Unfolding Pathway for a Beta Hairpin Fragment of Protein G

Vijay S. Pande and Daniel S. Rokhsar, University of California, Berkeley and Lawrence Berkeley National Laboratory

A typical unfolding trajectory at 400°K demonstrates discrete unfolding steps. Beta-sheet hydrogen bonds (if formed) are shown as sheets, and the hydrophobic core is shown in wireframe with van der Waals radii (TRP red, PHE blue, TYR purple, VAL gray). The time in picoseconds is given in the upper left of each frame.

 

Research Objectives

To study the unfolding and refolding pathway of a beta-hairpin fragment of protein G using all-atom molecular dynamics simulation. While this fragment is small, it possesses several of the qualities ascribed to small proteins: cooperatively formed beta-sheet secondary structure and a hydrophobic core of packed side chains.

Computational Approach

This 16-residue peptide folds rapidly and cooperatively to a conformation with defined secondary structure and a packed hydrophobic cluster of aromatic side chains. Since the beta-hairpin is small, its unfolding can be studied in much more detail than the larger proteins whose high temperature unfolding have been examined previously. Using simulations a few nanoseconds in duration, we studied complete unfolding events at temperatures as low as 400°K, and the initial stages of unfolding at 350° and 370°K (77° and 97°C). The availability of many simulations over a range of temperatures permitted the determination of the complete unfolding pathway as well as an extrapolation of this pathway to refolding conditions.

We then tested the hypothesis that refolding under physiological conditions occurs by the reverse of the high-temperature unfolding mechanism. The computationally long time scale for refolding makes a full simulation at low temperature unfeasible. However, we were able to simulate the refolding of the beta-hairpin peptide from conformations in its transition state ensemble. The critical advance that made this possible is analysis techniques that have been developed in the study of lattice models which allowed us to identify the transition states for the various transitions of the unfolding pathway. Even for slow kinetic processes, the actual passage through the transition state can be quite fast (tens of picoseconds); most of the folding time is spent waiting for the fluctuations to reach the transition state. By directly identifying the transition state, we bypassed this time-consuming part of the simulation.

Accomplishments

At high temperatures, we found that the beta-hairpin unfolds through a series of sudden, discrete conformational changes. These changes occur between states that are identified with the folded state, a pair of partially unfolded kinetic intermediates, and the unfolded state. To study refolding at low temperatures, we performed a series of short simulations starting from the transition states of the discrete transitions determined by the unfolding simulations. These simulations showed that refolding at low temperatures can proceed by reversing the unfolding pathway found at high temperatures.

Significance

The direct simulation of protein folding is a "holy grail" of computational biology. Since straightforward molecular dynamics can typically examine trajectories only tens of nanoseconds in duration, however, the milliseconds needed to fold even small proteins are far too long to simulate. A clever stratagem that allows progress to be made in studying conformational changes in proteins is to instead simulate unfolding, under conditions (high temperature, acid pH, high denaturant) such that the unfolding reaction rate is accelerated into an accessible range. These simulations have yielded insights into the initial stages of unfolding to an expanded conformation, which is assumed to reflect the later stages of refolding. The transition state for this process is in good agreement with experimental determinations of the folding transition state under physiological conditions. Important open questions pertain to the relationship between extremely rapid unfolding at 500°K and the much slower refolding process at physiological temperatures, as well as the underlying physical reason for the surprisingly good agreement between high- and low-temperature transition states.

Publications

V. S. Pande and D. S. Rokhsar, "Folding pathway of a lattice model for proteins," Proceedings of the National Academy of Sciences (in press, 1998).