Graph-based Approaches to Protein Structure- and Function Prediction

The three-dimensional structure of a protein is determined by the network of covalent and non-covalent interactions. An exact description of the governing forces requires to take into account quantum effects which makes the system too complex for most computational analyses. Depending on the application, a simpler representation can make such analyses feasible while still capturing the relevant aspects of the system. Here we explore a number of applications which are based on representing a protein as a graph of interacting residues. This representation has some conceptual advantages over an all-atom representation. It can be shown that the graph representation captures the three dimensional information up to an average accuracy of 2 Ångstrom C-alpha RMSD. The deviation stems from the fact that the network is equivalent to an ensemble of structures which satisfy the contact constraints. This can be used to represent some degree of flexibility. Furthermore, the representation makes it possible to apply algorithms from graph theory to common protein analysis problems such as structure alignment and structure prediction. Part 1: Multiple Structure Alignment and the Sample Mean of Graphs. In contrast to the alignment of sequences, structure-based alignments allow us to look further back in evolutionary time when comparing proteins. For the pairwise case, it has been shown that graph-based methods yield very sensitive alignments which are able to detect remote evolutionary relationships. Here we extend this approach to the case of aligning multiple proteins represented as graphs. This gives rise to a mathematically rigorous definition of the optimal multiple alignment. We analytically derive that calculating an optimal alignment is equivalent to calculating the sample mean for a set of graphs. This sample mean theory for graphs has only very recently been developed and makes a number of powerful algorithms applicable to protein structure analysis. We propose a new multiple structure alignment algorithm based on the sample mean theory and compare its performance to current alternative methods. We show that our algorithm is more efficient than other graph-based algorithms while retaining the same advantages. We further show that the quality of the alignments are as good as other current methods when benchmarked on a large set of structural alignments. Part 2: Consensus Prediction of Residue-Residue Contacts. Accurate prediction of the non-covalent interactions in a protein is equivalent to predicting the three-dimensional structure. Results from the CASP experiments show that current contact prediction methods are inferior to methods which attempt to predict the three dimensional structure directly. However, contact prediction can sometimes give complementary information and hence has been included in some of the top-performing structure prediction methods. Here we present a contact prediction method which is based on calculating the graph-mean of a number of input predictions to create a consensus prediction. We tested the method with CASP server predictions as inputs which are converted to contact graphs before calculating the sample mean. The parameters of the method are trained on targets from the CASP 7 experiment and evaluated on targets from CASP 8. Predicted contacts are evaluated in terms of accuracy and coverage compared to the native contacts. For 50% of the targets, our prediction is better than any of the input models. For 85% of the targets, our prediction is in the top 5% and in all cases it is better than the median score. When compared to the individual methods from which input models were taken, our method predicts contacts more accuractely than any other method. This shows that even though many state-of-the-art methods already make use of consensus information for template picking and model selection, consensus information at the contact level can be further exploited to improve current prediction methods. Part 3: The Structural Impact of Cancer-Associated Mutations in Oncogenes and Tumor Suppressors. Since the availability of high-throughput sequencing methods, the first complete cancer genomes have been published. By comparing the sequence variation between tumor cells and healthy tissue from the same patient, somatic mutations can be identified which are potentially linked with tumorigenesis. However, the consequence of the mutations on a structural and functional level remains to be characterized. We applied computational methods to study the effects of somatic mutations on known and predicted protein structures of well-known cancer genes. For each of ≈2000 mutations, we investigate surface accessibility, proximity to known functional sites, clustering of mutations within the structure, and stability change upon mutation. We obtain significant differences between mutations in oncogenes and tumor suppressors. While mutations in oncogenes tend to occur at the protein surface, are highly clustered and directly affect sites important for protein function, mutations in tumor suppressors tend to affect primarily protein stability. We also find that the alteration of oncogenic activity is often associated with mutations at ATP or GTP binding sites. With these results we can confirm and statistically validate the hypotheses for the gain-of-function and loss-of-function mechanisms of oncogenes and tumor suppressors, respectively. We further show that the differences in the mutational patterns can be used to predict for previously uncharacterized genes, identified in cancer sequencing studies, whether they will likely function as an oncogene or a tumor suppressor. This method can be a valuable tool in the analysis of the increasing amount of data that is being generated by the current cancer sequencing projects. Summary: Starting from a theoretical result, the equivalence of structure alignment and calculating the sample mean of graphs, we present novel methods for the multiple alignment of protein structures and for the prediction of residue-residue contacts. These methods have direct applications in protein structure analysis. In the third part we apply structure prediction to the analysis of human disease mutations. The results confirm the gain of function vs. loss of function hypothesis of oncogenes and tumor suppressors, respectively and give rise to a method for predicting functional properties of cancer-associated proteins from their mutational patterns obtained from sequencing of cancer genomes.