A simple method for probing the mechanical unfolding pathway of proteins in detail

Abstract

Atomic force microscopy is an exciting new single-molecule technique to add to the toolbox of protein (un)folding methods. However, detailed analysis of the unfolding of proteins on application of force has, to date, relied on protein molecular dynamics simulations or a qualitative interpretation of mutant data. Here we describe how protein engineering Phi value analysis can be adapted to characterize the transition states for mechanical unfolding of proteins. Single-molecule studies also have an advantage over bulk experiments, in that partial Phi values arising from partial structure in the transition state can be clearly distinguished from those averaged over alternate pathways. We show that unfolding rate constants derived in the standard way by using Monte Carlo simulations are not reliable because of the errors involved. However, it is possible to circumvent these problems, providing the unfolding mechanism is not changed by mutation, either by a modification of the Monte Carlo procedure or by comparing mutant and wild-type data directly. The applicability of the method is tested on simulated data sets and experimental data for mutants of titin I27.

Fig 1.

Two-state model for the interpreting mechanical unfolding experiments. The activation energies for folding and unfolding are given by ΔΔG_‡-D and ΔΔG_‡-N respectively, and x_u and x_f are respectively the distances along the reaction coordinate from the native state (N) and denatured state (D) to the transition state (‡). The reaction coordinate is taken here to be the distance between N and C termini, r_NC.

Fig 2.

Force spectra for (a) L60A and (b) V13A mutants of titin I27 shown together with that for wild type. Mutant (squares) and wild type (circles) are shown together with the best fit curve to the two-state model by Monte Carlo simulation (solid line for wild type and dashed line for mutants). Pulling speed ν is in m⋅s⁻¹.

Fig 3.

(a) Normalized probability density p(x_u, k) for a Monte Carlo fit of a two-state model to the force spectrum of titin I27 wild type. Reasonable fits are obtained for a range of unfolding rate constants k of about an order of magnitude (Inset) (x_u, k) pairs of similar probability selected for plotting. (b) Plot of the fits for the parameters x_u = 3.20 Å, k = 8.30 × 10⁻⁵ s⁻¹ (A), x_u = 3.33 Å, k = 5.00 × 10⁻⁵ s⁻¹ (B), x_u = 3.46 Å, k = 3.01 × 10⁻⁵ s⁻¹ (C) and x_u = 3.55 Å, k = 1.81 × 10⁻⁵ s⁻¹ (D). Units of x_u, k, and ν are m, s⁻¹, and m⋅s⁻¹ respectively.

Fig 4.

Synthetic data sets for TI I27, generated by using the unfolding rate constant for wild type and values of k 10 (“mutant” 1) and 100 (“mutant” 2) times faster. The lines show the fit of each data set to a mean slope (parameters used to generate data: x_u = 3.3 Å, k = 5 × 10⁻⁵ s⁻¹ for wild type, L = 100 nm, T = 298 K). Pulling speed ν is in m⋅s⁻¹.