Statistical Evidence for a Helical Nascent Chain

Abstract

We investigate the hypothesis that protein folding is a kinetic, non-equilibrium process, in which the structure of the nascent chain is crucial. We compare actual amino acid frequencies in loops, α-helices and β-sheets with the frequencies that would arise in the absence of any amino acid bias for those secondary structures. The novel analysis suggests that while specific amino acids exist to drive the formation of loops and sheets, none stand out as drivers for α-helices. This favours the idea that the α-helix is the initial structure of most proteins before the folding process begins.

Keywords: folding pathway; protein folding; secondary structure prediction; single amino acid distributions.

Figure 1

Average abundance, ${\overline{f}}_a\left(a\right)$ (cf. Equation (3)), of amino acid a, in the protein set used. The values are given in percentage of the total number of amino acids (see text).

Figure 2

Distributions/histograms for a few of the frequencies $f(a,s,p)$, where the amino acid a is specified at the top of each plot and where red is for $s=\alpha$-helix, blue is for $s=\beta$-sheets and green is for $s=$ loops. In this figure, the variable $f(a,s,p)$ (the x-coordinate) runs from zero (which means that none of the amino acids a are found in s) to 30 (which means that 30% of the amino acids in the protein are a’s found in s). The y-coordinate is proportional to the number of proteins with a given value of $f(a,s,p)$. The scale of the y-coordinate is the same for all plots and all distributions are normalised. The horizontal dotted lines are the FWHM of the distributions (see text).

Figure 3

Average frequency of finding an amino acid a in $\alpha$-helices (top plot), $\beta$-strands (middle plot) and loops (bottom plot). The values are given in percentage for each secondary structure, i.e., summing all the values in each line leads to 100. The amino acids are specified by their one letter codes.

Figure 4

Distributions/histograms for a few of the ratios $R(a,s,p)$ (cf. Equation (10)), where the amino acid a is specified at the top of each plot and where red is for $s=\alpha$-helix, blue is for $s=\beta$-sheets and green is for $s=$ loops. The variable $R(a,s,p)$ (the x-coordinate) runs from zero to four, the scale of the ordinates is the same in all plots and all histograms are normalised. The vertical dotted line marks the value $R(a,s,p)=1$, when the actual number of amino acids a in secondary structure s is equal to what is expected in the absence of any correlation between a and s. The horizontal dotted lines are the FWHM of the distributions (see text).

Figure 5

Most probable values for the ratios $R(a,s,p)$ (cf. Equation (10)) for $\alpha$-helices (top plot, red), $\beta$-sheets (middle plot, blue) and loops (bottom plot, green). The most probable value is taken from the full distributions for each ratio $R(a,s,p)$ and the uncertainty around that value is given by the FWHM.

Figure 6

Most probable values for the ratios $R(a,s,p)$ (cf. Equation (10)) for $\alpha$-helices (top plot, red), $\beta$-sheets (middle plot, blue) and loops (bottom plot, green). The most probable value is taken from the middle peak in the distributions for each ratio $R(a,s,p)$ and the uncertainty around that value is given by the FWHM of that middle peak.