Energy landscape and multiroute folding of topologically complex proteins adenylate kinase and 2ouf-knot

Abstract

While fast folding of small proteins has been relatively well characterized by experiments and theories, much less is known for slow folding of larger proteins, for which recent experiments suggested quite complex and rich folding behaviors. Here, we address how the energy landscape theory can be applied to these slow folding reactions. Combining the perfect-funnel approximation with a multiscale method, we first extended our previous atomic-interaction based coarse grained (AICG) model to take into account local flexibility of protein molecules. Using this model, we then investigated the energy landscapes and folding routes of two proteins with complex topologies: a multidomain protein adenylate kinase (AKE) and a knotted protein 2ouf-knot. In the AKE folding, consistent with experimental results, the kinetic free energy surface showed several substates between the fully unfolded and native states. We characterized the structural features of these substates and transitions among them, finding temperature-dependent multiroute folding. For protein 2ouf-knot, we found that the improved atomic-interaction based coarse-grained model can spontaneously tie a knot and fold the protein with a probability up to 96%. The computed folding rate of the knotted protein was much slower than that of its unknotted counterpart, in agreement with experimental findings. Similar to the AKE case, the 2ouf-knot folding exhibited several substates and transitions among them. Interestingly, we found a dead-end substate that lacks the knot, thus suggesting backtracking mechanisms.

Fig. 1.

Free energy surfaces and a representative trajectory of the folding of AKE. (A) Crystal structure of the AKE [Protein Data Bank (PDB): 4ake]. (B) Free energy profiles along Q_tot at temperatures T = 0.98T_F, 0.99T_F, 1.00T_F, 1.01T_F, and 1.02T_F. (C) A representative folding trajectory monitored by Q_tot, (black), Q_LID (gray), Q_NMP (red), and Q_CORE (green). (D) Two-dimensional kinetic free energy landscape on the reaction coordinates Q_tot and Q_CORE at 0.90T_F, and its one-dimensional projections. The seven substates and completely unfolded (U) and native states (N) are labeled. The substate 1 may correspond to the denatured state (D).

Fig. 2.

Folding routes and structural features of the substates of AKE. (A) Folding routes and residue-resolved contact scores of every substate at T = 0.90T_F. Color code: red, unstructured; blue: fully structured. The five most probable folding routes that reach the native state are represented by colored arrows with the line widths representing the abundance of each folding route. Different colors represent different folding routes. (B, C) Same as A but at T = 0.92T_F (B) and 0.94T_F (C) with the substates represented by circled numbers.

Fig. 3.

Folding of a designed knotted protein 2ouf-knot and its unknotted counterpart 2ouf-ds. (A, B). Crystal structures of 2ouf-knot (PDB: 3 mlg) (A) and 2ouf-ds (PDB: 3mli) (B). The eight helices are labeled by H1, H2, …, H8, and the loop is labeled by L1. Two cysteines forming the disulfide bond in 2ouf-ds are explicitly shown. (C, D) Time courses of the Q score of the entire protein for the knotted protein (C) and the unknotted protein (D) at the folding temperature T = T_F. (E) One-dimensional free energy profiles for the knotted (solid line) and unknotted (dashed line) proteins at T = 0.98T_F, 1.00T_F, and 1.02T_F. (F) The ratios of the successful folding with four different models when started from fully unfolded structures.

Fig. 4.

Two-dimensional free energy surfaces of knotted (A, C) and unknotted (B, D) proteins on the reaction coordinates Q_tot and Q_H1–H4 (A, B) and on coordinates Q_tot and Q_H4–H6 (C, D) at T_F. The unit of the free energy is k_BT.

Fig. 5.

Results of kinetic simulations for the knotted protein. (A, B) Two representative folding trajectories monitored by the Q scores of the entire protein (black), and the number of native contacts between the H1 and H4 (red), H2 and L1 (yellow), H2 and H5 (green), H2 and H6 (blue), H2 and H8 (cyan), and H4 and H6 (purple). Note that the two trajectories have different time scales. The knot formed by concerted threading mechanism (A) or by slipknot intermediate mechanism (B). (C) Two-dimensional kinetic free energy surface at T = 0.90T_F on the reaction coordinates Q_tot and rmsd and its one-dimensional projections. The six substates are labeled by numbers.

Fig. 6.

Folding routes and structural features of the substates of the knotted protein, 2ouf-knot.