morphology, tubulin acetylation, colchicine sensitivity, flagellar length, swimming rate, flagellar regeneration kinetics, or low calcium–induced flagellar resorbtion kinetics (Kozminski et al., 1993a). Therefore, we con- clude that expression of this construct does not perturb flagellar microtu- bule dynamics. Fla10-1 mt mutant strain cc-1919 and lf2-5 mt mutant strain cc-2287 were obtained from the Chlamydomonas Genetics Center (Duke University, Durham, NC). Strains expressing HA-tubulin in fla10 and lf2 mutant back- grounds were constructed by crossing 5C12G12 with cc-1919 or -2287, and selecting tetrad products (Harris, 1989) that showed the mutant phenotype and that expressed tagged tubulin as judged by immunofluorescence. Mating procedure Gamete cultures of 5C12G12 mt and 6145c mt were obtained using standard methods (Harris, 1989). 500 L of each culture was then mixed together and allowed to mate for 15 min. To arrest mating, 5 ml of low ni- trogen medium (Harris, 1989) was added to the mating mixture, which was then allowed to sit undisturbed for 15 min. During this time, the nega- tively phototactic mt cells swam to the bottom of the tube to form a pel- let, along with the majority of the quadriflagellated dikaryons, which be- come negatively phototactic after mating. The mt cells, which were nonphototactic under these conditions, remained in suspension. The top 4 mL of medium was removed and replaced with 4 mL fresh medium. This procedure was repeated twice more to remove unmated mt cells, thereby arresting further mating. The remaining cells were diluted to a total volume of 10 mL to further discourage additional mating. Immunofluorescence Immunofluorescence was performed as described (Cole et al., 1998). Pri- mary antibodies were mouse monoclonal anti-HA antibody 12CA5 diluted 1:10, and affinity-purified rabbit anti-Fla10 (Cole et al., 1998) diluted 1:250. Affinity-purified rabbit anti-IFT52 antibodies were provided by James Deane (Deakin University, Melbourne, Austrailia) and diluted 1:50. Sec- ondary antibodies were Oregon green goat anti–rabbit (Molecular Probes) plus Texas red goat anti–mouse (Jackson ImmunoResearch Laboratories), each diluted 1:500. We note that when Chlamydomonas cells adhere to polylysine-coated coverslips for long periods of time, the tips of the flagella begin to curl up, such that even antibodies that stain the flagellum uni- formly along its length sometimes give a brighter signal at the tip. There- fore, we minimized the time (always 5 min) that the cells were allowed to adhere to the coverslips. Cells fixed immediately after mating showed no tip labeling, indicating that the tip labeling observed in Fig. 1 was not simply an artifact due to tip curling. For distinguishing central pair from outer doublet microtubules, flagella on intact cells were de-membranated and splayed using NP-40 plus ATP as previously described (Johnson, 1998). The partial regeneration experi- ment of Fig. 4 was performed as described (Johnson and Rosenbaum, 1992). Slides were imaged with a 63 NA1.4 oil immersion objective. Lengths were measured using a calibrated reticule mounted in the ocular. For imaging IFT52 staining versus flagellar length, wild-type cells were deflagellated by pH shock. Cells were stained with antibodies to IFT52 and acetylated tubulin, and imaged using a cooled CCD using a uniform expo- sure time. Average intensity was measured in a series of 20 20 windows that spanned the length of the flagella. Appendix Mathematical model of flagellar length control Derivation of differential equation describing length regu- lation. To obtain the differential equation describing flagel- lar tubulin turnover (Eq. 1), we assume that IFT-mediated precursor transport is the rate-limiting step that determines the addition rate of new tubulin subunits at the distal end. Direct measurements have shown that IFT particles move at a constant rate of va 2 m/s in the anterograde direction, and vr 3.5 m/s in the retrograde direction (Kozminski et al., 1993b). The time it takes for a particle to move from the base to the tip and back again over a length L is given by 2L/v, where v is an effective velocity equal to 2vavr/(va vr) which, given the measured values for IFT, is equal to 2.5 m/s. This simple model assumes that the number of parti- Flagellar length control | Marshall and Rosenbaum 413 cles moving anterograde equals the number moving retro- grade, which may not be strictly true. However, the funda- mental predictions of these simulations are not affected if one changes the relative ratio of anterograde to retrograde particles. If there are N transport complexes moving in a sin- gle flagellum, we obtain the expression vN/2L as the as- sembly rate at the tip, where is a proportionality constant reflecting the effective transport capacity of each IFT parti- cle. We assume that disassembly occurs at a constant rate D, estimated to be 0.011 m/s, based on the rate at which fla- gella resorb during the rapid disassembly period after mating (10 m in 15 min). We can then solve for by considering the steady-state situation where D vN/2L. We set N 10 based on typical DIC images, but any other number would give the exact same results because we solve for in terms of N. The plot of Fig. 8 B was obtained by computing the value of vN/2L for different values of L. Prediction of flagellar regeneration kinetics. The flagel- lar regeneration plot (Fig. 8 C) was produced by solving Eq. 1 to yield: T {A DL Aln|A DL|}/D2 C (A1) where A vN/2, D is the disassembly rate, T is time, and C is a constant of integration. We fit Eq. A1 to a published time-course of flagellar regeneration (Rosenbaum et al., 1969). The solution plotted in Fig. 8 C corresponds to A 2.67 m2/min, D 0.22 m/min, and a lag before initia- tion of regeneration (determined by letting the constant of integration C vary to obtain the optimal fit) of 3.0 min. The r.m.s. error in T was 7.4 min. Simulation of flagellar severing experiments. To simu- late experiments in which flagellar length reequalizes follow- ing perturbations such as severing one flagellum, it is neces- sary to model the effects of flagellar severing on the pool of flagellar precursor proteins. The simplest assumption is that axonemal proteins are loaded onto IFT particles according to a simple binding equilibrium so that the amount of mate- rial transported by each IFT particle is proportional to the available pool of flagellar precursor proteins. Let P represent the total pool of flagellar precursor protein, including both free precursor and that already incorporated into flagella. Specifically, P refers to the quantity of which- ever flagellar structural protein is limiting. At present it is not known whether this is tubulin or some other protein. We find P by noting that Chlamydomonas cells contain a free protein pool sufficient to build two half-length flagella with- out additional protein synthesis if both flagella are cut off (Rosenbaum et al., 1969). Therefore, the total pool size P is found by solving for steady state conditions, both for normal cells in which a complete pool gives two full-length flagella, and for deflagellated cells for which a pool reduced by two flagella worth of material yields two half-length flagella at steady state. For any given total pool size, the free pool of protein will be P minus the quantity of protein incorporated into the two flagella, or P L1 L2. Therefore, we replace the original rate coefficient in Eq. 1 with a pool-dependent rate coefficient (P L1 L2) where is a constant. To simulate the severing of one flagellum, the length of the severed flagellum was set to 0.1 m (to avoid division by zero) and the initial length of the unsevered flagellum was