Thermodynamically speaking

In the context of reversible unfolding, protein stability is defined as the difference between the free energies of the unfolded and folded states, ΔG. That is, as long as we can safely talk about a ‘two state’ unfolding process. 

So the greater this difference, the more stable the protein. 

Although it is easy to derive the formula that gives ΔG with respect to temperature (see the curve in the figure below) it is much harder, and not always possible, to experimentally determine the two parameters of the formula that differ for different proteins and determine the exact shape of the curve (for an enlightening discussion on thermodynamic stability see the relevant section of this review or the original work of Nojima et al.).

Typical stability curve of a protein (G. Feller, J. Phys.: Condens. Matter, 2010)

A couple of months ago, there came to light a very interesting work, by C.C. Liu and V.J. LiCata, on the detailed thermodynamic study of the thermal stability of two highly structurally homologous proteins. The thermophilic Taq polymerase and its homologous mesophilic Pol I polymerase from E.Coli. The authors, by decomposing the ΔG curve into its two competing enthalpic and entropic components, show that the increased stability of Taq polymerase is entropic in nature. But, lo and behold, this pair is not the only such case. In fact, the authors use the same analysis on another 17 available pairs of homologous proteins, which are pretty much all the existing published data there are for which this analysis is applicable. In almost all the cases, for the thermophilic homologue the stabilizing enthalpic contribution has to compensate a smaller entropic penalty than for the mesophilic one. Why “penalty”? Well, in all temperatures above the maximal stability temperature, the entropic contribution is unfavorable for the folded state (look at the signs of ΔH and TΔS in the figure above and remember that ΔG=ΔΗ-ΤΔS). 
Now, the entropy of protein folding in general has two major opposite contributions: the favorable hydrophobic effect and the unfavorable loss of conformational entropy that comes with the protein collapse. Thus when thermophiles have to compensate a smaller entropic penalty, they either have a rather compact or structured denatured state that already isolates the hydrophobic groups from the water or … a more flexible folded state. Or both.

Unfolding is a crack!

The atomic force microscopy and other single molecule techniques have inspired a body of theoretical work aimed to detail the unfolding process of proteins.

A related intriguing question is: at which extent the unfolding due to a perturbative external mechanical force overlaps with the temperature (or chemically) induced process? There is not reason to think the two processes to be identical, and in principle a thermostable protein could lacks resistance along the pulling direction. However, it is tempting to follow the unfolding mechanism in different cases (temperature, chemical, and force induced) and see whether or not they can be mapped onto a similar problem-class.

I cite here a very interesting work by de Graff, Shannon, Farrel, Williams and Thorpe appeared in Biophysical Journal in 2011, see the pdf here. They used a simplified, but realistic enough, model to describe force induced unfolding of a protein as the crack propagation in a network. The model describes the protein matrix as a network of interactions between rigid units, and these interactions can break as effect of the applied external force mimicking the pulling of the protein's terminals. The progress of the cracking is followed and successfully compared to the unfolding processes caused by external force and generated by molecular dynamics simulations at the atomistic resolution. The great advantage of the model introduced by Thorpe and coworker is the computational cost, quite low as compared to the cpu-time required to perform atomistic simulations. The dissolution of a connected rigid network induced by progressively scaled interactions has been previously used to model thermal denaturation. In particular some investigations were devoted to thermophilic proteins and their thermal stability, see Rader, PhysBio(2009) and Rodestock&Gohlke, Protein(2010). The authors showed that in the matrix of thermophilic proteins the dissolution process of the network is more difficult to occur as effect of a more robust connectivity of the rigid motifs. The idea to compare temperature and force unfolding path echoes also in other recent papers, more or less innovative, see Srivastava&Granek, PhysRevLett(2013) and Prasanth&Andricioaei, NatureComm(2012).

Unfolding pathway of barnase protein. de Graff et al, Biophy J (2011),  101, 736.