Bayesian methods for protein structure calculation from sparse, heterogenous and lowquality data
Final Report Abstract
The aim of this project was to develop computational methods for biomolecular structure determination with challenging experimental data, including sparse and low-resolution data. We tackled the problem from three different angles: (1) Incorporation of data-independent prior knowledge, (2) support for hybrid structural data, and (3) improved conformational sampling. All of these developments were integrated into a Bayesian statistical approach to biomolecular structure determination. To improve structure calculation with sparse data, we adopted a strategy that is highly successful in protein structure prediction: the assembly of protein models from structural parts, so-called fragments, that correspond to recurrent secondary or super-secondary structure. We have developed highly practical tools to search for fragments based on sequence information and/or experimental data. The use of structural fragments alleviates problems with data sparseness and lack of resolution only to some extent, because fragments mostly provide local information. Therefore a complementary strategy was to learn statistical potentials from known protein structures. Our methods for learning statistical potentials can be used to coarse-grain biomolecular structures, i.e. to represent biomolecular structures at lower resolution by lumping groups of atoms together into pseudo-atoms. One of the future efforts will be to develop a multi-scale description of biomolecular structures that can pass through multiple levels of resolution and describes intra-molecular interactions on a coarse-grained level. There are a number of recent developments in structural biology that allow the determination of increasingly large and fragile biomolecular complexes. Cryo-electron microscopy has witnessed a tremendous boost during the funding period. Also solid-state NMR is now routinely used to characterize the structure of large, and often symmetric, assemblies. We developed several computational methods that facilitate structure determination with cryo- EM and solid-state NMR. We developed methods in 3D image processing and structural modeling for cryo-EM data. A very promising development is a Bayesian reconstruction algorithm for single-particle analysis. A particular strength of our reconstruction algorithm is the use of pseudo-atoms, which nicely connects with our efforts in estimating coarse-grained representations of biomolecular structures. We also made progress in improving methods for conformational sampling of biomolecules. We applied and developed several algorithms that can be used for general Bayesian computation. These include a generalization of nested sampling and an adaptive ensemble annealing algorithm. The key quantity that is estimated by these algorithms is the density of states. The density of states does not only allow us to formulate adaptive algorithms with fewer algorithmic parameters. It can also be used to solve other computational challenges in Bayesian inference such as the computation of marginal likelihoods and Bayes factors. In several structure determination projects, we showed that our methods are of great practical use. We used our sharpening method to improve the structure of the eukaryotic ribosome from cryo-EM data. We merged X-ray and NMR data to determine the structure of a kinase/inhibitor complex in solution. We calculated the structure of a trimeric autotransporter adhesin; our structure is among the first membrane protein structures determined by solid-state NMR. Another successful application of ISD was the determination of a helical type 1 pilus from hybrid experimental data. The successful completion of these structure determination projects became possible only through the methods that were developed in this project. We expect that our tools and future improvements will continue to be of high practical relevance and assist in other challenging structure determination projects.
Publications
- A Blind Deconvolution Approach for Improving the Resolution of Cryo-EM Density Maps. Journal of Computational Biology 18:335- 346 (2011)
M. Hirsch, B. Schölkopf & M. Habeck
- HHfrag: HMM-based fragment detection using HHpred. Bioinformatics 27:3110-6 (2011)
I. Kalev & M. Habeck
- Statistical mechanics analysis of sparse data. Journal of Structural Biology 173:541-8 (2011)
M. Habeck
- Bayesian estimation of free energies from equilibrium simulations. Physical Review Letters 109:100601(2012)
M. Habeck
(See online at https://doi.org/10.1103/PhysRevLett.109.100601) - Inferential NMR/X-ray based structure determination of a dibenzo[a,d]cyclo-heptenone inhibitor/p38α MAP kinase complex in solution. Angewandte Chemie 51:2359–62 (2012)
V. S. Honndorf, N. Coudevylle, S. Laufer, S. Becker, C. Griesinger & M. Habeck
(See online at https://doi.org/10.1002/anie.201105241) - Membrane-protein structure determination by solid-state NMR spectroscopy of microcrystals. Nature Methods 9:1212–7 (2012)
S. Shahid, B. Bardiaux, T. Franks, L. Krabben, M. Habeck, B. Rossum & D. Linke
(See online at https://doi.org/10.1038/NMETH.2248) - A probabilistic model for secondary structure prediction from protein chemical shifts. Proteins 81: 984–993 (2013)
M. Mechelke & M. Habeck
(See online at https://doi.org/10.1002/prot.24249) - Estimation of interaction potentials through the configurational temperature formalism. Journal of Chemical Theory and Computation 9: 5685– 5692 (2013)
M. Mechelke & M. Habeck
(See online at https://doi.org/10.1021/ct400580p) - Hybrid Structure of the Type 1 Pilus of Uropathogenic E. coli. Angewandte Chemie 54: 11691–11695 (2015)
B. Habenstein, A. Loquet, K. Giller, S. Vasa , S. Becker, M. Habeck & A. Lange
(See online at https://doi.org/10.1002/ange.201505065) - Structure inference in cryo-electron microscopy using Gaussian mixture models. Biophysical Journal 108(5): 1165-1175 (2015)
P. Joubert & M. Habeck
(See online at https://doi.org/10.1016/j.bpj.2014.12.054)
