SUMMARY
In order to characterize the energy expenditure of Paramecium, we simultaneously measured the oxygen consumption rate, using an optic fluorescence oxygen sensor, and the swimming speed, which was evaluated by the optical slice method. The standard metabolic rate (SMR, the rate of energy consumption exclusively for physiological activities other than locomotion) was estimated to be 1.18×10^{–6} J h^{–1} cell^{–1} by extrapolating the oxygen consumption rate into one at zero swimming speed. It was about 30% of the total energy consumed by the cell swimming at a mean speed of 1 mm s^{–1}, indicating that a large amount of the metabolic energy (about 70% of the total) is consumed for propulsive activity only. The mechanical power liberated to the environment by swimming Paramecium was calculated on the basis of Stokes' law. This power, termed Stokes power, was 2.2×10^{–9} J h^{–1} cell^{–1}, indicating extremely low efficiency (0.078%) in the conversion of metabolic power to propulsion. Analysis of the cost of transport (COT, the energy expenditure for translocation per units of mass and distance) revealed that the efficiency of energy expenditure in swimming increases with speed rather than having an optimum value within a wide range of forced swimming, as is generally found in fish swimming. These characteristics of energy expenditure would be unique to microorganisms, including Paramecium, living in a viscous environment where large dissipation of the kinetic energy is inevitable due to the interaction with the surrounding water.
INTRODUCTION
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 O_{2} h^{–1} for a single cell (Paramecium caudatum). These values can be converted to the power, 0.38–8.8×10^{–5} J h^{–1} cell^{–1}, by the conventional transformation of liters of O_{2} into 20.1 kJ (SchmidtNielsen, 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 `nonmotile' 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.
MATERIALS AND METHODS
Cells and culture
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} Na_{2}HPO_{4}, 1.0 mmol l^{–1} NaH_{2}PO_{4}, 1.5 mmol l^{–1} CaCl_{2}, 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 lowspeed, handoperated centrifugation (<170 g) and were adapted to the experimental solution (KCM: 1.0 mmol l^{–1} KOH, 1.0 mmol l^{–1} CaCl_{2}, 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).
Recording setup
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 3.5×10^{3}–1.9×10^{4} 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 (FO960, 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 (halfmaximum intensity width of 0.2 mm; SU42C63510, Audio Technica, Tokyo, Japan), and darkfield images of cells that swam in the slit of light were recorded with a CCD camera (XC77RR, 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.
Data processing
In each experiment, the partial pressure of oxygen (P_{O2}, relative value to equilibrium with atmospheric air) was recorded every 30 s. Data were revised according to the temperature during measurements, following the builtin correction protocol. The rate of change in P_{O2} (ΔP_{O2}/Δt) was calculated by numerical differentiation of the plot of P_{O2} vs time (t) by the partial leastsquares fitting. Thus, the oxygen consumption rate per cell (V̇_{O2}, in ml O_{2} h^{–1}) was calculated as follows: (1) where S is oxygen solubility (in ml O_{2} ml^{–1}) at the temperature recorded, V_{ch} is the volume of the chamber (in ml) and N is the number of cells contained in the chamber.
To measure the swimming speed, darkfield 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 laboratorymade, computerassisted, 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 ttest. The partial leastsquares fitting was done using every seven data points obtained.
RESULTS
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 poststirring 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 leastsquares 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.
The simultaneous measurement of V̇_{O2} and U was also made at increased K^{+} ion concentrations, aiming at reducing the swimming speed of cells. Paramecium has been known to reduce its swimming speed in response to the experimental depolarization of the membrane (Machemer, 1989). In the present study, we changed K^{+} concentration from 1 mmol l^{–1} (standard solution) to 4 mmol l^{–1} for this purpose. In a depolarizing solution of 4 mmol l^{–1} K^{+}, cells swam slower as expected (0.76±0.16 mm s^{–1} N=14 in this solution compared with 0.99±0.26 mm s^{–1} N=54 in the standard solution, P<0.01). Fig. 3 shows plots of V̇_{O2} vs U measured in solutions of different K^{+} concentrations. These plots show a positive correlation (R=0.57, N=68) between increasing U and increasing V̇_{O2}. The linear regression of plots in the range of U=0.4–1.5 mm s^{–1} gave the following equation of V̇_{O2} vs U (mm s^{–1}): (2) Because the standard metabolic rate (SMR) is defined as the energy spent independent of locomotion (Hill et al., 2004), it can be estimated to be V̇_{O2} at a zero swimming speed. The linear regression of V̇_{O2} vs U gives us a primary approximation of SMR of a single Paramecium cell as 1.18×10^{–6} J h^{–1} by extrapolating V̇_{O2} down to U=0 and equating 1 liter of oxygen with 20.1 kJ (SchmidtNielsen, 1984). The energy spent by Paramecium especially for swimming (swimming power, P_{s}) is obtained by subtracting SMR from the total energy expenditure converted from V̇_{O2} using Eqn 2 at a given swimming speed; at its standard speed U_{s}=1 mm s^{–1} in our analysis, the calculated values of the total expenditure and P_{s} are 4.02×10^{–6} J h^{–1} and 2.84×10^{–6} J h^{–1}, respectively. When Paramecium swims at U_{s} and consumes oxygen at the rate expected from Eqn 2, SMR and P_{s} are therefore 29.3% and 70.7% of the total energy expenditure, respectively. This means that Paramecium uses a large part of its metabolic energy only for swimming.
DISCUSSION
We evaluated V̇_{O2} only from measurements of cells up to 10^{4} because of the limited resolution (signaltonoise 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).
For statistical analysis of V̇_{O2} vs U, there may be alternatives to Eqn 2, which we used for Paramecium and has the form: (3) where a and b are leastsquares parameters.
To assess the relationship with fish physiology, an empirical nonlinear function of the following form was used with similar parameters of a and b: (4) where the exponent c is generally about 2.5 for fish (Alexander, 2003). The nonlinear leastsquares fitting of Eqn 4 to the Paramecium data presented in this study gave the following function: (5) which is shown by a broken line in Fig. 3. Root mean squares of the fitting (a measure of goodness of fit) of the linear and nonlinear functions were 5.45×10^{–8} and 5.48×10^{–8}, respectively, indicating that there is little difference in goodness of fit between the two functions. Indeed, both functions are indistinguishable for assessing the relationship between the rate of oxygen consumption and the swimming speed in the range of observations, although the intercept obtained on the basis of the nonlinear function is about 54% larger than that obtained on the basis of the linear function (Fig. 3). However, it should be noted that the exponent c was calculated to be 1.67±2.66 (mean±95% confidence interval), which was not significantly different from the unity. For the simplification of the results, we took the resultant linear function (Eqn 2) as the primary approximation, in order to assess the relationship between the rate of oxygen consumption and the swimming speed of P. caudatum.
The power liberated by swimming Paramecium can be estimated to be the work per unit time, which is done against the viscous drag. As a ciliated microorganism swims through a fluid, energy is generally being dissipated by the viscosity in the fluid both inside and outside the cilia layer (Keller and Wu, 1977). While an estimate of the former is difficult as argued by these authors, the latter can be evaluated by hydrodynamics about a prolate spheroid moving and rotating in a viscous fluid. In low Reynolds number states, such as in the case of swimming Paramecium, energy dissipation due to translation (propulsion) can be calculated on the basis of Stokes' law. The power, termed `Stokes power (StP)', at speed U is: (6) where η is the viscosity of the medium and D is the drag coefficient of the object. For a sphere of radius r, D=6πr. More realistically, Paramecium can be assumed to be a spheroid moving along its long axis. For a prolate spheroid with short rotating radius r_{b} and long axial radius r_{a}, D is calculated to be: (7) whereτ =r_{a}/(r_{a}^{2–}r_{b}^{2})^{1/2} (Happel and Brenner, 1986). For P. caudatum with a mean size (r_{a}=8.3×10^{–5} m, r_{b}=2.0×10^{–5} m), swimming in water (η=1.0×10^{–3} Pas) at U_{s}, StP is calculated to be 2.2×10^{–9} J h^{–1}. This value indicates that the efficiency of Paramecium swimming forward, i.e. the ratio of the power exerted to the environment to P_{s}, is only 0.078%. The rest of P_{s} is dissipated for rotation of the cell body (rolling and yawing, while yawing is significantly small compared with rolling in Paramecium) and inside the cilia layer as described above. Energy dissipation due to rolling (P_{roll}) of a prolate spheroid, i.e. rotation about its major axis, can be estimated by: (8) where C_{M} is the moment coefficient and ω is the rate of rolling (Chang and Wu, 1974). C_{M} is a function of the ratio of minor to major axis r_{b}/r_{a} and has been given by a numerical expression [equations 40b and 45 in Chang and Wu (Chang and Wu, 1974)]. For the rate of rolling ω=1 rps=2πs^{–1}, using the same values for r_{a}, r_{b} and η as described above, and C_{M}=0.72 at r_{b}/r_{a}=0.24, P_{roll} is calculated to be 8.5×10^{–11} J h^{–1}. This value is 3.9% of StP. Because P_{roll} thus evaluated is substantially small compared with StP, the rest of P_{s} is mostly dissipated inside the cilia layer. Studies investigating the swimming of largerscale animals, however, have reported higher efficiency; about 10% and 5%, for a rainbow trout (Salmo gairdneri) swimming with undulating body and/or fins (Webb, 1971) and a squid (Illes illecebrosus) with jet propulsion (Webber and O'dor, 1986), respectively. These facts demonstrate that the energy cost of swimming in Paramecium is about twoorders of magnitude lower than in these larger animals.
Paramecium gains propulsive thrust from beating cilia, by which metabolic energy is converted to the mechanical work. Gueron and LevitGurevich computed the mechanical thrust of Paramecium cilia beating in metachronal coordination with neighboring cilia (Gueron and LevitGurevich, 1999). If we take 2×10^{–16} J to be the mechanical work per cilium per beat [cf. fig. 2 in Gueron and LevitGurevich (Gueron and LevitGurevich, 1999)], the total power of beating cilia on the entire surface of a single cell (10^{4} 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 efficiency of animal locomotion has also been discussed in terms of the cost of transport (COT, in ml O_{2} m^{–1} kg^{–1}), which is defined as energy consumption for the translocation of the unit weight of an animal per unit of distance, and is formulated as follows: (9) where M is the cellular mass for Paramecium. In this study, M was obtained based on the assumption that a spheroidal cell body has the mean density of 1.04 g cm^{–3} (Ooya et al., 1992). Fig. 4 shows COT as a function of U. As shown by the line in Fig. 4, a linear assessment of the relationship of V̇_{O2} vs U (Eqn 2) gives a hyperbolic curve, indicating a monotonic decrease in COT with an increase in U. In the case of the swimming of fish, by contrast, COT curves have a Jshape with a minimum COT within the range of the ordinary U (Claireaux et al., 2006). The Jshaped curve of COT in fish is possibly derived from the highly nonlinear relationship of V̇_{O2} vs U, which is represented by the exponent c in Eqn 4 significantly greater than the unity. The minimum COT corresponds to the optimum efficiency of locomotion (Videler, 1993). If we take nonunity c (1.67) into the calculation of COT in Paramecium swimming obtained from the leastsquares fitting of Eqn 4, the minimum COT would be found at 1.45 mm s^{–1}, which is nearly the maximum speed. It is, therefore, argued that the efficiency of energy expenditure of swimming in Paramecium increases with speed. This is the second characteristic of Paramecium swimming, which we discovered for the first time from experiments carried out in this study, which have enabled us to measure oxygen consumption and swimming speed simultaneously.
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 energyrequiring 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 gravitydependent changes in proliferation activity to gravikinesis (gravitydependent 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 reexamine 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
 leastsquares parameter
 b
 leastsquares 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
FOOTNOTES

This work was supported by the GrantinAid for Scientific Research (No. 18570067) from the Ministry of Education, Sports, Science and Technology of Japan and also by `Groundbased Research Announcement for Space Utilization' promoted by Japan Space Forum. We thank Dr K. Hasegawa for lending us the optic fluorescence oxygen sensor.
 © The Company of Biologists Limited 2009