The Relations Between Membrane Potential and Parameters of Ciliary Beat in Free-Swimming Paramecium Caudatum

It has been known for many years that electric currents flowing through a suspension of Paramecium modify the beating characteristics of the cilia in such a way that the organisms turn and move towards the cathode (Ludloff, 1895; Jennings, 1906). Jahn (1961) has accounted for this behaviour by supposing that current flows through the cell membrane and either enhances or reverses the normal ciliary beat, depending on the direction of the current. Naitoh & Kaneko (1972) have recently shown that the important parameter in controlling the direction of ciliary beat in models of Paramecium extracted with Triton X-100 is the internal calcium ion concentration, and Eckert (1972) has proposed a unifying theory of bioelectric control of ciliary activity in which the internal calcium concentration is governed by the cell-membrane potential. The response of Paramecium to electric fields can then be understood in terms of a variation in membrane potential causing local changes in the direction and frequency of ciliary beat.

This paper describes experiments on Paramecium caudatum in which the normal movement is perturbed by external electric fields. The underlying changes in the parameters of ciliary beat are then deduced and interpreted in terms of changes in membrane potential. This method obviates the need for micro-electrodes which would otherwise be necessary to perturb the membrane potential, and the results furnish a useful check on the reliability of the usual micro-electrode studies.

Specimens of Paramecium caudatum, reared in hay infusion, were washed in distilled water containing 1 mm CaCl₂ and 4 mM KC1/1. Most of the observations were made in this medium. Organisms moving in a shallow glass dish were photographed from above with a Vinten Mk. 3 scientific cine camera coupled to a low-power Zeiss microscope. Horizontal illumination was provided by a projector lamp and condenser lens. Electric fields were applied between two long parallel stainless-steel electrodes placed a distance 40 mm apart in the dish. Organisms were kept away from the electrodes by filter paper barriers 10 mm away from each electrode.

Field-tracing experiments showed that these barriers produced a less than 5 % deviation from a uniform field over the central region of the dish.

Swimming velocity (u), axial spin (W) and orientation rate (β) were inferred from the cine record. Tracks lying in the plane of the dish were selected to eliminate geometrical errors. The curvature of the trajectories could be measured directly in electric fields above 100 V m⁻¹ (Fig. 1). At lower field strengths track curvatures were too small to be measured in this way, and instead the ‘pile up’ distribution adjacent to the cathodal barrier was measured from the film. Under these conditions the number density of organisms falls exponentially with increasing distance from the barrier, and if the scale length of the distribution is δ, the mean orientation rate is given by

When a field is applied there is an immediate increase in swimming velocity, the degree of the increase depending on the field strength. Fig. 2 shows the swimming velocity 10 s after applying the field. Above about 37 V m⁻¹ the organisms move in straight lines towards the cathode, and begin to exhibit their characteristic anterior swinging motion above about 70 V m⁻¹. The velocity starts to fall off above 100 V m⁻¹, and this peaking appears to coincide with the onset of large-amplitude swinging.

Fig. 3 shows the swimming velocity as a function of time for E₀ = 50 V m⁻¹. During the second pulse the swimming velocity is returning to its pre-field value, even in the presence of the field. Accommodation to the field takes longer, the stronger the field, but for all field strengths appears to be complete within 2 min.

Fig. 4 shows the orientation rate β as a function of field strength for equilibrated specimens. Within the accuracy of the experiments all the points lie on the solid line indicated; no significant differences were noted as the concentrations of potassium and calcium ions were varied separately over a range limited by half and twice the standard concentrations. No evidence of accommodation of β was observed over periods of up to 15 min in field strengths below about 100 V m⁻¹.

The marked increase in swimming velocity with E₀ can only be interpreted in terms of equation 1 as an increase in frequency. Ф is typically 10–15° in normal locomotion (Kinosita, 1954; Machemer, 1972) so that cos Ф cannot increase by more than 3 %. Studies of beating cilia show that their amplitude is generally close to the geometrically permitted maximum (Sleigh, 1968). Thus, for example, if E_o= 50 V m⁻¹ the velocity increases by 72 % (Fig. 2), and equation 1 implies that the average frequency has also increased by this amount.

The change in membrane potential over the organism can readily be calculated (Appendix A). For an average Paramecium moving towards the cathode in a field of 50 V m^-1 the maximum depolarization (at the cathodal end) is ∼ 6 mV and the maximum hyperpolarization (at the anodal end) is also ∼ 6 mV ; the membrane potential varies linearly along the length of the organism. If the frequency depends uniquely on the membrane potential then the frequency will be unchanged at the centre of the organism when the field is applied, and will exhibit maximal changes at cathodal and anodal extremities. The very fact that metachrony exists in ciliary arrays implies that the frequency is influenced by neighbouring cilia; this and the smooth co-ordinated motion at low field strengths suggests that in an electric field all the cilia beat at virtually the same frequency, which is itself a function of the perturbing field. If either depolarizing or hyperpolarizing perturbations of the membrane caused a decrease in frequency then to a first approximation no mechanism would exist for increasing swimming velocity, since the mean frequency would be unchanged. The present observations are therefore consistent with only one hypothesis, namely, that depolarizations and hyperpolarizations both produce increases in frequency. The magnitude of the increase in previously unexposed organisms 10 s after application of the field is (23 ± 3) % mV⁻¹ (Fig. 2), although the magnitude of the increase is highly dependent upon the previous history of the organism (Fig. 3).

The changes in swimming velocity with higher field strengths are considered after the next section.

The present results therefore suggest that the angle of ciliary beating is strongly dependent on depolarizing deviations of the membrane potential from its resting value, that the relationship is probably quasi-linear, and that hyperpolarizations cause little or no change in the direction of beat. Micro-electrode studies (Kinosita, 1954) indicate that when the ionic constitution of the outside medium is changed both Φ and V_m change simultaneously; whilst V_m reaches a new equilibrium level, <D soon returns to its original value. Both types of experiment therefore suggest that the angle of beat depends upon the perturbation in membrane potential rather than upon its absolute value.

If the above picture is correct some further consequences follow. As the field strength is increased the cilia on the anterior half of the organism will turn progressively backwards, and the swimming velocity will decrease accordingly. The expected decreases have been calculated for an organism spinning uniformly about its longitudinal axis (Appendix B) and are shown in Table 1. At low field strengths the swimming velocity increases with increasing field strength because the frequency increases. Assuming that the swimming velocity increases at the same rate at higher field strengths (the dotted line in Fig. 2) the percentage reductions in actual swimming speed can be calculated, and are shown in Table 1. The general agreement between the measured and predicted values suggests that changes in angle of beat can account for the variations in swimming velocity in electric fields.

The theoretical model predicts the rate at which axial spinning should occur (Appendix B). If Φ₀ ∼ 10–15° the predicted rate of spin is about 0·5–0·75 Hz, which is what is in fact observed. This clearly confirms the idea that the spiralling of Paramecium is due to transverse components of ciliary thrust (Machemer, 1972) and not to any asymmetry in body geometry.

As the electric field is applied, the rate of spinning should increase to a maximum of about 1·25 Hz at 150 V m⁻¹, and decrease at higher field strengths. In real organisms, however, uniform spinning about one axis does not occur at fields above about 70 V m⁻¹ ; instead, the anterior end traces out a cone, and the organism spirals forward in such a way that the same parts of the membrane tend to be on the outside of the spiral. This could be due to variations in electrical sensitivity along the surface of the organism, to asymmetries produced by the presence of the oral groove, or to a combination of both. The present experiment cannot distinguish between the two possibilities, however.

The gyration in the electric field can explain Dryl ‘s (1963) observation that organisms near a boundary exhibit oblique orientation to the field direction in fields above 70 V m⁻¹ ; the boundary prevents full gyration from occurring, and the organism moves along the boundary at an angle determined by the asymmetry of the ciliary forces.

The present results can be correlated with the observations of Naitoh & Kaneko (1972) on the changes in swimming velocity with internal calcium concentration. The angle of beat (Φ) changes almost linearly from zero to 90° (this follows from equation 1) as the internal calcium concentration is increased logarithmically from 0·1to 1·0 μM I⁻¹. The average rotation is thus 90° per calcium decade. Since the present results show that this rotation is also produced by a depolarization of 10 mV, the internal calcium ion concentration must vary with membrane depolarization at the rate of approximately one decade/10 mV. Thus the increase in calcium ion concentration at the ciliary apparatus is about 25 % for a depolarization of 1 mV. The two principal problems now are to elucidate the mechanism by which the membrane potential governs the internal calcium concentration, and to determine how this governs the direction of ciliary beat.

We thank Mr R. Silva for technical assistance, and the Central Research Fund of the University of London for an equipment grant.

The multiples of 1·08 and 1·86 in equations (A4) and (A 5) are within 8% of 1·0 and 2·0, which are the appropriate values for a cylindrical body with length much greater than the diameter. This is the justification for using a cylindrical model for the electro-mechanical analysis presented in Appendix B.

For the reason given in Appendix A a cylindrical model of P. caudatum is utilized here.

The maximum turning effect in electric fields arises when the organism is at right angles to the field direction. Cilia on the hyperpolarized (anodal) half beat as usual whilst on the depolarized (cathodal) half they beat at an angle determined by the membrane depolarization ΔV_m (equation 2). Consider a transverse section (Fig. B 1) and the corresponding elements (1, 1′) and (2, 2′)-The propulsive force from (2, 2′) is, for each, and for (1, 1′) is (symbols are defined in Table 2). The resultant torque dT due to these strips is then given by