Fuzzy oil drop model to interpret the structure of antifreeze proteins and their mutants

Abstract

Mutations in proteins introduce structural changes and influence biological activity: the specific effects depend on the location of the mutation. The simple method proposed in the present paper is based on a two-step model of in silico protein folding. The structure of the first intermediate is assumed to be determined solely by backbone conformation. The structure of the second one is assumed to be determined by the presence of a hydrophobic center. The comparable structural analysis of the set of mutants is performed to identify the mutant-induced structural changes. The changes of the hydrophobic core organization measured by the divergence entropy allows quantitative comparison estimating the relative structural changes upon mutation. The set of antifreeze proteins, which appeared to represent the hydrophobic core structure accordant with "fuzzy oil drop" model was selected for analysis.

Fig. 1

The ES model definition. (a) the Ramachandran map with low energy area distinguished (b) the relation between V-angle (dihedral angle between two sequential peptide bond planes) and R – radius of curvature (in logarithmic scale to avoid large values for β-structural forms) as calculated for structures belonging to low energy fragments on Ramachandran map (shown in a) together with the approximation function (2nd degree polynomial). (c) the Ramachandran map with points representing the structures accordant with the approximation function shown in b). (d) the ellipse path assumed to represent the limited conformational sub-space for early-stage intermediate. (e) the ellipse path linking all secondary structures area

Fig. 2

The ES model applicability to 7MSI and 1MSI – proteins of lower and higher (respectively) discordance with the assumed model although both of them are treated as representing the structure not accordant with the ES model (D_average above 1.). The dark blue symbols – theoretical dependence between V-angle and Ln(R), pink squares – observed parameters and yellow triangles – the residues of the higher than 1.0 unit difference between expected and observed values of ln(R) for particular V-angle

Fig. 3

The 3-D presentation of the 7MSI (left) and 1MSI (right) proteins differing their lower and higher (respectively) accordance with the LS model. The fragments marked in white – residues of difference higher than 1.0 unit shown in Fig. 1 as yellow triangles. The residues shown in red – mutations versus the wild type

Fig. 4

The hydrophobic density profile for 3MSI and 9MSI showing the idealized and observed distributions. The proteins were selected to show the lowest and the highest respectively accordance between the idealized (T) and observed (O) hydrophobicity distribution. The yellow line shows the random distribution (R). The residues mutated versus the wild type are shown by cyan circles

Fig. 5

3-D presentation of 3MSI (left) and 9MSI (right) with the residues of hydrophobicity density differing more than 0.004 versus the expected one given in white. The residues shown in red – the mutated residues

Fig. 6

The relation between traditional similarity measurements expressed as RMS-D values and D _KL measurements. The correlation coefficient calculated is equal to 0.2268 with the statistical significance on the level p < 0.0001