Target function

The CYANA target function (Güntert et al., 1991; Güntert et al., 1997) is defined such that it is zero if and only if all experimental distance restraints and torsion angle restraints are fulfilled and all non-bonded atom pairs satisfy a check for the absence of steric overlap. A conformation that satisfies the restraints more closely than another one will lead to a lower target function value. The CYANA target function for distance restraints and torsion angle restraints is defined by

$V=\sum _{c=u,l,v}w_{c}\sum _{(\alpha ,\beta )\in I_{c}}w_{\alpha \beta }^{c}(d_{\alpha \beta }-b_{\alpha \beta })^{2}+w_{a}\sum _{i\in I_{a}}w_{i}\left[1-{\frac {1}{2}}\left({\frac {\Delta _{i}}{\Gamma _{i}}}\right)^{2}\right]\Delta _{i}^{2}$

Upper and lower bounds, b_αβ, on distances d_αβ between two atoms α and β, and restraints on individual torsion angles θ_i in the form of allowed intervals $\scriptstyle [\theta _{i}^{\min },\theta _{i}^{\max }]$ are considered. I_u, I_l and I_v are the sets of atom pairs (α,β) with violated upper, lower or van der Waals distance bounds, respectively, and I_a is the set of restrained torsion angles. w_u, w_l, w_v and w_a are overall weighting factors for the different types of restraints, and $\scriptstyle w_{\alpha \beta }^{c}$ and w_i are relative weighting factors for individual restraints. The half-width of the forbidden range of torsion angle values is denoted by $\scriptstyle \Gamma _{i}=\pi -(\theta _{i}^{\max }-\theta _{i}^{\min })/2$, and Δ_i is the size of the torsion angle restraint violation.

The target function may include additional terms for restraints on vicinal scalar coupling constants, residual dipolar couplings, and pseudocontact shifts, as well as identity and symmetry restraints for symmetric multimers. Alternatives to the simple square potential for violated distance restraints have also been implemented.