FIG. 3.
Natural degrees of freedom that are used on protein structure. (a) A sandwich of two three-stranded anti-parallel β-sheets (β-strands are shown as rectangular slabs) with natural degrees of freedom that treat the β-sheets as rigid bodies. These independent variables, Xi are Shift (Dx), Slide (Dy), Rise (Dz), Tilt (τ), Roll (ρ), and Twist (ω). (b) Two rigid helical segments (α-helices are shown as cylinders) with the natural degrees of freedom that describe their relative orientation. These independent variables, Xi, are Shear (Sx), Stretch (Sy), Stagger (Sz), Buckle (κ), Propeller (π), and Opening (σ). (c) Illustration of the move along Shear (Sx), one of the natural degrees of freedom describing the relative orientation of a three-stranded β-sheet and an α-helix. All the remaining independent variables, Xi, are identical to the ones in (b) and can be derived if one aligns the α-helix with the central strand of the β-sheet. (d) Showing one possible arrangement of the flexible protein loops (dashed line) that connect individual β-strands and α-helices. The red rectangle illustrates a loop segment containing a molten zone with Nm = 7 between magenta atoms. Recursive Stochastic Closure (RSC) changes the conformation of the molten zone, so that the broken connection between segments (β-strands, α-helices) is repaired. In the lack of torsion or bond angle constraints (e.g., peptide planes are not described explicitly in coarse grain representation), there are 19 dependent degrees of freedom, Xd (magenta).