Advanced likelihood-based methods in structural biology

A global community of structural biologists work to unravel the arrangements of atoms that constitute vital molecules within the cell, such as proteins and DNA, and the way they interact. By visualising these molecules and interactions, we gain profound insights into the chemical reactions of life, how their disruption manifests as disorders of health, and how to develop treatments.

To visualise these molecules, structural biologists mostly employ two techniques: X-ray crystallography, which involves growing crystals of the molecules, and electron cryo-microscopy (cryo-EM), which images molecules frozen in a thin layer of ice. Both methods need intricate computational methods to construct an atomic structure. The best methods are built on a statistical technique called maximum likelihood (ML).

Maximum likelihood (ML) is about finding the parameters of a statistical model that make the observed data most likely, and is powerful because it includes uncertainties. As a simple example, imagine you are an archer shooting arrows at a bullseye, and you have a friend who wants to know how accurate a shot you are. As you shoot a dozen times, factors like wind and your skill will mean that that although you aim at the bullseye, your arrows will miss, to different degrees.

To try to hide your accuracy, you then remove the paper marking the target on the board, so your friend can only see the positions of the hits, not the bullseye. They must now estimate both the bullseye's position and your accuracy; the best estimate will be found using ML. They will first need to assume that the hits are randomly distributed in a Gaussian distribution, which has 3 parameters, the bullseye position (x,y), and sigma, which represents how spread out your hits are, and they should then adjust (x,y) and sigma until the observed hits are most probable according to the Gaussian distribution.

Hence, ML not only estimates (x,y), but also how error-prone you are, and these are intrinsically linked in the calculations.

In the case of structural biology, the data from X-ray crystallography ('reflections') and cryo-EM ('maps') are statistically modelled and the best atomic coordinates are the ones with the highest likelihood given the errors in the data and the atomic coordinates. Our work is advancing the statistical model (a complicated equivalent of the simple Gaussian in the example above) so that ML can be applied.

With our ML methods we can find molecules in cryo-EM maps even when the data are extremely poor, such as when there is only a rudimentary outline of the molecule. Part of our proposal is to build on this work and use the data from which the cryo-EM maps are constructed to assess our atomic models, rather than pre-processed map data as currently. We also propose to develop a statistical model for an exciting extension of cryo-EM, cryo-electron tomography, which permits the visualisation of entire cells or cell sections.

This innovative approach offers insights into cellular machinery within its natural environment, albeit with less precise imaging than cryo-EM. Likewise, our ML methods are able to find atomic coordinates from crystallographic reflection data even when the data are extremely poor, such as when the crystals grow in certain problematic ways ('pathologies').

Our proposal includes improving ML methods for a common form of crystal pathology not currently well accounted for.

Although structural biology relies on ML methods, structural biologists themselves are largely unaware of the details of the ML methods because the methods are hidden within highly automated software. Our proposal also includes expanding the number of experiments that can be completed automatically, to empower structural biologists to swiftly and conveniently obtain high-quality structures.

This, in turn, accelerates progress in comprehending the complexities of biology and medicine, ultimately advancing the frontiers of human health.