What Drives Protein Folding Despite Entropic Barriers?

[knulp]

I have a question about protein folding. I have heard that there is a free energy barrier to overcome in going from the unfolded (ensemble) to folded states, and that this barrier is largely entropic -- i.e., as the (idealized, general) protein starts to fold, it loses more in entropy than it gains (loses) in enthalpy. If so, then why does the protein take these steps (of going from the unfolded to the transition state) spontaneously in the first place?

 

[chemisttree]

Are you familiar with chaperone proteins? These proteins are implicated in the folding mechanism of nascent unfolded protein segments. It may require energy to correctly fold a protein in the cytosol... it may not be merely a thermodynamic inevitability.
http://www.jbc.org/cgi/content/abstract/265/27/16324

The chaperones GroES and GroEL require 14 ATP molecules to complete a folding of a protein.
http://www.wiley.com/legacy/college/boyer/0470003790/animations/protein_folding/protein_folding.swf

 

[knulp]

Sure, but I'm really talking about those (many) proteins that don't seem to require chaperones.

Also, I'll just modify what I first wrote -- the nature of the barrier probably varies from protein to protein, but I still think that it's usually an entropy-dominated effect. The conformational entropy of the protein is lost more quickly than enthalpic gains (enthalpy losses) are made, up to the transition state...

 

[Mike H]

Disclaimer: I do not work in the area of protein folding. I do not keep up with the literature on the latest experiments and simulations. I've ended up in the midst of some heated discussions about this field, which I thought were vaguely silly, that I would rather have not been involved in as they were a waste of perfectly good oxygen.

I want to make sure that I'm understanding you correctly. You want to know how a thermodynamically favorable process (a protein folding to its native state) occurs despite an activation barrier. In this case, welcome to the club. Everyone (metaphorically) wants to understand how protein folding works and its mechanisms and kinetics. Sadly, completely general answers applicable to every possibility will have to wait. I wouldn't hold my breath though.

I did manage to dig up a review I remember reading on the topic (it's not quite a decade old now). Some choice quotes...

Folding of a protein must overcome the thermodynamically unfavourable loss of
conformational entropy associated with the dynamic heterogeneity of the conformationally
disordered polypeptide in the unfolded state. Various estimates of this entropy have been
made, both from theoretical considerations of the statistics of random coil polypeptides and
extracted from experimental data (Schellman, 1955; Privalov, 1979; Brooks et al. 1988).
Values range from 15 - 25 J K-1 mol-1 per residue arising from backbone conformational
freedom (φ-ψ rotations, etc.), with additional contributions arising from restriction in side
chain conformational mobility (Doig & Sternberg, 1995). This corresponds to a free energy
(T.ΔS) of order 6 kJ mol-1 or more per residue that must be overcome by a net negative
contribution from changes in interactions between protein and solvent groups, either
separately or collectively, in the folding process.

Perhaps, too, we are asking rather too much at present when attempting detailed molecular interpretation of the empirical thermodynamic data. Even much simpler systems defy such analysis. The melting of a simple organic solid, for example, is not understood in the same detail that we seem to be demanding for protein unfolding.

Why proteins fold is still a bit of a mystery. That is, the opposing thermodynamic forces are so delicately balanced that it is difficult to decide which, if any, are predominant - and indeed the balance may be different in different proteins. Nevertheless, the more we get into this intriguing problem the more we learn about the nature of biomolecular interactions and how they have been fine tuned during evolution to meet biological needs. Chris Anfinsen himself was often pessimistic about the protein folding problem, expressing it this way: that if there are N proteins in the entire world, then by the time we have solved the structure of (N-1) of them perhaps (and only perhaps!) might we accurately predict the structure of the Nth. We still have some way to go.

-- Alan Cooper (1999) "Thermodynamics of Protein Folding and Stability." Protein: A Comprehensive Treatise Volume 2, pp. 217 - 270. Series Editor: Geoffrey Allen. Publisher: JAI Press Inc.

Now, I haven't rigorously gone back through the paper to see how well every point Cooper makes holds up at the current moment (nor am I going to - but I'll be happy to send you an Adobe Acrobat version of the paper if you'd like to do so), but the spirit of these quotes is still dead-on, I'd say.

 

[Ygggdrasil]

I'll also repeat Mike's disclaimer that I am not an expert on protein folding. My only qualification is having read a few papers and the following review that I will share with you (Shakhnovich E. Protein Folding Thermodynamics and Dynamics: Where Physics, Chemistry, and Biology Meet. Chem. Rev. 2006 May 10;106(5):1559-1588. doi:10.1021/cr040425u).

One point that the author makes in the review is that protein folding can be thought of like other disorder-order transitions found in nature: as a phase transition. In many phase transitions (e.g. the formation of ice), the barrier is nucleation, the formation of a minimal fragment of the ordered phase. Following Mike's lead, I'll pull a few quotes from the review:

With regard to folding kinetics, an important theoretical discovery of a nucleation mechanism via formation of a specific folding nucleus⁹⁸ was made using coarse-grained-lattice-models. As defined in ref 98, a nucleus is a minimal folded fragment that results in inevitable subsequent unidirectional downhill descent to the native conformation. Such a defined nucleus was termed "postcritical" in ref 98 to emphasize that no recrossing back to the unfolded basin occurs after its formation. [. . .] The specificity of the nucleus means that a well-defined obligatory small fragment of the structure needs to be formed in order to guarantee fast decent to the native state. This conclusion was reached in ref 98 based on the analysis of folding trajectories, i.e., the search for the invariant minimal set of contacts whose appearance preceded subsequent fast folding. This way, a putative nucleus was identified. Then control simulations were run to make sure that simulations starting from conformations with a preformed nucleus indeed rapidly descended to the native state without recrossing to the unfolded basin, i.e., that formation of the nucleus guaranteed subsequent rapid downhill folding.

(ref 98. Abkevich, V. I.; Gutin, A. M.; Shakhnovich, E. I. Biochemistry 1994, 33, 10026)

Based on this idea of nucleation, the author proposes to consider protein folding as a phase transition rather than as a "chemical reaction" with a free energy barrier:

While the chemical reaction analogy organically focuses on the transition states for the folding reaction, the key in the phase transition analogy is also the transition state, but with its emphasis on entropy, it focuses on the TSE, i.e., the ensemble of conformations that is defined dynamically: as having probability pfold = 1/2 to fold and 1/2 to unfold.⁹⁹ The advantage of the "phase transition" analogy is that it gets physics right; that is, from the beginning it recognizes the crucial role of entropy, along with energy, in determining the kinetics mechanism. The difficulty is that there is no universal theory of kinetics of first-order phase transitions and many aspects of it are very system-dependent so that exploiting this analogy does not bring us automatically to a satisfactory theory of folding kinetics.

The author concludes the section by writing:

In summary, while the debate of what is the best approach to theoretically describe protein folding kinetics is ongoing, it is this author's opinion that a "physical" approach based on the nucleation scenario within the phase transition analogy is more physically sound than a "chemical" approach motivated by the "energy landscape" picture of simple chemical reactions. While the latter certainly claimed some success in quantitatively reproducing folding rates, failure to get it qualitatively right (e.g. incorrect chain length scaling) perhaps diminishes the success of quantitative agreements. However, in all fairness, a fully satisfactory folding kinetics theory is a matter of the future, not the past, and we can only guess its form and source of inspiration.

So, knulp's question is still very much an open question in the field of protein folding.

 

[knulp]

Okay. My question was pretty vaguely stated but I meant it to be pretty general, and I think I've become a little more comfortable with the idea.

The question was, for the protein folding processes that involve a free energy barrier, how do the proteins get over the energy barrier, if it's unfavorable to do so?

I guess the thing is that despite the barrier, it's generally really only a matter of time before the protein overcomes the barrier just by virtue of random events -- and the higher the barrier, the longer it generally takes.

The protein might diffuse into a less probable state of lower entropy, thus increasing its free energy -- or the noncovalent bonds between different parts of the protein might weaken on the whole, giving higher potential energy or enthalpy (and free energy)...

Thanks for your replies.. I think that some of the thinking has changed a bit since the time those papers you cited were written. Nucleation is now more usually thought of as a process that can start in various different parts of the polypeptide, rather than being something that has to happen in one way (in one region of the polypeptide, for instance). And I don't know what the consensus view on protein folding theory prospects might be, but I think Anfinsen sounded overly and unreasonably pessimistic (only after solving n-1 proteins experimentally can we predict the structure of the nth protein, with n being the total number of proteins in the universe? He might have been a pioneer, but come on!).

 

[Mike H]

In the review by Shakhnovich that Ygggdrasil quoted, Shakhnovich mentions at the end of the paper:

In a certain sense, such atomic-level simulations will represent a “final solution” of the problem of the protein folding mechanism. However, protein folding has been an active field for more than 30 years, and probably all conceivable mechanisms have been proposed in the literature either as pure speculations or as insights from coarse-grained models. In this sense, “the final solution” of the problem of the protein folding mechanism will most likely look like a multiple-choice problem rather than an “essay”-like solution presenting an entirely novel mechanism that nobody thought of in the past. Most likely, the “final solution” will combine elements of many mechanisms that researchers observed in simplified models in more pure forms, so that in a sense the best “multiple choice” answer will sound like “all of the above”. Nevertheless, we are bound to witness decisive progress in studies of protein folding in the coming years.

I take the opinion that the above is a pretty reasonable answer - while you might be prepare a set of all possible mechanistic elements that are responsible for protein folding, the mix of elements and each one's contribution to the process for that particular protein or protein family is going to vary.

Even for something that is modeled as a two-state (or nearly so) equilibrium process, the kinetics don't have to be that simple. So having multiple contributions crop up as the protein folds makes a certain intuitive sense in that regard, such that it just doesn't have to be one factor. The possibility that the internal environment of the cell might also be a factor, from viscosity effects to its heterogeneity. I've skimmed across mentions of where dewetting can, in principle, be a major contribution to facilitating folding processes as well (don't have the citation on me, but I think it was in PNAS last year).

So, for example, if someone told me that protein A had a hydrophobic collapse at one end of the polypeptide chain that served as a nucleation site for the rest of the protein, and spontaneous formation of secondary structure elsewhere that collided where dewetting then occurred, followed by formation of a disulfide bridge which restricted a mobile linker region which initiated the collided secondary structure to wrap around the nucleation site...it sounds perfectly reasonable. Maybe not as straightforward as some may like, but such it goes.

I actually thought that sentiment of Anfinsen's was both funny and true. After all, there's a vague sense that we can usually trust macromolecular structures (after all, it's our quantitatively and physics-inclined colleagues doing crystallography and NMR doing that work) as the "native" structure. When you hear about NMR spectroscopists playing fast and loose with the sample conditions so as to minimize linewidth (without much concern about its reasonableness as a faux-biological environment) and how crystal structures are frequently done under cryogenic conditions...well, anyway.

(FYI, I'm an NMR type who has fiddled around with crystallography. Some honest self-reflection never hurt anyone, I figure...)