Diane C Jamrog | PubMed Health

PubMed2004

On the equivalence between a commonly used correlation coefficient and a least-squares function.

Many objective functions have been proposed in X-ray crystallography to solve the molecular replacement (MR) problem and other optimization problems. This paper establishes the equivalence of optimizing two of these target functions, a commonly used correlation coefficient and a least-squares function. This equivalence may exist only in the neighborhoods about the global optima or the entire MR variable space depending on whether the mean values of the observed and calculated data are subtracted from the data. In addition, an argument is presented that the correlation coefficient between structure-factor magnitudes is likely to perform better than the correlation coefficient between intensities, especially when low-resolution data are used. This prediction was tested during coarse grid searches at low resolution using the MR program SOMoRe.

Journal Article↗

PubMed2003

SOMoRe: a multi-dimensional search and optimization approach to molecular replacement.

Commonly used traditional molecular-replacement (MR) methods, though often successful, have difficulty solving certain classes of MR problems. In addition, MR problems are generally very difficult global optimization problems because of the enormous number of local minima in traditionally computed target functions. As a result, a new MR program called SOMoRe is introduced that implements a new global optimization strategy that has two major components: (i) a six-dimensional global search of a target function computed from low-resolution data and (ii) multi-start local optimization. Because the target function computed from low-resolution data is relatively smooth, the global search can coarsely sample the MR variable space to identify good starting points for extensive multi-start local optimization. Consequently, SOMoRe was able to straightforwardly solve four realistic test problems, including two that could not be directly solved by traditional MR programs, and SOMoRe solved a problem using a less complete model than those required by two traditional programs and a stochastic six-dimensional program. Based on these results, this new strategy promises to extend the applicability and robustness of MR.

Algorithms↗