(A) Schematic of I27 for target pulling [1TIT]. The key interactions for the unfolding intermediate are the hydrogen bonds (blue) between β-strand-A' and β-strand-B, and between β-strand-A and β-strand-G. In the pulling experiments and simulations, the anchor points for the pulling are the N and C terminii (red). (B) The trajectory for a target velocity of 6.0 Å/ps shows constant velocity motion with a fitted slope of 5.9 Å/ps. (C) The pre-pulse velocities fluctuate around 4.1 Å/ps except for the early part of the trajectory where the velocities is close to zero. (D) The applied forces derived from the change in velocities from the pre-pulse velocities to the target velocity (dark blue). As the forces fluctuate ∼150 pN, to find the general shape of the curve (light blue), a low-pass FFT filter was used to filter out the fluctuations. The fitted curve has a maximum of 280 pN near the beginning of the trajectory before dropping down to ∼20 pN. In the second column are the results for the trajectory with a target velocity of 1.00 Å/ps. (E) The system is effectively trapped as the distance between the anchor points do not change. (F) The pre-pulse velocities are negative −0.7 Å/ps, due to the reflection against the free-energy barrier. (G) The applied forces. The fitted curve has a maximum of 93 pN that is maintained throughout the simulation.

(A) In the distance response curves, the points along each column represents the distance evolution of the trajectory for a given target velocity. If the last point approaches the gray dotted line, the protein is unfolding at the target velocity rate. Otherwise the protein is trapped by an unfolding barrier. (B) In the velocity response curves the averaged pre-pulse velocity is plotted for each trajectory. Negative values means the protein is trapped in an intermediate or is completely extended. When the protein is unfolding without barriers, the values approaches the positive dotted curve. (C) In the fitted force response curves, the forces can be compared to the theoretical maximum force (2MV_target) indicated by the gray line. When the system is trapped or completely extended, the maximum force is close the the theoretical maximum. When the system is unfolding with no barriers, the maximum force plateaus at the unfolding force of the protein.

(A) The evolution of the end-to-end distance of the trajectories from the initial state. The trajectory at V_target = 0.6 Å/ps (cyan trace) is trapped in the folded state. At V_target = 0.8 Å/ps (red trace), the system is trapped in an unfolding intermediate. At higher velocities (green trace, V_target = 1.4 Å/ps), the system works through a kinetic barrier before unfolding without impedance. The following snapshots show the key backbone hydrogen bonds between β-strand-A (green sticks), β-strand-G (purple sticks) and β-strand-B (blue sticks). (B) The last snapshot of the trapped trajectory (cyan trace, V_target = 0.6 Å/ps), with hydrogen bonds intact between β-strands-A, B – G. (C) The last snapshot from the trajectory trapped in the unfolding intermediate (red trace, V_target = 0.8 Å/ps) where the hydrogen-bonds between β-strand-A' and B are broken. The following snapshots are from a trajectory that unfolds through the kinetic barrier (green trace, V_target = 1.4 Å/ps): (D) three hydrogen-bonds between β-strand-A and G are broken; (E) all hydrogen bonds between β-strand-A and G are broken; and (F) the protein can now unfold without kinetic barriers at a constant velocity.

The pulling geometries are (A,B) N-C pulling in e2lip3, (C,D) N-41 pulling in e2lip3, (E,F) N-C pulling in ubiquitin, and (G,H) 48-C pulling in ubiquitin. The left column shows the schematic whilst the right column shows the distance-response curve as explained in the captions for . By identifying where the major drop-off in distance response occurs, we can identify the critical target velocity, from which we can derive a critical unfolding force.

The first row shows a trajectory with a large relaxation time of 200 fs, with plots of (A) the pre-pulse velocities and (B) the force response. The pulses here are applied so infrequently that the system cannot escape out of the folded state, indicated by the negative pre-pulse velocities. The second row corresponds to the default relaxation time of 100 fs, with (C) pre-pulse velocities that oscillates around zero before rising to the target velocity of 6.0 Å/ps, and (D) forces rising to a peak and then falling. The third row corresponds to a small relaxation time 10 fs, where (E) the target velocity is easily maintained with small fluctuations, and the system is never allowed to relax to negative values, which corresponds to (F) a very small force response.