This dissertation presents the development of quadrupole magnetic tweezers, which are capable of actuating, measuring, and controlling biological samples at nanometer scale. Magnetic force, with the advantages of biocompatibility and specificity, is employed as the actuation force for biological manipulation. Quadrupole magnetic tweezers are designed and implemented to realize force generation in arbitrary two-dimensional (2D) directions. To characterize the relationship between the applied currents to the coils and the resulting magnetic force on the magnetic probe, a lumped parameter model with magnetic monopole approximation is employed to describe the magnetic field generated by the magnetic poles. The magnetic force model is then developed based on this approximation. According to the force model, the magnetic force exerted on the magnetic probe is nonlinear with respect to the applied currents to the coils and is position dependent.
Three-dimensional (3D) particle tracking algorithm based on microscope off-focus images is developed to measure the motion of the magnetic probe. Subnanometer resolution in all three axes at 400 Hz sampling rate is achieved using a high speed CMOS camera in bright-field illumination. At each sampling, the lateral position of the particle is first estimated by the centroid method. The axial position is then estimated by comparing the radius vector, which is converted from the off-focus 2D image of the probe with no information loss, with an object-specific model, calibrated automatically prior to each experiment. By normalizing the radius vectors, the algorithm becomes a shape-based method, thus invariant to image intensity change and robust to photobleaching. The algorithm is therefore updated and utilized to measure the 3D position of fluorescent particles by analyzing the fluorescent images acquired by a high sensitivity CCD camera. Furthermore, according to a detailed analysis of measurement noise, variance equalization and correlation-weighted optimization are employed to enhance the measurement resolution by achieving the best linear unbiased estimation (BLUE) of the axial position.
Feedback control is then established to realize a stable trapping of the magnetic probe. The inverse force model is first derived to cancel the nonlinearity and the position dependency in magnetic force generation. Linear controllers are then designed to regulate the motion of the probe. The force gain, the damping coefficient, the system time delay, as well as the maximum current that can be applied without saturating the magnetic materials are calibrated using the results of proportional control. The accuracy of the force model is also verified using experiments. Furthermore, a minimum variance controller is designed and implemented to minimize the thermal fluctuation of the bead in water.
To demonstrate the capabilities of the developed system, experiments with living cells are performed. A modified setup is developed to improve the accommodation of living cells. Magnetic beads are attached on cell membrane through the specific binding between fibronectin and integrin, and magnetic forces are applied through the magnetic beads to the cells. Mechanical properties of the cells can be estimated from the cells’ response to applied forces. The cellular response anisotropy and cell adaptation to forces are also investigated.