Effect of Low-Pass Filtering in Force Calibration of Magnetic Tweezers

In typical experiments where magnetic tweezers are involved, precise measurement of the magnetic forces is of crucial importance. To achieve this, a widely applied method is to track the bead's Brownian motion trajectory and to calculate the force from its mean-squared-displacement. However, this method does not take into account the fact that the bead-tracking device always has a finite bandwidth, acting effectively as a low-pass filter. The result could be subjected to significant system errors, which overestimates the magnetic force. We analyze the power spectrum of the bead's Brownian motion, and provide a corrected formula to calculate the magnetic force, which is free of system errors induced by limited detection bandwidth. A dsDNA force-extension curve is experimentally measured. The curve is consistent with the WLC model, exhibiting correctness of the new formula. On the other hand, the force given by the traditional method shows significant deviation from the WLC model, which is 3 times larger at most.