On the thermodynamic hypothesis of protein folding (protein evolutionylattice modelsyfolding simulationyfolding kinetics)

The validity of the thermodynamic hypothesis of protein folding was explored by simulating the evolution of protein sequences. Simple models of lattice proteins were allowed to evolve by random point mutations subject to the constraint that they fold into a predetermined native structure with a Monte Carlo folding algorithm. We employed a simple analytical approach to compute the probability of violation of the thermodynamic hypothesis as a function of the size of the protein, the fraction of the total number of possible conformations which are kinetically accessible, and the roughness of the free-energy landscape. It was found that even if the folding is under kinetic control, the sequence will evolve so that the native state is most often the state of minimum free energy. Understanding how proteins fold not only is one of the most interesting theoretical problems in molecular biophysics but also has far-reaching medical and biotechnological consequences. Levinthal pointed out that it is impossible for an unfolded protein to find the native state by randomly searching through the entire space of possible conformations (1). This led him to postulate that a protein must follow a specific path that guides it to the native state, and therefore folding must be under kinetic control. According to him, ‘‘If the final folded state turned out to be the one of lowest configurational energy, it would be a consequence of biological evolution and not of physical chemistry’’ (2). In contrast, Anfinsen concluded from the results of his numerous denaturation–renaturation experiments that the native state of the protein is indeed the global minimum of free energy, a conjecture that he called the thermodynamic hypothesis of protein folding (3). The debate between these two viewpoints has continued, with numerous experimentalists and theoreticians investigating whether proteins reach their global energy minimum in a pathway-independent manner under thermodynamic control, or whether they follow a specific pathway to a possibly local minimum under kinetic control. Experiments have suggested that some small monodomain proteins obey the thermodynamic hypothesis (4, 5). There are also examples of proteins where the active state is not the thermodynamically most stable state. For instance, the plasminogen activator inhibitor (PAI-1) active conformation is metastable, and the protein takes a more stable inactive conformation within hours (6). Similar observations have been made with other members of the serpin family. Protein misfolding, as is the case in many diseases such as Alzheimer’s disease, Creutzfeldt–Jakob disease, and bovine spongiform encephalopathy, have been attributed to kinetic traps or folding to an alternate state of lower energy (7). Similarly, it has been possible to modify proteins so that they are no longer able to fold, although the stability of the native state is unaltered (8, 9). On the theoretical side, Thirumalai used molecular dynamics simulations to support his hypothesis that proteins fold into a metastable state (10). Shakhnovich and co-workers questioned whether a protein could consistently find the same native state by using this mechanism (11), and they proposed that a sufficiently large ‘‘energy gap’’ separating the native state from others was a necessary and sufficient condition for rapid folding (12), consistent with the results of simple models based on spin-glass theory (13, 14). Such an energy gap would necessarily imply the thermodynamic hypothesis. In other work, Shakhnovich showed that lattice proteins under strong evolutionary pressure to fold as quickly as possible evolve so that the native state is a deep and global minimum (15). On the other hand, proteins have not evolved to fold at the maximum possible rate. In addition, in lattice models almost the entire conformation space is kinetically accessible, so the absence of other deeper minima is not surprising. Onuchic, Wolynes, and Dill and their co-workers postulated that the distinguishing characteristic of foldable proteins is the existence of a ‘‘folding funnel’’ that directs the folding protein into the native state without the need for a definite pathway (16–18). This approach leaves open the possibility of kinetically inaccessible lower-energy states outside of the folding funnel. More elaborate theoretical models have been developed that have further explored the relationship between the free-energy landscape and the folding kinetics, including the role of traps and intermediates in the folding process (19–21). In this paper we attempt to address the challenge posed by Levinthal, and investigate whether the thermodynamic hypothesis could result through the process of protein evolution. During evolution, protein sequences undergo random mutations. If the mutation does not interfere with the folding and function of the protein, it is possible for this mutation to be accepted and fixed in the population. Mutations that destabilize the native state are likely to interfere with successful folding, and thus will have a low acceptance rate. Conversely, mutations that destabilize alternative deep minima are more likely to be accepted. With evolutionary time, energy minima representing nonnative states are likely to become higher in energy than the native state, so that the thermodynamic hypothesis becomes fulfilled. This can occur even if the folding is under kinetic control. To test this hypothesis, we performed simulations of protein evolution by using simple lattice model proteins. We first designed protein sequences that fold under kinetic control to a native state different from the ground state of lowest energy. We then allowed the protein to evolve by random mutations. Mutations were accepted only if the protein still folded into the original native conformation. At each generation we calculated the energies of the native state, the initially designed ground state, and the current ground state of the sequence. As The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked ‘‘advertisement’’ in accordance with 18 U.S.C. §1734 solely to indicate this fact. © 1998 by The National Academy of Sciences 0027-8424y98y955545-5$2.00y0 PNAS is available online at http:yywww.pnas.org. This paper was submitted directly (Track II) to the Proceedings office. ‡To whom reprint requests should be addressed. e-mail: richardg@ umich.edu.