Why does minimization of free energy result into an almost uniform distribution of protein foldings?

Question

I have just found out that proteins (at least in some cases) are folded into their functional conformation (i.e. their functional folding), through thermal fluctuations, and that this conformation minimizes free energy. i.e. that the reason that a protein has a certain conformation, is because this conformation minimizes free energy.

I am surprised by this, because if all proteins of a certain type (sequence of amino acids) have the same conformation, this actually minimizes entropy. I would have expected that if we would just leave the protein folding to random fluctuation, it would tend towards a reasonably high-entropy distribution of conformation, i.e. lots of different conformations for individual protein molecules of the same type.

What explains this?

Answer 1

You are forgetting about the aqueous environment the protein is folding in. Typically proteins fold in such a way that hydrophobic sections of the protein are hidden from the aqueous environment and hydrophilic sections are not. This means that even though the entropy decreases in just the confirmation of the protein, the entropy of the aqueous environment increases much more. The environment has many more accessible orientations when the hydrophobic sections are hidden and the hydrophilic sections are exposed, and thus entropy overall still increases.

A recent SciShow video covers this exact idea in the context of protein folding as well as other biological scenarios.

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A somewhat more quantitative picture is given here

In biology, entropy is very often the driving force, for instance for the burial of hydrophobic protein domains. Imagine a water molecule in a tetrahedron. The tetrahedron has four corners, and the water has two hydrogens, so you can place the molecule in $4\text{ choose }2 = 6$ orientations. If you add a nonpolar group of a neighboring molecule at one corner of the tetrahedron, only three of the six states remain favorable (by still allowing hydrogen bonding). So $\Delta S_\text{hydrophobic} = k_b\ln(3) - k_b\ln(6) < 0$, meaning that entropy has decreased.

An incorrect and simplistic view of protein folding is as follows. An unfolded protein has high configurational entropy but also high enthalpy because it has few stabilizing interactions. A folded protein has far less entropy, but also far less enthalpy. There is a trade-off between $H$ and $S$ here. Note that because $\Delta G = \Delta H - T\Delta S$, increased temperature weights the $S$ term more heavily, meaning that higher temperature favors unfolding.

That entire explanation only considers the energy of the protein and not that of the solvent. In fact, hydrophobic domains of a protein constrain the possible configurations of surrounding water (see explanation above), and so their burial upon folding increases the water’s entropy. Moreover, it turns out that the hydrogen bonding of polar residues and the backbone is satisfied both in an unfolded state (by water) and in a folded state (by each other). Therefore enthalpy is “zero sum,” and protein folding is driven almost entirely by entropy.

A much more detailed description can be found here, although I will say I have only skimmed this; I have not read through it carefully.

Answer 2

An important factor here is that protein functioning requires specific conformation. If it misfolds, then, at best, it will be disfunctional, at worst it may result in harmful effects for the cell (indeed, protein misfolding is the cause of some serious illnesses). Note also, that proteins fold into the required configuration only under specific normal conditions - temperature, pressure, acidity, etc.

Proteins that we observe nowadays have evolved over millions of years to be functional - in other words, all the proteins that had a high risk of misfolding, resulted in the extinction of the species that possessed these proteins. This is why there are only about a thousand of known functional protein configurations, despite millions of different protein sequences.

It is not entirely true that a protein folds in one lowest energy configuration - there is plenty of evidence that it explores the phase space around this configuration.

There is nothing wrong with the fact that the entropy is not maximized, since we are dealing with a non-equilibrium situation - called life. A cell can be thought of as a heat engine, which obtaines energy from one reservoir in the form of sugars, etc., uses this energy to perform useful work - constructing proteins and other molecules, and dumps the unused energy into the environment. Thus, in some cases proteins are chaperoned by other molecules to a specific configuration - they are not guaranteed to adopt in a lab the same configuration that they adopt in a cell.

A useful introductory text in protein folding is Kerson Huang's short book.

Answer 3

A system undergoing thermal fluctuations implies that internal energy, volume, or particles numbers are being exchanged freely in and out of the system of interest - for example by fixing an intensive variable such as T, P, or chemical potential. Systems held at constant temperature (for example a large reservoir or heat bath surrounding the system of interest) will not tend toward states of maximum entropy. They tend toward states of minimum free energy. The Helmholtz free energy F = U - TS is a balance of internal energy and entropy, thus to minimize Helmholtz free energy, the system will tend towards both high entropy and low energy depending on the temperature.

One can say, for example, the conditions under which two residues in your protein will form dimers (a low entropy state relative to monomers) by computing the free energies of both the undimerized and dimerized states. If the interaction energy of the dimerized state is such that it overcomes the penalty of reduced entropy, then a higher temperature is needed to dissociate them. Such a system will be dominated by dimers at low temperatures and by monomers at high temperatures. If we had only maximized the entropy, we would conclude that dimers should never form.

If the combined system (system plus heat bath) is completely isolated, then its equilibrium will indeed be a state of maximum entropy of the combined system - but not necessarily an isolated part of it. So in general it is easier to think in terms of free energies rather than entropy maximization in typical laboratory conditions.