# Live-cell measurement of protein binding to chromatin allows probing cellular biochemistry

Live-cell measurement of protein binding to chromatin allows probing cellular biochemistry in physiological conditions, which are difficult to mimic measurements are essential for determining how cellular reactions proceed in the complex milieu of the live cell. are in theory more direct since bound molecules can be visualized (2). However, accurately identifying which segments of a trajectory reflect binding is complicated by the fact that even a completely stationary molecule will appear to move due to the precision limit of localization and a freely diffusing molecule will appear to be bound transiently if it undergoes a few small displacements. Therefore, different strategies have been developed to discriminate between bound and free molecules in SMT (2,10,11). For example, bound molecules have been identified by setting two thresholds, an upper bound with an integer, and the time between consecutive images). The resultant displacements for different tracks were then used to either calculate an ensemble-averaged mean-squared displacement (MSD) curve (25) or to populate a ME-143 supplier time-dependent histogram of displacements (26), or in other words the distribution of jumps obtained at different time lags which was corrected for photobleaching as described below, represents the probability of observing a displacement between represents the diffusion coefficient, or with a hindered (anomalous) diffusion model, of each binding event. We then computed the cumulative histogram will be erroneously counted as bound as: For the selected thresholds, and the average residence time on chromatin is usually then calculated as and the survival probability of bound molecules and which was either fixed to the value obtained for H2B or kept as a free parameter to be determined from the data. A second free parameter in the model was the diffusion PPIA rate of free p53 molecules. Finally, the model also contained two other free parameters, the association and dissociation rates of binding that specified the exchange between the bound and free states. This kinetic model was applied to fit the complete set of p53 displacements obtained from all trajectories (Figure 2d) and this yielded an estimated bound fraction and residence time that were similar to those estimated using the thresholding procedure (Table 1) both when was fixed to the value obtained from the H2B ME-143 supplier data or when was kept as a free parameter. In the latter case, the estimated diffusion constant for bound p53 molecules was faster than that measured for H2B (0.0027?m2/s versus 0.0019?m2/s), consistent with our comparison of the MSD plots for bound p53 versus H2B molecules (Figure 2c). Thus, the kinetic model and the objective thresholding procedure yield very similar conclusions. While the preceding kinetic model yielded a good fit to the smaller p53 displacements (which reflect bound molecules), the fit was poor for the larger displacements (which reflect free molecules). To investigate whether improving this fit to the larger displacements would influence the binding estimates, we added a second freely diffusing state to the kinetic model. This added two more free parameters to the model, namely the diffusion constant of this second freely diffusing state and the fraction of molecules in this state. As expected with the addition of more free parameters, the new kinetic model yielded a better fit to the p53 displacement histogram. However, the estimates for the p53 bound fractions and residence times were not significantly changed. This provides further confidence that our binding estimates from SMT are reasonably accurate. It is important to point out that the good fit of the SMT data obtained by presuming two freely diffusing components does not prove that two such states actually ME-143 supplier exist. Instead, it is likely that these two states provide a simple way.