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Resonance energy transfer has become an indispensable experimental tool for single-molecule and single-cell biophysics. Its physical underpinnings, however, are subtle: it involves a discrete jump of excitation from one molecule to another, and so we regard it as a strongly quantum-mechanical process. And yet its kinetics differ from what many of us were taught about two-state quantum systems, quantum superpositions of the states do not seem to arise, and so on. Although J. R. Oppenheimer and T. Förster navigated these subtleties successfully, it remains hard to find an elementary derivation in modern language. The key step involves acknowledging quantum decoherence. Appreciating that aspect can be helpful when we attempt to extend our understanding to situations in which Förster’s original analysis is not applicable.

Standard pedagogy introduces optics as though it were a consequence of Maxwell’s equations and only grudgingly admits, usually in a rushed aside, that light has a particulate character that can somehow be reconciled with the wave picture. Recent revolutionary advances in optical imaging, however, make this approach more and more unhelpful: How are we to describe two-photon imaging, FRET, localization microscopy, and a host of related techniques to students who think of light primarily as a wave? I was surprised to find that everything I wanted my biophysics students to know about light, including image formation, x-ray diffraction, and even Bessel beams, could be expressed as well (or better) from the quantum viewpoint pioneered by Richard Feynman. Even my undergraduate students grasp this viewpoint as well as (or better than) the traditional one, and by mid-semester they are already well positioned to integrate the latest advances into their understanding. Moreover, I have found that this approach clarifies my own understanding of new techniques.

Myosin V is biomolecular motor with two actin-binding domains (heads) that take multiple steps along actin by a hand-over-hand mechanism. We used high-speed polarized total internal reflection fluorescence (polTIRF) microscopy to study the structural dynamics of single myosin V molecules that had been labeled with bifunctional rhodamine linked to one of the calmodulins along the lever arm. With the use of time-correlated single-photon counting technology, the temporal resolution of the polTIRF microscope was improved ∼50-fold relative to earlier studies, and a maximum-likelihood, multitrace change-point algorithm was used to objectively determine the times when structural changes occurred. Short-lived substeps that displayed an abrupt increase in rotational mobility were detected during stepping, likely corresponding to random thermal fluctuations of the stepping head while it searched for its next actin-binding site. Thus, myosin V harnesses its fluctuating environment to extend its reach. Additional, less frequent angle changes, probably not directly associated with steps, were detected in both leading and trailing heads. The high-speed polTIRF method and change-point analysis may be applicable to single-molecule studies of other biological systems.

The force generated between actin and myosin acts predominantly along the direction of the actin filament, resulting in relative sliding of the thick and thin filaments in muscle or transport of myosin cargos along actin tracks. Previous studies have also detected lateral forces or torques that are generated between actin and myosin, but the origin and biological role of these sideways forces is not known. Here we adapt an actin gliding filament assay to measure the rotation of an actin filament about its axis (“twirling”) as it is translocated by myosin. We quantify the rotation by determining the orientation of sparsely incorporated rhodamine-labeled actin monomers, using polarized total internal reflection microscopy. To determine the handedness of the filament rotation, linear incident polarizations in between the standard s- and p-polarizations were generated, decreasing the ambiguity of our probe orientation measurement fourfold. We found that whole myosin II and myosin V both twirl actin with a relatively long (∼1μm), left-handed pitch that is insensitive to myosin concentration, filament length, and filament velocity.

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters—the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632nm–7.03μm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length pwlc depended on L; even for moderately long DNA molecules (L=1300nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the “finite wormlike chain (FWLC),” to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of pwlc on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of pfwlc on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

Long life expectancy, demand for high activity levels, and bone loss at the time of revision motivate the search for reliable and successful nonce-mented hip stem designs. It is hypothesized that improved implant fit may increase the longevity of noncemented total joints. Quantitative X-ray CT has enabled the use of a computerized stem design program, which designs an optimal-fit hip stem for individual femurs. Computed tomography and interactive image processing methods are used to generate the individual three-dimensional femoral models, which are used by the stem design program. Optimal-fit design provides maximum stem-bone contact while satisfying the requirement of being surgically insertable. Previous methods of custom implant design, including those that use three-dimensional CT modeling, have not provided optimal stem-bone fit. Quantitative results of this new process are presented.

Tethered particle experiments use light microscopy to measure the position of a micrometer-sized bead tethered to a microscope slide via an approximately micrometer-length polymer, to infer the behavior of the invisible polymer. Currently, this method is used to measure rate constants of DNA loop formation and breakdown mediated by repressor protein that binds to the DNA. We report a new technique for measuring these rates using a modified hidden Markov analysis that directly incorporates the diffusive motion of the bead, which is an inherent complication of tethered particle motion because it occurs on a timescale between the sampling frequency and the looping time. We compare looping lifetimes found with our method, which are consistent over a range of sampling frequencies, to those obtained via the traditional threshold-crossing analysis, which vary depending on how the raw data are filtered in the time domain. Our method does not involve such filtering, and so can detect short-lived looping events and sudden changes in looping behavior.