Hidden Intermediate State and Second Pathway Determining Folding and Unfolding Dynamics of GB1 Protein at Low Forces

Atomic force microscopy experiments found that GB1, a typical two-state model protein used for study of folding and unfolding dynamics, can sustain forces of more than 100 pN, but its response to low forces still remains unclear. Using ultrastable magnetic tweezers, we discovered that GB1 has an unexpected nonmonotonic force-dependent unfolding rate at 5–160 pN, from which a free energy landscape with two main barriers and a hidden intermediate state was constructed. A model combining two separate models by Dudko et al. with two pathways between the native state and this intermediate state is proposed to rebuild the unfolding dynamics over the full experimental force range. One candidate of this transient intermediate state is the theoretically proposed molten globule state with a loosely collapsed conformation, which might exist universally in the folding and unfolding processes of two-state proteins.

Figure 1

Unfolding of $\mathrm{GB}{1}_8$ in force-ramp experiments. (a) Sketch of magnetic tweezers with a protein construct ${\mathrm{GB}1}_8$ linked between glass surface and paramagnetic bead. (b) Force-extension curve of $\mathrm{GB}{1}_8$, measured in force-ramp experiments with constant loading and unloading rates of $\pm 1\mathrm{pN}/\mathrm{s}$. Each extension jump step corresponds to an unfolding event of a single GB1 domain. (c) Unfolding force distribution from four different tethers at constant loading rate of $0.2\mathrm{pN}/\mathrm{s}$ (black and gray circles for two tethers) and $1\mathrm{pN}/\mathrm{s}$ (black and gray squares for two tethers). Force distribution is fitted by prediction of Bell’s model (Eq. S1) with $k_u^0=(7\pm 3)\times {10}^{-4}{\mathrm{s}}^{-1}$ and $x_u=0.25\pm 0.03\mathrm{nm}$ [26]. Numbers of unfolding events are given in the legend.

Figure 2

Unfolding and refolding dynamics of $\mathrm{GB}{1}_8$ at constant forces. (a) $\mathrm{GB}{1}_8$ domains unfold in stepwise fashion after force increases from 2.0 to 60 pN. When force drops to 6 pN, entropic collapse of peptide (gray circle area) is followed by the folding process (gray square area). (b) Average folding time courses at 5.0, 4.5, and 3.5 pN from more than four folding time courses are fitted with exponential decay function to get $k_f(f)$. (c) Extension time course of 4000 s at 8.0 pN shows equilibrium folding and unfolding dynamics of $\mathrm{GB}{1}_8$. Relative frequency of 0.5 s smoothed extension exhibits distribution peaks with zero to eight unfolded domains. (d) Unfolding and folding probability of GB1 was obtained by cumulative distribution of pseudo dwell time [19]. Dashed line and solid line show exponential fitting curves to determine $k_u$ and $k_f$ of GB1 at 8.0 pN, respectively.

Figure 3

Force-dependent folding and unfolding rates and two-pathway model for GB1 unfolding. (a) Folding rates and unfolding rates from force jump experiment and equilibrium measurement from 3 to 160 pN are summarized (Fig. S10). Slope determined by data points at 140 and 160 pN gives unfolding distance of $\sim 0.13\mathrm{nm}$ (red line). Linear fitting in force range 15–140 pN determines $x_u=0.25\pm 0.01\mathrm{nm}$ (black line), consistent with force-ramp experiment. Folding rate is fitted by Eq. S7 with folding transition state of size 3.65 nm and zero-force folding rate of $k_f^0=150\pm 50{\mathrm{s}}^{-1}$ (gray line). Error bar of folding and unfolding rates is given by standard error, and force is estimated to have 5% uncertainty. (b) Unfolding rates at 5–30 pN in (a) are enlarged. The unfolding rates in force range 5–9 pN obtained by equilibrium measurements are fitted with parameters $x_u=1.0\pm 0.2\mathrm{nm}$ (blue dashed line). Nonmonotonic force-dependent unfolding rates at force-range 5–30 pN are fitted with a model with a hidden intermediate state and second catch-bond pathway (blue curve, Eq. S9). The dashed red line shows fitting result of model C in Ref [8] (Eq. S19), which is discussed in Supplemental Material [20]. (c) Diagram of a two-dimensional free energy landscape with three local minima (states $N$, $I$, $U$) and two unfolding pathways. Transition states are marked by dashed lines. (d) Model to explain the experimental results of $k_u(f)$. Solid arrows indicate the dominant pathway at different force range. The red double-dagger symbol represents the highest energy barrier position along the dominant unfolding pathway.