Investigating correlations is the key to understanding the nature of biological systems. In general, correlations describe the relationship between data sets or specific characteristics of data. To investigate correlations among and within biomolecules we discussed two complementary approaches to advance the understanding of evolution. Mutational dynamics can mainly be seen in the space of sequences whereas the altered phenotype is selected in the biophysical realm. By mutual information, an information-theoretical measure, we can identify potentially coevolving nucleotide or amino acid positions from a set of sequences combined into a multiple sequence alignment. In the biophysical realm, the mechanics of a biomolecule, which is important for its structure and function, is examined by various methods. Since molecular dynamics simulations and normal mode analysis are computationally expensive approaches, coarse-grained protein representations such as elastic network models have been developed. We used such protein models, particularly the Gaussian and the anisotropic network model, to jugde the importance of single residues or amino acid contacts on the dynamics of the biomolecule or distinct portions.
In this thesis, we applied this analysis to distinct sets of hammerhead ribozyme sequences of type I and III to reveal coevolutionary hot spots shared among the different sequences. We observed a weaker coevolution of ribozymes originating from prokaryotes and eukaryotes compared to viroid sequences. Additionally, we obtained signals between helical stems I and II which is well-known from experiments. However, we noticed a coevolutionary connection between stems I and III throughout all sets of sequences that have not been reported yet.
We applied an established protocol to a structural model of the small viral potassium channel Kcv, where we deleted single contacts and measured the resulting change in dynamics using the Frobenius norm. Here, we observed a mechanical connection of N- and C-terminal residues, whereas the selectivity filter seems almost mechanically uncoupled to the rest of the channel. A similar study was performed for the acetylcholinesterase as well where we additionally correlated mechanical changes with coevolutionary information. By means of coarse-grained protein models, we proposed a protocol for the Kcv to identify the transition from a functional to a non-functional channel upon N-terminal deletions.
Furthermore, we utilized reduced molecular models to derive amino acid specific interaction constants directly from a set of protein structures obtained from e.g. from molecular dynamics simulations. To this end, we examined the performance of three approaches to retrieve the input parameters from an artificially constructed system. As it turned out, semidefinite programming is an efficient method for this task and was employed for a realistic application as well
