Past exam of the biological physics course of the University of Oxford / 2019 / 1 / d

Use a short inducer pulse to release DNA-bound fluorescent LacI, then remove extracellular IPTG rapidly and start the search clock after washout. The supplied entry, binding and dissociation times imply a synchronization uncertainty of order a few tenths of a second, which must be measured and separated from the search latency. If rebinding is faster than that dead time, the protocol alone cannot resolve the true mean without a kinetic correction or faster triggering.

Image individual cells rapidly enough to distinguish freely diffusing proteins from a persistent immobilized fluorescent spot at the single operator. Prelocate that locus from an independent position marker or a previous binding event. Score the first specific capture after each reset; controls lacking a functional target distinguish stable operator binding from nonspecific DNA residence. Correct for localization error, bleaching, blinking, missed brief events and target motion, and verify that the fluorescent tag does not substantially change the search kinetics.

With four independent freely searching molecules, each having an approximately exponential single-molecule target-arrival time of mean ${\tau }_1$, the first-arrival survival isThus report both the observed first capture among four and the inferred mean for one searcher. If the number of visible available molecules varies, use $S(t)=\exp [-{\int }_0^{t}n(s)ds/{\tau }_1]$ and account for censoring rather than blindly multiplying by four. Repeated resets and many cells estimate the distribution; deviations from an exponential test the independent well-mixed approximation. The rapid inducer manipulation defines a synchronization strategy, not an assumption that all subsequent intracellular search paths are identical.