We detail the design of an electromagnetic assembly capable of generating a constant magnetic field superimposed to a large magnetic field gradient (between 40 and 100 T/m), which was uniform over a large gap (between 1.5 and 2 cm). Large gaps allowed the use of wide high numerical-aperture lenses to track microspheres attached to DNA molecules with an inverted light microscope. Given the geometric constraints of the microscope, computer-aided design was used to optimize the magnetic field gradient linearity, homogeneity, and amplitude, as well as the arrangement of the magnetic coils, the currents, and the mechanical stability of the assembly. The assembly was used to apply forces of controlled amplitude, direction, and time dependence on superparamagnetic microspheres by using magnetic coils instead of permanent magnets. A streptavidin-coated microsphere was attached to the 3′ end of a λ-phage DNA molecule through a single biotin molecule. The 5′ end of the λ-phage DNA molecule was tethered to a glass coverslip by conjugating the DNA's overhang to a complementary 12 base-pair primer, which was itself cross-linked to a heterobifunctional group placed on the glass coverslip. By tracking the centroid of this microsphere, the mechanical response of a single λ-phage DNA molecule was measured as a function of the applied magnetic force. The resulting force-extension curve was fitted with the worm-like-chain model to obtain λ-phage DNA's persistence length and contour length, which were in agreement with previous reports.
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