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I am studying Differential Scanning Calorimetry (DSC) and am not quite understanding why most proteins have a bell shape when the heat capacity is plotted against the temperature.

Also, I would appreciate if you could provide good sources on this topic (books, articles, etc).

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This is just a guess, but it's probably because the heat measurement is actually measuring the sum of many, many molecules reactions. It is a fact of mathematics, rather than natural science, that forces such phenomena to approximately follow bell curves (i.e., Gaussian functions). Basically, the central limit theorem states that if you have many instances of the same (random) variables and average them together, then the result will look like a bell curve. Here, the local thermodynamic change induced by a single individual protein molecule, as a function of the temperature, is presumably that random variable, since the thermodynamic behaviour of each protein is roughly similarly distributed. The randomness comes from the essentially chaotic random movements of the molecules.

See here or here for more.

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    $\begingroup$ I guess the symmetry can be explained by the cumulative states of the ensemble. However, I can't think of a no reason for this peak to be Gaussian. People often confuse most symmetric shapes (including the bell shape) as Gaussian. $\endgroup$
    – WYSIWYG
    Mar 26 '19 at 12:56
  • $\begingroup$ @WYSIWYG True, the CLT is not always appropriate. I am not familiar enough withe subject to comment definitively, but from looking up a few curves, they are decidedly non-Gaussian far from the peak point. I had merely guessed that each molecule's "peak" (denaturation/unfolding) could be viewed as an RV (so the solution is an IID sample), and the observation was composed of the avg over molecules. This formulation, of course, only says that there should be near-Gaussianity close to that point! But even this may well be physically inaccurate. Hopefully someone more knowledgeable can jump in. :) $\endgroup$ Mar 26 '19 at 16:41

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