Theoretical study of the nonlinear force loading control in single molecule stretching experiments

Force spectrum measurements with constant loading rate are widely used in single molecule manipulation experiments to study the mechanical stability and force response of biomolecules. Force-dependent transition rates can be obtained from the transition force distribution, but it is limited to the force range with non-zero force distribution. Though constant loading rate control can be realized in magnetic tweezers, but the loading rate range is limited due to the slow movement of permanent magnets. Non-linear exponential and exponential squared force loading functions are more feasible in magnetic tweezers, while there is no theoretical result available for these two kinds of non-linear force loading functions. In this study we solved the unfolding process of a protein following Bell's model under nonlinear exponential and exponential squared force loading functions, which offer a broader range of unfolding force distribution compared to the traditional constant loading rate experiments. Furthermore, we derived two force loading functions which can produce uniform unfolding force distribution. This research contributes fundamental equations for the analysis of experimental data obtained through single molecule manipulation under nonlinear force loading controls, and pave the way of using nonlinear force control in magnetic tweezers experiment.