This paper discusses numerical simulations of the magnetic field produced by an electromagnet for generation of forces on superparamagnetic microspheres used in manipulation of single molecules or cells. Single molecule force spectroscopy based on magnetic tweezers can be used in applications that require parallel readout of biopolymer stretching or biomolecular binding. The magnetic tweezers exert forces on the surface-immobilized macromolecule by pulling a magnetic bead attached to the free end of the molecule in the direction of the field gradient. In a typical force spectroscopy experiment, the pulling forces can range between subpiconewton to tens of piconewtons. In order to effectively provide such forces, an understanding of the source of the magnetic field is required as the first step in the design of force spectroscopy systems. In this study, we use a numerical technique, the method of auxiliary sources, to investigate the influence of electromagnet geometry and material parameters of the magnetic core on the magnetic forces pulling the target beads in the area of interest. The close proximity of the area of interest to the magnet body results in deviations from intuitive relations between magnet size and pulling force, as well as in the force decay with distance. We discuss the benefits and drawbacks of various geometric modifications affecting the magnitude and spatial distribution of forces achievable with an electromagnet.
Force spectroscopy based on magnetic tweezers is a powerful technique to manipulate single biomolecules and study their interactions. The resolution in a magnetic probe displacement, however, needs to be commensurate with molecular sizes. To achieve the desirable sensitivity in tracking displacements of the magnetic probe, some recent approaches have combined magnetic tweezers with total internal reflection fluorescence microscopy. In this situation, a typical force probe is a polymer microsphere containing two types of optically active components -a pure absorber (magnetic nanoparticles for providing the pulling force) and a luminophore (semiconducting nanoparticles or organic dyes for fluorescent imaging). In order to fully assess the system's capability for tracking the position of the force probe with sub-nanometer accuracy, we developed a body-of-revolution formulation of the method of auxiliary sources (BOR-MAS) to simulate absorption, scattering, and fluorescence of microscopic spheres in an evanescent electromagnetic field. The theoretical formulation uses the axial symmetry of the system to reduce the dimensionality of the modeling problem and produces excellent agreement with the reported experimental data on forward scattering intensity. Using the BOR-MAS numerical model, we investigated the probe detection sensitivity for a high numerical aperture objective. The analysis of both backscattering and fluorescence observation modes shows that the total intensity of the bead image decays exponentially with the distance from the surface (or the length of a biomolecule). Our investigations demonstrate that the decay lengths of observable optical power are smaller than the penetration depth of the unperturbed excitation evanescent wave. In addition, our numerical modeling results illustrate that the expected sensitivity for the decay length changes with the incident angle, tracking the theoretical penetration depth for a two-media model, and is sensitive to the bead size. The BOR-MAS methodology developed in this work for near field modeling of bead tracking experiments fully describes the fundamental photonic response of microscopic BOR probes at the sub-wavelength level and can be used for future improvements in the design of these probes or in the setup of bead tracking experiments.
We demonstrate in detail a semisupervised scheme to classify unexploded ordnance (UXO) by using as an example the data collected with a time-domain electromagnetic towed array detection system during a live-site blind test conducted at the former Camp Butner in North Carolina, USA. The model that we use to characterize targets and generate discrimination features relies on a solution of the inverse UXO problem using the orthonormalized volume magnetic source model. Unlike other classification techniques, which often rely on library matching or expert knowledge, our combined clustering/Gaussian-mixture-model approach first uses the inherent properties of the data in feature space to build a custom training list that is then used to score all unknown targets by assigning them a likelihood of being UXO. The ground truth for the most likely candidates is then requested and used to correct the model parameters and reassign the scores. The process is repeated several times until the desired statistical margin is reached, at which point a final dig is produced. Our method could decrease intervention by human experts and, as the results of the blind test show, identify all targets of interest correctly while minimizing false-alarm counts.
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