An Exploration of the Universe of Polyglutamine Structures

Abstract

Deposits of misfolded proteins in the human brain are associated with the development of many neurodegenerative diseases. Recent studies show that these proteins have common traits even at the monomer level. Among them, a polyglutamine region that is present in huntingtin is known to exhibit a correlation between the length of the chain and the severity as well as the earliness of the onset of Huntington disease. Here, we apply bias exchange molecular dynamics to generate structures of polyglutamine expansions of several lengths and characterize the resulting independent conformations. We compare the properties of these conformations to those of the standard proteins, as well as to other homopolymeric tracts. We find that, similar to the previously studied polyvaline chains, the set of possible transient folds is much broader than the set of known-to-date folds, although the conformations have different structures. We show that the mechanical stability is not related to any simple geometrical characteristics of the structures. We demonstrate that long polyglutamine expansions result in higher mechanical stability than the shorter ones. They also have a longer life span and are substantially more prone to form knotted structures. The knotted region has an average length of 35 residues, similar to the typical threshold for most polyglutamine-related diseases. Similarly, changes in shape and mechanical stability appear once the total length of the peptide exceeds this threshold of 35 glutamine residues. We suggest that knotted conformers may also harm the cellular machinery and thus lead to disease.

Fig 1. Scatter plot relating the specified variables for four differentsets, from left to right, Q₂₀, Q₆₀, V₆₀ and CATH.

The empty black points represent the conformers with less than 50% secondary structure content, while the filled red dots represent the more structured conformers. The vertical dotted lines in the middle panels mark the simply stiff limits of stability for each case (see the S1 Text). The conformers to the left of this line are more volatile. The horizontal dashed lines in the middle and bottom panels mark off the top five conformers with respect to the value of F _max.

Fig 2. Distributions of F _max for the studied species.

The top left panel shows the distribution for Q₂₀ in a thick line. The conformations with no force peaks are not plotted in the histograms but contribute to normalization. The amount of such non-mechanostable conformers is (79 ± 2)% for Q₂₀, (34 ± 3)% for Q₆₀, (16.5 ± 0.2)% for V₆₀, and (47 ± 3)% and (20.2 ± 0.5)% for CATH₆₀ and CATH, respectively. The errors were computed using a bootstrapping method and the size of the error bar indicates the standard deviation.

Fig 3. Time evolution of the studied structures.

For each set in Q₆₀, Q₂₀ and V₆₀, 100 randomly chosen structures have been placed under a free-dynamics evolution for 10 ns. After that, the RMSD has been studied and the last time when it fluctuates above 2 Å is recorded as the residence time (t _R). The top graph shows the escape probability (P _e(t)), defined as the probability of having left the initial state of a conformer at time t. We can see how Q₂₀ fluctuates out of the initial structure much faster than Q₆₀, while V₆₀ starts more slowly but rapidly outruns both Q₆₀ and Q₂₀. The inset shows the average evolution of the RMSD for the three sets compared to an example of a similar-sized globular protein, an immunoglobulin binding domain of protein G (PDB code 1GB1, 56 residues). The latter lasts for longer than 10 ns fluctuating around 2 Å, while the other three rapidly evolve out of the initial structure. The bottom graphs show scatter plots of ⟨z⟩ vs. t _R. No simple relation can be established between these two quantities above the stiff limit (dashed vertical lines), while below it residence times never exceed 1 ns.

Fig 4. Knots in the studied conformers.

The top left panel shows an example of a Q₆₀ conformation containing a trefoil (3₁) knot with the knot ends highlighted with yellow spheres. To its right, the same conformation has been partially stretched, and the region inside the knot is highlighted in red and zoomed in. The middle panels represent histograms of the knot end positions, k _±, for Q₆₀ (left) and V₆₀ (right). The bottom panel shows their corresponding extension, Δk. The percentage of knotted structures relative to to the total number of independent conformers found for Q₆₀ and V₆₀ are (9.3 ± 1.8)% and (3.6 ± 0.5)%, respectively. Shallow knots have an extension closer to 60 (the system size). Protein representations have been done with VMD [48].

Fig 5. Variability of the specified parameters with the length, n, of the polyQ chain (circles).

The values for V₆₀ are indicated by a square. χ _F represents the fraction of conformers with at least one force peak for that particular length. The dotted fits correspond to a logarithmic function (top left.352 ln(x/8.115)) and a polynomial behavior (top right, y = 0.236x ^0.562), which is typical for avalanches. The bottom panels show average over the structures of R _g and w. ⟨R _g⟩ has a saturating behavior up to n = 40, but jumps for higher values. ⟨w⟩ presents a transition around n = 35 from slightly elongated to more globular proteins.