Probabilistic graphical models in structural biology and protein science

How it is used

Structural biology works out the shapes of proteins and other large molecules, and how shape explains what they do. Probabilistic graphical models describe a set of variables as a graph: each variable is linked to the others it depends on, and the model learns the strength of those links. In protein science the variables are often the positions in a protein sequence, and the links are pairs of positions that change together across related proteins from many species. One example fitted a maximum entropy model to an alignment of a protein family, matching how often each amino acid appears at each position and in each pair of positions, then scored pairs of positions by the strength of their direct coupling.

The same way of thinking is used on experimental data rather than on sequences. One example treats the images from an electron microscope as arising from hidden variables, the unknown orientation and class of each particle, and works out how likely each possible orientation is before using those probabilities to update a three-dimensional map. Another passes raw, unscaled X-ray diffraction measurements, along with information about where and how each was recorded, to a model that merges them. Related work uses measures of shared information to choose which protein variants to build and test, and to pick features of candidate segments of a sequence.

Why researchers use it

Proteins fold because many parts of the chain press on one another at once, and experiments record only indirect, noisy traces of that. A graphical model suits both problems because it separates direct dependence from indirect dependence. If position one affects position two, and two affects three, simple correlation makes one and three look connected; the model can attribute the link to the chain of direct couplings instead. That matters when a coupling is read as evidence that two residues touch in the folded structure.

The models also give a natural place to put what is unknown. Quantities that cannot be measured, such as the orientation of a single particle in a microscope image, enter as hidden variables, and the model carries a distribution over them rather than a single guess. Noise and measurement conditions enter the same way, as further variables. This lets a single fit combine the data with prior expectations and report how uncertain the result is, instead of relying on a separate, hand-tuned correction step.

In the record

structural-biologyProtein shapes computed from patterns of change across families of related sequencesFitted a maximum entropy model of a protein family's sequences to single and paired amino acid frequencies, scoring directly coupled residue pairs.structural-biologySoftware works out protein shapes from electron microscope images using statisticsTreated particle orientation and class as hidden variables, weighting each image's contribution to the three-dimensional map by its posterior probability.structural-biologyBayesian program merges X-ray diffraction data from three experiment types in one stepTook unmerged, unscaled diffraction intensities with per-reflection metadata such as resolution and detector position, and merged them in one model.structural-biologyMachine learning picked which engineered enzymes to build for fatty alcohol productionChose seed sequences from a large chimera library by maximising shared information with the whole library, then built and measured them.

Limits

These models describe dependence, not mechanism. A strong coupling between two sequence positions can arise from shared ancestry, from a shifted copy of the same protein in the alignment, or from a contact in a different structural state, so it need not mean two residues touch. The fits need many related sequences, and families with few known members are poorly served. The assumptions built in, which variables may depend on which, and the approximations used to make the fitting tractable, both shape the answer, and a confident posterior can still be confidently wrong if those assumptions are off.

Written by AIxSci: the background from general knowledge, the examples from checked records.