We demonstrate a proof of concept for detecting heterogeneities and estimating lifetimes in time-correlated single-photon-counting (TCSPC) data when photon counts per molecule are low. In this approach photons are classified as either prompt or delayed according to their arrival times relative to an arbitrarily chosen time gate. Under conditions in which the maximum likelihood (ML) methods fail to distinguish between heterogeneous and homogeneous data sets, histograms of the number of prompt photons from many molecules are analyzed to identify heterogeneities, estimate the contributing fluorescence lifetimes, and determine the relative amplitudes of the fluorescence, scatter, and background components of the signal. The uncertainty of the lifetime estimate is calculated to be larger than but comparable to the uncertainty in ML estimates of single lifetime data made with similar total photon counts. Increased uncertainty and systematic errors in lifetime estimates are observed when the temporal profile of the lifetime decay is similar to either the background or scatter signals, primarily due to error in estimating the amplitudes of the various signal components. Unlike ML methods, which can fail to converge on a solution for a given molecule, this approach does not discard any data, thus reducing the potential for introducing a bias into the results.

Chromatin remodelers are molecular motors that play essential roles in the regulation of nucleosome positioning and chromatin accessibility. These machines couple the energy obtained from the binding and hydrolysis of ATP to the mechanical work of manipulating chromatin structure through processes that are not completely understood. Here we present a quantitative analysis of nucleosome repositioning by the imitation switch (ISWI) chromatin remodeler and demonstrate that nucleosome stability significantly impacts the observed activity. We show how DNA damage induced changes in the affinity of DNA wrapping within the nucleosome can affect ISWI repositioning activity and demonstrate how assay-dependent limitations can bias studies of nucleosome repositioning. Together, these results also suggest that some of the diversity seen in chromatin remodeler activity can be attributed to the variations in the thermodynamics of interactions between the remodeler, the histones, and the DNA, rather than reflect inherent properties of the remodeler itself.

Here we demonstrate the benefits of a new curriculum for introductory calculus-based physics that motivates classical mechanics using a modified version of Hamiltonian mechanics. This curriculum shifts the initial focus of instruction away from forces and the associated vector mathematics, which are known to be problematic for students, to the scalar quantity energy, which is more closely aligned with their previously established intuition, and associated differential and integral calculus. We show that implementation of this calculus-enhanced "energy-first" curriculum resulted in higher normalized gains on the Force Concept Inventory exam for all students and improved performance in downstream engineering courses for students with lower ACT math scores. In other words, the downstream benefits were largest for students with lower math abilities who also pose a larger retention risk. This new curriculum thus has the potential to improve student retention by specifically helping the students who need help the most, including traditionally underserved populations who often have weaker mathematics preparation. We propose future work to investigate whether this new curriculum has lowered the math transference barrier to learning in introductory physics, resulting concomitantly in improvements in student learning of classical mechanics and in student fluency with applied mathematics.

One issue in genome maintenance is how DNA repair proteins find lesions at rates that seem to exceed diffusion-limited search rates. We propose a phenomenon where DNA damage induces nucleosomal rearrangements which move lesions to potential rendezvous points in the chromatin structure. These rendezvous points are the dyad and the linker DNA between histones, positions in the chromatin which are more likely to be accessible by repair proteins engaged in a random search. The feasibility of this mechanism is tested by considering the statistical mechanics of DNA containing a single lesion wrapped onto the nucleosome. We consider lesions which make the DNA either more flexible or more rigid by modeling the lesion as either a decrease or an increase in the bending energy. We include this energy in a partition function model of nucleosome breathing. Our results indicate that the steady state for a breathing nucleosome will most likely position the lesion at the dyad or in the linker, depending on the energy of the lesion. A role for DNA binding proteins and chromatin remodelers is suggested based on their ability to alter the mechanical properties of the DNA and DNA-histone binding, respectively. We speculate that these positions around the nucleosome potentially serve as rendezvous points where DNA lesions may be encountered by repair proteins which may be sterically hindered from searching the rest of the nucleosomal DNA. The strength of the repositioning is strongly dependent on the structural details of the DNA lesion and the wrapping and breathing of the nucleosome. A more sophisticated evaluation of this proposed mechanism will require detailed information about breathing dynamics, the structure of partially wrapped nucleosomes, and the structural properties of damaged DNA.

The packaging of the eukaryotic genome into chromatin regulates the storage of genetic information, including the access of the cell’s DNA metabolism machinery. Indeed, since the processes of DNA replication, translation, and repair require access to the underlying DNA, several mechanisms, both active and passive, have evolved by which chromatin structure can be regulated and modified. One mechanism relies upon the function of chromatin remodeling enzymes which couple the free energy obtained from the binding and hydrolysis of ATP to the mechanical work of repositioning and rearranging nucleosomes. Here, we review recent work on the nucleosome mobilization activity of this essential family of molecular machines.