(a) A schematic presentation of the rebinding and unbinding measurements. [(b)–(e)] Hysteresis in the force-extension curves calculated with Eq. (1) for the Morse [(b) and (c)] and Lennard-Jones [(d) and (e)] potentials and for two values of the spring constant [(b) and (d)] and [(c) and (e)]. Black and gray (blue and red online) curves show force traces for unbinding and rebinding processes, respectively. Parameter values: , , , , , , and .
The total potential experienced by the pulled molecule for three different positions of the cantilever, (a), (b), and (c). Panels (a) and (c) give the potential at the critical positions and , for which the barriers for rebinding and unbinding vanish, respectively. Panel (d) presents the positions of the local minima and maximum of the potential as functions of . Variations in the bound and free states and the maximum are shown by dotted, dashed, and solid curves, respectively. For clarity we use the logarithmic scale to present variation in and with . Parameter values: , , , and .
(a) Barrier heights for the unbinding and rebinding as a function of the applied force, and (b) PDFs for unbinding and rebinding forces. Circles and squares and the corresponding curves show the results for the unbinding and rebinding processes, respectively. (a) Solid curve presents results of numerical calculations of ; dashed and dotted curves show predictions of analytical scaling Eqs. (5) with given by Eq. (6), and the scaling relation for the unbinding barrier with the fitting parameter , respectively. (b) Symbols and curves show results of numerical calculations of and and the corresponding analytical results [Eq. (7)]. For unbinding we used . The inset demonstrates considerable difference between analytical PDFs for unbinding obtained with (solid line) and without (dashed line) introduction of the fitting parameter . , other parameters as in Figs. 1(a) and 1(b).
Pre-exponential factors entering the rate equation (4) for unbinding (a) and rebinding (b) as functions of the applied force. Solid and dashed curves present results of numerical calculations and analytical scaling relations (5). Parameters as in Fig. 2.
The most probable unbinding and rebinding forces vs the pulling velocity. Analytical and numerical results for unbinding are presented by black curves and symbols (blue online), while those for rebinding are shown by gray curves and symbols (red online). Calculations have been done for the Morse potential and two values of the spring constants: (solid lines and circles and squares) and (dashed lines and triangles). In analytical calculations for and 1 N/m we used and , respectively. Other parameters as in Fig. 1.
[(a) and (b)] PDFs of the dissipated energy calculated for the Morse potential and two values of the spring constant, (a) and (b). Circles, squares, and triangles show PDFs for , 50, and 300 nm/s, respectively. The curves are simple connectors between the data. (c) The mean dissipated energy vs pulling velocity calculated for (circles and solid curve) and (squares and dashed curve). Symbols and curves present results of Langevin simulations and analytical calculations with Eqs. (6) and (11). Parameters as in Fig. 3, and for the description of unbinding we used the fitting parameters and for and 0.2 N/m, respectively.
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