Prediction of protein folding rates from simplified secondary structure alphabet.

Protein folding is a very complicated and highly cooperative dynamic process. However, the folding kinetics is likely to depend more on a few key structural features. Here we find that secondary structures can determine folding rates of only large, multi-state folding proteins and fails to predict those for small, two-state proteins. The importance of secondary structures for protein folding is ordered as: extended ß strand > α helix > bend > turn > undefined secondary structure>310 helix > isolated ß strand > π helix. Only the first three secondary structures, extended ß strand, α helix and bend, can achieve a good correlation with folding rates. This suggests that the rate-limiting step of protein folding would depend upon the formation of regular secondary structures and the buckling of chain. The reduced secondary structure alphabet provides a simplified description for the machine learning applications in protein design.

Reduced alphabet for protein folding prediction.

What are the key building blocks that would have been needed to construct complex protein folds? This is an important issue for understanding protein folding mechanism and guiding de novo protein design. Twenty naturally occurring amino acids and eight secondary structures consist of a 28-letter alphabet to determine folding kinetics and mechanism. Here we predict folding kinetic rates of proteins from many reduced alphabets. We find that a reduced alphabet of 10 letters achieves good correlation with folding rates, close to the one achieved by full 28-letter alphabet. Many other reduced alphabets are not significantly correlated to folding rates. The finding suggests that not all amino acids and secondary structures are equally important for protein folding. The foldable sequence of a protein could be designed using at least 10 folding units, which can either promote or inhibit protein folding. Reducing alphabet cardinality without losing key folding kinetic information opens the door to potentially faster machine learning and data mining applications in protein structure prediction, sequence alignment and protein design.

How the folding rates of two- and multistate proteins depend on the amino acid properties.

Proteins fold by either two-state or multistate kinetic mechanism. We observe that amino acids play different roles in different mechanism. Many residues that are easy to form regular secondary structures (α helices, ß sheets and turns) can promote the two-state folding reactions of small proteins. Most of hydrophilic residues can speed up the multistate folding reactions of large proteins. Folding rates of large proteins are equally responsive to the flexibility of partial amino acids. Other properties of amino acids (including volume, polarity, accessible surface, exposure degree, isoelectric point, and phase transfer energy) have contributed little to folding kinetics of the proteins. Cysteine is a special residue, it triggers two-state folding reaction and but inhibits multistate folding reaction. These findings not only provide a new insight into protein structure prediction, but also could be used to direct the point mutations that can change folding rate.

Inter-residue interaction is a determinant of protein folding kinetics.

In recent years, there have been many breakthroughs in the prediction of protein folding kinetics using empirical and theoretical methods. These predictions focus primarily on the structural parameters in concert with contacting residues. The non-covalent contacts are a simplified model of the interactions found in proteins. Here we investigate the physico-chemical origin and derive the approximate formula ln k(f)=a+b×Σ1/d(6), where d is the distance between different residues of the protein structure. It achieves -0.83 correlation with experimental over 57 two- and multi-state folding proteins, indicating that protein folding kinetics is determined by the interactions between all pairs of residues. The interaction is a short-range coupling that is effective only when two residues are in close proximity, consistent with the dominant role of the contacts in determining folding rates.

Choice of synonymous codons associated with protein folding.

Bioinformatical studies suggest that additional information provided by nucleic acids is necessary to construct protein three-dimensional structures. We find underlying correlations between the contents of bases. All correlations occur at the third codon position of a gene sequence. Four inverse relationships are observed between u(3) and c(3), between a(3) and g(3), between u(3) and g(3), and between c(3) and a(3); and two positive relationships are apparent between u(3) and a(3), and between c(3) and g(3). Their correlation coefficients reach -0.92, -0.89, -0.83, -0.85, 0.83, and 0.66, respectively, for large proteins with multistate folding kinetics. The interconnection of bases can be ascribed to choice of synonymous codons associated with protein folding in vivo. In this study, the refolding rate constants of large proteins correlate with the contents of the third base, suggesting that there is underlying biochemical rationale of guiding protein folding in choosing synonymous codons.

Relationship between protein folding kinetics and amino acid properties.

The successful prediction of protein-folding rates based on the sequence-predicted secondary structure suggests that the folding rates might be predicted from sequence alone. To pursue this question, we directly predict the folding rates from amino acid sequences, which do not require any information on secondary or tertiary structure. Our work achieves 88% correlation with folding rates determined experimentally for proteins of all folding types and peptide, suggesting that almost all of the information needed to specify a protein's folding kinetics and mechanism is comprised within its amino acid sequence. The influence of residue on folding rate is related to amino acid properties. Hydrophobic character of amino acids may be an important determinant of folding kinetics, whereas other properties, size, flexibility, polarity and isoelectric point, of amino acids have contributed little to the folding rate constant.