Maintaining and breaking symmetry in homomeric coiled-coil assemblies

In coiled-coil (CC) protein structures α-helices wrap around one another to form rope-like assemblies. Most natural and designed CCs have two–four helices and cyclic (Cn) or dihedral (Dn) symmetry. Increasingly, CCs with five or more helices are being reported. A subset of these higher-order CCs is of interest as they have accessible central channels that can be functionalised; they are α-helical barrels. These extended cavities are surprising given the drive to maximise buried hydrophobic surfaces during protein folding and assembly in water. Here, we show that α-helical barrels can be maintained by the strategic placement of β-branched aliphatic residues lining the lumen. Otherwise, the structures collapse or adjust to give more-complex multi-helix assemblies without Cn or Dn symmetry. Nonetheless, the structural hallmark of CCs—namely, knobs-into-holes packing of side chains between helices—is maintained leading to classes of CCs hitherto unobserved in nature or accessed by design.


Analytical ultracentrifugation (AUC)
The sedimentation-velocity experiments for CC-Type2-II, CC-Type2-LI, CC-Type2-LV and CC-Type2-VI (formerly known as AIKEIA, CC-Hept, ALKEVA and AVKEIA) have been reported previously. 1 Due to low α helicity, the AUC experiments were not conducted for the sequence CC-Type2-FV. CC-Type2-FL aggregated at 3,000 rpm and CC-Type2-FF slowly precipitated during the SE experiment.             . Residuals for sedimentation-velocity experiments are shown as a bitmap in which the greyscale shade indicates the difference between the fit and raw data. Scans are ordered vertically, with earlier scans at the top. The horizontal axis is the radial range over which the data were fitted. Right: sedimentation-equilibrium data (top, dots) and fitted single-ideal species model curves at 21k (blue), 24k (red), 27k (green) and 30k (purple) rpm. The fit returns a mass of 21,950 Da (6.6 × monomer mass, 95% confidence limits 21,816 -22,078). Bottom: residuals for the above fits using the same colour scheme as above.
Conditions: 70 µM peptide concentration, PBS (pH 7.4).               . continuous c(s) distribution from sedimentation-velocity data at 50k rpm returning s = 1.748 S, s20,w = 1.871 S, f/f0 = 1.157 and mw = 14,833 Da (4.2 × monomer mass) at 95% confidence level. Conditions: 150 µM peptide concentration, PBS (pH 7.4). Residuals for sedimentation-velocity experiments are shown as a bitmap in which the greyscale shade indicates the difference between the fit and raw data. Scans are ordered vertically, with earlier scans at the top. The horizontal axis is the radial range over which the data were fitted. Intensity values displayed are normalised to blank readings. K d to peptide not determined due to not reaching saturation.

30.69
Supplementary Table 3 Crystallisation data collection and refinement statistics. Highest-resolution shell shown in parentheses. R free represents the R-factor calculated from 5% of reflections that were not used during refinement.

CC-Type2-FI iSOCKET Knobs-into-holes interactions
Chain   to create a truncated octahedron cell of TIP3P water molecules setting the padding to 6 Å and the closeness to 0.75 Å. The charge of the system was neutralised using NaCl and additional ions were added to simulate a concentration of 0.1 M in NaCl. Using the cpinutil.py program, every ionisable residues of CC-Type2-LL-L17E and CC-Type2-IL-SG-L17E, that is every Lys and Glu residues, were made titratable, leading to a total of 60 and 70 titratable residues respectively.

CC-Type2-LF iSOCKET Knobs-into-holes interactions
Minimisation, heating and equilibration -The two systems were minimised in 6 phases, first the water, hydrogen atoms and ions were minimised applying a restraint on the protein atoms of 25 kcal.mol -1 .Å -2 , then the side chains, except the Lys and Glu residues were minimised, first keeping a 25 kcal.mol -1 .Å -2 restraint on the backbone as well as on the Lys and Glu residues, and then decreasing it to 10 and then 5 kcal.mol -1 .Å -2 , finally only the Cα and Lys and Glu atoms were restrained, first with a 2 then 1 kcal.mol -1 .Å -2 restraint. Each minimisation phase consisted in up to 1000 steps of steepest descent followed by up to 10000 steps of conjugate gradient. The systems were then heated to 300 K over 100 ps applying a 5 kcal.mol -1 .Å -2 restraint on backbone atoms as well as on Lys and Glu residues. This was followed by a 500-ps initial equilibration in the NPT ensemble at a temperature of 300 K controlled via Langevin dynamics using a collision frequency of 5 ps -1 and a pressure 101325 Pa maintained with a Berendsen barostat and a pressure relaxation time of 1 ps and using a 5 kcal.mol -1 .Å -2 restraint on backbone atoms, Lys and Glu residues.
Using the same pressure and temperature regulations, a careful equilibration protocol was initiated in which the ionisable residues were allowed to titrate with an exchange between states attempted every 100 steps, using a relaxation dynamic of 100 steps, an implicit salt concentration of 0.1 M and a pH of 4.0 as it is the pH at which both CC-Type2-LL-L17E and CC-Type2-IL-SG-L17E are the most stable experimentally. Although running CpHMD simulation in the NPT ensemble is not recommended in AMBER 16, we found that the fully protonated internal Glu residues (each having 4 protons on the carboxylate, named GL4 in AMBER) led to a destabilisation of the coiled coils yielding significant deviations from the crystal structures, leading in turn to a poor starting point for the CpHMD and pH-REMD simulations. Keeping restraints throughout the NPT equilibrations could prevent this but the relaxation of the protein upon shifting to NVT without restraint would lead to changes in pressure, thereby defeating the purpose of the NPT equilibration. We therefore decided to allow the ionisable residues to titrate during the NPT equilibration, carefully monitoring the equilibration. To further test the validity of our approach we also ran equilibrations in which the protonation states were allowed to change for a short period of time and fixing them again afterwards.
We found no differences in the outcome of the equilibration except for a lower sampling of the protonation states and the possibility to stop the simulation at unfavourable protonation states leading to deviations from the crystal structure. In light of these results we therefore performed the NPT equilibration allowing the ionisable residues to titrate.
The NPT CpHMD equilibration was first run for 1 ns using the same 5 kcal.mol -1 .Å -2 restraint on backbone atoms, Lys and Glu residues, then for 1 ns using 2 kcal.mol Analysis of the pH-REMD simulations -Protonation state statistics were calculated with the cphstats program part of AMBER 16. MD trajectories were pre-processed (to remove unwanted translational and rotational motions of the protein) and analysed with the CCPTRAJ program. 8 The radii of the channels were calculated using HOLE 9 with the MDAnalysis toolkit. 10 From the pH-REMD simulations, the pKa of the ionisable residues can be calculated using the generalised Henderson-Hasselbalch (HH) equation or Hill equation: where f d is the deprotonated fraction and n the Hill coefficient. In the ideal case of an ionisable residue not interacting with any other ionisable residue, n=1 and the standard HH equation describe the titration curve. However, as interactions with other ionisable residues increases, the HH equation will less accurately describe the titration curve, leading to n<1 in the case of anti-cooperativity between protonation state changes or n>1 in the case of cooperativity. One major exception is replica 7 with parameter set 2 for which conformations sampled at very high pH were suddenly brought to pH 3 leading to the dissociation of the barrel. This replica was then unable to exchange with higher pH walkers, except for some exchanges at pH 3.5. -The X-ray crystal structures of CC-Type2-LL-L17E and CC-Type2-IL-Sg-L17E were used as reference for the calculations. All the atoms except hydrogen atoms were used for the calculations. The regions indicated with an asterisk correspond to the populations of structures for which one or more Glu17 has its side chain pointing toward the outside of the structure. Curves are coloured by pH value according to the key on the right-hand side. A logarithmic RMSD scale was used so that large RMSD values corresponding to dissociation of chains can be visualised. Figure 95 Occupancy of a sodium ion interacting with the inner ring of Glu17 residues in CC-Type2-LL-L17E (blue) and CC-Type2-IL-Sg-L17E (green) between pH 3 and 10.5 -A sodium ion is considered as interacting inside the ring of Glu17 residues if it is at a distance of less than 12 Å from each Glu17 residues. From pH~7 and above the occupancy diminish mainly because of the increased sampling of opened and dissociated barrels, but also partly because the metrics is sensitive to conformations for which more than one side chains of Glu17 point toward the outside of the structure. A colour spectrum is used to represent the clash scores for each atom. No clashes are coloured white and minimal to extensive clashes are coloured from pink to red respectively. At very short distance, atoms that are not covalently bound are rendered as being covalently bound.

Supplementary Figure 100
Rescoring of the sequence-threading matrix with alternative force fields. Total energy from scoring with (left) amber99-SB-ILDN forcefield 11 with amber99 OBC implicit solvent (a physicalbased force field) and (right) DFIRE2.0 12 (a statistical-based force field). Scores are normalised to the diagonal line and are divided by the number of chains in the assembly. Figure 101 Standard deviation of the chain scores for each sequence threading -The standard deviation of chain BUDE scores from modelling sequences discussed in the manuscript onto all parallel structures discussed in the manuscript. Colormaps show the (left) standard deviation in BUDE points (a pseudo-energy function) and extracted from this (right) the standard deviation of the steric component of the BUDE score.