Hidden symmetries in the primary sequences of beta-barrel family

How the Sequence of a Gene Specifies Structural Symmetry in Proteins

Internal symmetry is commonly observed in the majority of fundamental protein folds. Meanwhile, sufficient evidence suggests that nascent polypeptide chains of proteins have the potential to start the co-translational folding process and this process allows mRNA to contain additional information on protein structure. In this paper, we study the relationship between gene sequences and protein structures from the viewpoint of symmetry to explore how gene sequences code for structural symmetry in proteins. We found that, for a set of two-fold symmetric proteins from left-handed beta-helix fold, intragenic symmetry always exists in their corresponding gene sequences. Meanwhile, codon usage bias and local mRNA structure might be involved in modulating translation speed for the formation of structural symmetry: a major decrease of local codon usage bias in the middle of the codon sequence can be identified as a common feature; and major or consecutive decreases in local mRNA folding energy near the boundaries of the symmetric substructures can also be observed. The results suggest that gene duplication and fusion may be an evolutionarily conserved process for this protein fold. In addition, the usage of rare codons and the formation of higher order of secondary structure near the boundaries of symmetric substructures might have coevolved as conserved mechanisms to slow down translation elongation and to facilitate effective folding of symmetric substructures. These findings provide valuable insights into our understanding of the mechanisms of translation and its evolution, as well as the design of proteins via symmetric modules.

Identification of latent periodicity in domains of alkaline proteases

Internal repeats in protein sequences have wide-ranging implications for the structure and function of proteins. A keen analysis of the repeats in protein sequences may help us to better understand the structural organization of proteins and their evolutionary relations. In this paper, a mathematical method for searching for latent periodicity in protein sequences is developed. Using this method, we identified simple sequence repeats in the alkaline proteases and found that the sequences could show the same periodicity as their tertiary structures. This result may help us to reduce difficulties in the study of the relationship between sequences and their structures.

Symmetric key structural residues in symmetric proteins with beta-trefoil fold

To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric.

Effects of external interactions on protein sequence-structure relations of beta-trefoil fold

Proteins with symmetric structures are ideal models to investigate the sequence-structure relations. We investigate proteins with beta-trefoil fold and find they have different degrees of sequence symmetries although they show similar symmetric structures. To understand this, we calculate the strength of interactions of the beta-trefoil folds with surrounding environments and find the low degrees of sequence symmetries are often correlated with large external interactions. Our results give an additional confirmation of Anfinsen's thermodynamic hypothesis that protein structures are not only determined by their sequences but also by their surrounding environments. We suggest the external interactions should be considered additionally in protein structure prediction through ab initio folding.

Identification of protein latent periodicities using recurrent correlation analysis

Many large proteins have evolved by internal duplication and fusion. For proteins with internal structural symmetry, this means that their sequences should be made up of identical repeats. However, many of these repeat signals can only be seen at the structural level yet. We suggested a method of recurrent correlation analysis to detect the sequence repeats of proteins directly from their sequences. It showed that the internal repetitions of the representative proteins in six folds of mainly beta class could be identified directly at the sequence level.

A simple method of identifying symmetric substructures of proteins

Accurate identifications of internal symmetric substructures of proteins are needed in protein evolution study and protein design. To overcome the difficulties met by previous methods, here we propose a simple quantitative one by using a similarity matrix plus Pearson's correlation analysis. The distance root-mean-square deviation (dRMSD) is used to measure the similarity of two substructures in a protein. We applied this method to the proteins of the beta-propeller, jelly roll, and beta-trefoil families and the results show that this method cannot only detect the internal repetitive structures in proteins effectively, but also can identify their locations easily.