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.

Stay flexible, Stay stable...

For some time thermophilic proteins have been considered more rigid than their mesophilic homologues. The "rigidity paradigm" was introduce to explain both the extreme stability of thermophiles as well as their lack of activity at ambient conditions. According to this view functionality is then recovered at the high optimal growth temperature because of the activation of the protein flexibility. Experimentally, one of the strongest support to this "corresponding states" picture comes from H/D exchange experiments, see this beautiful comment from R. Jaenicke in PNAS(2000). However, recent works using the H/D exchange, Neutron Scattering and NMR techniques have questioned the paradigm. Inspired by this querelle we have used extensive MD simulations to play with the concept for a model system, a pair of homologous G-domains of different stability content. The paper is just out in JPCB(2013). Quite surprisingly for our system we see that the hyperthermophilic protein show comparable and even enhanced flexibility than the mesophilic less stable variant. The more intriguing feature pops up when the global flexibility is considered. The conformational spaces sampled by the proteins were projected on a reduced network of linked kinetic separated states; and the hyperthermophiles is systematically characterised by a larger number of conformational substates! This flexibility (conformational entropy) is proposed to stabilise the protein by broadening the stability curve and consequently raising the melting temperature. I will get back on this........

Graphical Abstract, JPCB (2013), 117 (44), pp 13775–13785. 

Ideal proteins?

How do proteins form or maintain a unique fold, stable and biologically preferred when at the same time the unfolded or misfolded states are the vast majority of the possible conformations? We know that the information of the three dimensional structure of a protein is encoded in its amino acid sequence (Anfinsen's dogma) [1]. In particular, the funneled energy landscape approach prescribes that amino-acid sequences tend to choose the three dimensional structure that minimizes their free energy. But not everybody embraces the folding-funnel approach, especially since it has been well known that for most proteins the free energy difference between the folded and the unfolded states is only marginally negative [2]. At the same time the protein folding problem has been suggested as an NP-complete one [3], or otherwise no fast solution to it is known, while at the same time nature copes with it very efficiently in biological systems.

So the question remains. Or doesn’t it?
It seems that, through the field of protein design, the recent approach of Baker and colleagues [4] gave a big push towards the answer. The ansatz was: forget about the sequence; there must be a mapping or a relation between specific secondary structure patterns and tertiary structure motifs. Indeed, the authors formulated concrete, unambiguous rules connecting the alternation and length of 2 or 3 secondary structure elements with their supersecondary structure. Specifically, they first defined the notion of chirality (left or right) for the motif βlβ and the notion of orientation (parallel or antiparallel) for the motifs βlα and αlβ, where β, α and l stand for beta, alpha and loop respectively. They then gave the three following fundamental rules. 
1) βlβ rule: the chirality of β-hairpins is determined by the length of the loop between the two strands. Two- and three-residue loops almost always give rise to left-hairpins, whereas five-residue loops give rise primarily to right-hairpins. 
2) βlα rule: The preferred orientation of βlα-units is parallel for two-residue loops and antiparallel for three-residue loops.
3) αlβ rule: The preferred orientation of αlβ-units is parallel. 
At a next level of complexity, from these 3 fundamental rules follow 4 emergent rules concerning βlβlα-, αlβlβ- or βlαlβ-units. Their validation included both Rosetta folding simulations of sequence-independent backbone models as well as analysis of motifs in known protein structures. Both approaches were in agreement with each other. More notably, the authors, following strictly these rules, designed ab initio five different protein folds that exhibited extraordinary thermal stability reaching melting temperatures greater than 95 C. They thus called these models “ideal”.

What triggered a subsequent, recent work by L. Vitagliano and coworkers [5], was the fact that naturally occurring proteins might not follow the rules as strictly as in the above designing, they are however - even if marginally - stable. The overall analysis of crystal structures from the thermophiles Thermotoga maritima, the genus Pyrococcus and the genus Sulfolobus, revealed an adherence to the above rules, with the notable over-representation of the βlβ-l2 (i.e. two-residue loop), a state with exclusive preference for left-chirality.So could the adherence to those rules be driving an evolutionary selection for thermostable proteins? It is possible. Let’s not forget at this point that there is no divine hand defining these rules. As the authors of [4] note, they follow from either minimization of torsional strain or backbone bendability. And this is also the reason why proteins that follow these rules not only have stable native states but also unstable non-native states, a fact partially responsible for the funnel-shaped resulting energy landscapes. A question that naturally arises from Baker’s group's result concerns the functionality of the designed proteins at ambient temperature or not. It is either outside the scope their work or it is implicitly assumed that since one can drive the fold (and decide of course on the sequence) he can design proteins with the desired function. But protein function requires the appropriate, or let’s say the perfect, amount of flexibility. It was very nicely demonstrated by Hans Frauenfelder and co-workers [6] that protein dynamics is slaved by both the hydration shell and the bulk solvent, it is thus controlled by the solvent viscosity which in turn depends on the temperature. As the authors in [5] note, “exceptions to the (above) rules are not rare in naturally thermostable proteins. This observation suggests that in these cases a certain level of “frustration” is likely essential for proteins to carry out their biological functions.”

Bottom line, could we ever succeed in mimicking nature exactly? All it takes after all is to mimic its perfect deviation from the rules.


[1] C.B. Anfinsen, The formation and stabilization of protein structure. Biochem. J. 1992, 128(4), 737-749.
[2] A.D. Robertson and K.P. Murphy, Protein Structure and the Energetics of Protein Stability. Chem. Rev. 1997, 97, 1251−1268.
[3] B. Berger and T. Leighton. Protein folding in the hydrophobic-hydrophilic (hp) is np-complete. In Proceedings of the second annual international conference on Computational molecular biology, RECOMB ’98, pages 30–39, New York, NY, USA, 1998. ACM
[4] Koga N, Tatsumi-Koga R, Liu G, Xiao R, Acton TB, Montelione GT, Baker D (2012) Principles for designing ideal protein structures. Nature 491:222–227.
[5] Balasco N, Esposito L, De Simone A, Vitagliano L., "Role of loops connecting secondary structure elements in the stabilization of proteins isolated from thermophilic organisms", Protein Sci. 2013 Jul;22(7):1016-23. doi: 10.1002/pro.2279.
[6] Hans Frauenfelder, Guo Chena, Joel Berendzena, Paul W. Fenimorea, Helén Janssonb, Benjamin H. McMahona, Izabela R. Stroec, Jan Swensond and Robert D. Younge, A unified model of protein dynamics, vol. 106 no. 13, 5129–5134 (2008)

Nobel 2013, three legs better than two(?)

The 2013 Nobel prize in Chemistry was a great news for all of us working in the field of computer modeling of biomolecules. M. Karplus, M.Levitt and A. Warshel were recognized for their seminal work on multi-scale modeling of bio-systems, namely for having posed the basis of mixed quantum/classical simulations. However, I like to think the award in a more broad sense, modern science is not anymore solely a duet between experiments and theory. Computation is up there as the third leg of knowledge, a new world with its algorithms, its theory and its in silico experiments. On this regards,  I remember a nice discussion by G. Ciccotti on the role of computing in modern theoretical physics, see here.

Back to the topic of this blog, I just wanted to cite three works from the Nobel’s laureates that are especially important when investigating protein thermostability. The first is a work from V.Daggett and M.Levitt (J.Mol.Biol.1993, see here) where the unfolding pathway of a globular protein is explored by performing high-temperature simulations. The second one is from T.Lazaridis, I. Lee and M. Karplus (Protein Sci. 1997, see here)  where the stability of the hyperthermophilic protein Rubredoxin from Pyrococcus furiosus is compared to that of the mesophilic homologue and discussed vis-à-vis of protein rigidity and flexibility. The final one is from M. Roca, H.Liu, Messer and A. Warshel (Biochemistry, 2007, see here). Here, the authors tackle the problem of protein function at high temperature, and in particular they challenge the common view according to which the lack of activity of thermophiles at ambient conditions relates to a more rigid behavior of the protein.

The first Molecular Dynamics simulation of hard-spheres run on a Univac calculator (BJ Alder and TE Wainwright, JCP, 1957, 27, 1208).  For historical curiosity, see the interview to BJ Alder here and an overview by WW Wood on Monte Carlo methods, here.