A cartoon of the often-assumed dependence of the protein free energy on its extension (Refs. 2 and 10) (i.e., the mechanical unfolding reaction coordinate). The native state is separated from the condensed denatured state (CD) by a barrier. The extended denatured state (ED) corresponds to larger extensions.
The native configuration of the ubiquitin-type domain using the model of Refs. 49–51.
The computed free energy as a function of the domain extension at different temperatures.
The free energy of the domain in the presence of a force at and at different values of .
Representative configurations and average contact maps for the equilibrium ensemble of conformations of the ubiquitin domain at , constrained to have its extension equal to (a) , (b) , and (c) , corresponding to the points I, II, and III in Fig. 4. The value was constrained by a spring to be equal to those values. The plots of protein structures were created by using the PYMOL software (Ref. 82).
Two-dimensional contour maps for the free energy as a function of (a) the protein extension and the rmsd from the native conformation and (b) the protein extension and its radius of gyration at . The white area in the lower right-hand corner of each plot corresponds to very high values of free energy and is not visited by folding/refolding trajectories.
Slices of the two-dimensional free surface plotted in Fig. 6(a), taken at different values of the protein extension .
A typical refolding trajectory observed when the domain is initially stretched by a high force and the force is then removed at . (a) rmsd vs for this trajectory plotted against the free-energy contour map . The trajectory originates at a large value of , corresponding to an extended conformation. (b) The time dependence of , , and for this trajectory. The unit of time is . The arrow indicates the time at which rmsd attains its native value. Only the part of the trajectory preceding this moment is shown in Fig. 8(a). The simulation was performed for .
(a) The trajectory observed when the domain is initially stretched by a high force and the force is then reduced to at . This trajectory is plotted against the free-energy contour plot . (b) A typical unfolding trajectory in the presence of a high stretching force . In the beginning of the simulation the domain is in the native state. The temperature is in each case.
The free energy of the polyprotein chain that consists of domains as a function of its extension . The free energy of a single domain is described by Eqs. (14) and (15). The theoretical curve is given by Eqs. (16) and (24) with and .
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