ABSTRACT
Mammalian ciliary beat frequency (CBF) is regulated by the intracellular calcium concentration. It has been shown by us and others, using a variety of methods, that CBF follows the direction of cytoplasmic calcium concentration ([Ca2+]i) changes (1-8). At the molecular level, however, it remains unclear how changes in [Ca2+]j are transduced into changes in CBF. Recent advances in measuring [Ca2+]j and CBF simultaneously, a technique first described by Komgreen and Priel (4), and the introduction of high-resolution, simultaneous measurements, where accurate kinetic relationships between these two signals can be assessed (9,10), have advanced our understanding of how Ca2+ regulates CBF. We have measured CBF and [Ca2+]i (indicated by fura-2) at room temperature in response to activation of the G-protein coupled M3 muscarinic receptor by 10 |lM acetylcholine (ACh). When CBF was estimated by a Fourier transform method with a CBF time resolution of <100 ms (10), the difference in the onset of the CBF increase compared to [Ca2+]j was 70 ± 30 ms (mean ± SEM; n = 20 cilia). 59
During the slower return to baseline, a lag of 8 ± 3.2 s was observed, indicative of hysteresis. These data are in agreement with the ones presented by Sanderson et al. in this book (Fig. 1). While calmodulin inhibitors (calmidazolium and W-7; each n — 5) decreased baseline CBF by an average of 1.1 ± 0 .1 Hz, they did not alter the kinetic relationship between [Ca2+]i and CBF. Similarly, phosphatase inhibitors (okadaic acid and cyclosporin A; each n = 5) changed neither baseline CBF nor the kinetic coupling between [Ca2+]j and CBF. These data suggested that the timing of Ca2+ action on CBF in ovine airway epithelial cells is unlikely to be determined by phosphorylation reactions involving calmodulin or kinase/ phosphatase reactions. Based on these observations, we developed a model for calcium action on ciliary beating, which is presented here. MODELING THE COUPLING OF [Ca2+]i AND CBF Three basic models of Ca2+/CBF coupling were considered. A linear coupling model was rejected by the data (Fig. 1). A simple cooperative binding model was also rejected since a Hill plot (not shown) did not reveal a linear relation between [Ca2+]i and CBF. A more complex model that takes the action of dynein arms into account was therefore needed. For a discussion on current understanding of the principles of dynein motor activity during ciliary beating, see Chapter 2 in this book.Our model of the effect of [Ca2+]i on CBF was based on three assumptions:
1. Ciliary dynein arms move microtubules with either a ‘ ‘slow’ ’ or ‘ ‘fast’ ’ duty cycle, in accordance with experimental microtubule sliding results using Chlamydomonas inner dynein arms (11).2. Dynein ATPase activity is shifted between fast and slow modes by a change in [Ca2+]j.3. Ntotai complete and sequential dynein ATPase cycles are necessary to complete one ciliary stroke, in accordance with the ciliary motility model by Holwill et al. (12,13). Thus,
CBF = 1/(Ntotai X Tdyneincycle) (1) where Tdynein cycle is the time (in seconds) that the dynein arm actively interacts with the microtubule (thereby moving it) and not necessarily the full duration of a dynein arm cycle (which is roughly 33 ms in vitro; see Chapter 2). Using published data on dynein conformational changes, we estimated the minimum number of sequential dynein arm actions necessary for one single ciliary stroke as follows (12,13). Two outer doublets separate by ~0.1 |im at the end of a full ciliary bend, and a single dynein arm cycle can move a microtubule 4-16 nm (8 nm currently being favored; see Chapter 2). Thus, anywhere between 12 and
where ffast is the fraction of the dynein arms that are operating in fast mode, fS|0W is the fraction of the dynein arms that are operating in slow mode (and fslow = 1 — ffast)? Tfast is the time (in seconds) required for an active dynein cycle (interacting with the microtubule) in fast mode, and Tslow is the active dynein cycle time (in seconds) in slow mode.First, we wanted to illustrate the calcium dependence of the fraction of slow (no calcium bound) vs. fast dynein arms (all binding sites with bound calcium) using the Hill equation assuming, for this example, a total Kd for all cooperative binding sites of 150 nM (Fig. 2C). CBF at low [Ca2+] is determined by the slow dynein cycle time. With increasing [Ca2+], the fraction of fast dynein will increase and therefore speed up CBF. The traces shown in the graph simulate the relationship between [Ca2+]j and the fraction of fast dynein arms assuming 1 (no cooperative binding) to 2-5 cooperative Ca2+-binding sites, respectively. With this use of the Hill equation to calculate the fast and slow dynein arm fraction’s dependence on [Ca2+], CBF can be estimated.Figure 2D shows a simulation for which the slow dynein arm duration was chosen to result in a “ resting” CBF of 7 Hz (based on our data from recordings at 20°C), whereas the switch to all fast dynein arms was chosen to result in a maximal CBF of 12 Hz. This frequency range was only used for the purpose of simulation, and these specific values are not a general feature (or limit) of the model. The fraction of fast vs. slow was taken from the simulated Hill equation as mentioned above (Fig. 2C). Such graphs now start to resemble recorded data, especially when used with three or more cooperative Ca2+-binding sites.Finally, we fit this model to recorded data as shown in Figure 3. The slow and fast dynein cycle duration, and the Kd were free parameters of the fit, thereby allowing basal and maximal frequencies to assume any value. These fits suggested that models with four cooperative Ca2+-binding sites best fit the recorded data (in a least-squares sense). Using the fit parameters for four cooperative Ca2+- binding sites, the average Kd was 50 nM, the slow dynein cycle duration 9 ms, and the fast dynein cycle duration 4.5 ms (n = 9 cells). These nine experiments were also combined into a single data set and again fitted with the model (Fig. 3B). Again, using four cooperative Ca2+-binding sites resulted in the best fit.
