The force, the heat and the shear. Three weaknesses for three perturbations!

Shear unfolding chapter two. Same question: Can proteins unfold in shearing fluid flows, and to what extent? How do the tensile forces exerted by the solvent affect the protein compared to other types of external perturbations such as thermal denaturation, or directional pulling forces used in optic/magnetic tweezers or atomic force microscopy (AFM) experiments? Before the answer: conventional all-atom molecular dynamics simulations often require too much computational effort, hence, we have developed an original methodology using Lattice Boltzmann Molecular Dynamics (LBMD) and the Optimized Potential for Efficient peptide folding Prediction (OPEP) coarse-grained model to inquire the unfolding features of a small Cold Shock Protein subjected to three different perturbations: shear flow, heat shock and pulling force. Since the implicit-solvent OPEP model inherently lacks hydrodynamics, the Lattice Boltzmann framework allowed us to realistically simulate the flow interaction with the protein, while retaining good computational efficiency with respect to explicit-solvent approaches. Here the answer: The direct comparison of the unfolding mechanisms evidenced that the three perturbations act on different weaknesses of the protein, and thus lead on average to very different unfolding pathways. Funny enough, for this small globular protein shear flow acts more similarly to thermal excitation then a direct mechanical force. Our results suggest that the interpretation of experimental studies that rely on force-spectroscopy techniques to investigate natural shear-activated systems, such as the von Willebrand factor or the bacterial adhesin FimH, is not straightforward. The paper is out here.

When solvent breaks a protein: protein unfolding under shear

Proteins break under the action of different perturbations, the temperature, chemicals, mechanical forces. Fluid flow too, in special condition, unfolds a protein. In some biological processes, the fluid induced perturbation is even functional. That is the case of blood coagulation where the long chain of the von Willibrend factor unrolls and extends under the action of blood shear flow caused by a vessel injury. Other proteins, known as catch-bonds, use the tensile force to strength the binding with their substrate via a sort of allosteric conformational change. It is therefore intriguing to understand in which conditions a protein unfolds in shear flow, and the molecular mechanism of the process. We have dedicated a recent paper to this by exploiting the power of the lattice Boltzmann MD technique. Surf it here.

In vivo stability! Cell type matters.....

In a very recent PNAS, J. Danielsson et al. [see here] present a very interesting work focusing on protein stability in cell. They used in-cell NMR to reconstruct the stability curve of the protein SOD1. The interesting finding is that when the protein is moved in two different types of cells, a bacterial (E. coli)  and a mammalian cell (A2780) the protein is destabilised in both cases. Firstly, this finding questions the common believe that under crowding a protein gets stabilised because of an excluded volume effect. In short, if the available space is reduced because of the presence of a large numbers of macromolecules acting as crowders, the highly entropic and extended unfolded state should be unfavored. This picture is however very simplified since in both folded and unfolded states, a targeted protein interacts with its neighbours, and the results of these specific interactions, i.e. electrostatic, could alter the equilibrium favouring unfolding. The effect of different specific interactions, is actually probed by the authors, showing that by changing the local environment, moving from E.coli to a mammalian cell, the destabilisation effect is different. Last, but not least, the destabilisation results as an increase of the specific heat of unfolding that shrinks the stability curve. This calls for a particular effect of the crowders on the nature of the unfolded state. Stay tune, because the life of proteins in cell is where our interest is going....  

Molecular view of molecular crowding. Project at the Riken HPC center, Japan [see here]

Unfolding Under Shear

What does it happen to a protein in fluid shear flow? According to some studies, a protein could be forced to unfold. However there is not agreement on the necessary strength, or more technically, on the magnitude of the shear rate that could cause the unfolding to happen. Jaspe and Hagen for example estimated that only an extraordinary value of the shear rate (10⁷ s^-1) is effective for unfolding globular proteins, read their work in Biophys. J.(2006)  here.

In our group we have recently combined an effective coarse-grained model for simulating protein motion with an engine for considering hydrodynamic interactions. A first glance to this coupling is presented in a recent review in ChemSocRev(2014), see here. We also presented the preliminary results of an investigation aimed to understand how shear flow acts on the stability of proteins. We actually show the unfolding process of a simple β-hairpin peptide under laminar shear flow. We have used a very strong shear rate, 10¹⁰s^-1, and the unfolding occurs in about 10 ns. We are now checking how the unfolding rate changes by decreasing the shear rate.

Fig.9 in Sterpone et al, Chem.Soc.Rev. (2014) DOI:10.1039/C4CS00048J.  Unfolding of β-hairpin under shear. 

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.