Abstract
Previous studies show that the same type of bond lengths and angles fit Gaussian distributions well with small standard deviations on high resolution protein structure data. The mean values of these Gaussian distributions have been widely used as ideal bond lengths and angles in bioinformatics. However, we are not aware of any research done to evaluate how accurately we can model protein structures with dihedral angles and ideal bond lengths and angles.Here, we introduce the protein structure idealization problem. We focus on the protein backbone structure idealization. We describe a fast O(nm/ε) dynamic programming algorithm to find an idealized protein backbone structure that is approximately optimal according to our scoring function. The scoring function evaluates not only the free energy, but also the similarity with the target structure. Thus, the idealized protein structures found by our algorithm are guaranteed to be protein-like and close to the target protein structure.We have implemented our protein structure idealization algorithm and idealized the high resolution protein structures with low sequence identities of the CULLPDB_PC30_RES1.6_R0.25 data set. We demonstrate that idealized backbone structures always exist with small changes and significantly better free energy. We also applied our algorithm to refine protein pseudo-structures determined in NMR experiments.
Highlights
When studying the functions of a protein, it is crucial to know the three-dimensional structure consisting of the Cartesian coordinates of all the atoms of the protein
It has been observed that the bond lengths and angles of the same type assume a Gaussian distribution with a small standard deviation (STDEV) in high resolution protein structure data
We introduce a novel dynamic programming algorithm with a run-time complexity of O(n/ 8), where is a small constant, to find the optimal idealized protein backbone structure according to our scoring function
Summary
When studying the functions of a protein, it is crucial to know the three-dimensional structure consisting of the Cartesian coordinates of all the atoms of the protein. We introduce a novel dynamic programming algorithm with a run-time complexity of O(n/ 8), where is a small constant, to find the optimal idealized protein backbone structure according to our scoring function. If this constraint is satisfied, the distance between the target coordinate and any generated coordinate representing the same atom is upper bounded by r It is reasonable for any generated idealized structure Pi to be considered similar to target structure P0. The scoring function should evaluate the similarity between generated idealized structure Pi and target structure P0, but should evaluate the free energy of Pi, to ensure that Pi is protein-like. The target side-chain structure might be a poor reference for defining the search space and for evaluating the structure similarity score for generated idealized side-chain structures. Similar to the backbone scoring function, DH (Pi, P0) and Dχ (Pi, P0) serve as distance metrics to conserve the side-chain structure
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