Sequence determinants of protein folding rates: Positive correlation between contact energy and contact range indicates selection for fast folding

Abstract

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.

Detecting selection for negative design in proteins through an improved model of the misfolded state

“…Through this procedure, we rationalize important qualitative features of real HPs as a consequence of negative design, such as the fact that chain termini tend to be more hydrophobic than expected based on their solvent exposure, and we are able to predict the strength of interaction energies as a function of structural profiles. The deviations from this prediction allow identifying potential sites that are subject to selective pressure for fast folding …”

“…The deviations from this prediction allow identifying potential sites that are subject to selective pressure for fast folding. 21 Last, this theory can be applied for simulating protein evolution with stability constraint, and it predicts that there is an optimal hydrophobicity that depends on population size. These results will be reported elsewhere.…”

Detecting Selection on Protein Stability through Statistical Mechanical Models of Folding and Evolution

“…These two design principles cannot be achieved at the same time, which induces frustration in protein evolution. Nevertheless, despite the signal for negative design being stronger, the signal for selection on the protein folding rate can be detected from a statistical analysis of the PDB [74]. This analysis shows that short-range native contacts tend to have high energy, and the energy decreases with contact range, consistent with negative design, but it attains a minimum at | i − j | ≈ 8.…”

“…Moreover, this effect is larger for proteins characterized by larger absolute contact order $\text{ACO}={\sum }_{ij}{C}_{ij}^{\text{nat}}false|i-jfalse|/{\sum }_{ij}{C}_{ij}^{\text{nat}}$, a structural parameter that is negatively correlated with the protein folding rate [75]. Structures with large ACO tend to fold more slowly, and they are expected to be subject to stronger selective pressure for sequence features that accelerate the folding rate, such as the strong short-range contacts described in Plotkin's theory [74]. …”

“…One can see that short-range contacts are more attractive than expected on a stability ground, and this effect increases with chain length and with the absolute contact order (ACO). Reproduced with permission from [74] (Wiley © ).…”