Local versus global fold switching in protein evolution: insight from a three-letter continuous model.

Recent design experiments have demonstrated that some proteins can switch their folds in response to a small number of point mutations either directly, in a single mutational step, or via intermediate bistable sequences, which populate two different folds simultaneously. Here we explore the hypothesis that bistable intermediates are more common in switches between structurally similar folds while direct switches are more common between dissimilar folds. To this end, we use a reduced model with seven atoms per amino acid and three amino acid types as a biophysical basis for protein folding and stability. We compare a set of mutational pathways, selected for optimal stability properties, that lead to switches between ß-hairpin and α-helix folds with 16 amino acids and between [Formula: see text] and [Formula: see text] folds with 35 amino acids, respectively. Fold switching in each case is sharp, taking only a few mutations to be completed. While the sharpness of mutationally driven protein fold switching can be traced to a shift in the energy balance of the two native states, conformational entropy contributes to determining the point at which fold switching occurs along a pathway.

Smooth functional transition along a mutational pathway with an abrupt protein fold switch.

Recent protein design experiments have demonstrated that proteins can migrate between folds through the accumulation of substitution mutations without visiting disordered or nonfunctional points in sequence space. To explore the biophysical mechanism underlying such transitions we use a three-letter continuous protein model with seven atoms per amino acid to provide realistic sequence-structure and sequence-function mappings through explicit simulation of the folding and interaction of model sequences. We start from two 16-amino-acid sequences folding into an α-helix and a ß-hairpin, respectively, each of which has a preferred binding partner with 35 amino acids. We identify a mutational pathway between the two folds, which features a sharp fold switch. By contrast, we find that the transition in function is smooth. Moreover, the switch in preferred binding partner does not coincide with the fold switch. Discovery of new folds in evolution might therefore be facilitated by following fitness slopes in sequence space underpinned by binding-induced conformational switching.

Hybrid Monte Carlo with non-uniform step size.

The Hybrid Monte Carlo method offers a rigorous and potentially efficient approach to the simulation of dense systems, by combining numerical integration of Newton's equations of motion with a Metropolis accept-or-reject step. The Metropolis step corrects for sampling errors caused by the discretization of the equations of motion. The integration is usually performed using a uniform step size. Here, we present simulations of the Lennard-Jones system showing that the use of smaller time steps in the tails of each integration trajectory can reduce errors in energy. The acceptance rate is 10-15 percentage points higher in these runs, compared to simulations with the same trajectory length and the same number of integration steps but a uniform step size. We observe similar effects for the harmonic oscillator and a coarse-grained peptide model, indicating generality of the approach.

Mutation-induced fold switching among lattice proteins.

Recent experiments uncovered a mutational pathway between two proteins, along which a single mutation causes a switch in fold. Searching for such paths between real proteins remains, despite this achievement, a true challenge. Here, we analyze fold switching in the minimalistic hydrophobic/polar model on a square lattice. For this analysis, we generate a comprehensive sequence-structure database for chains of length ≤ 30, which exceeds previous work by five units. Single-mutation-induced fold switching turns out to be quite common in the model. The switches define a fold network, whose topology is roughly similar to what one would expect for a set of randomly connected nodes. In the combinatorially challenging search for fold switches between two proteins, a tempting strategy is to only consider paths containing the minimum number of mutations. Such a restricted search fails to correctly identify 40% of the single-mutation-linked fold pairs that we observe. The thermodynamic stability is correlated with mutational stability and is, on average, markedly reduced at the observed fold switches.