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Evidence for the principle of minimal frustration in the evolution of protein folding landscapes

Link to the actual article can he found here.

The article beings by describing what an energy landscape is, and how the principal of minimal frustration manifests itself through the energy landscape model of protein folding (and unfolding).

A useful video I found in understanding how the funneled energy landscape describes protein folding is shown below.

Image Credit: C. Fennell, Junior Fellow, Laufer Center for Physical and Quantitative Biology, Stony Brook University.

The graph shown on the right depicts the funneled energy landscape. The z-axis the free energy, and the x and y axis represent the configurational entropy of the protein. The black dot shows the current state of the protein, in terms of these representative coordinates. The animation on the left follows the proteins current state by animating its length and connections.

This landscape model is used to predict how the protein will evolve over time, thus this energy landscapes essentially "contains" all the information about the proteins configuration, mechanics, and dynamics. One way to probe the energy landscape of a protein is to measure the protein's unfolding and refolding rates, these rates are associated with how "bumpy" the energy landscape is.

Image credit: The Dill Research Group

If you imagine the diffusion down the energy landscape as a ball rolling down a hill. The ball will essentially fall down the smooth funnel instantaneously, but will take longer to roll down the bumpy funnel because it will have to overcome many of the small hills and valleys down it's path.

Now to the article, the principal of minimal frustration, “...quantifies the dominance of interactions stabilizing the specific native structure over other interactions that would favor nonnative, topologically distinct traps”’. What this essentially says is that proteins want to have smooth energy landscapes - rather than bumpy ones. Because proteins need to be in the folded (native) state to perform their biological function, it is strictly advantageous for proteins to fold as quickly as possible - in order to restore themselves to their native state. The authors continue to claim, “The principle of minimal frustration suggests that naturally evolved proteins with the same structure should have similar folding rates and that modulation of thermodynamic stability should occur via unfolding rates.” Graphically, this means that the "depth" of the energy landscape is modulated based on thermodynamic stability, but the upper energy landscape structure stays the same.

The authors of this article claim that proteins that have evolved from ancient proteins (billions of years old) will have similar folding rates, but vary only in their unfolding rates.

First, it is proven that the more ancient proteins are more thermophilic and stable, by probing their specific heat as a function of temperature and their unfolding rates as a function of denaturant concentration (urea). The proteins that are indeed more thermophilic and resilient to urea are more ancient. (Figure Above)

Then, by probing the proteins unfolding and folding barrier size (shown as delta G), they show that the unfolding step size is the only one of the two that is modulated by the protein's thermodynamic stability. (Figure Above)

These results manifest themselves as an alteration on the proteins energy landscape, as a function of the proteins stability, and correspondingly - it's "age". The relatively unaffected folding rate corresponds to an unchanged "top" of the energy landscape, while the longer unfolding rate is associated with the deeper native state barrier.

The authors results corroborate the principal of minimal frustration, and show how the energy landscape of a protein is modulated with with is stability, and that the protein's stability is directly correlated with it's age.

Article citation:

Franco O. Tzul,Daniel Vasilchuk, and George I. Makhatadze, Evidence for the principle of minimal frustration in the evolution of protein folding landscapes PNAS 2017 114 (9) E1627-E1632; published ahead of print February 14, 2017, doi:10.1073/pnas.1613892114