Protein structures and a-helices

Theoretical approaches to structural biophysics, like the theories of transport and reaction kinetics explored in other chapters of this book, are grounded in physical chemistry concepts. Here we explore a few problems in molecular structural dynamics using those concepts. The first two systems presented, helix-coil transitions and actin polymerization, introduce classic theories. The material in the remainder of the chapter arises from the study of macromolecular interactions and is motivated by current research aimed at uncovering and understanding how large numbers of proteins (hundreds to thousands) interact in cells [7], 

Both the structures and the dynamics of macromolecules are studied in terms of statistical thermodynamics. In the following section, we introduce the helix-coil transition theory that accounts for formation of the ubiquitous a-helical structure of peptide chains in aqueous solution. To a large extent, current research on protein 

1 In the era of systems biology, great attention is paid to the structures of networks of reactions and interacting molecules (i.e., the topological connectivities). In some ways network structures have replaced molecular structures as the central object of biological attention. 

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Figure 8. Matrix listing the number of times a particular amino acid exchange was observed in a pentapeptide pair involving two unrelated protein structures and a secondary structural change from j9-strand to Q -hellx. For example, a jQ-strand going to an a-helix by changing only one residue in five was observed 12 times in different pentapeptides and proteins Positions marked are the respective row and column sum of counts, indicating general trends in the secondary structural transition. For example, alanine (column count sum at 63) is the residue most often changed in moving away from a helical structure and toward a jQ-structure.

Recently, a vibrational analysis was reported that assigns the characteristic amide bands of p turns (Bandekar and Krimm, 1979). An interesting conclusion is that amide I bands observed in proteins near 1690 cm can be correlated with p turns as well as structures. The amide II frequencies correlated with P turn type I are expected near 1550-1555 cm and 1567 cm" S those for type II near 1545,1555, and 1560 cm" The turns are characterized by amide II modes with frequencies higher than those of p structures and a helices. 

Figure 2.17 Two adjacent parallel p strands are usually connected by an a helix from the C-termlnus of strand 1 to the N-termlnus of strand 2. Most protein structures that contain parallel p sheets are built up from combinations of such p-a-P motifs. Beta strands are red, and a helices are yellow. Arrows represent P strands, and cylinders represent helices, (a) Schematic diagram of the path of the main chain, (b) Topological diagrams of the P-a-P motif.

On the basis of simple considerations of connected motifs, Michael Leviff and Cyrus Chothia of the MRC Laboratory of Molecular Biology derived a taxonomy of protein structures and have classified domain structures into three main groups a domains, p domains, and a/p domains. In ct structures the core is built up exclusively from a helices (see Figure 2.9) in p structures the core comprises antiparallel p sheets and are usually two P sheets packed... 

Chofhia, C., Levitt, M., Richardson, D. Structure of proteins packing of a-helices and pleated sheets. 

Figure 10.2 (a) Amino acid sequence of a fragment of the Zif 268 protein that contains three zinc fingers. Residues forming the p strands and a helices are red and green, respectively, and those involved in the turn between the last p strand and the a helix are blue, (b) The nucleotide sequence of the DNA fragment that was used in the x-ray structure determination of the Zif 268 fragment complexed with DNA. 

FIGURE 19.21 These structures show how a protein first forms a helices and p sheets and then how the coils and sheets fold together to form the shape of a protein. Finally, if the protein has a quaternary structure, the protein subunits stack together, (a) Newly formed polypeptide (b) intermediate (c) subunit ... 

Figure 5-6. Examples of tertiary structure of proteins. Top The enzyme triose phosphate isomerase. Note the elegant and symmetrical arrangement of alternating p sheets and a helices. (Courtesy of J Richardson.) Bottom Two-domain structure of the subunit of a homodimeric enzyme, a bacterial class II HMG-CoA reductase. As indicated by the numbered residues, the single polypeptide begins in the large domain, enters the small domain, and ends in the large domain. (Courtesy ofC Lawrence, V Rod well, and C Stauffacher, Purdue University.)...

The PPII conformation is abundant in known protein structures, although PPII helices are not particularly common. Sreerama and Woody (1994) found that around 10% of all protein residues are in the PPII helical conformation. However, the majority of those are not part of a PPII helix. Stapley and Creamer (1999) and Adzhubei and Sternberg (1993) found that only 2% of the residues in the proteins examined were part of PPII helices four residues or longer in length. Moreover, on average, each protein possesses just one such PPII helix. The PPII helices found tend to be very short. Stapley and Creamer (1999) found that 95% of the PPII helices in their protein data set were only four, five, or six residues long. 

The influence of adsorption on the structure of a -chymotrypsin is shown in Fig. 10, where the circular dichroism (CD) spectrum of the protein in solution is compared with that of the protein adsorbed on Teflon and silica. Because of absorbance in the far UV by the aromatic styrene, it is impossible to obtain reliable CD spectra of proteins adsorbed on PS and PS- (EO)8. The CD spectrum of a protein reflects its composition of secondary structural elements (a -helices, / -sheets). The spectrum of dissolved a-chymotrypsin is indicative of a low content of or-helices and a high content of //-sheets. After adsorption at the silica surface, the CD spectrum is shifted, but the shift is much more pronounced when the protein was adsorbed at the Teflon surface. The shifts are in opposite directions for the hydrophobic and hydrophilic surfaces, respectively. The spectrum of the protein on the hydrophilic surface of silica indicates a decrease in ordered secondary structure, i.e., the polypeptide chain in the protein has an increased random structure and, hence, a larger conformational entropy. Adsorption on the hydrophobic Teflon surface induces the formation of ordered structural elements, notably an increase in the content of O -helices (cfi, the discussion in Sect. 3.1.4). 

Jones, D., Taylor, W., and Thornton, J. (1994). A model recognition approach to the prediction of all-helical membrane protein structure and topology. Biochemistry 33, 3038-3049. 

Before doing so, we briefly examine the influence of conformation and flexibility. Indeed, formation of succinimide is limited in proteins due to conformational constraints, such that the optimal value of the and ip angles (Sect. 6.1.2) around the aspartic acid and asparagine residues should be +120° and -120°, respectively [99], These constraints often interfere with the reactivity of aspartic acid residues in proteins, but they can be alleviated to some extent by local backbone flexibility when it allows the reacting groups to approach each other and, so, favors the intramolecular reactions depicted in Fig. 6.27. When compared to the same sequence in more-flexible random coils, elements of well-formed secondary structure, especially a-helices and 13-turns, markedly reduce the rate of succinimide formation and other intramolecular reactions [90][100],... 

The a-helix is the classic element of protein structure. A single a-helix can order as many as 35 residues whereas the longest strands include only about 15 residues, and one helix can have more influence on the stability and organization of a protein than any other individual structure element. a-Helices have had an immense influence on our understanding of protein structure because their regularity makes them the only feature readily amenable to theoretical analysis. 

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