CARPe Diem

When a protein folds on a rough but funneled energy landscape, there are generally multiple low free energy paths open (1). However, for proteins of relatively low symmetry, such as λ-repressor fragment, these paths are not likely to be exactly degenerate in free energy (2). Thanks to the exponential sensitivity of the Boltzmann factor, exp[−ΔG/RT], paths even slightly higher in free energy than the lowest one are not going to be populated very much. Thus a dominant path emerges, and mutations or changes in solvent condition are required to turn off that dominant path and turn on an alternative one (2).

It would be very nice for comparison with simulations, ranging from single trajectory molecular dynamics to Markov state models (3–5), to create highly symmetrically funneled energy landscapes, so that paths are likely to be degenerate and alternative paths can be observed and modeled under just one solvent condition, for just one sequence, in a single simulation. Can it be done? The answer given by Aksel and Barrick (6) in this issue of the Biophysical Journal is a clear “yes.” Their recipe is CARPe diem: seize the day with CARPs!

CARPs, or consensus ankyrin repeat proteins, provide a linear sequence of identical folding modules that are nearly degenerate in free energy, and variable in number. In a truly parallel pathway situation, any one of the repeats can fold at any time with the characteristic time constant τ. If one has n of them doing it simultaneously, the time constant of the complete CARP will speed up to τ/n. Thus, we have a seemingly paradoxical prediction: the bigger the protein, the faster it folds. In practice, the speedup may not be quite as much because not all repeats fold completely independently, but the apparent paradox of bigger-is-faster remains.

That is exactly what Aksel and Barrick (6) observe in their experiments. They started out by creating a consensus ankyrin repeat sequence first. In natural ankyrin repeat proteins, each repeat has a slightly different sequence, ruining the almost perfect degeneracy that is possible with identical sequences (7). In their consensus repeats, the only breaking of degeneracies comes from the slightly different N- and C-terminal constraints. Of course, the more repeats (the bigger n), the less these edge effects come into play.

Next, Aksel and Barrick (6) collected stopped-flow kinetic data. As expected, less denaturant in solution yields faster folding; but going up from n = 1 to n = 4 also speeds up folding considerably, with half-lives of just a few milliseconds for the biggest and fastest repeat proteins. Comparison with simple alternative models unambiguously shows that the consensus repeat proteins are close to a perfect parallel pathways mechanism, and without denaturant they speed up into the microsecond regime. That speed is perfect for comparison with single trajectory molecular dynamics simulations, or with multiple trajectories stitched together by Markov models. It would be beautiful to see in such simulations how the subtle end effects break the degeneracy a little, producing a preference for folding from the inside-out or vice versa. Fig. 1 A, adapted from Aksel and Barrick (6), shows such a lifting of degeneracy at the ends based on their analysis of the experiments—but can simulations get it right?

Figure 1.

(A) The parallel-path Ising model of Aksel and Barrick (6), with the single-sequence approximation that states like (1–2)+(4–5) do not contribute. The thickness of arrows indicates kinetic contribution of parallel paths, revealing the edge effect discussed in the text. (B) The normal v-shaped chevron plot (black dotted curve) can turn into a χ-plot instead (solid curve) when intramolecular aggregation (red dotted curve) begins to compete with correct folding in an artificial tethered repeat protein (9).

Interesting things are also going on upon unfolding. Aksel and Barrick (6) observe a nonlinear dependence of ln(τ) on denaturant concentration, a so-called rollover of the chevron plot, indicating that within the various parallel paths, fewer and fewer repeats must unfold to reach the transition state. All of these folding and unfolding behaviors can be modeled using a simple but powerful Ising model (Fig. 1 A).

Consensus repeat proteins have a rich history in protein chemistry and engineering (8), and CARPs in particular offer all kinds of opportunities to observe interesting structural effects that perturb the basic parallel assembly mechanism. For example, repeats can interact to form transient chimeras, i.e., proteins where part of one repeat folds together with its complement from another. Such transient aggregation during folding has been observed for artificial U1A repeat proteins (see Fig. 1 B) (9), and there is also strong evidence for it from single molecule experiments studying titin repeat proteins, in which some monomer sequences are very similar, whereas others are very different (10).

Intramolecular misfolded states could also explain the rollover of the chevron plot observed by Javadi and Main (11) for another set of consensus repeat proteins. For the Rop proteins, such alternative arrangement of repeats even requires a double-funneled energy landscape (12,13). Aksel’s and Barrick’s CARPs, which minimize intramolecular aggregation effects, are also a great starting point for a future mutation-perturbation analysis: how much of a perturbation does it take to lift the near-perfect degeneracy and destroy the parallelism? Are analogous sites near the ends more sensitive or less sensitive than in the center? Such experiments could answer quantitatively the question of how (un)likely ordinary low-symmetry proteins are to display parallel pathways with similar populations, as opposed to succumbing to the Boltzmann factor exp(−ΔG/RT).