Abstract 
A simple method is presented to assess the information that is provided by distance constraints for pairs of residues in proteins. The probability that the distance d_ij between the C^α atoms of residues i and j lies within a given range is computed for all N(N-1)/2 pairs in a molecule of N residues, and a quantity H is defined in terms of these probabilities; H is a measure of the ambiguity in the computed conformation of the molecule (consistent with the given distance constraints) and is related to the root-mean-square deviation of the computed conformation from the native one. The quantity H is used to determine the number, kind, and quality of the distance constraints required to define the conformation of a protein within given limits of error, using the 58-residue molecule bovine pancreatic trypsin inhibitor as an illustration. For example, to obtain the computed conformation with a root-mean-square deviation of less than 2 A from the native conformation, the values of d_ij of more than 〜80 pairs (half of them with 5 ≦　|i-j | ≦ 20 and the other half with 21≦ |i-j | ≦ 57) must be known exactly, or of more than 〜150 pairs (half of them with 5 ≦　|i-j | ≦ 20 and the other half with 21≦ |i-j | ≦ 57) must be known with an error no greater than 〜2 A; alternatively, the same root-mean-square deviation of less than 2 A from the native structure can be achieved by the computed conformation if more than 〜160 pairs are chosen so that 20 A is assigned as the lower limit for half of these d_ij's (for those pairs in the native protein that are separated by ≧ 20 A) and 10 A is assigned as the upper limit for the other half of these d_ij's  (for those pairs in the native protein that are separated by ≦ 10 A). In all of the above examples, all values of d_i,i+1  were fixed at 3.8 A, and all values of d_i,i+2  were confined to the range 4.5-7.2 A (the minimum and maximum possible values for a polypeptide chain). We also examined the kind of constraints (in terms of their distance both along the chain and through space) that are most effective to obtain a small root-mean-square deviation. For a given number of constraints, information about pairs with large |i-j | or small d_ij  is more effective in determining the conformation than is information about pairs with small |i-j |  or large d_ij. It is found, however, that information that includes both small and large |i-j | or both small and large d_ij is the most effective.
 
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