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Let ''X'' = {''X''<sub>''b''</sub>, ''X''<sub>''s''</sub>} be the random variables representing the entire protein structure. ''X''<sub>''b''</sub> can be represented by a set of 3-d coordinates of the [[backbone]] atoms, or equivalently, by a sequence of [[bond length]]s and [[dihedral angle]]s. The probability of a particular [[conformation]] ''x'' can then be written as:
:<math>p(X = x|\Theta) = p(X_b = x_b)p(X_s = x_s|X_b,\Theta), \,</math>
where <math>\Theta</math> represents any parameters used to describe this model, including sequence information, temperature etc. Frequently the backbone is assumed to be rigid with a known conformation, and the problem is then transformed to a side-chain placement problem. The structure of the graph is also encoded in <math>\Theta</math>. This structure shows which two variables are conditionally independent. As an example, side chain angles of two residues far apart can be independent given all other angles in the protein. To extract this structure, researchers use a distance [[threshold]], and only pair of residues which are within that threshold are considered connected (i.e. have an edge between them).
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