Fig 1.
Structures of the investigated proteins: MJ0366 (residue 6-87, pdb code 2efv), MJ0366_CC (residue 6-92), VirC2 (pdb code 2rh3), DndE (pdb code 4lrv) and AvtR (pdb code 4hv0).
First on the left is the simplified representation of the smallest-known trefoil knotted protein (MJ0366 residues 6–92, pdb code 2efv). For each structure of knotted protein are marked the N-terminal knot tail length (red) and the C-terminal knot tail length (blue).
Fig 2.
Model of the chaperonin cage, a cylindrical box with a characteristic length L, implemented and applied in this study.
Unfolded, unknotted conformations of DndE in a cage with L = 2 nm (left) and L = 3.0 nm (right).
Fig 3.
Thermodynamic properties of investigated knotted (MJ0366, MJ0366_CC, DndE, VirC2) and unknotted (AvtR) proteins.
Results are calculated at the folding temperature Tf, which varies across different confinement sizes. Left column: Heat capacity as a function of temperature for several different sizes of the cage, L. Right column: Free energy profiles as functions of native contacts fraction Q (represented by solid lines) and corresponding knot probability PK(Q) (dashed lines) for different confinement sizes.
Table 1.
Average times between folding-unfolding transitions in different confinements for investigated knotted (MJ0366, MJ036_CC, VirC2, DndE), and unknotted (AvtR) proteins.
Times are given in simulation steps and divided by 106.
Fig 4.
Left: Average times between folding-unfolding transitions as a function of chaperonin box size (L) in logarithmic scale. Right: Median folding and unfolding times for VirC2 in a bulk solvent (dashed lines, magenta and dark blue squares) and in the chaperonin box with L = 2.5 nm (solid lines, red and light blue squares) as a function of temperature. The heat capacity is presented with green lines (dashed for bulk solvent, and solid for confinement).
Fig 5.
Characteristic folding pathway for MJ0366.
The key moment during the folding process is a formation of the β-sheet at the N-terminal. The threading of the C-terminal through the loop is the final event of the process.
Fig 6.
Typical folding pathway for VirC2.
First the C-terminal end is wrapped by the consecutive fragment of the chain. In this way the loop is created, and finally the N-terminal is being threaded through it.
Fig 7.
Probability differences of finding formed native contacts for ensambles with Q equal to 0.55 and 0.5 for VirC2 in the bulk and in the chaperonin with L = 2.5 nm.
Circled groups of contacts are involved in backtracking.
Fig 8.
Difference between average contact maps in the bulk and in the chaperonin cage with L = 2.3 nm for MJ0366_CC for selected values of Q: 0.45, 0.5, 0.55, and 0.6.
Above the diagonal, the structure of the protein is colored to reflect the changes for each amino acid.
Fig 9.
Difference between average contact maps in the bulk and in the chaperonin cage with L = 2.3 nm for MJ0366_CC for selected values of Q: 0.45, 0.5, 0.55, and 0.6.
For bulk data was collected at the highest accessible temperature for the folding process in these conditions, T = 127. Data for folding in confinement were collected at T = 140.5. Above the diagonal, the structure of the protein is colored to reflect the changes for each amino acid.
Fig 10.
Left: Mean asphericity of the native (N), unfolded (U) and at Qmax (QM) ensembles for DndE and AvtR. Right: Mean asphericity of the ensemble representing Qmax, for which F(Q) reaches maximum, as a function of confinement for the studied proteins.