Figure 1.
(a) Schematic of amino acid backbone dihedrals
and
, and (b) a corresponding Ramachandran plot. In a typical Ramachandran plot of a glutamine residue, each pixel represents a
bin, whose intensity represents its relative population, ranging from 1,2,
,9, and 10 or more conformations, sampled in our simulations. Blue, yellow, grey, and pink clusters identify PPII,
,
, and
regions, respectively.
Table 1.
Secondary structure definitions.
Figure 2.
, PPII and
content of selected polyQ peptides.
Here, given are the contents (as a percentage) of individual glutamine residues found in: (a,b) -region (c,d) PPII-region (e,f)
. These percentages are plotted against the Glu residue numbers for (a,c,e)
[red],
[blue] and (b,d,f)
[red],
[blue]. These percentages are obtained from clustering the conformations based on their dihedral angles in the Ramachandran plot.
Figure 3.
Helical, turn and coil content of selected polyQ peptides.
Here, given are the contents (as a percentage) of individual glutamine residues found in the following conformations: (a,b) helical (,
) (c,d) turn (H-bonded,bend) (e,f) coil. These percentages are plotted against the Glu residue numbers for (a,c,e)
[red],
[blue] and (b,d,f)
[red],
[blue]. These percentages are obtained from the DSSP [58], [59] analysis code.
Figure 4.
and
. Cartoon representation of sample conformations of (a)
and (b)
. Purple, blue, cyan, and orange represent
-helix,
-helix, turn, and coil secondary structural motifs, respectively. The licorice-like representation of the proline segment of
is given in (b). These structures are plotted by VMD [61] using STRIDE [60] for secondary structure prediction.
Figure 5.
Selected extended conformations of
peptides. Here, we give (a) cartoon and (b) licorice-like representation of select conformations of the
peptide with (
,
,
,
)
and (
,
,
,
)
strands. (a) The coloring is similar to Fig. 4 with yellow and green representing
and
strands respectively. We used a dihedral angle-based algorithm to detect the
strands and for other secondary structures in these plots we used STRIDE [60] distributed with VMD [61]. (b) The residues involved in (
)
-hairpin, (
) isolated
-strand, (
)
-harpin, and (i
) isolated
-strand are highlighted. The rest of residues are grey and all the side chains are represented by thin lines.
Figure 6.
Correlation analysis results for selected polyQ peptides.
Here is given the (a) odds ratio based between any two glutamine residues (
and
) of
[red] and
[blue] in terms of (
). From each side of the peptide
ending residues are omitted in the calculations to reduce the end effects. (b) Similar to (a) for
[red],
[blue], and
[black]. Here
residues from each end are omitted. (c,d) Correlation coefficient between
dihedral angles of any two glutamine residues (
and
) in terms of (
) for (c)
[red],
[blue] and (d)
[red],
[blue], and
[black]. The end residues were omitted according to the same protocol used for odds ratio analysis. (e,f) Similar to (a,b) but with the odds ratio calculated using the probabilities that residues belong or not to an
repeat region.
Figure 7.
Correlation analysis results for selected polyQ peptides.
Specifically, we give for (a)
(b)
and (c)
based on OR(
)[red] OR(PPII)[blue] and OR(
)[black]. (d) To compare the linear and OR-based results we plotted
(r) versus the correlation coefficient corr
(r) for
that suggests an almost linear behavior with a correlation coefficient of 0.97.
Figure 8.
Distribution of radius of gyration of polyQ peptides.
(a) The estimated distribution for
[red] and
[blue]. (b) The estimated
distribution for
[red] and
[blue]. The blue curve can be estimated as the sum [black] of three Gaussian distributions [dotted]. (c) The estimated
distribution for
, considering only the structures with an all-trans proline segment [green]. Similarly the green curve can be estimated as the sum [black] of four Gaussian distributions [dotted]. Considering only the structures that at least have one cis-proline results in the magenta curve for the
distribution. All the histograms are obtained using a window of width
. (d) The exponent
in
relation estimated from select pairs of
(x axis) and
(
for blue circles and
for yellow squares). Inset: The average
(in
) of Q
peptides for
.
Table 2.
Secondary structure analysis of the polyQ peptides.
Table 3.
Helix and turn populations of the polyQ peptides.