COVARIATION ANALYSIS OF LOCAL AMINO ACID SEQUENCES IN RECURRENT PROTEIN LOCAL STRUCTURES

An amino acid packing code for α-helical structure and protein design

This work demonstrates that all packing in α-helices can be simplified to repetitive patterns of a single motif: the knob-socket. Using the precision of Voronoi Polyhedra/Delauney Tessellations to identify contacts, the knob-socket is a four-residue tetrahedral motif: a knob residue on one α-helix packs into the three-residue socket on another α-helix. The principle of the knob-socket model relates the packing between levels of protein structure: the intra-helical packing arrangements within secondary structure that permit inter-helix tertiary packing interactions. Within an α-helix, the three-residue sockets arrange residues into a uniform packing lattice. Inter-helix packing results from a definable pattern of interdigitated knob-socket motifs between two α-helices. Furthermore, the knob-socket model classifies three types of sockets: (1) free, favoring only intra-helical packing; (2) filled, favoring inter-helical interactions; and (3) non, disfavoring α-helical structure. The amino acid propensities in these three socket classes essentially represent an amino acid code for structure in α-helical packing. Using this code, we used a novel yet straightforward approach for the design of α-helical structure to validate the knob-socket model. Unique sequences for three peptides were created to produce a predicted amount of α-helical structure: mostly helical, some helical, and no helix. These three peptides were synthesized, and helical content was assessed using CD spectroscopy. The measured α-helicity of each peptide was consistent with the expected predictions. These results and analysis demonstrate that the knob-socket motif functions as the basic unit of packing and presents an intuitive tool to decipher the rules governing packing in protein structure.

The use of information theory in evolutionary biology

Information is a key concept in evolutionary biology. Information stored in a biological organism's genome is used to generate the organism and to maintain and control it. Information is also that which evolves. When a population adapts to a local environment, information about this environment is fixed in a representative genome. However, when an environment changes, information can be lost. At the same time, information is processed by animal brains to survive in complex environments, and the capacity for information processing also evolves. Here, I review applications of information theory to the evolution of proteins and to the evolution of information processing in simulated agents that adapt to perform a complex task.

Methods for optimizing the structure alphabet sequences of proteins

Protein structure prediction based on fragment assemble has made great progress in recent years. Local protein structure prediction is receiving increased attention. One essential step of local protein structure prediction method is that the three-dimensional conformations must be compressed into one-dimensional series of letters of a structural alphabet. The traditional method assigns each structure fragment the structure alphabet that has the best local structure similarity. However, such locally optimal structure alphabet sequence does not guarantee to produce the globally optimal structure. This study presents two efficient methods trying to find the optimal structure alphabet sequence, which can model the native structures as accuracy as possible. First, a 28-letter structure alphabet is derived by clustering fragment in Cartesian space with fragment length of seven residues. The average quantization error of the 28 letters is 0.82 A in term of root mean square deviation. Then, two efficient methods are presented to encode the protein structures into series of structure alphabet letters, that is, the greedy and dynamic programming algorithm. They are tested on PDB database using the structure alphabet developed in Cartesian coordinates space (our structure alphabet) and in torsion angles space (the PB structure alphabet), respectively. The experimental results show that these two methods can find the approximately optimal structure alphabet sequences by searching a small fraction of the modeling space. The traditional local-optimization method achieves 26.27 A root mean square deviations between the reconstructed structures and the native one, while the modeling accuracy is improved to 3.28 A by the greedy algorithm. The results are helpful for local protein structure prediction.