The mucociliary epithelium is a synchronized and highly effective waste-disposal system. It uses mucus as a vehicle, driven by beating cilia, to transport unwanted particles, trapped in the mucus, away from the organs. The ability of cilia, tiny hairlike protrusions (diameter 0.25 μm, length 5–7 μm and packing density 100–200 per cell), to propel steel beads of 1 mm in diameter at a speed of 0.5 mm/s is amazing (1). This titanic task is achieved due to the high degree of coordination between the individual cilia, and due to the ability of cilia to respond, quickly and for prolonged periods of time, to various stimuli, by increasing drastically the ciliary beat frequency (CBF). Owing to the physiological importance of mucociliary function in respiratory, digestive, and reproductive systems, and the rapidly growing list of diseases caused by dysfunction of the cilia, from chronic respiratory disease to abnormal organ development in the embryo (2), coordinated movement of cilia in time and space (metachronism) and signal transduction pathway(s) which lead to CBF enhancement have been intensively investigated. It was shown that extracellular adenosine-triphosphate (ATP) or acetylcholine (ACH) induces robust CBF enhancements from 10 Hz up to 30 Hz (3–11). Moreover, it was found that, when CBF was rapidly increased by extracellular ATP or ACH, the degree of coordination between beating cilia was not affected (12). These results suggest that transport rate will increase with ciliary stimulation. Nevertheless, the degree of correlation between ciliary frequency and the forces applied by cilia remains to be established. Moreover, since the forces applied by cilia depend not only on the beat frequency, but also on the beat pattern, it remains to be resolved whether the beat pattern depends on the CBF, and to what extent. These fundamental questions remain open, partly due to technical difficulties to measure directly the force produced from intact explants and to estimate the form of ciliary beat versus increase of CBF. Several studies have been made of the dependence of the pattern of ciliary beat upon ciliary beat frequency (13–15). These studies have relied on optical methods, attempting to describe three-dimensional movement from two-dimensional images of moving, dense cilia, thinner than the diffraction limit. The conflicting conclusions about the beat pattern at basal frequencies are an outcome of the inherent complexity of these systems. For example, a recent study (16) concluded that the effective stroke and the recovery stroke are in the same planes, contrary to the common concept (13,17–19).

To address this issue, in this study we examined the activity of cultured mucociliary cells from frog esophagus using simultaneous atomic force microscope (AFM) and photoelectric measurements. We applied our recently developed experimental setup (20) to examine the dependence between the amplitudes of both AFM and photoelectric signals on CBF, stimulated with two chemical stimulants (ATP and ACH) and temperature. Based on these measurements we draw conclusions regarding the dependence of the ciliary beat form on the beat frequency.

FIGURE 1 Cilia tips hitting the AFM tip. Four cilia, along an imaginary line perpendicular to the page, are depicted performing their effective stroke from right to left. The arc described by the tip of the gray colored cilium is indicated with dashed lines. It (more ...)

The optical setup is comprised of two opposing optical microscopes, focused in the plane of the ciliary culture, when one of them serves as a condenser, thus focusing light on the tissue and the opposed one collects the light scattered while passing through the active ciliary tissue. An optic fiber positioned in the intermediate image plane of the second microscope collects light from a circular area with a diameter of ~5 μm in the plane of the sample, adjacent to the AFM cantilever, and delivers it to a photomultiplier tube for conversion to an electric signal. The ability to simultaneously acquire both signals, from the same position on the sample not only allows the validation of the AFM measurements by the well-established electro-optical method, but enables us new insights into the change of the ciliary beat pattern during change of beat frequency.

For the measurements of stimulation by increase of temperature, the glass substrate was heated with a laser (Mira Optima, with a Verdi-V5 pump laser, both by Coherent, Santa Clara, CA) coupled through a multimode optical fiber. After temperature stimulation, cells were stimulated with ATP, to verify their normal response and ensure that no temperature-induced damage had occurred.

• Consecutive segments of the signal were analyzed, each 1–4 s long, with the purpose of calculating the CBF and amplitude representative of that segment.
• Segments of the data were selected, in which the frequency was well defined and stable (see further details below). In these sections, the signal was close to periodical, and therefore the standard deviation value was used as the representative value for the signal amplitude.
• After identifying the first maximum in the fast Fourier transform (FFT) power spectrum of a one second sampling duration, the program accepts or rejects the segment based on the ratio between the major peak and the next maxima. A clear, prominent peak indicates a period where the frequency is stable and well defined. The program then attempts to widen the segment of data, by adding more sampling points, for as long as the acceptance criterion is met. This way, the longest segments of signal are being selected, for which the frequency is stable and well defined, over the whole stimulation event.

The amplitude of the AFM signal is proportional to the force applied on it by the cilia. A thorough calibration of the AFM system may be performed, allowing readings of this amplitude in force units, as we have previously demonstrated (20). For the purpose of this study the absolute force units are not required (therefore the calibration steps were skipped); however, it is important to realize that the amplitude of the AFM signal is proportional to the force applied on it by the beating cilia. The various measurements, on various samples, were performed with uncalibrated AFM probes, and no attempt was made to establish the precise distance of the AFM tip from the base of the cilia. Therefore, in various measurements, the AFM tip may measure the force applied by a different number of cilia.

FIGURE 2 Stimulation of ciliary beat frequency with extracellular ATP (10 μM). (a) Frequency as extracted from AFM signal, according to the protocol described in Materials and Methods. Frequency is at its basal level (~10 Hz) during the first 50 (more ...)

To test whether the linear relationship depends on stimulant concentration, we performed experiments with ATP concentrations of 1, 10, 100 μM, on different cultures, from different frogs. The results were practically identical to the experiment described in Fig. 2 and are detailed in Table 1. The linear relationship between force and frequency is concentration-independent, over the whole duration of the experiment, i.e., through acceleration and deceleration of the beat frequency.

TABLE 1 Force-CBF relationship for stimulation of the beat frequency with various stimulants

The results are summarized in Table 1, where we report the slopes of the amplitude versus frequency plots on a log-log scale (plots not shown). The linear force-frequency relationship is maintained with ACH as a stimulant, despite the fact that it acts through different receptors. For ATP as stimulant we obtained an average slope of 1.0 ± 0.2 (three samples, two frogs, concentration 10 μM), and with ACH the average slope is 1.1 ± 0.1 (eight samples, three frogs, concentration 10 μM). A t-test comparison of the two sets of measurements, for the two stimulants, shows the sets of data are identical with a confidence >95%.

We used a powerful laser coupled to an optical fiber, to heat the sample. We chose this method of heating, to avoid electrical wires contacting the AFM liquid cell, which would have induced mechanical vibrations. The setup is described schematically in Fig. 3. The end of the optic fiber was placed under the glass substrate on which the ciliary tissue resided, 2.2 mm away (horizontally) from the position of the AFM probe.

FIGURE 3 Experimental setup for temperature stimulation of the ciliary beat frequency. An optic fiber connected to a powerful laser is positioned underneath the coverslip on which the ciliated tissue culture resides. The graph shows the temperature profile in (more ...)

We took extensive measures to ensure that the heating of the chamber did not damage the ciliary tissue. Tissue damage may be followed by cell death and release of ATP to the growth medium, thus causing stimulation of the CBF indirectly by ATP and not directly by temperature. Before beginning experiments, we measured the temperature profile in the liquid chamber with a copper-constantan thermocouple at three points, after shining the laser for several minutes. The temperatures at this time are representative of thermal equilibrium, therefore the temperature profile in the whole cell can be assumed to be a Gaussian centered above the optic fiber (see Fig. 3). The distance of the fiber from the bottom of the liquid chamber was adjusted so that the temperature did not exceed 35°C at the point where the AFM cantilever was positioned. The temperature directly above the fiber did not exceed 65°C. Then, the bare glass substrate was replaced with an identical glass substrate with ciliated tissue culture, for measurement. Importantly, it was verified that no tissue was placed directly above the optic fiber (see Fig. 3).

The AFM probe measured in a region where the temperature raised from room temperature to ~33°C, when heating. Temperature was not monitored during the experiment, to avoid mechanical vibrations induced by a thermocouple connected to the AFM liquid chamber. The scope of this study is to characterize the force-frequency relationship, and not the frequency-temperature relationship, thus, once it has been established that attained temperatures are not damaging, we treated the temperature as a stimulant of CBF. The measurements were started with the heating laser off, verification of the AFM reported frequency with the electro-optical system reported frequency, then the laser radiation was shone on the sample for ~60 s and shut off again. AFM signal was continuously collected before, during, and after heating, for a total of ~10 min. The optical subsystem signal was also continuously collected during this time. After completion of the measurement, it was verified that the ciliary tissue responded to ATP stimulation in the usual fashion, to ensure yet again that no damage was inflicted by heating.

In Fig. 4 we plot on a log-log scale the amplitude versus the frequency from one experiment and show that in this case the dependence is linear as well (the slope is 1). The average slope of three experiments from three different frogs is 1.0 ± 0.2. For temperature stimulation of CBF, the relationship force-frequency is also linear.

FIGURE 4 Dependence of AFM signal amplitude on the frequency, upon stimulation of CBF by temperature. Plot is on a log-log scale and the slope of the linear fit is 1; the amplitude of the AFM signal has a linear dependence on the frequency.

In our measurements, we find that, while the AFM signal amplitude rises linearly with the beat frequency, the amplitude of the optical signal decreases with increasing frequency, simultaneously and colocally. A typical result is shown in Fig. 5. All data presented have been acquired on the same patch of cilia during an ATP stimulation experiment. ATP was slowly added to the liquid chamber between 450 and 480 s. Frequency is increasing at ~550 s (~9 min) from the start of the experiment. The frequencies of the optical signal and AFM signal (Fig. 5, a and c, respectively) are identical, confirming proper operation of the AFM system and the fact that we are measuring the same cilia by both systems. The amplitude of the AFM signal increases (linearly) with increase of the frequency (Fig. 5 d) while simultaneously, the amplitude of the optic signal decreases (Fig. 5 b). The apparent decay of the optic signal before the rise in frequency occurs within the signal noise.

FIGURE 5 Optical and AFM simultaneous and colocal measurement during a stimulation experiment with extracellular ATP (10 μM). (a) Frequency of the optical signal. (b) Amplitude of the optical signal (normalized). (c) Frequency of the AFM signal. (d) Amplitude (more ...)

Previous measurements of the amplitude of the optic signal while changing the CBF by stimulation were performed (3) showing a decrease of the optic amplitude with the increase of the CBF. Our results show that this effect is not disconnected from the linear increase of the AFM signal amplitude, but in fact provides additional information regarding the change of the ciliary beat patterns. We discuss in depth these findings in what follows.

The measurement of the force applied by cilia as a function of beat frequency is reported here for the first time. It is important to mention that the absolute values of force have not been measured in each experiment. Not only is this not required to assess whether the force depends linearly on the beat frequency, but in fact it strengthens the reliability of the results: the linear dependence is not a function of the initial force sensed by the AFM cantilever at the beginning of the experiment (initial approach and dipping of the tip into the field of cilia). The log-log plots in Fig. 2 c and Fig. 4 represent on a logarithmic scale the relationship y = ax^α + b, where y is the force sensed by the AFM tip and x is the beating frequency. In this equation, a is the proportionality coefficient, that has dimensions of N/Hz, and describes how much force per Hz of beating frequency is sensed by the cantilever. We have shown previously that this number is in its essence a geometrical factor describing the number of cilia that hit the AFM tip, the angles and position along the individual cilia where they meet the pyramidal tip, and the geometry of the tip (in addition, it includes the proportionality between the bending of the AFM cantilever and the actual voltage difference that is reported by the AFM electronics). It can be extracted from an experiment with a calibrated cantilever, by varying the depth to which the AFM tip penetrates the field of cilia (20). This a-value changes very sharply as a function of the initial dipping depth (approximately one order of magnitude for 2 μm change in penetration depth), and in this study it varies between the various experiments; however, it is constant along a single experiment. The results reported here are therefore an average over several experiments in which the geometry was different, the cantilever force coefficient was different and the initial alignment of the AFM was different (the monitoring laser hitting the back of the cantilever is manually adjusted for each mounted cantilever, thus the voltage recorded by the acquisition electronics varies from one cantilever to another). The fact that the force-frequency dependence is linear under these conditions lends much credibility to these results, and shows that it is a general effect, not just a coincidence of a specific system setup. This information provides a unique opportunity to analyze the form of the ciliary beat upon change of frequency in a mucociliary system. The obtained results have a number of implications on the form of beat of these cilia, discussed below.

FIGURE 6 Schematic representation of the form of ciliary beat. (a) A cilium performing its effective stroke in the direction indicated by the arrow. L is the length of the cilium, θ is the angle swept by the cilium during the effective stroke, l = (more ...)

Thus, the measured AFM amplitude, Z, is proportional to the tangential velocity of the cilium's tip V_cilium: Z V_cilium (the same conclusion can be drawn also from momentum transfer considerations).

Since our measurements show that Z is linear in the beat frequency, f, it follows that

It is important to note that an alternative scenario could have taken place: as we sketch in Fig. 6 b, the angle swept during the effective stroke could have been decreased to a minimal value of θ′ (between the two dashed lines) while still displacing the mucus layer by the same distance during each cycle, since during the rest of the stroke the cilium tip is not embedded in the mucus layer. However, our findings indicate that this is not the case; instead, the arc length remains constant while the frequency changes. A hypothetical scenario like the one described in Fig. 6 b would have saved energy consumption; however, this would have decreased the tangential velocity of the cilium's tip, leading to a reduced transport velocity (since a reduced length of arc swept at a given frequency means a lower tangential velocity). Our results indicate that the cilia follow a scenario that leads to the maximal increase of transport velocity, by keeping the length of the effective stroke constant.

Both ATP and ACH activate phospholipase C, in turn mobilizing Ca²⁺ from intracellular Ca²⁺ stores (10,23). However, extracellular ATP acts through the Purinergic receptors to cause continuous influx of Ca²⁺ from outside the ciliary cell (8), while ACH does not (10). Instead, ACH acts through muscarinic receptors on the ciliary cell membrane to directly increase intracellular cAMP levels (11), which enables maintaining the CBF higher than prestimulation level, independent of (resumed prestimulation) Ca²⁺ level. Thus, seemingly, two different ways are utilized to maintain increased CBF activity, by each stimulant.

There is a very limited amount of data describing the form of beat of mucociliary systems, nevertheless it is instructive to compare our findings with other members of the cilia family, even though they perform different functions.

In a comparative study of native and mutant Chlamydomonas, the mutants beat with a slower frequency, but with an arc of identical length (24). A study of the waveform of the metachronal wave at various CBFs, in Mytilus edulis' short (lateral) cilia and other organisms' cilia (25), led to the conclusion that the angular velocity of the effective stroke is higher in cilia that beat faster, since the waveform remains unchanged. A study of the metachronal wave in the same cilia as used in this study (12) also demonstrated that the metachronal wavelength does not change with CBF increase. In a photoelectronic measurement of the beats of respiratory tract cilia (6), both recovery and effective strokes were faster with increase of CBF. These studies support the conclusion from our AFM measurements of faster tangential velocity during effective stroke with CBF increase and independence of arc length on CBF.

Other imaging results in the literature are less straightforward for comparisons with our results. In optic measurement of cilia from Paramecium (14) the angular velocity of the effective stroke first sharply increased with CBF increase, followed by plateau with further CBF increase. In a study of rabbit tracheal cilia (26), the effective stroke shortened its duration linearly with CBF increase within the range 4–12 Hz but did not change at higher frequencies.

In addition, since the length of the effective stroke arc is constant, the recovery stroke is also performed faster. However, since the cilium is more erect during recovery stroke at high frequencies, the total path traveled by the cilium during a whole beat cycle shortens. To illustrate this, we schematically draw a top-down projection of the path described by the cilium tip in Fig. 6, e and g, during basal and stimulated frequency, respectively. Thus, when increasing the beat frequency, the cilium maintains a constant effective stroke arc, resulting in a linear increase in the tangential velocity and consequently a linear increase in mucus transport velocity, while during recovery stroke it becomes more erect, thus shortening the distance to the end of the cycle and the beginning of the next recovery stroke. The shortening of the total path should save on energy consumption, without sacrificing maximal transport velocity increase.

The simultaneous electro-optical and AFM measurements performed in this study reveal new details about the beat form of mucus propelling cilia, when they accelerate their beating frequency.

The length of the arc swept by the cilia during effective stroke remains constant during stimulation of CBF. This leads to a tangential velocity of the cilium tip precisely linear with the beating frequency. Consequently, the mucus transport velocity is expected to increase linearly with the beating frequency.

This feature does not depend on the type of stimulant (chemical or temperature), on the species of chemical stimulant (ATP or ACH), or on the concentration of the chemical stimulant (ATP: 1 μM, 10 μM, 100 μM). This seems to indicate that the switching occurs at constant positions of the cilium, presumably related to its inner structure, positions that are not affected by the mechanism leading to CBF increase.

While the effective stroke geometry remains unchanged, the recovery stroke is being performed in an increasingly perpendicular (to the cell surface) plane with increasing beat frequency, as indicated by the optical measurement. This fact leads to a shortening of the total path swept by the tip of the cilium during a beat cycle.