Figure 4: Force-dependent conformational free energy difference between RecA filament and ssDNA. The force-dependent conformational free energy difference per nucleotide between RecA filament and ssDNA, , is negative in the force range of 0–90 pN and shows a non-monotonic force dependence. is obtained by WLC fitting and is obtained by cubic spline interpolation to experimental data of RecA filament and naked ssDNA in Figure 1B, respectively. Insert shows the experimentally measured polymerization (circles) and de-polymerization (tri-angles) rates of MtRecA filament at multiple forces. Shadow indicates the force range at which no observable de-polymerization of the MtRecA filaments for > 1000 s (Supplementary Figure S10). Note that the polymerization rate was not measured for force <10 pN to avoid formation of secondary structure that may hamper the polymerization of MtRecA on ssDNA.

Mentions: The force-dependent conformational free energies of RecA filament and ssDNA can be calculated from their respective force-extension curves and through relations: and . were directly measured in our buffered reaction solution conditions (Figure 1B), which were used to calculate per nucleotide ssDNA. As is negative up to 90 pN, force in this range facilitates RecA polymerization by reducing the free energy cost for polymerization and is optimized in force range of 20–25 pN (Figure 4). The equilibrium between RecA polymerization and de-polymerization depends on the rates of polymerization and de-polymerization, kon and koff, respectively, through . Therefore, the effect of force on shifting the equilibrium must be through either increasing kon or decreasing koff, or both.