A theoretical and experimental treatment of fitting methods for localizing the centers of diffraction-limited spots is presented. Use of an analytical point spread function shows that maximum likelihood fitting is superior to both unweighted and weighted least squares Gaussian fitting. We optimally localized isolated fluorescent beads and molecules imaged as diffraction-limited spots, determined the orientation of molecules and present reliable formulas for the precision of various localization methods. Both theory and experimental data showed that unweighted least-squares fitting of a Gaussian squanders one-third of the available information, a popular formula for its precision exaggerates beyond Fisher's information limit, and weighted least-squares may do worse, whereas maximum-likelihood fitting is practically optimal.

Molecular motors are responsible for numerous cellular processes from cargo transport to heart contraction. Their interactions with other cellular components are often transient and exhibit kinetics that depend on load. Here, we measure such interactions using ‘harmonic force spectroscopy’. In this method, harmonic oscillation of the sample stage of a laser trap immediately, automatically and randomly applies sinusoidally varying loads to a single motor molecule interacting with a single track along which it moves. The experimental protocol and the data analysis are simple, fast and efficient. The protocol accumulates statistics fast enough to deliver single-molecule results from single-molecule experiments. We demonstrate the method’s performance by measuring the force-dependent kinetics of individual human β-cardiac myosin molecules interacting with an actin filament at physiological ATP concentration. We show that a molecule’s ADP release rate depends exponentially on the applied load, in qualitative agreement with cardiac muscle, which contracts with a velocity inversely proportional to external load.

We demonstrate a novel, yet simple tool for the study of structure and function of biomolecules by extending two-colour co-localization microscopy to fluorescent molecules with fixed orientations and in intra-molecular proximity. From each colour-separated microscope image in a time-lapse movie and using only simple means, we simultaneously determine both the relative (x,y)-separation of the fluorophores and their individual orientations in space with accuracy and precision. The positions and orientations of two domains of the same molecule are thus time-resolved. Using short double-stranded DNA molecules internally labelled with two fixed fluorophores, we demonstrate the accuracy and precision of our method using the known structure of double-stranded DNA as a benchmark, resolve 10-base-pair differences in fluorophore separations, and determine the unique 3D orientation of each DNA molecule, thereby establishing short, double-labelled DNA molecules as probes of 3D orientation of anything to which one can attach them firmly.