Constraining volume by matching the moments of a distance distribution

The problem of computing a molecular structure from a set of distances arises in the interpretation of NMR data as well as other experimental methods that yield distance information. Techniques for computing structures must find conformations consistent with the distance data. There are often other constraints on the structure that must be satisfied as well. One of the most problematic constraints is the constraint on the total volume occupied by the atoms. In this paper, we use the first two moments (mean and variance) of an estimated distance distribution to constrain the volume of a computed structure. We show that a probabilistic algorithm for matching the first two moments of the estimated distance distribution significantly improves the quality of the solution, especially when the distance information alone is not sufficient to define the structure precisely. We also show that our method is not sensitive to small errors in the estimates of mean and variance of the distance distribution. Finally, we demonstrate the use of this constraint in computing a low-resolution structure of the 30S prokaryotic ribosomal subunit. Quantitative analysis of our results allows us to assess the information content contained in constraints on volume, and to show that in some cases addition of a volume constraint adds information roughly equivalent to doubling the number of input distances. Our results also demonstrate the flexibility of probabilistic representations of structural constraints, and the importance of including volume information to constrain structural computations-especially in the case of sparse data.