Phi-psi maps

IK Roterman, MH Lambert, KD Gibson, HA Scheraga. A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. II. PHI-PSI maps for N-acetyl alanine N -methyl amide Comparisons, contrasts and simple experimental tests. J Biomol Stiaict Dyn 7 421-453, 198. 

We have developed a new representation of conformational space and a computer program to prepare it U). This representation, the n-h map, allows many combinations of monomeric geometry and glycosidic linkage angle to be considered. A bonus in our method is that representations for the various polymers are quite different, whereas the Phi-Psi maps (without the iso-n and iso-h contours) are all very similar (3 ). Some polymers are characterized by n-b maps that have large, continuous allowed areas, while others have small or multiple, disconnected areas. 

Fig. 5. Subdivisions of the phi/psi or Ramachandran map labeled with the range of propensities for the 18 amino acids (glycine and proline are excluded) as they map to each subdivision calculated from a large collection of folded protein structures. The propensity is defined by the probability that amino acid x will be found in a subdivision divided by the probability that an average amino acid will be found in a subregion. Data are taken from Table 1 of Shortle (2002).

The favoured dihedral angles for protein main chains were derived from energy considerations of steric clashes in peptides giving the well known Ramachandran plot (Ramachandran and Sasisekharan, 1968). These phi/psi combinations characterize the elements of secondary structure. Accurate main chain models can be constructed from spare parts, that is short pieces of helices, sheets, turns, and random coils taken from highly refined structures, provided a series of C-alpha positions can be established from the electron density map... 

Comparison of the maps reveals significant differences in the location of the minima. The protein based energy surface (Figure 2a). shows minima in the vicinity of phi, psi value.s of —60, —40 —120, —160, and 60,40°. The first two correspond... 

Conformational maps show values of phi and psi that fall into two regions the first region contains points that are always allowable and the second region contains points that are sometimes allowed. As shown in Figure 2.11, all points within the inner lines are always allowed and those within the outer solid lines are sometimes allowed. Hence the entropy (or rotational freedom of a peptide) is obtained from the area surrounded by the solid lines on a conformational map (Figure 2.11) and is proportional to the number of allowable conformations of a dipeptide unit. Please note a flexible chain with a lot of rotational freedom is easier to stretch than a rigid chain. We define the flexibility of a polypeptide as the natural logarithm of the number of allowable conformations,, times Boltzmann s constant (Equation (2.1)). 

---