Characterization of protein-folding pathways by reduced-space modeling

Abstract

Ab initio simulations of the folding pathways are currently limited to very small proteins. For larger proteins, some approximations or simplifications in protein models need to be introduced. Protein folding and unfolding are among the basic processes in the cell and are very difficult to characterize in detail by experiment or simulation. Chymotrypsin inhibitor 2 (CI2) and barnase are probably the best characterized experimentally in this respect. For these model systems, initial folding stages were simulated by using CA-CB-side chain (CABS), a reduced-space protein-modeling tool. CABS employs knowledge-based potentials that proved to be very successful in protein structure prediction. With the use of isothermal Monte Carlo (MC) dynamics, initiation sites with a residual structure and weak tertiary interactions were identified. Such structures are essential for the initiation of the folding process through a sequential reduction of the protein conformational space, overcoming the Levinthal paradox in this manner. Furthermore, nucleation sites that initiate a tertiary interactions network were located. The MC simulations correspond perfectly to the results of experimental and theoretical research and bring insights into CI2 folding mechanism: unambiguous sequence of folding events was reported as well as cooperative substructures compatible with those obtained in recent molecular dynamics unfolding studies. The correspondence between the simulation and experiment shows that knowledge-based potentials are not only useful in protein structure predictions but are also capable of reproducing the folding pathways. Thus, the results of this work significantly extend the applicability range of reduced models in the theoretical study of proteins.

Fig. 1.

CABS energy (E) and its standard deviation (E_sd) as a function of T for barnase. Each point represents a single isothermal simulation. The transition temperature (Tt = 2,025) is identified by the steep drop of the energy and the peak of the heat capacity. Tt cannot be strictly identified with the TS. Sometimes, as for CI2, conformations observed at Tt may be relatively unstructured, with some features of a molten globule state. See also Figs. 2 and 3b.

Fig. 2.

Acquisition of structure elements in side-chain contact maps from simulations of barnase (a) and CI2 (b) at various temperatures: highly denaturing (hds), denaturing (ds), just before Tt, and at Tt. Native contact maps are provided for reference. For CI2, additional simulations below Tt (T = 1.6) are presented. The colors indicate the frequency of contacts. Short-range contacts (up to i, i+2) are omitted for clarity. (a) At T = 2.7, the most frequently appearing nonhelical turn (94, 97) is marked. Circled areas indicate α1 helix and interactions pattern of β3–β4 with the rest of the chain. (b) Cooperative substructures are circled in blue, interactions A16–L49 and A16–A58 for simulations at T = 1.6 are marked in red, and interactions of I20 with V47 and L49 are in gray.

Fig. 3.

Folding pathways of barnase (a) and CI2 (b), as illustrated by snapshots from the simulation at different temperatures (see Fig. 2) and experimentally derived native (N) structures (Protein Data Bank ID codes: 1BNR and 2CI2, respectively). (a) Highly denaturing (hds) with residual α1 helix structure and β3–β4 turn (side chains W94 and Y97 marked with red sticks). A representative hydrophobic cluster is shown with the most frequently contacting side chains marked with lines (ds) and an example of a distorted structure at Tt, with a relatively loose, planar central part of the β sheet interacting with the helix. (b) Highly denaturing with residual α helix structure. The most nucleating area at Tt is β3–β4. Shown are the first stage of docking of the α helix to β3–β4 (I20 and V47 marked with yellow sticks, L49 in red), the conformation with properly ordered β3–β4 and β5 strands before the formation of the N-terminal strands (nucleus residues A16, L49, and A58 marked with red sticks, I57 with its side chain pointing opposite to the helix in dark gray), and the best-formed structure (at T = 1.6). Coordinate root mean square deviation, 3.8 Å.

Fig. 4.

Location of the main nucleation site of barnase at Tt. Shown is a map of distances between C^α displayed above the diagonal; color indicates average values in angstroms (color legend on the Left). The map shows close contacts of β3–β4 strands with the majority of the protein. Standard deviations of the C^α distances are in angstroms (color legend on the Right) are presented below the diagonal. The map shows that the α1 helix (7–17) and β3 (87–91)–β4 (96–99) form the most stable tertiary area. The main nucleation site is marked with the white circles.