Thermodynamics of protein folding

[jhirlo]

My textbook’s explanation for spontaneous renaturation of defolded protein is this:

“Although in defolded state protein has grater entropy, greater degree of disorder, it folds into original conformation (lower entropy), and this seems to be in collision with the II law of thermodynamics. But by refolding molecules of water surrounding him increase its own entropy by forming maximum number of hydrogen bonds (they’re squeezing, pushing in hydrophobic regions from protein surface inside of protein, allowing hydrophilic regions to come out to surface to form H-bonds with water), so net change in entropy of solute and protein is than increase of entropy, and process is spontaneous.”

Thing that I disagree in this that by forming hydrogen bonds water is increasing its own entropy, how can this be true ?
By forming maximum number of (or generally forming) hydrogen bonds water increases its order, by organizing own molecules in ordered fashion dictated by hydrogen bonds. Than how can this H-bond forming could be S increasing?

Please help.
Regards.

 

[Bystander]

You are dealing with a textbook written by someone who doesn't know his(her) thermo too well --- THE SECOND LAW: for any spontaneous process, the entropy of the UNIVERSE increases --- PERIOD, end of statement of the second law. The second law places no constraints on the sign of the entropy change observed in the system of interest; it constrains the sum of the entropy changes of the system AND of the surroundings to be greater than zero.

If the system is the protein molecule at the beginning (initial state of the process), the system is the protein molecule at the final state of the process --- the implicit redefinition of the final state system as protein plus water is --- what shall we say? Flaky.

This is where an enormous number of mistakes are made in thermo, the definitions of systems and of surroundings.

 

[jhirlo]

Thank you Bystander, you’ve moved discussion from dead point.
Let’s define parameters of change like this:

Consider observed system: tube with water and protein in it. (+surrounding if needed)
1) It’s on 37 degrees of Celsius (body temperature).
Protein is properly folded hydrophilic regions outside forming H-bonds with water, hydrophobic inside.

2a) We heat up tube to 70 degrees of Celsius, protein defolds to random coil (it’s sad that that how it increases its entropy), while system cools down protein spontaneously refolds to active state (increasing its entropy).


2b) Or even better, we’re introducing no heat, we are at 37C const. We put some denaturizing agent into the tube, denaturize protein to random coil, remove denaturizing agents, and protein spontaneously goes back to active conformation.

We can consult here dG = dH - TdS , and say that this happens only when we have decrease of free energy.
Now in my textbook they say that crucial parameter for this change is distribution of H-bonds between protein and water, and change in entropy resulting it. That’s fishy and an understandable part for me…

 

[Bystander]

Let's take it a step at a time: (that'd be a good user name, "stepatatime") 1) define the system; 2) define an initial state for the system; 3) define a final state for the system.

1) System: protein plus water.

2) Initial state: folded protein "hydrate" at some {T, P, X }_Initial.

3) Final state: unfolded protein plus water at {T, P, X }_Final.

Here's where I, the physical chemist, am going to require that we tighten up the definitions a bit, but first, a couple questions:

a) Do you understand that thermodynamic properties, state functions, etc., are defined only for matter in bulk, or for macroscopic systems? That is, that we do not discuss the entropy change associated with the unfolding of a protein molecule, or the hydration and refolding of that molecule?

b) Do you understand that you are discussing a reversible process? That is, that this is an equilibrium? That there is some concentration of unfolded protein present in the initial, folded, state, and some folded protein remaining in the unfolded state?

c) Do you understand that the word "spontaneous" and it's derivatives are used only for discussion of irreversible processes in the "high and holy" practice of thermodynamics? I realize we're talking through a language barrier here, both literally and figuratively (your language vs. mine, and biochem vs. thermo), so don't take this comment as a personal slam at you.

d) Almost forgot --- what all have you had for chem courses? General, I presume. Any p-chem?

 

[arwelbath]

I've been stuck on problems like this too. Here's how I'm thinking about it at the moment...

For our protein, let's say that we are discussing the free energy difference between the states. Generally we'd think of it as DG = DH - tDS. So for a given transformation of the system, the direction of the reaction is in the direction of the negative free energy change. However, the negative free energy change isn't the same as a negative entropy change - you also have the enthalpy change of the system to think about. It's the combination of both that has to lead to the negative DG.

Making things more complicated still, when you change the temperature of the system (and this leads to some unfolding), you also have a change in the heat capacity of the protein. So then the best way to think about dG is with this modified form of the Gibbs-Helmholtz equation...

dG = dG-T(dH/Tm)+dCp(T-Tm-T*ln(T/Tm))

where Tm is a reference temperature where dG is zero. dCp has been found to correlate with the change in the solvent accessible surface area as the protein unfolds. Basically, enthalpy, entropy and heat cpacity changes as a polypeptide unfolds.