We calculate the displacement of a single spherical particle from the minimum of a harmonic well positioned near a plane wall and immersed in a uniform flow. A failure to account for the fluctuations in particle position orthogonal to the plane (leading to fluctuations in hydrodynamic drag) results in large discrepancies, with the naive displacement calculated by assuming no fluctuations in the balance of forces. The chief criterion for neglecting such fluctuations is that the stiffness of the harmonic potential exceeds the thermal stresses on the particle by at least two orders of magnitude. For micrometer-diameter particles typically employed in force spectroscopy of DNA, macromolecules, and molecular motors, this can lead to errors of up to 100% in the measured properties. The Supporting Material to the article provides an implementation of this model intended to fit experimental measurements for the stiffness of the harmonic potential constraining the particle.
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