Many problems in crystallography can be approached in terms of the principle of maximum likelihood. Intuitively, the principle of maximum likelihood means that the best model is the one that agrees best with the data. Agreement is measured by the probability of measuring the data. So likelihood is the probability that you would measure the set of observed data, given whatever model you have of the experiment.
Probability distributions in experimental science are often Gaussian, and then likelihood becomes equivalent to least squares. In the case of crystallography, the (phased) structure factors have Gaussian distributions, but the phase information is lost when we measure intensities, and the distributions of the measurements are no longer Gaussian. This is why it is necessary to go to first principles and apply likelihood.
It turns out that likelihood provides a good basis for a variety of crystallographic experiments, including molecular replacement, model phasing, experimental phasing with isomorphous replacement and anomalous dispersion, and model refinement. We have developed or contributed to likelihood-based programs in all these areas: model phasing (SIGMAA), molecular replacement (Beast, Phaser), experimental phasing (Phaser) and refinement (CNS).
Much of the background material can be obtained from the web pages from the macromolecular crystallography course that was presented here in the 1999-2000 academic year. In addition, here are links to overheads presented at lectures at a workshop on protein structure refinement held in September 1997 in York.
Currently, our efforts in crystallographic methods are focused on the development of our program Phaser. More information can be found on the Phaser website.
In our structural work, we focus on the structures of medically-relevant proteins, particularly those for which the structure may be useful in the development of new therapies. For a number of years we have worked on bacterial toxins, particularly pertussis toxin and the Shiga-like toxins involved in E. coli food poisoning (often called "hamburger disease" in North America). Most recently, we have been working to understand the enzymatic mechanism of pertussis toxin.
In an area largely led by Dr. Aiwu Zhou, we are working on a number of serpins, with an emphasis on non-inhibitory members of the family. These include the hormone-binding globulins and angiotensinogen.
Last updated 19 September, 2008