Free-energy landscape of two-state protein acylphosphatase with large contact order revealed by force-dependent folding and unfolding dynamics

Acylphosphatase (AcP) is a small protein with 98 amino acid residues that catalyzes the hydrolysis of carboxyl-phosphate bonds. AcP is a typical two-state protein with slow folding rate due to its relatively large contact order in the native structure. The mechanical properties and unfolding behavior of AcP has been studied by atomic force microscope. Here using stable magnetic tweezers, we measured the force-dependent folding rates within a force range 1–3 pN, and unfolding rates 15–40 pN. The obtained unfolding rates show different force sensitivities at forces below and above ∼27 pN, which determines a free-energy landscape with two energy barriers. Our results indicate that the free-energy landscape of small globule proteins have general Bactrian camel shape, and large contact order of the native state produces a high barrier dominate at low forces.

Figure 1

Sketch of magnetic tweezers measuring the force response of AcP protein and representative experimental data. (a) Schematic of protein-tethered magnetic bead: Construct of AviTag(biotin)-FH1-AcP-FH1-SpyTag was attached to streptavidin-coated paramagnetic bead and the SpyCatcher-coated coverslip surface. Zoomed-in shows the crystal structure of AcP (PDB:1APS). (b) Force-extension curve shows AcP unfolding with step size of 22 nm at force of ∼19 pN during the force-increasing process with a loading rate of 1 pN/s. The dashed frame shows the unfolding-folding transitions of SpyTag/SpyCatcher. Raw data were recorded at 200 Hz (grey line) and smoothed in a time window of 0.25 s (black line).

Figure 2

Force-dependent folding/unfolding rates and unfolding step sizes of AcP. (a) The folding rates and unfolding rates of AcP were obtained from force-jump experiment. The average unfolding rates were fitted with Bell's model in the force ranges 15–25 and 30–40 pN, which determined two different $x_u$: $x_{u,1}=0.69\pm 0.06$ nm, $x_{u,2}=1.85\pm 0.06$ nm, and corresponding parameters $k_{u,1}^0=\left(6\pm 3\right)\times {10}^{-3}{\mathrm{s}}^{-1}, k_{u,2}^0=\left(2.8\pm 0.6\right)\times {10}^{-6}{\mathrm{s}}^{-1}$, respectively. Critical force of 5.3 pN is estimated from the extrapolation of force-dependent folding/unfolding rates. The unfolding rate came from six different tethers and the folding rate came from three different tethers (Fig. 7). Error bar is obtained from the standard error of the mean lifetime. Force is estimated to have 5% uncertainty. (b) Force-dependent folding rates (Figs. 6 and 7) are fitted by Arrhenius’ law to determine the size of folding transition state as 5.0 ± 0.5 nm. (c) The average unfolding step sizes of AcP were obtained from force-jump measurement. Error bar is the standard deviation. The black curve represents the worm-like chain fitting with contour length of ∼35.8 nm and persistence length of ∼0.8 nm.

Figure 3

Unfolding dynamics of AcP under different forces in the force-jump experiment. (a) Typical force-jump measurement of the unfolding process of AcP. It shows an example of six force-jump cycles on the same protein tether. Before each cycle, the protein folded to its native state at a force of 0.5 pN for 20 s. When applying forces of 15 or 20 pN for 60 s, we can see the unfolding step of AcP with probabilities of ∼14% and ∼76%, respectively. When applying forces of 25 pN for 25 s, 30 pN for 7 s, 35 pN for 5 s, and 40 pN for 5 s, unfolding transitions were recorded in all force cycles. Raw data were recorded at 200 Hz (grey line) and smoothed in a time window of 0.25 s (black line). (b) The survival probability of native state of AcP at 20 and 35 pN. The red solid line shows exponential fitting curve to determine $k_u$ of AcP. Similarly, $k_u$ of AcP under other forces was determined (Fig. 4).

Figure 4

The survival probability of native state of AcP at 15, 25, 30, and 40 pN. The red solid line shows exponential fitting curve to determine the unfolding rate of AcP. Statistics of data points come from six independently measured tethers. Deviation of data points from the straight lines at the long unfolding times is due to the intrinsic properties of the stochastic unfolding process, which has been confirmed by simulations.

Figure 5

Measurement of AcP folding rate. (a) The measurement of the folding rate at 1 pN. First, force of 30 pN was applied to unfold AcP. Then force was dropped to 1 pN and let protein to fold at 1 pN for 1 s. Due to large fluctuation of extension at 1 pN, we cannot observe the clear folding process directly. Therefore, we increased force to 30 pN and recorded the extension time course from which we determine if the folding at 1 pN for 1 s was successful or not. The same measurement was done for 3, 6, 11, and 17 s. Before each measurement, 0.5 pN was applied for 20 s to make sure the protein can successfully fold. Raw data were recorded at 200 Hz (grey line) and smoothed in a time window of 0.25 s (black line). (b) The folding probability at different folding time at 1 pN. Exponential fitting determines the folding rate of AcP as $0.08{\mathrm{s}}^{–1}$ at 1 pN (red solid line). More independent measurements are given in Fig. 6.

Figure 6

Data points from three independently measured tethers represent folding probability at different folding time, and the exponential fitting curves determine the folding rates of AcP as $0.10{\mathrm{s}}^{–1}$ at 1 pN, $0.04{\mathrm{s}}^{–1}$ at 2 pN, $0.009{\mathrm{s}}^{–1}$ at 3 pN (red solid line).

Figure 7

Force-dependent unfolding and folding rates from individual protein tether. (a) Force-dependent unfolding rates from six independently measured protein tethers are plotted with different symbols. Circular data points are determined by a single exponential fitting to the survival probability of native state at different forces. Square data points are the reciprocal of the mean unfolding time. (b) Force-dependent folding rates from three independently measured tethers. Fitting curves in Fig. 2 are shown in both (a) and (b).

Figure 8

Using the NIU model to fit the force-dependent unfolding rates, we found the interdependence among the parameters. Detailed equation can be found in Ref. [17]. (a) Fixing the parameter values in the figure, parameters $k_{IN}^0$ and $k_{IU}^0$ are proportional to each other. (b) Fixing the parameter values in the figure, parameters $x_{IU}$ and $x_{IN}$ are anticorrelated to each other.

Figure 9

Free-energy landscape of AcP constructed from force-dependent folding and unfolding rates. Folding free energy of AcP of $10.9k_{\mathrm{B}}\mathrm{T}$ was obtained from the extrapolated critical force of 5.3 pN [Fig. 2]. Unfolding distances $x_{u,1}$ and $x_{u,2}$ were obtained from the slope of force-dependent unfolding rate at forces greater than 30 pN and smaller than 25 pN, respectively. Unfolding barriers were estimated based on an assumption of the intrinsic unfolding rate of ${10}^6 {\mathrm{s}}^{-1}$. The dashed line between TS1 and TS2 represents an unstable intermediate state which was not observed in the extension time course. Size of the unfolded state is estimated from the room mean square of the end-to-end distance of random coil polypeptide.