Dynamic torsion angle

The key idea of the fast torsion angle dynamics algorithm in Dyana is to exploit the fact that a chain molecule such as a protein or nucleic acid can be represented in a natural way as a tree structure consisting of n+1 rigid bodies that are connected by n rotatable bonds (Fig. 2.1) [74, 83]. Each rigid body is made up of one or several mass points (atoms) with invariable relative positions. The tree structure starts from a base, typically 

The role of the potential energy is taken by the Dyana target function [8, 28] that is defined such that it is zero if and only if all experimental distance constraints and torsion angle constraints are fulfilled and all nonbonded atom pairs satisfy a check for the absence of steric overlap. A conformation that satisfies the constraints more closely than another one will lead to a lower target function value. The exact definition of the Dyana target function is  

Upper and lower bounds, bap, on distances da/3 between two atoms a and b, and constraints on individual torsion angles 0i in the form of allowed intervals [f 111, 13 ] are considered. Iu, h and Iv are the sets of atom pairs (a, /I) with upper, lower or van der Waals distance bounds, respectively, and Ia is the set of restrained torsion angles. wu, Wj, wv and wa are weighting factors for the different types of constraints. 

The angular velocity vector tok and the linear velocity vk of the reference point of the rigid body k (Fig. 2.1b) are calculated recursively from the corresponding quantities of the preceding rigid body p(lc)  

Denoting the vector from the reference point to the center of mass of the rigid body k by Yi , its mass by and its inertia tensor by h (Fig. 2.1b), the kinetic energy can be computed in a linear loop over all rigid bodies 

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Recently, MD constrained to torsion angle space [torsion angle dynamics (TAD)] was introduced to refinement calculations [33,57,58]. Earlier versions of the equations of... 

Standard calculation methods developed for small proteins are sufficiently powerful to solve protein structures and complexes in the 30 kDa range and beyond [97,98] and protein-nucleic acid complexes [99]. Torsion angle dynamics offers increased conver-... 

Giintert P, Mumenthaler C, Wiithrich K. Torsion angle dynamics for NMR structure calculation with the new program DYANA. J Mol Biol 1997 273 283-298. 

The calculation of the torsional accelerations, i.e. the second time derivatives of the torsion angles, is the crucial point of a torsion angle dynamics algorithm. The equations of motion for a classical mechanical system with generalized coordinates are the Lagrange equations... 

Stage 2. Torsion angle dynamics calculation at constant high temperature One fifth of all N torsion angle dynamics steps are performed at a constant high reference temperature of, typically, 10,000 K. The time step is initialized to 2 fs. 

Stage 3. Torsion angle dynamics calculation with slow cooling close to zero temperature The remaining 4N/5 torsion angle dynamics steps are performed during which the reference value for the temperature approaches zero according to a fourth-power law. 

Throughout the torsion angle dynamics calculation the list of van der Waals lower distance bounds is updated every 50 steps using a cutoff of 4.2 A for the interatomic distance. 

Perform structure calculation using DYANA torsion angle dynamics... 

Rice, L.M. and Brunger, A.T. (1994) Torsion angle dynamics reduced variable conformational sampling enhances crystallographic structure refinement. Proteins 19,277-290. 

Residual dipolar couplings have been used by Mittermaier and Kay187 to probe the torsion angle dynamics of protein side-chains. Using the B1 domain of peptostreptococcal protein L, they show that the residual dipolar couplings can be used to distinguish static from mobile side-chains, and that the motions of most mobile side-chains can be adequately explained by rotamer-jump models. 

The molecular dynamics for NMR structure determination and the torsion angle dynamics were extensively reviewed by Giintert.35 The method was also reviewed by Clore and Schwieters.20 The molecular dynamics programs, e.g., CHARMM,42 AMBER,43 and GROMACS44 can be used for the structure determination. XPLOR,38 its successor CNS,45 and XPLOR-NIH12... 

Guntert P, Wuthrich K (2001) Sampling of conformation space in torsion angle dynamics calculations. ComputPhys Commun 138(2) 155-169... 

Herrmann T, Guntert P, Wuthrich K (2002) Protein NMR structure determination with automated NOE assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA. J Mol Biol 319 209-227... 

Upon cryo-cooling, the unit cell dimensions of the l-Ppol crystals shrunk 0.6-1 A on each edge (e.g. from a=59.19A to a=58.58 A, from b=62.13 A to b=61.10 A, and from c=l 12.69 A to c=l 11.70 A for the metal soaked crystal). Simple rigid body minimization followed by Powell minimization of the partially refined room temperature structure or the AMoRe solution did not did not drop the R ge below 40 % for either cryo-cooled data set. The structures were then subjected to torsion angle dynamics protocols (48) at several temperatures. Both starting models, with either data set, failed to produce a structure with an Rfree below 39 % for data between 8 and 2 A. In addition, the resulting maps did not look very good. 

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