Table I.

Probability Density Expressions Extracted from the Torsion Angle Database

Residue type	Probability density functiona	Statistical approximationb
Gly, Ala		None
Thr, Val, Ser, Cys		None
cis-Pro, trans-Pro		determines other ring torsion angles
Asp, Asn, Ile, Leu, His, Trp, Tyr, Phe
Met, Glu, Gln
Lys, Arg
prePro		None
		None

^aFor simplicity, probability density functions omit conditionals whenever possible. For example, for residue types Gly and Ala, p(ϕ, ψ) implies p(ϕ, ψ|Gly) and p(ϕ, ψ|Ala), respectively. In the case of prePro, the explicit use of a conditional is informative. For example, the probability density function of pre-proline arginines is represented by p(ϕ, ψ, χ₁|prePro) p(χ₂, χ₃, χ₄), where p(ϕ, ψ, χ₁|prePro) corresponds to all non-glycine, non-proline pre-proline residues (with at least one side chain torsion angle), and p(χ₂, χ₃, χ₄) to all arginines, regardless whether they precede a proline (see text for another example).

^bThe statistical approximations used to arrive at the different probability density expressions are indicated, where the orthogonality sign (⊥) means “independent of”.