bkoep Staff Lv 1
This is the first of a three-part blog post. In the first part, we’re going to review the concept of energy landscapes, which some of you may already be familiar with. In the second part, we’ll discuss how a concept from physics, called a partition function, can help us think about energy landscapes. In the last part, we’ll propose a way that we might use these concepts of energy landscapes and partition functions to improve protein design in Foldit.
The energy landscape
There’s a problem with the way we currently design proteins in Foldit—and not just in Foldit, but also in Rosetta. In fact, it’s a problem in any protein design strategy that optimizes the absolute energy of the design. This strategy is the premise of a Foldit design puzzle. The Foldit score measures the absolute energy of a solution (with a negative multiplier), so that when players compete to find solutions with the highest score, they are actually competing to find solutions with the lowest absolute energy.
However, the success of a protein design (i.e. whether or not the protein folds) does not depend only on the absolute energy of the design. Rather it depends on the protein’s energy landscape. The energy landscape is a concept we use to think about all the possible ways that a string of amino acids can fold. As any Foldit player knows, there are a lot of different ways to fold up a string of amino acids, and they all have different energies (or Foldit scores). We can imagine the energy landscape as a surface where every (x,y) coordinate represents a different fold, or state, and the height of the surface (the z-coordinate) represents the energy of that state. In some places there will be hills, which represent states with a high energy (low Foldit score), and in other places there will be valleys, where folds have a low energy (high Foldit score).
Conceptual illustration of a protein energy landscape, from Dill, K.A. and MacCallum, J.L. (2012)
One of the reasons we like the analogy of energy landscapes is that we intuitively understand how things tend to “prefer” low points in the landscape. If you place an object randomly on the energy landscape, it will tend to slide downhill, from a high-energy state to a low-energy state. If we consider the effect of thermal motion that is constantly jostling around the object (imagine a Mexican jumping bean that randomly jumps around the landscape), then the object will explore all the different valleys of the energy landscape. Nevertheless, the Mexican jumping bean will spend the most time in the deepest valleys of the landscape.
A protein behaves the same way in its energy landscape. At room temperature, there is a considerable amount of thermal motion that allows the protein to explore its energy landscape, although the protein will spend the most time in the states with lowest energy. Every amino acid sequence has a different energy landscape, with different valleys in different places. When you mutate amino acids in a Foldit puzzle to find higher scores for your design, what you’re really doing is looking for an energy landscape where your design is in a deeper valley. However, the Foldit score only tells you about the energy of your designed folded state—or the “depth” of your desired valley. What we’re not considering in Foldit is the rest of the landscape, and whether there might be other low-energy “decoy states”—other deep valleys for your protein to explore.
This is a difficult problem to solve because the energy landscape for a protein is vast. It’s difficult to account for the decoy states because we don’t know what they might look like. We don’t know where to search in the energy landscape for other low-energy valleys, and the landscape is too big to search exhaustively.
The search for decoys
As many of you are probably aware, a lot of the recent De-novo Freestyle prediction puzzles have targeted Foldit player-designed proteins. The purpose of these puzzles is to look for low-energy decoy states, or alternative valleys in the energy landscape. We already run Foldit designs through Rosetta@home to look for decoy states—and for the most part, Rosetta@home seems to do a pretty good job. But occasionally Foldit players find solutions that Rosetta@home misses.
In the following example we're going to pick on fiendish_ghoul, because this energy landscape problem is clearly illustrated by two of their designs, shown below:
The protein on the left is a design originally from Puzzle 1331; the protein on the right is a design from Puzzle 1239. Beneath each cartoon protein structure is a scatter plot with the results from corresponding De-novo Freestyle puzzles that we posted using the sequence of each design. Each black point represents a solution, plotted with respect to its RMSD to the folded state (x-axis) and its energy (y-axis). Together these points give us a profile of the energy landscape for each protein. We see that the design on the left has a “funnelled” landscape, such that the lowest-energy solutions are those close to the folded state (RMSD close to zero) and solutions very different from the folded state (large RMSD) all have higher energies. In the design on the right, however, Foldit players identified a number of decoy states that are very different from the folded state (large RMSD), and have energy just as low as the folded state. These decoy states (marked with colored circles in the scatter plot) appear as “valleys” in the energy landscape of the protein.
The cartoon structures of these decoy states are shown below using the same rainbow coloring as above, with the N-terminus of the protein colored blue, and the C-terminus of the protein colored red:
In each of the decoy structures, all of the α-helices and β-strands are there, but it appears there is some ambiguity about where the helices should go. According to the solutions from the De-novo Freestyle puzzle, the three α-helices can fold in different arrangements around the central β-sheet, and all of these arrangements have similar energies. Since all of these states have similar energy, the protein will not have a strong preference for any single one of them.
Both of fiendish_ghoul's proteins were designed by optimizing their absolute energy, but the protein on the right has a problematic energy landscape. If we made these proteins in the lab, we would expect the protein on the left to be well-folded, and to spend most of its time in the designed state, since it appears to be the only deep valley in the landscape. However, we would expect the protein on the right to be poorly-folded, and to spend its time sampling all the different decoy states discovered by Foldit players.
Check back on Monday for the next blog post, where we’ll discuss these energy landscapes in more detail!
