Is protein unfolding the reverse of protein folding? A lattice simulation analysis¹

Abstract

Simulations and experiments that monitor protein unfolding under denaturing conditions are commonly employed to study the mechanism by which a protein folds to its native state in a physiological environment. Due to the differences in conditions and the complexity of the reaction, unfolding is not necessarily the reverse of folding. To assess the relevance of temperature initiated unfolding studies to the folding problem, we compare the folding and unfolding of a 125-residue protein model by Monte Carlo dynamics at two temperatures; the lower one corresponds to the range used in T-jump experiments and the higher one to the range used in unfolding simulations of all-atom models. The trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations. At the lower temperature, the system unfolds through a mandatory intermediate that corresponds to a local free energy minimum. At the higher temperature, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble most closely those that make up the “fast track” of folding. The transition state for unfolding at the lower temperature (above T_m) is determined and is found to be more structured than the transition state for folding below the melting temperature. This shift towards the native state is consistent with the Hammond postulate. The implications for unfolding simulations of higher resolution models and for unfolding experiments of proteins are discussed.

Introduction

The most direct method of determining the mechanism by which a protein folds would be to use an accurate high-resolution model and to follow a series of trajectories from the denatured state to the native structure. Since folding times range from milliseconds to hours, an all-atom representation of a protein in explicit solvent subject to classical dynamics Brooks et al 1983, Brooks et al 1988 would require on the order of 10²years to reach the native state with present computing power Caflisch and Karplus 1994a, Caflisch and Karplus 1994b, Berendsen 1998 (even though simulations of fast events that precede the rate-limiting step, such as helix formation and collapse, are now feasible (Duan & Kollman, 1998)). While simulations can be accelerated by the addition of a potential specifically designed to drive the protein to its native state Brunger et al 1986, Boczko and Brooks 1996, such an approach does not address the problem in an unbiased manner. Further, because little is known about the transition state region, which is likely to involve many configurations, activated dynamics methods, that have been so successful in studying small molecule reactions Chandler 1978, Brooks et al 1988, Truhlar et al 1996, are difficult to apply to the protein folding problem. In fact, delineation of the details of the transition state region, for which substantial experimental data now exist (Fersht, 1995b), remains one of the essential questions to be addressed by computer simulations.

Given the difficulty of the direct approach, researchers have turned to indirect methods of studying the mechanism of protein folding. One such technique is to follow the events that occur in an all-atom simulation of a protein unfolding from the native state at high temperature. Such calculations are possible because the increase in temperature drastically speeds up the reaction and reduces the computational time to a manageable level. Unfolding simulations have the additional benefit that they begin with a single, well-defined state, in comparison to folding simulations in which one must begin with a series of configurations that make up the denatured state.

Published high temperature unfolding simulations include studies of BPTI (Daggett & Levitt, 1992), lysozyme Mark and van Gunsteren 1992, Kazmirski and Daggett 1998, chymotrypsin inhibitor 2 Li and Daggett 1996, Daggett et al 1996, Lazaridis and Karplus 1997, ubiquitin (Alonso & Daggett, 1995), and barnase Caflisch and Karplus 1994a, Caflisch and Karplus 1994b, Caflisch and Karplus 1995, Li and Daggett 1998, Daggett et al 1998. One example is a series of all-atom unfolding simulations of barnase in the presence of explicit solvent molecules at 600 K(Caflisch & Karplus, 1994a). This temperature speeds up the reaction by about six orders of magnitude relative to experimental measurements at 327 K. Although the root-mean-square deviation from the native structure began to increase within the first few picoseconds, the radius of gyration changed only after 30 ps, suggesting that the protein initially underwent a local conformational search to find a pathway for unfolding. Such calculations could provide information about the transition state region and the role of intermediates in the folding reaction, even though identification of the transition state in such simulations is not straightforward (Li & Daggett, 1996).

One reason such simulations are of particular interest at present is that experimental high temperature unfolding is being done on time scales that correspond to those of the simulations. Temperature-jump (T-jump) techniques, in which one heats the protein solution within nanoseconds by irradiating an inert dye, have been applied to ribonuclease A (RNase A) (Phillips et al., 1995) and apomyoglobin Gilmanshin et al 1997a, Gilmanshin et al 1997b. Monitoring the protein with time resolved infrared measurements has provided some information on the role of secondary structure during the early events of unfolding. For example, in the study of RNase A (Phillips et al., 1995), which monitored the β-sheet population by measuring the absorbance at 1633 cm⁻¹, no change was observed until 1 ns after the T-jump from 59.0 °C to 62.5 °C (the melting temperature is T_m=62 °C (Chen & Lord, 1976)). This delay is analogous to that of 30 ps which preceded the increase in the radius of gyration in the barnase simulations (Caflisch & Karplus, 1994a).

Although the results obtained with computational studies of unfolding under denaturing conditions are not inconsistent with those of kinetic folding studies Caflisch and Karplus 1994a, Finkelstein 1997, the available data are insufficient for a definitive comparison. Consequently, it would be very useful to study the folding and unfolding behaviors of a single system by simulations. For this purpose, it is necessary that the model be simple enough that its folding reaction can be simulated in an unbiased manner. The only systems that allow such studies are highly reduced models, in which the residues of the polypeptide are typically represented by single quasiparticles (beads) that interact by a short-range potential of mean force. Although the beads need not be constrained to the vertices of a lattice to observe folding Guo and Thirumalai 1997, Zhou and Karplus 1997, doing so allows a more thorough treatment of the system (for reviews of lattice models, see Karplus and Sali 1995, Shakhnovich 1997, Pande et al 1998).

We have made a detailed analysis of one such system: a 125-residue chain subject to Monte Carlo dynamics on a simple cubic lattice Dinner et al 1996, Dinner et al 1998, Dinner and Karplus 1999. This model is of particular interest because its folding mechanism exhibits many of the complexities observed experimentally for that of lysozyme (Dobson et al., 1998), a well-studied protein that is comparable in length (129 residues). After a fast (<10⁶MC steps) collapse to a disorganized globule, the system makes a relatively slow (∼10⁷-10⁸MC steps) search through the compact states for a specific set of about 30 contacts (non-bonded spatial nearest-neighbors) which make up a stable core that leads to a rapid (∼10⁶MC steps) accumulation of additional structure. Although the chain can fold directly from the core to the native state (“fast track” folding), it often becomes trapped in low-energy, misfolded intermediates with substantial native structure. In these cases, completion of folding requires rearrangement and condensation of non-core residues, which is often slow due to the need to disrupt stable contacts (“slow track” folding). One of the key elements of the mechanism is that, in contrast to smaller models (Šali et al., 1994), specific pathways (each of which involves a rather broad ensemble of structures at any given point) predominate in going from the denatured state to the native state. This means that a comparison of high-temperature unfolding to low-temperature folding can determine whether corresponding pathways are followed in the forward and backward reactions.

Here, we focus primarily on the representative 125-mer sequence for which detailed kinetic and thermodynamic results are available (Dinner & Karplus, 1999). We compare the observed folding trajectories for that sequence with unfolding trajectories calculated at two temperatures. The first temperature (T=1.10T_m) is a little higher than but comparable to temperatures used in T-jump experiments Phillips et al 1995, Gilmanshin et al 1997b and the second (T=1.67 T_m) is comparable to temperatures used in all-atom molecular dynamics simulations of unfolding Caflisch and Karplus 1994a, Caflisch and Karplus 1994b. We monitor both the evolution of overall chain properties and the dissolution of individual contacts (native and non-native). Overall, the trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations (Dinner & Karplus, 1999). Indeed, at T=1.10 T_m, the system unfolds through a mandatory intermediate in which the core (which involves primarily residues 53 to 100) and the last 25 residues are in a native conformation while the first 50 residues are completely disordered. At T=1.67 T_m, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble those that make up the fast track of folding more closely than those that make up the various slow tracks of folding. We discuss the relation of our results to other comparisons of high-temperature unfolding to low-temperature folding. In general, unfolding studies are most likely to provide useful information on the folding of proteins that employ nucleation (core formation) and condensation (sequential growth) mechanisms and lack off-pathway intermediates. If misfolded states contribute, it is likely that they will be missed in high temperature unfolding simulations.