Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

The response of single DNA molecules to externally applied forces and torques was directly measured using an angular optical trap. Upon overwinding, DNA buckled abruptly as revealed by a sharp extension drop followed by a torque plateau. When the DNA was held at the buckling transition, its extension hopped rapidly between two distinct states. Furthermore, the initial plectonemic loop absorbed approximately twice as much extension as was absorbed into the plectoneme upon each additional turn. The observed extension change after buckling and the postbuckling torque support a recent DNA elasticity model.

The primary goal of a dividing somatic cell is to accurately and equally segregate its genome into two new daughter cells. In eukaryotes, this process is performed by a self-organized structure called the mitotic spindle. It has long been appreciated that mechanical forces must be applied to chromosomes. At the same time, the network of microtubules in the spindle must be able to apply and sustain large forces to maintain spindle integrity. Here we consider recent efforts to measure forces generated within microtubule networks by ensembles of key proteins. New findings, such as length-dependent force generation, protein clustering by asymmetric friction, and entropic expansion forces will help advance models of force generation needed for spindle function and maintaining integrity.

DNA melting under torsion plays an important role in a wide variety of cellular processes. In the present Letter, we have investigated DNA melting at the single-molecule level using an angular optical trap. By directly measuring force, extension, torque, and angle of DNA, we determined the structural and elastic parameters of torsionally melted DNA. Our data reveal that under moderate forces, the melted DNA assumes a left-handed structure as opposed to an open bubble conformation and is highly torsionally compliant. We have also discovered that at low forces melted DNA properties are highly dependent on DNA sequence. These results provide a more comprehensive picture of the global DNA force-torque phase diagram.