Solvent disorder and protein dynamical transition

Protein dynamical transition (PDT) indicates the sudden activation of protein fluctuations above a critical temperature, Td ~ 220-240 K. The phenomenon has attracted the attention of scientists along the years because the possible implications. First, it has been strongly related to the role of the solvent environment surrounding the protein, and namely its physical changes. It is not surprising that many concepts coined in the community of liquids were transposed to scratch insights on the problem. Secondly, this problem represented the door through which the community active in neutron scattering entered heavily in the discussion about protein dynamics and function. Yet today, numerous  interesting works focusing on the protein dynamical transition appear in top-notch magazines, see e.g. Weik and coworkers discussed the correlation among water translation and protein fluctuation across the PDT [here] while Hong and coworkers claim that the transition is an intrinsic feature of the dry protein energy landscape [here]. We are participating to the debate, as presented in the post dedicated to Lindemann criterion. To better understand the relationship among protein motion and solvent behaviour, we have recently developed a methodology that using data from particle based simulations, can fruitfully estimate the change in the water  hydrogen bond connectivity, in space, in time, and in temperature. We show the PDT correlates to the sudden increase in the configurational disorder of the water HB network enveloping the proteins. Our finding links, in the spirit of the Adam–Gibbs relationship, the diffusivity of protein atoms, as quantified by the hydrogen mean-square displacements, and the thermodynamic solvent configurational entropy. Enjoy the paper here, and a comment in the P. Ball's blog Water in Biology.

Protein melting: the Lindemann criterion applied to proteins

The full knowledge of the structural and dynamic properties of the native, transition, intermediate, and denatured states of proteins is a key goal of life and physical sciences. Indeed, this kind of information can lay the foundation for the deep understanding of folding and unfolding of proteins which, in turn, are crucial processes in the metabolism of cells, regulating biological activity and targeting proteins to different cellular locations. In our work (Katava et. al., PNAS (2017) here)we focus the attention on the sub-nanosecond dynamics of a model protein in correspondence of the melting transition, when it is embedded in three different solvents. We show that, although the different solvents modify the protein melting temperature, a common scaling toward a constant value for the local fluctuations is attained when approaching the unfolding temperature.
Quite remarkably, this result is reminiscent of the famous criterion for melting of solids proposed by F.A. Lindemann in 1910, which states that crystals liquefy when their atomic root mean square fluctuations exceed a certain threshold value. The common scaling we found for protein mean square displacements at melting not only sheds unique light on the relationship between protein flexibility and stability, but also opens the possibility to predict protein unfolding in special environments (e.g., the cell interior) by following thermal local fluctuations.
The striking analogy between the melting of inorganic crystals and native biomolecules suggests that these seemingly very different systems may share similar behavior in correspondence of phase transitions. On these grounds, we may speculate that simplified theories of solids can also be effectively applied to interpret the behavior of complex biological systems.

Corresponding state hypothesis along the GTPase cycle in homologues

Marina Katava et al. have tracked the effect of substrate binding on the conformational flexibilities of two homologous GTPase domains of different stability contents by mimicking the catalytic cycle. The notable finding is that for the hyperthermophilic specie only at its high working temperature the release of entropy in the domain upon the hydrolysis of the GTP molecule matches that of the mesophilic domain at ambient condition. This was probed following several functional modes of the protein considered important for signalling propagation upon reaction as well as for the allosteric activation. It was also confirmed that the key region ensuring the flexibility for the conformational change upon catalysis (the switch I region) is also the weakest part in the mesophilic domain, confirming a sort of stability/function trade-off. You can enjoy the paper here.

And yet it functions!

A nice paper adressing the issue of how mesophilic/thermophilic enzymes functions at differents temperatures is just out in Biochemistry [see here].

The work by the group of EA Eisenmesser focuses on the behavior of the cyclophilin enzyme from Geobacillus kaustophililus (GeoCyp), a bacterium found in the the deep see sediment of the Mariana Trench,  and compared to its mesophilic homologous from humans (CypA). The study demonstrates that, at variance with other mesophilic/thermophilic pair, here, the thermophile maintains up to 70% of its catalytic power at low temperature where most of thermophiles do not function or have very limited activity. We have already posted on the "corresponding state principle", introduced to explain why most of thermophiles lack activity at ambient conditions. According to this view, the lack of activity is due to the enhanced rigidity of the protein matrix which compromises mobility essential to the catalytic turn-over. At the same time mechanical rigidity is postulated as the source of the enhanced stability of the protein and its resistance to thermal stress. The universality of this principle has been questioned by showing that in many cases thermophiles can be as flexible as their mesophilic variants at the same thermodynamic conditions, thus stability is the results of a smaller entropy penalty between folded (less entropic) and unfolded (more entropic) states. 

According to the work by Eisenmesser and coworkers, the thermophilic GeoCyp is highly similar from the structural point of view to the human CypA, and its dynamics at different timescales is comparable even if its mobility seems more sensitive to temperature increases. What probably causes the 30% drop of activity at low temperature (10°C) with respect to activity at its optimal temperature (60°C) is a reduced local motion of binding-site loop, which gating is affected by the presence of a charged amino-acid, and a slightly less strong electric field measured at the level of the catalytic site and supposed to ease the isomerization of the peptide bond. In summary, this study shows us another deviation from the common believe based on the observation of reduced thermophilic activity at low temperatures. Nice work!

Volume fluctuation of reaction intermediates determines reactivity

Fig. 6. in Terazima et al, PNAS (2014) shows that a monoactivated protein decamer expands in volume and consequently dissociates, while a polyactivated decamer shrinks in volume and doesn't dissocitate.

 

Proteins are subjected to thermal fluctuations that occur at all length- and timescales, ranging from bond vibrations to large-scale domain rearrangements. The fluctuations affect the volume of the protein and vice versa. The close relationship between protein conformation and protein activity is a well established concept, while the role of fluctuations in protein activity is yet to be elucidated. A recent experimental study on a blue-light photosensor (TePixD) from the thermophile T. elongatus has shown that the flexibility of reaction intermediates is crucial in the overall reaction kinetics.

In solutions and crystals, TePixD proteins form pentameric rings, which further associate to decameric structures. An equilibrium between the pentamers and decamers is impaired by light illumination, upon which the decamers dissociate to pentamers. If the light-source is then removed, the pentamer-decamer equilibrium is restored within 5 s.

Using a pulse laser-based technique, two intermediate states have been identified in the decamer dissociation upon light illumination. These intermediates are named I1 and I2, and they exhibit different volume compressibilities with respect to the ground state. It has been shown that the change in compressibility, which is proportional to change in volume, is positive and about 10% of the compressibility of the protein, meaning that the intermediate species’ volume is larger as compared to the ground state. The volume change is related to different fluctuation levels. It is presumed that the fluctuations are unequally distributed and that the enhancement of the fluctuations at the interface regions of the decamers facilitates the dissociation.

The light illumination causes a conformational change in the immediate vicinity of the photoreactive center, but this center is not near the protein interfaces that are affected by dissociation and association. Evidently, the protein flexibility is changed by the conformational change around the photoactive center, which causes a greater protein flexibility, which in turn increases the volume of the intermediate species and drives protein dissociation.

This is also confirmed by the fact that high-intensity light, which activates more than one protein in the decamer, produces less pentamers because the volume of these species is decreased as well as the protein fluctuations. Thus, there exists an experimental proof that relates higher protein flexibility to enhanced reactivity.

Coarse-graining can track protein thermal stability?

Molecular simulation based on coarse-grained (CG) models is commonly used to explore large scale molecular motion or folding/unfolding processes. However, it is questionable wether these simplified models are good enough to capture the different thermal-stabilities of proteins.

Here several problems come upfront. Not all CG models are apt to monitor protein unfolding and stability. In some cases external biases are glued on top of the model in order to ensure proteins stability during a simulation; without these biases the structures just do not hold. As consequence the effect of physical/chemical perturbations to the folded structure cannot be appreciated. In other models, the folded state is encoded in native-biases -as in the Go-like model- so one wonder wether the detected unfolding paths that are key to distinguish the stabilities of homologues are "real". Finally, one should always keep in mind that a CG hamiltonian is made up of effective interactions, and, if a rigorous bottom-up graining approach is used, this implies that the model is temperature and concentration and pressure dependent. That is, the thermodynamic reference state is embedded in the interactions. This makes troubles when simulations are performed at different temperatures as in the case of the Replica Exchange Method. Despite the limitations, the possibility to use a CG model to explore the kinetic and thermodynamic stabilities of mesophilic and thermophilic proteins is rather appealing. We have tackled the problem recently, and nice results have been obtained. The paper is out here.  If you have not access, just ask!

Tracking the corresponding state principle

Maria KALIMERI just graduated from Univ Paris VII. Congratulations! Her thesis focused on mechanical properties of thermophilic proteins explored via an innovative framework based on network analysis. Here a bite of her work "Understanding the relation between protein flexibility, stability and function remains one of the most challenging, open questions in biophysical chemistry. For example, proteins need to be flexible to facilitate substrate binding but locally rigid to sustain substrate specificity. Exemplary cases are enzymes from microorganisms that thrive at elevated temperatures, also referred to as thermophiles. These proteins are stable and functional at the high temperature regime but generally lack activity at ambient conditions. Therefore, their thermal stability has been correlated to enhanced mechanical rigidity through the corresponding states paradigm. The generality of this view, however, has been questioned by a number of

experimental and computational studies. In the present study, we employ the gold standard of computational techniques, namely Molecular Dynamics simulations, in order to identify microscopical characteristics that distinguish thermophilic from mesophilic proteins, elaborating in particular on the rigidity paradigm mentioned above." For a more complete reading see here.

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.

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)