1-4 & 2-3 Correlation model

The pattern of residues are important for the ß-turn prediction. This is equivalent to saying that the correlation between different amino acids play an important role in the ß-turn prediction. In view of this, a model called 1-4 & 2-3 correlation model was proposed to predict ß-turns in proteins. When a tetrapeptide folds into a ß-turn, the interaction between its 1st and 4th residues and the interaction between its 2nd and 3rd residues becomes remarkable. Particularly, a H-bond may form between the backbone C=O of the 1st residue and the backbone NH of the 4th residue. Therefore, the 1-4 & 2-3 correlation model reflects in some sense the essence of the intrachain interaction of a ß-turn.

The ß-turn structure involves four consecutive residues, and hence can be generally expressed by

where X₁ represents the amino acid at the 1st position, X₂ represents the amino acid at the 2nd position, and so forth. Since there are 20 different amino acids, the number of possible tetrapeptides would be 20*20*20*20=1.6*10⁵. Tetrapeptides can be classified into two categories: the ß-turn set denoted by S(t), and non ß-turns set denoted by S(nt). An attributive function is used to describe the relevancy of a tetrapeptide to the ß-turn set S(t).

An attributive function Ø used to define intrachain interaction between the 1st and 4th residues and between the 2nd and 3rd residues is of the following form:

where g=10⁴ is an amplifying factor used for making the data in a range easier to handle. P₁(X₁) is the probability of amino acid X₁ occurring at 1st position, P₂(X₂) is the probability of amino acid X₂ occurring at second position, P₃(X₃|X₂) is the probability of amino acid X₃ occurring at the 3rd position given that X₂ has occurred at the 2nd position and P₄(X₄|X₁) is the probability of amino acid X₄ occurring at the 4th position given that X₁ has occurred at the 1st position. All these probabilities can be derived from a training set of data consisting of tetrapeptides known to be folded into a ß-turn in proteins.

The larger the Ø of a tetrapeptide, the closer its attribute to the ß-turn set S(t), and hence the higher its propensity to form a ß-turn in proteins. For a given tetrapeptide, when the attributive parameter Ø is greater than the threshold value T, it is assumed to be able to form a ß-turn; otherwise, it is not. Thus the criterion for predicting the propensity to form a ß-turn for a given tetrapeptide in proteins can be defined by the value of D, as formulated as follows:

a tetrapeptide will form a ß-turn, if its D>=0,

a tetrapeptide will not form a ß-turn , otherwise.

where the discriminant function D is given by

D(X₁X₂X₃X₄)=Ø(X₁X₂X₃X₄)-T

where the value of the threshold T can be determined via an optimization procedure.

Table3 : The probabilities and conditional probabilities derived from training set S(t)

1. The probabilities P₁(X₁)

2 The probabilities P₂(X₂)

3 The conditional probabilities P₃(X₃|X₂)

4. The conditional probabilities P₄(X₄|X₁)

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