Flexible fitting of proteins and nucleic acids using Gaussian Mixture Models

Abstract

Fundamental aspect of cryo-electron microscopy (cryo-EM) is deriving atomic models from the 3D reconstructions. A number of advances have been made in detector technology and image processing that has enabled some dramatic improvements in resolution. Still, low resolutions continue to plague the field. Cryo-EM reconstructions, which rely on many images of molecules with different orientations, are limited by the noise and conformational heterogeneity often inherent to the molecules of interest. Classification of these structures into distinct classes, enables insights into the conformational space that they inhabit, and can indeed improve the quality of individual reconstructions. However, even within classes, atomic motions are an unavoidable fact of nature. The inherent noise in low-dose electron imaging, along with the number of particles in the sample, limits to what degree classes can accurately be assigned. It is thus an accepted matter, that many reconstructions will by their very nature contain features from many molecule which are only approximately identical. This manifests itself in heterogeneous resolutions, where fluctuations can be attributed to changes in the local similarity of the averaged molecules.

To build atomic models from these low resolution reconstructions, a common approach known as flexible fitting, employs atomic structures which have been solved using high-resolution techniques. In this thesis, I explore a flexible fitting and refinement method which attempts to improve the interpretability of atomic models by estimating the local resolution of the atoms in the underlying data. Using a Gaussian Mixture Model, a single atomic model is used to describe the experimental map, with atoms modelled as isotropic three-dimensional Gaussians with widths determined from the reconstruction. This allows better interpretation of the atomic structure, as coordinate uncertainty is accounted for. Of course, isomorphic Gaussians are limited in their accuracy at representing atomic motions of bonded atoms. Instead, a second representation is derived by modifying the atomic models in the context of a molecular dynamics simulation with perturbations derived from the local resolution information. This representation, composed of an ensemble of atomic structures was shown to produce an improved fit with the data.

Unfortunately, the initial model which is fitted to the experimental data, often requires significant rearrangement of its coordinates in order to fit the cryo-EM map before local resolutions can be estimated. This is because high resolution starting models are typically derived from X-ray experiments, where crystallisation can result in structural change. Frequently, cryo-EM experiments are elucidating structures which have never been seen before. In such cases, structural predictions are used instead. These can be highly accurate, often down to the level of domains, but may require some rearrangement to better fit the data. Flexible fitting approaches are able to fit such models but require the use of restraints to prevent distortions. In the past, the RIBFIND approach has been successfully used to this end, but has been limited to protein structures. RIBFIND2, which is presented in this thesis is able to decompose RNA structures into rigid bodies which can be restrained during flexible fitting procedures.

Combining the GMM method with these RIBFIND2 restraints enabled a diverse set of structural predictions from the recent CASP15 challenge to be flexibly fit into cryo-EM maps, resulting in models with similar quality to the target structures.