Magic Numbers in Protein Structures

Generalized Klein-Gordon models: behavior around the ground state condensate

In this work, we investigate the balance between the nonlinear and linear interaction energy of an interparticle anharmonic system in the vicinity of the ground state condensate. As a result, we find that the nonlinear interaction energy is very significant in the vicinity of each degree of freedom. We address some potential applications of the findings to miscellaneous areas of interests such as soliton theory, hydrodynamics, solid state physics, ferromagnetic and ferroelectric domain walls, condensed matter physics, and particle physics, among others.

Descriptor-based protein remote homology identification

Here, we report a novel protein sequence descriptor-based remote homology identification method, able to infer fold relationships without the explicit knowledge of structure. In a first phase, we have individually benchmarked 13 different descriptor types in fold identification experiments in a highly diverse set of protein sequences. The relevant descriptors were related to the fold class membership by using simple similarity measures in the descriptor spaces, such as the cosine angle. Our results revealed that the three best-performing sets of descriptors were the sequence-alignment-based descriptor using PSI-BLAST e-values, the descriptors based on the alignment of secondary structural elements (SSEA), and the descriptors based on the occurrence of PROSITE functional motifs. In a second phase, the three top-performing descriptors were combined to obtain a final method with improved performance, which we named DescFold. Class membership was predicted by Support Vector Machine (SVM) learning. In comparison with the individual PSI-BLAST-based descriptor, the rate of remote homology identification increased from 33.7% to 46.3%. We found out that the composite set of descriptors was able to identify the true remote homolog for nearly every sixth sequence at the 95% confidence level, or some 10% more than a single PSI-BLAST search. We have benchmarked the DescFold method against several other state-of-the-art fold recognition algorithms for the 172 LiveBench-8 targets, and we concluded that it was able to add value to the existing techniques by providing a confident hit for at least 10% of the sequences not identifiable by the previously known methods.

Efficient expansion, folding, and unfolding of proteins

We consider a nonstatistical, computationally fast experiment to identify important topological constraints in folding small globular proteins of about 100-200 amino acids. In this experiment, proteins are expanded mechanically along a path of steepest increase in the free space around residues. The pathways are often consistent with folding scenarios reported in kinetics experiments and most accurately describe obligatory or mechanic folding proteins. The results suggest that certain topological "defects" in proteins lead to preferred, entropically favorable channels down their free energy landscapes.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.