Thornton's frequencies

In 1988, Janet Thornton developed a prediction program based on the statistical method employed by Chou and Fasman (1977). Initially, the absolute amino acid occurrences for each of the 4 positions in the ß-turn type categories were calculated. These were then normalized to give positional frequencies f(i), f(i+1), f(i+2), f(i+3), which were used by the predictive algorithm. Conformational parameters for the turn categories, P(t), were also calculated for each amino acid. The conformational parameters for helix, P(a) and ß-sheet, P(b) were taken from Chou & Fasman (1978).

The parameters used by the program were defined as follows:

p(Aa)=f(Aa)/<f>

where:

f(Aa)=no.of particular amino acid type of secondary structure/no.of particular amino acid in proteins studied

<f>=total no. of amino acids in type of secondary structure/total no. of amino acids in proteins studied

for positions i to i+3:

f(iAa)=no.of particular amino acid in position i of turn/no.of particular amino acid in proteins studied

The algorithm used the following criteria to test for a particular ß-turn type:

1. p(t)=f(i)*f(i+1)*f(i+2)*f(i+3) was greater than a calculated cutoff value.

cutoff value for Type-I ß-turn=4.00

cutoff value for Type-II ß-turn=2.70

2. <P(t)> was greater than unity.

3. <P(t)> was greater than either <P(a)> or <P(b)>.

The cutoff values were obtained by the "fine tuning" of the average probability of occurrence of that particular ß-turn type. The average probability is the average of the p(t) values for every possible 4 residue sequence. The fine tuning was in the form of a multiplication factor, which , when applied to the average probability, maximized the number of database-located turns of a particular type found by criterion 1, and minimized the number of 4-residue sequences in the proteins studied that were not turns, but satisfied criteria 2 and 3.

Table2: Conformational parameters and positional frequencies

A. Type I ß-turns

Amino acid P(t) f(i) f(i+1) f(i+2) f(i+3)
Ala 0.742 0.0136 0.0296 0.0210 0.0173
Arg 0.879 0.0039 0.0309 0.0502 0.0116
Asn 1.788 0.0924 0.0139 0.0531 0.0370
Asp 1.977 0.0687 0.0452 0.0741 0.0289
Cys 1.379 0.0518 0.0239 0.0359 0.0398
Gln 0.791 0.0240 0.0150 0.0210 0.0269
Glu 1.121 0.0176 0.0418 0.0352 0.0286
Gly 1.141 0.0236 0.0130 0.0201 0.0686
His 0.781 0.0408 0.0082 0.0204 0.0163
Ile 0.389 0.0047 0.0166 0.0047 0.0166
Leu 0.612 0.0117 0.0190 0.0175 0.0190
Lys 0.697 0.0130 0.0277 0.0228 0.0130
Met 0.661 0.0001 0.0001 0.0081 0.0645
Phe 0.768 0.0169 0.0056 0.0225 0.0393
Pro 0.953 0.0279 0.0721 0.0047 0.0001
Ser 1.468 0.0446 0.0533 0.0421 0.0211
Thr 1.252 0.0383 0.0383 0.0304 0.0304
Trp 1.345 0.0268 0.0134 0.0336 0.0738
Tyr 0.711 0.0145 0.0145 0.0202 0.0289
Val 0.394 0.0072 0.0130 0.0101 0.0130

B. Type-II ß-turns

Amino acid P(t) f(i) f(i+1) f(i+2) f(i+3)
Ala 0.943 0.0148 0.0136 0.0012 0.0123
Arg 1.215 0.0039 0.0077 0.0116 0.0309
Asn 0.986 0.0046 0.0069 0.0254 0.0069
Asp 0.711 0.0072 0.0072 0.0001 0.0163
Cys 0.985 0.0159 0.0040 0.0040 0.0199
Gln 1.454 0.0180 0.0180 0.0030 0.0240
Glu 0.840 0.0066 0.0110 0.0066 0.0132
Gly 2.608 0.0083 0.0047 0.0875 0.0106
His 0.642 0.0041 0.0122 0.0082 0.0041
Ile 0.426 0.0142 0.0024 0.0001 0.0024
Leu 0.525 0.0146 0.0029 0.0001 0.0058
Lys 0.732 0.0065 0.0098 0.0001 0.0163
Met 0.725 0.0081 0.0161 0.0001 0.0081
Phe 0.757 0.0112 0.0169 0.0001 0.0056
Pro 1.801 0.0186 0.0581 0.0001 0.0001
Ser 0.756 0.0087 0.0136 0.0025 0.0074
Thr 0.665 0.0176 0.0016 0.0001 0.0096
Trp 0.151 0.0001 0.0067 0.0001 0.0001
Tyr 0.909 0.0087 0.0087 0.0058 0.0173
Val 0.610 0.0101 0.0058 0.0014 0.0087

Using the appropirate average probability of ß-turn occurence as a starting probability of ß-turn occurence as a starting point, the cut-off was adjusted to maximize the number of observed turns predicted and minimize the number of incorrectly predicted turns (Thornton 1988).

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