The overarching theme for the two main experiments presented here is that standard biochemical and cell biological techniques, which need fairly large samples and hence average over large numbers of things, be they molecules or cells, tend to smear out interesting phenomena that occur to a small fraction of those things. Averaging also collapses the entire population distribution into one single value, and furthermore prevents tracking properties of individuals over the lifetime of the experiment. The first project described here involves mechanically tying knots into linear DNA molecules stretched out between optically trapped beads. Without mechanical intervention, the molecules we used contained knots only rarely, and those knots are expected to involve small portions of the DNA contour and hence give only small perturbations to the overall polymer dynamics. By tying and observing them singly, we were able to show that, while knots collapse and tighten under tension, even the most complex ones we tied retained mobility to quite a surprising degree. The observed knot sizes and diffusivities correlated well with theoretical predictions for knots in ideal ropes of finite thickness, indicating that even under high tension the different parts of the molecular knots are kept away from each other because of electrostatic repulsion. The differences between knots of different topologies, both in size and speed, open up the possibility that, with further refinement, this approach may allow us to observe the stepwise actions of single topoisomerases in chemically undoing complex knots. The second project was to develop a microfluidic system to perform many signaling experiments on cells simultaneously within a single field-of-view of a microscope. Single cell sensitivity has been pivotal both in verifying data quality and in understanding cell-to-cell variabilities in signaling strengths. In the course of these two projects I also had a few side ideas which, sadly, I wasn’t able to develop to the degree that I would have liked. I've included them here as minor digressions, in the hopes that someone will see them and find them useful
