Inversion of the Hydrophobic/Hydrophilic Paradigm Demystifies the Protein Folding and Self-Assembly of Problems

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Kauzmann’s idea was bold and brilliant and had captured the imagination of many scientists. It is not surprising therefore, that the dominance of the HΦO effect has prevailed for over half a century. The fact that HΦO groups are in the interior of the protein, and the fact that the transfer of HΦO molecules from water to an organic liquid is large and negative are undeniable. The former lends credibility to Kauzmann’s model, while the latter provides the large negative Gibbs energy change.

It is not surprising that the usage of the HΦO effect has flourished in explaining many biochemical processes such as protein folding, protein-protein association and molecular recognition. Very few have questioned the validity of Kauzmann’s model for the process of protein folding, or the validity of its explanation based on Frank and Evans’ ideas of iceberg formation. The HΦO paradigm seemed to have been unassailable, and became the central dogma in the biochemical literature ^{[5, 13]}.

3. The Fall of the Hydrophobic (HΦO) Effect and the Rise of the Hydrophilic (HΦI) Effects

The title of this section might seem to most biochemists to be misplaced and overly exaggerated. After no recent textbook even mentions that there are cracks in the HΦO dogma, let alone its “fall.” And what are the HΦI effects? These are unheard of. Everyone had already been convinced that hydrogen bonds (HBs) contribute insignificantly to the stability of the native structure of the protein. Nevertheless, some murmurs of doubts have been heard during the past twenty years.

In 1980, in the preface of my book “Hydrophobic Interactions,” I wrote: ^[13]

“In spite of my researches in this field over almost 10 years, I cannot confirm that there is at present either theoretical or experimental evidence that unequivocally demonstrates the relative importance of the HΦO interactions over other types of interactions in aqueous solutions.”

My doubts were based on lack of evidence in favor of the contention that the HΦO effect is the most important effect in the “driving force” for protein folding. How can one claim that one factor is more important, or most important when one does not have a full inventory of all the factors involved in protein folding? Remember that Kauzmann’s paper was on “some factors in the interpretation of protein denaturation” – not on all factors involved. No one knew what were all the factors especially those that are solvent-induced. The only factor that could have competed with the HΦO effect was the HB, but the HBs were already deemed to be unimportant in aqueous solutions.

Kauzmann’s model of inference from transferring of molecules from water to organic liquid, and the fact that most HΦO groups are found in the interior of the protein were so convincing that the mere expression of doubts could not have rattled the dominance of the HΦO dogma. One needs more than doubts. One needs facts! “Lack of evidence” for an idea cannot be used as evidence against that idea.

This was the main motivation for the examination of the entire question of the solvent-induced effects on the protein folding and protein-protein association that I undertook late in the 1980s ^{[14, 15, 16, 17, 18, 19]}. The results of this examination were stunning; initially to me, then slowly diffusing into the literature.

First, came the realization that the HB-inventory argument was fundamentally faulty ^[17]. Second, Kauzmann’s model, appealing as it was, for over 50 years was found irrelevant to the protein folding process ^{[14, 15, 16, 17, 18, 19]}. Finally, a logical pitfall: The fact that HΦO groups are found in the interior of the protein cannot be used as an argument in favor of the role of the HΦO effect in protein folding.

I shall briefly explain here in qualitative terms each of the abovementioned findings. More can be found in references 4 and 5. The HB-inventory argument was based on the stoichiometric equation (1). The first serious challenge to the HB-inventory argument was expressed in 1990 ^[17]. It was shown that the very writing of the stoichiometric equation in the form (1) is faulty for two reasons:

1. What is lost on the left hand side are not HB energies but solvation Gibbs energies of the HΦI groups. On the other hand, a genuine HB energy is gained on the right side of (1).

2. Whatever the water molecules do when they are released from the solvation sphere of the two HΦI groups is irrelevant to the driving force. These water molecules “flow” from the solvation sphere into the pool of water at constant chemical potential. Therefore, they cannot contribute anything to the driving force. This argument has demolished the foundations on which the HΦO has risen.

Figure 2. (a) Solvation of a non-polar molecule in water. (b) onditional solvation of a non-polar group attached to non-polar backbone. (c) onditional solvation of a non-polar group attached to polar backbone

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Second, the analysis of all the solvent-induced factors revealed that Kauzmann’s model does not feature in the “driving force” for the process of protein folding ^{[15, 16, 17, 18, 19]}. Instead of the Gibbs energy of solvation of a HΦO molecule in water, the conditional solvation Gibbs energy of a HΦO group features in the “driving force.” These Gibbs energies are very different from the Gibbs energies of solvation in water. The difference could be one or two orders of magnitudes. The main reason is that a HΦO group attached to the backbone (BB) of the protein is surrounded by water molecules which are perturbed by the BB. Figure 2b. On the other hand, the solvation of a HΦO molecule is by unperturbed water molecules, Figure 2a. Thus, at this stage not only the basis on which the HΦO model was built upon was demolished, but the HΦO - model itself was now shown to be inadequate ^{[4, 5]}.

It is unfortunate that despite these findings people still propagate the non-evidential “evidence” in favor of the HΦO effect.

In a recent review, Dill et al write: ^[20]

“There is considerable evidence that hydrophobic interactions must play a major role in protein folding. (a) Proteins have hydrophobic cores, implying nonpolar amino acids are driven to be sequestered from water. (b) Model compound studies show 1-2 kcal/mol for transferring a hydrophobic side chain from water into oil-like media , and there are many of them. (c) Proteins are readily denatured in nonpolar solvents.(d) Sequences that are jumbled and retain only their correct hydrophobic and polar patterning fold to their expected native states…, in the absence of efforts to design packing, charges or hydrogen bonding.”

Unfortunately, none of these can be used as evidence in favor of the role of hydrophobic interaction in protein folding. (a) The fact that hydrophobic groups are found in the interior of the protein does not necessarily mean that the hydrophobic interactions are responsible for bringing these groups to the interior of the protein. Such a conclusion is an illusion and cannot be supported by theory. It is similar to the conclusion that the mixing of two ideal gases is the cause of the entropy increase upon mixing, or that the “entropy of mixing” is the “driving force” for the process of mixing ^[21]. Similarly, one cannot say anything about the “driving force” for protein folding merely by watching the hydrophobic groups occupying the interior of the protein. (b) The Gibbs energies of transfer of small model compounds from water to an oil-like media were shown to be irrelevant to the driving force in protein folding ^{[4, 5]}. (c) The fact that proteins are readily denatured in non-polar solvent means that water is important. It says nothing on the relative importance of hydrophobic vis-à-vis hydrophilic effects. (d) The last "evidence" is anything but evidence in favor of hydrophobic effects. It says nothing even on the role of water, certainly nothing about the relative importance of the hydrophobic vis-à-vis the hydrophilic effects.

It is regrettable that these non-evidence appear in the literature almost twenty years after the strong evidence in favor of the HΦI effects was published!

The evidence in favor of the HΦI effects are overwhelming. First, it was shown that direct HB in aqueous solutions is not insignificant, as believed ^[17]. Furthermore, the analysis of the solvent-induced effects on protein folding has also opened the door to a host of new solvent-induced effects that were never considered before. These effects involved HΦI rather than HΦO groups. The most important one, and so far the most studied, was the pairwise HΦI interactions between pairs of HΦI groups at a distance between 4-5Å. For this particular HΦI interaction there is overwhelming evidence that it is far stronger than any of the HΦO effects. The evidence comes from theoretical estimates ^{[4, 5]}, simulations ^{[22, 23]}, and experimental data ^{[4, 5, 24]}. This HΦI effect was estimated to contribute about -12kJ/mol, a far larger contribution compared with the corresponding HΦO effect. It should be noted that the number of pairs of HΦI groups in any protein is much larger than the number of HΦO groups.

The qualitative reason for such a strong HΦI interaction at this particular configuration, is shown in Figure 3 where the two HΦI groups can be bridged by a water molecule. It should be stressed however that this effect is not due to a formation of long-lived HB-bridge, as some have misunderstood. Such a “permanent” bridge could provide two HB energies, i.e. about -48 kJ/mol. The real effect is a mutual solvation of the two HΦI groups. This effect involves HB energy, but also involves probability of finding a water molecule that can form a HB-bridge between the two HΦI groups. The most direct evidence for the existence of such a HΦI effect is the second peak in the radial distribution function of pure liquid water ^[4]. Other experimental evidence comes from the relative solubilities of two isomers of the same molecule, having two HΦI groups at two different distances ^[5]. We have mentioned only one HΦI effect. Other effects involving simultaneous solvation of three or more HΦI groups were found to be even stronger, albeit perhaps less frequent ^[5].

Figure 3. Two HΦI groups at a distance of 25A (a), can be bridged by a water molecule. This is the same distance as the second nearest neighbors in ice (b)

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4. The Problem of Protein Folding and Its Answer

There are several problems that are associated with the process of protein folding. Some aspects of the problem such as the existence of a code that translates from a sequence of amino acids into a 3-D structure, or the existence of a global minimum in the Gibbs energy landscape were inspired by Anfinsen’s thermodynamic hypothesis ^{[25, 26]}. These aspects were discussed in reference 5. Here we shall discuss the question that was raised by Levinthal ^{[27, 28]}and later formulated by the editors of Science ^[29]. Levinthal made a quick estimate that if the protein were to move at random in its configurational space, it would take eons to reach the native 3-D structure. This question was chosen as one of the 125 “big questions” of Science ^{[29, 30, 31]}.

“Can we predict how proteins will fold? Out of near infinitude of possible ways to fold, protein picks one in just tens of microseconds.”

There are essentially two questions in this quotation. One, is the question of prediction of the 3D proteins. In my opinion there is no general answer to this question ^[31]. The second, is the question about the speed of the folding process. A hint to the solution to this question was already provided by Levinthal: ^{[27, 28]}

“We feel that protein folding is speeded and guided by rapid formation of local interactions.” Levinthal was almost right in his speculative answer. He did not specify what are the “local interactions” that “speeded and guided” the protein in its folding pathway. The answer to the question of how and why protein folds in a relatively short time is simple and straightforward: a protein will fold, if it folds, in a short time because at each stage of the folding process strong forces are exerted on the various groups along the protein. The main question is not how and why proteins fold, but rather what the strong forces are that force the protein to fold in a narrow range of pathway? This question could not be answered within the HΦO paradigm, simply because the HΦO effect could not deliver strong forces.

It is ironic that in a review article entitled “Dominant Force in Protein Folding” you cannot find a word on real force, and certainly nothing about dominant forces ^[32]!The situation has radically changed once strong HΦI forces - real forces, the existence of which was not even suspected - were discovered. Recognizing the existence of strong HΦI forces rendered all the speculations about the shape of the Gibbs energy landscape superfluous. One does not even need to mention the Gibbs energy landscape in connection with the problem of protein folding. The general problem of how and why protein folds is now answerable. There remains the question however of the implementation of this general answer to specific proteins. In my opinion this should not pose any insurmountable difficulty. At each initial configuration of the unfolded protein, one can calculate the total forces- both direct and solvent-induced forces exerted on all the groups of protein. The resultants of these forces should “speed and guide” the protein into its folding pathway.

5. The Problem of Protein-Protein Association and Its Answer

In the editorial of Science in 2005, one finds another “big question” in science: ^{[29, 30]}

“How do proteins find their partners?” Protein-protein interactions are at the heart of life. To understand how partners come together in precise orientations in seconds, researchers need to know more about the cell’s biochemistry and structural organization.

Again, this question could not be answered within the HΦO paradigm. It was therefore deemed to be one of the “big questions” of Science. Indeed, the process of protein-protein association to form a stable and long lived dimer (or higher aggregate) is not less of a mystery than the process of protein folding ^[5].

In forming a stable dimer, one monomer loses its translational entropy. This is true for any association process. In most cases of dimerization a chemical bond is formed between the monomers. The energy of the bonds compensates for the loss of translational entropy making the dimerization process favorable. In protein association there is no covalent bond between the monomers. Hence the mystery: What is the factor that compensates for the loss of translational entropy? In some textbooks, you might find the answer that the HΦO effect is the dominant factor in this process. However, a careful examination of the process shows that this factor is minor and cannot account for the stability of the dimer (or of any other aggregate for that matter) ^[5]. On the other hand, the inclusion of the HΦI effect shows how an extremely unlikely process of dimerization turns into an extremely likely process. The details of the HΦI contribution to the process of association may be found in reference 5. Here, we provide only a qualitative description of the basic idea.

Consider two globular proteins at contact. Clearly, the direct interaction between the two monomers is minor. The Gibbs energy for this process will be large and positive. Next, we take into account the solvent-induced effect. We start with completely HΦO monomers, i.e. proteins on the surface of which consists of HΦO group. We find that in this case the Gibbs energy of the process of dimerization remains large and positive. This means an unfavorable dimerization process.

Next, we gradually increase the mole fraction of HΦI groups on the surface of the protein. Figure 4 shows the dependence of the Gibbs energy of dimerization as a function of the radius of the protein for several mole fractions of the HΦI groups. We see that once the mole fraction of the HΦI group is larger than about 0.4 or 0.6 the curve turns into a negative territory, i.e. making the process of dimerization favorable. The larger the mole fraction x₀ the more negative the Gibbs energy change.

Figure 4. The dependence of the standard Gibbs energy of dimerization of two globular proteins as a function of the radius of the protein, for different values of the mole fraction of the hydrophilic groups

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Figure 5. Water-bridges connecting two globular proteins

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