Substantial energy expenditure for locomotion in ciliates verified by means of simultaneous measurement of oxygen consumption rate and swimming speed

Paramecium inhabits an environment that is mechanically characterized by the dominant influence of viscous forces. In such a viscous environment, defined as low Reynolds number hydrodynamics, organisms move under conditions that greatly differ from those of our aerial environment, in which organisms move while being dominantly affected by the inertial force and the pressure of the surrounding fluid(Vogel, 1994). It is therefore not surprising that organisms perform a different mode of energy expenditure for locomotion in such a different mechanical environment.

As the viscous force dominates in the swimming of aquatic microorganisms, a large amount of energy should be dissipated through the interaction with the surrounding fluid. This means that the swimming of Paramecium is done with much lower efficiency than larger organisms, i.e. the ratio of efficient mechanical work to total energy expenditure for locomotion is low in Paramecium.

The total energy consumption of Paramecium was estimated on the basis of the oxygen consumption. Fenchel and Finlay summarized the data of the total oxygen consumption rate measured from the cells under various physiological conditions, such as growing or starved cells at different temperatures (Fenchel and Finlay,1983). They obtained 0.19–4.4×10^–9 l O₂ h^–1 for a single cell (Paramecium caudatum). These values can be converted to the power,0.38–8.8×10^–5 J h^–1cell^–1, by the conventional transformation of liters of O₂ into 20.1 kJ(Schmidt-Nielsen, 1984).

Mechanical work done by swimming Paramecium can be estimated on the basis of Stokes' law. For a sphere with a diameter of 50 μm moving with a speed of 1 mm s^–1, which is one of the simplest models for P. caudatum, the power of swimming (the mechanical work done per unit time) has been calculated to be 3.4×10^–9 J h^–1. This power calculated on the basis of Stokes' law, which is called Stokes power in this paper (StP), is only 0.004–0.09%of the total energy expenditure.

This very small percentage, however, does not correctly represent the efficiency of swimming of Paramecium. In order to estimate the efficiency, mechanical work should be compared with the energy used only for swimming. Little attention has been paid to the swimming behavior while measuring the oxygen consumption of microorganisms(Fenchel and Finlay, 1983; Scholander et al., 1952). We have therefore few data available in order to evaluate the amount of energy necessary for generating the locomotor activity of Paramecium. This is largely because it is difficult to simultaneously measure oxygen consumption and record the swimming behavior.

In this paper, we will present the energy expenditure of Paramecium in close relation to its swimming activity. For this purpose, paramecia were confined in a small volume of the chamber (<1 ml)and the oxygen consumption rate and the swimming speed were measured simultaneously from the same specimens. Oxygen consumption was measured by means of an optic fluorescence oxygen sensor(Okubo et al., 2008). Because this sensor has proved not to alter the amount of dissolved oxygen unlike oxygen electrodes, which consume a substantial amount of oxygen during the measurement procedure, it is ideal for measuring the oxygen concentration in a small volume of a sample. Swimming speed was measured from the recording obtained by the optical slice method (Kato et al., 2003).

Our measurements revealed a linear relationship between the rate of the oxygen consumption and the speed of freely swimming Paramecium. By extrapolating from the regression line between oxygen consumption rate and swimming speed, we could estimate that the energy expenditure of the cell in the `non-motile' state is about a quarter of the total energy consumed by the cell when swimming. This indicates that Paramecium uses a large amount (ca. 70%) of energy for swimming.

Paramecium caudatum Ehrenberg was cultivated at 23±1°C in hay infusion in Dryl's solution (2 mmol l^–1 sodium citrate, 1.2 mmol l^–1 Na₂HPO₄, 1.0 mmol l^–1 NaH₂PO₄, 1.5 mmol l^–1 CaCl₂, pH 7.2)(Mogami et al., 2001). We used cells at the early stationary phase of growth (18–22 days after incubation). Cells were collected by low-speed, hand-operated centrifugation(<170 g) and were adapted to the experimental solution(KCM: 1.0 mmol l^–1 KOH, 1.0 mmol l^–1CaCl₂, 0.25 or 1.0 mmol l^–1 MOPS, pH 7.2 adjusted by HCl) for longer than 1 h. The K⁺ concentration in the experimental solution was controlled by changing the amount of KOH added to the solution in order to achieve slower swimming by membrane depolarization (4 mmol l^–1 K⁺)(Machemer, 1989).

We measured the oxygen consumption and the swimming speed of Paramecium simultaneously. As shown in Fig. 1, 0.74 ml of cell suspension with a density of 3.5×10³–1.9×10⁴ cells ml^–1, which is close to the density during the stationary phase, were transferred, without air bubbles, into the columnar space of the recording chamber. The chamber was made of Plexiglas with inner dimensions of 12 mm in diameter and 5 mm in depth. The bottom of the chamber was sealed with silicone grease by a coverslip, through which the swimming of the cells could be recorded. The oxygen concentration in the chamber was measured by an optic fluorescence oxygen sensor (FO-960, ASR, Tokyo, Japan). The principle of the sensor procedure is based on the quenching of fluorescence caused by collisions between molecular oxygen and fluorescent dye molecules in the excited state. This means that measurements can be done without any consumption of oxygen by the sensor itself. The sensor is therefore utilized especially for measuring oxygen consumption in a small volume. In our recording chamber, the sensor was placed at the top of the columnar space with its probe surface facing the specimen.

The swimming behavior of Paramecium in the columnar space was recorded using the optical slice method(Kato et al., 2003). The chamber was illuminated by a horizontal slit laser with a known beam thickness(half-maximum intensity width of 0.2 mm; SU-42C-635-10, Audio Technica, Tokyo,Japan), and dark-field images of cells that swam in the slit of light were recorded with a CCD camera (XC-77RR, SONY, Tokyo, Japan).

The recording chamber was placed in a water bath with circulating water of a constant temperature. Specimens in the chamber were illuminated by the slit laser placed outside the water bath (Fig. 1). All of the recording devices were further enclosed in a constant temperature box in order to avoid changes in the temperature of the small volume containing the specimen, which may result from contact with the larger body of the sensing device. Temperature throughout the experiment was 23±1°C.

To measure the swimming speed, dark-field images of swimming Paramecium were recorded by a video recorder (DV format) for about 40 s and fed into a computer. The positions of individual cells were determined by a laboratory-made, computer-assisted, tracking software (Bohboh, Bohboh Lab., Tokyo, Japan) (Shiba et al.,2002), and the mean speed was calculated from the changes in distance at specific time intervals. In each experiment, swimming trajectories lasting >0.67 s (or 20 frames) were picked randomly, and the mean speed was obtained from the measurement of 40 cells.

The probability of statistical significance (P) was determined using Student's t-test. The partial least-squares fitting was done using every seven data points obtained.

The V̇_O2 of the cells in the experimental chamber (Fig. 1) while being stirred continually, by a small magnetic bar put into the cell suspension, was not significantly different from that measured after stirring had stopped and vice versa. Stirring and post-stirring measurements were done 5–10 min after the stirring was `on' and `off',respectively. The ratio of the rate with stirring to that without stirring was 0.97±0.56 (±s.d.) and was not significantly different from 1.0(N=8, P=0.87). This indicates that our procedure for measuring oxygen consumption using the sensor does not require any correction for heterogeneity of P_O2 in the chamber. Although the cells are focused on in order to record swimming some distance away from the sensor surface at the top of the columnar space, it seems safe to regard them as being representative in terms of the homogenous distribution of Paramecium cells usually found in a chamber of such small dimensions as used in Sawai et al. (Sawai et al., 2007).

Fig. 2A shows the time course of changes in P_O2 in the cell suspension. Time derivatives of the changes(ΔP_O2/Δt) were determined by the partial least-squares fitting, from which V̇_O2 was calculated using Eqn 1. Fig. 2B shows the time course of V̇_O2 thus obtained and the mean swimming speed (U) of cells simultaneously measured by the optical slice method. This gave a couple of pairs of V̇_O2 and U per each episode of replicated experiments.

We evaluated V̇_O2 only from measurements of cells up to 10⁴ because of the limited resolution(signal-to-noise ratio) of the sensor. However, we did not find any significant correlation between the cell number and V̇_O2 in the range we tested (correlation coefficient=0.28, data not shown).

Paramecium gains propulsive thrust from beating cilia, by which metabolic energy is converted to the mechanical work. Gueron and Levit-Gurevich computed the mechanical thrust of Paramecium cilia beating in metachronal coordination with neighboring cilia(Gueron and Levit-Gurevich,1999). If we take 2×10^–16 J to be the mechanical work per cilium per beat [cf. fig. 2 in Gueron and Levit-Gurevich (Gueron and Levit-Gurevich,1999)], the total power of beating cilia on the entire surface of a single cell (10⁴ cilia beating at 40 Hz) can be estimated to be 2.9×10^–7 J h^–1. This means that the conversion of the mechanical power of ciliary beating to propulsive power(StP) may be far less efficient (0.77%) than that of the conversion of the P_s to the mechanical power of ciliary beating(10.1%). Remarkably low efficiency of energy expenditure is one of the characteristics of Paramecium swimming in the mechanical environment governed by a viscous drag, where large dissipation of the kinetic energy is inevitable in the interaction with surrounding water.

The fact that Paramecium consumes a large amount of metabolic energy for swimming with extremely low efficiency suggests that it requires large changes in producing this metabolic energy when changing the propulsive thrust in response to external stimuli. In fact, Eqn 2 states that changes in U by 10% from U_s would change V̇_O2 by 7.1% of the total amount at U_s. It is, therefore, plausible that a subtle increase in the propulsive thrust might induce substantial effects on the other energy-requiring processes, such as cell proliferation, by reducing the energy supply to these processes in response to the increased demand for metabolic energy of locomotion.

Kato et al. hypothesized a close coupling of gravity-dependent changes in proliferation activity to gravikinesis (gravity-dependent modulation of the swimming speed) of Paramecium(Kato et al., 2003). Paramecium has been known to proliferate faster in microgravity(Planel et al., 1981; Richoilley et al., 1986)whereas it proliferates slower in hypergravity(Tixador et al., 1984; Planel et al., 1990; Richoilley et al., 1993; Kato et al., 2003). Paramecium also modulates its propulsive thrust depending on the swimming direction with respect to gravity; it increases the thrust when swimming upwards and decreases it when swimming downwards(Machemer et al., 1991; Ooya et al., 1992). Kato et al. considered how the energy supply to the proliferation activity would change in parallel with changes in the energy demand for modulating the thrust(Kato et al., 2003). They thought that a rapid increase in the demand for locomotion would complementally result in a decrease in the energy supply to proliferation and vice versa, as both proliferation and locomotion share a common metabolic resource within a cell. This hypothesis of what is essentially a counterbalance between proliferation and locomotion requires a substantial amount of energy change upon modulating the thrust either in microgravity or in hypergravity. The facts presented in the present study will make this requirement highly realistic.

SMR has not been, so far, distinguished from the total metabolic energy in unicellular organisms. It seems to be because of the far smaller amount of swimming power estimated by the theory of fluid dynamics than the total metabolic energy (Fenchel and Finlay,1983). The estimation of mechanical work should have been done taking account of a very low efficiency of energy conversion due to a large dissipation of energy through the interaction with the surrounding fluid. In this study we empirically estimated the swimming power in Paramecium,and demonstrated that a large amount of energy is consumed for swimming and,as a result, only part of the total metabolic energy could be regarded as SMR. It is therefore suggested that the definition of SMR should be reconsidered in light of the energetics of microorganisms as found in the present study. This will cause us to re-examine energetic relations, such as allometric metabolism–mass relations, in unicellular organisms, which has long been discussed on a similar basis to that established in large animals.

LIST OF ABBREVIATIONS

 
• a

  least-squares parameter

 
• b

  least-squares parameter

 
• c

  exponent

 
• C_M

  moment coefficient

 
• COT

  cost of transport

 
• D

  drag coefficient

 
• M

  cellular mass for Paramecium

 
• N

  number of cells

 
• P_O2

  partial pressure of oxygen

 
• P_roll

  energy dissipation due to rolling

 
• P_s

  swimming power

 
• r

  radius of sphere

 
• r_a

  long rotating radius

 
• r_b

  short rotating radius

 
• S

  oxygen solubility

 
• SMR

  standard metabolic rate

 
• StP

  Stokes' power

 
• t

  time

 
• U

  swimming speed

 
• U_s

  standard swimming speed

 
• V_ch

  volume in the chamber

 
• V̇ _O2

  rate of oxygen uptake

 
• η

  viscosity of medium

 
• ω

  rate of rolling