Figure 1.
Measuring correlated and uncorrelated noise in flagellar length control system
(A) Correlated and uncorrelated components of variation can be visualized in measurements of flagellar length in fixed Chlamydomonas cells with two equivalent flagella. The lengths of the two flagella in a cell are denoted L1 and L2 as illustrated in the diagram, where L1 is whichever flagellum happens to be to the left of the other in the field of view of the microscope. Graph plots length of one flagellum versus length of the other flagellum. Correlated variation is reflected by scatter along the diagonal L1 = L2 (gray line). Uncorrelated variation is reflected by scatter perpendicular to this axis. (Blue) Wild-type asynchronous culture; (red) wild-type gametes. (Inset) Diagram of a Chlamydomonas cell showing the three measurements reported in this paper.
(B) Dynamic changes in flagellar length. Image shows four successive time points, taken 10 min apart, of a 3D time series of a single living cell embedded in agarose and imaged with DIC microscopy. Graph below plots sample traces showing the length of two flagella within one cell versus time.
(C) Quantifying fluctuations in length observed in living cells. (Red) Mean-squared change in length plotted versus time, showing constrained diffusion-like behavior. Error bars signify standard error of the mean. (Black) Mean-squared change in length in glutaraldehyde-fixed cells as an indicator of measurement error.
(D) Correlation between length changes in successive 10-min intervals (red markers, r = 0.28) compared with length changes during 10-min intervals separated by 60 min (blue markers, r = 0.015). Inset gives autocorrelation of length changes (specified by the Pearson coefficient r, which is unitless) versus time lag.
(E) IFT-coupled model for length fluctuations. Tubulin subunits (green) are brought to the end of the flagellum by anterograde IFT particles (blue) and deposited onto the tip, elongating the flagellum. Tubulin subunits disassembling from the tip are immediately brought back to the cell body by retrograde IFT particles (orange), shortening the flagellum. At steady state, elongation and shortening events occur at the same average rate, but stochastic differences in the quantity of tubulin added or removed results in a net change in length of δ at a rate comparable to the frequency 1/τ of IFT trains arriving at or departing from the tip.
(F) IFT-uncoupled model for length fluctuations. IFT maintains a pool of tubulin monomers near the tip, which undergo association or dissociation events at rates Κ+ and Κ−, respectively. Assembly rate Κ+ is length dependent, creating an effective restoring force. The resulting Ornstein-Uhlenbeck process, which describes diffusion of flagellar length constrained by the presence of a restoring force, defines the slope and asymptote of the mean-squared length change versus time plot, as indicated by the diagram. This theoretical prediction can be directly compared with Figure 1C.