amino acid by amino acid. The proteins investigated are human fibrinopeptide A, guinea pig insulin, rattlesnake cytochromec, MS2 phage coat protein, rabbit triosephosphate isomerase, bovine pancreatic deoxyribonuclease A, bovine glutamate dehydrogenase, andBacillus thermoproteolyticus thermolysin. As a result of this study the experimentally testable hypothesis is put forth that for a large class of proteins the ratio of that fraction of the molecule which exhibits compositional non-randomness to that fraction which does not is on the average, stable about a mean value (estimated as 0.32 ± 0.17) and (nearly) independent of protein length. Stochastic and selective evolutionary forces are viewed as interacting rather than independent phenomena. With respect to amino acid composition, this coupling ameliorates the current controversy over Darwinian vs. non-Darwinian evolution, selectionist vs. neutralist, in favor of neither: Within the context of the quantitative data, the evolution of real proteins is seen as a compromise between the two viewpoints, both important. The compositional fluctuations of the electrically charged amino acids glutamic and aspartic acid, lysine and arginine, are examined in depth for over eighty protein families, both prokaryotic and eukaryotic. For both taxa, each of the acidic amino acids is present in amounts roughly twice that predicted from the genetic code. The presence of an excess of glutamic acid is independent of the presence of an excess of aspartic acid and vice versa. However, about twice as many prokaryotic families show observable deviations from randomness as eukaryotic families, although the magnitude of these deviations is the same for both taxa. The behavior of lysine and arginine is quite different, both qualitatively and quantitatively. For both taxa lysine is present in amounts roughly twice that predicted from the genetic code, but the deficiency of arginine is about twice as great for prokaryotes as for eukaryotes for which the amounts present are only half that expected from the code. Although in prokaryotic families the presence of a lysine excess is not correlated with the presence of an arginine deficit, in eukaryotic families a strong correlation exists. However, as for the acidic amino acids, the magnitude of the lysine excess is uncorrelated with the magnitude of the arginine deficit in both taxa. The greater arginine deficit in prokaryotes is thus due to the fact that fewer prokaryotic families seem to be able to utilize arginine effectively. These rather diverse experimental data with respect to electrical charge in proteins are unified by our finding that the genetic code possesses a hitherto undescribed dynamic property: namely, the transition probabilities for each of the 380 possible amino acid substitutions are quantitatively such as to maintain constant, on the average, under random mutation, the absolute proportions of acidic, basic and neutral amino acids about predictable numerical values which are closely the same independent of the type (minimal 1-, 2- or 3-base) or extent of amino acid substitution. This finding, together with the experimental data, lead to the conclusion that electrostatic stability of the experimentally observed type cannot be maintained in the absence of a certain minimum number of invariant amino acid residues. Theory permits a quantitative estimate of this number to be made for each protein family.

Notes: Many protein molecules, particularly those with high molecular weights, consist not of a single polypeptide chain, but form a complex made up from several polypeptide chains. This structure, which can be reversibly broken down, is known as the quaternary structure. A number of metabolic phenomena can be explained on a molecular basis by invoking the quaternary structure.

Notes: Casein from cow's milk is not a single substance, but can be resolved into numerous components. These include x-casein, which is the only fraction that contains appreciable quantities of sugars. This component plays a very important role in the clotting of milk by rennin, when it is split into an almost sugar-free fraction, para-x-casein, and a fraction containing sugars, x-caseinoglycopeptide. Caseinoglycopeptides have been isolated not only from the casein of cow's milk, but also from the caseins of sheep. Goat, and human milk. The second part of the paper deals with the clotting of milk by rennin and the amino acid sequence in caseinoglycopeptides.

Notes: The evolution of protein structures is discussed using cytochrome c, hemoglobin, and neurohypophyseal hormones as examples. Although these substances have different biological functions, their evolution is controlled by the same general rules: their primary structures vary at the level of the species, order, or class, but this variation is restricted by the fact that the biological activity of the protein must not be impaired. Alterations (i.e. substitutions, deletions, or additions of amino acid residues) can therefore occur only in certain positions of the peptide chains, although with different frequencies. The total number of alterations thus represents only the final state of a protein and does not take into account successive substitutions which may have taken place at the affected sites. It can therefore give only a rough indication of the phylogenetic distance between two species. The nature of the substituting residues, on the other hand, is a useful guide to zoological cognateness, since it allows the identification of transition molecules which simultaneously contain amino acid residues from the protein of the protein of the evolutionary ancestor and from the protein of the evolutionary descendant.

Notes: The protein hormone insulin occurs widely in the animal kingdom. Although its biological function is always the same, its amino-acid composition varies widely. Insulin consists of two polypeptide chains, which are linked by three cystine residues to form a bicyclic system with a 20-membered and an 85-membered ring. The protein crystallizes in various forms with foreign ions. In solution, insulin normally forms aggregates of 2n molecules. The hormone can be regenerated from the separated polypeptide chains, and its total synthesis has been achieved in a similar manner from synthesized peptide chains. In the biosynthesis of insulin, the two chains are evidently built up separately and subsequently linked together. Insulin promotes the synthesis of glycogen, fat, and protein in the organism; insulin deficiency leads to an increase in the blood-sugar level. At the molecular level, the mechanism of action of the hormone is still unknown. Current hypotheses are discussed. No specific active center has so far been detected in the insulin molecule, which contains several antigenic regions.