Myonemal Contraction of Spirostomum Ill. THE THERMAL DEPENDENCE OF CONTRACTION, RELAXATION AND EXCITATION-CONTRACTION COUPLING R. B. HAWKES AND D. V. HOLBERTON T h e Department of Zoology, University of H u l l , Hiill H U 6 7 R X , United K i n g d o m
ABSTRACT A microphotometric technique that displays rapid length changes of Spirostomum has been used to follow the variation with temperature of three kinetic parameters of myonemal contraction: contraction rate, relaxation rate and stimulus duration at threshold. In each case the exponential form of the relationship indicated that the gross rate constant might be equated with the limiting rate constant, k, of a driving chemical reaction, and from standard expressions of chemical kinetics the change in activation free energy appropriate to this reaction has been computed. The thermal dependence of contraction is described by an activation enthalpy (AH:) of 21.7 kcal mol-l, and the activation entropy (AS:) of 26.8 e.u. is consistent with a model of contraction requiring neutralization of fixed myonemal charges by divalent cations. The analysis of thermal dependence of relaxation gives a negative activation entropy, a result predicted for a rate-limiting reaction involving dissociation of a neutral molecule. On the other hand, values of AS: and AH: for relaxation fall close to an isokinetic correlation drawn in the literature from analysis of the thermal dependence of ciliary beat frequency in different organisms, and for which breakdown of a n ATP-ATPase complex could be the common ratelimiting reaction. AS for stimulus duration suggests that the rate-limiting step i n excitationcontraction coupling is a reaction between ions of like charge, or ion pair formation from a neutral molecule
From studies of the contraction of the peritrich stalk, both Hoffman-Berling ('58) and Weis-Fogh and Amos ('72) concluded that shortening depends on a mechanism quite distinct from that encountered in muscle. The molecular basis of contraction/relaxation of the spasmoneme is not understood, but evidence from stalk models favours a direct role for free Ca2+. Briefly, it has been proposed that at high Ca2+ concentrations (contracted) the spasmoneme resembles an isotropic rubber, comprising an array of long-chain protein molecules maintained in association by a small number of stable crosslinks. Network extension has been envisaged to occur in one of two ways; either the sequestration of Ca2+ permits the formation of Ca2+-sensitive crosslinks which extend the molecules, or in the absence of CaZ+ negative charge repulsion causes the spasmoneme to expand. In either case the spasmoneme J. CELL. PHYSIOL.,87: 25S264.
becomes anisotropic and birefringent and the decrease in configurational entropy that this implies is the source of energy for subsequent contraction. Some first results from Spirostomum suggest that similar mechano-chemical models may account for the shortening of body myonemes of contractile heterotrichs (Hawkes and Holberton, '75). We have attempted to investigate these models by a thermodynamic analysis of the kinetics of contraction and relaxation. While rigorous analysis is complex for such a gross system, a useful approach is suggested by earlier treatments of the thermal dependence of flagellar beating. Holwill and Silvester ('65) determined the molar changes in entropy (AS:) and enthalpy (AH:) of the reaction which is rate limiting on flagellar beat frequency in Strigomonas, by Received Feb. 4, '75. Accepted June 6, '75.
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R. B. HAWKES AND D. V. HOLBERTON
arguing that the theory of rate processes allows activation kinetics to be generally applied to complete systems even when the rate limiting step is not chemical, sensu strictu. The analysis relies on a statistical treatment of first-order reaction kinetics (Glasstone et al., ’41) summarized in the relation : lz
=EL’
(
-AG:/RT)
(1) h in which the k is the Boltzmann constant, h is Plancks constant, R is the gas constant, T is thermodynamic temperature, and k the rate constant of the system. AGT is the molar change in activation free energy and can be written in terms of activation enthalpy and entropy, thus:
AG: = AH: - TAS
(2)
To apply equation (1) to an in vivo biological process requires a suitable parameter for the rate constant k. Sleigh (‘56) successfully applied Arrhenius kinetics to the thermal dependence of peristomial ciliary beat in Stentor by taking k as either beat frequency or wave velocity. Holwill and Silvester (‘65, ’67) also used beat frequency as an indicator of reaction rate, and justified this approach by demonstrating a resemblance between the equation of a first order reaction and the rate of activation of “contractile units” related to the number of such units in the axoneme, if wave propagation is assumed to depend on repeated activation of such units and driven at a rate determined by the slowest reaction in the cycle. Length changes of Spirostomum may also be considered to depend on the activation of microscopic contractile units whose rate of change of configuration follows from the slowest step in the activating reaction sequence. On this view the time course of shortening and elongation will be an image of the kinetics of the driving chemical reaction. At constant temperature Spirostomum shortens with a velocity that is nearly constant for some 4-5 mS before the rate of change of length decays over a much longer interval. In simple terms, the response has two phases (Hawkes and Holberton, ’74), but examined in more detail it can be shown that the decay in shortening rate is of the form,
length beyond contracted length (Lc) at times denoted by the subscripts. Apart from the initial 1-3 mS of the response, shortening, including part of the apparently constant velocity phase, can be accounted for by this exponential decay (fig. 1) and can be assumed to be in phase with a reaction of the first order for which the rate constant k is measured by the shortening constant k‘. Elongation of Spirostomum is much slower, but oscillographs of rate of length change at constant temperature are similar in shape to shortening kinetics (Hawkes and Holberton, ’74; fig. 7 in that paper), and may be approximated by the exponential function (fig. 2), E o - E t = Eoe-k”t
(4)
in which the constant k” may be identified with the rate constant k of the driving first order reaction. Limitations to this argument include the fact that the photometric technique used in these studies measures projected area of a cell and not true length, so there is an inherent small error (of variable magnitude) when oscillographs are used to represent length changes, and that there may be alternative explanations for the particular form of the kinetics of length change. For instance, contraction kinetics have been simulated by determining the velocity at any length from Stokes’ law for the drag on the body of a shape appropriate to that length, assuming that drag is the load in balance with myonemal tension, and tension relates linearly to length (Hawkes, ’74). If this is the case then equation ( 3 ) describes a decay in myonemal tension in phase with a first order reaction. There is a very close parallel between this analysis of length change in Spirostomum and the reasoning applied by Burge and Elliott (‘63) to isometric tension decay following a muscle twitch, or isotonic elongation of some muscles after stimulation, which are also exponential in form. Equations (1) and (2) can now be rewritten
(5)
If the assumption that a first order reE t -- Eoe-k’t (3) action is rate limiting for length change where Et and & are the extensions in is correct, when either In (k‘/T) us. T-’
MYONEMAL CONTRACTION OF SPIROSTOMUM
I
Et cell
0
5
10
15
t i m e (mS) Fig. 1 Shortening kinetics of S p i r o s t o m i i m a t constant temperature. Semi-logarithmic plots of Et, the extension beyond contracted length, against time, to show the exponential form of the kinetics (text, equation 3) following a n early constant velocity phase of shortening. 0-0, averaged time course of contraction in response to electrical stimulation from 20 different cells using the data from an earlier paper (Hawkes and Holberton, '74; fig. 6). The prolonged early phase which is apparently not exponential arises i n part from averaging error a single contraction of Spirostomzim due to incomplete synchrony of the sample. 0-0, in response to electrical stimulation, length changes taken directly from an oscillograph. Shortening is not exponential with respect to time over only the first 1-2 mS.
0.5
0.1 Eo- E t cell lengths
0.01
0.001
time (S) Fig. 2 Relaxation kinetics of S p i r o s t o m z i m a t constant temperature. Semi-logarithmic plots of the extension deficit E,-Et against time. Each plot is the length change of one cell measured from a single relaxation oscillograph (Hawkes and Holberton, '74; fig. 7) and shows that the rate of re-extension becomes exponential as cells return to initial length (defined by equation (4) in text). 0-0, cell extending after a maximal stimulus (50 V, 20 mS). 0 -0 Cell extending after a supramaximal stimulus (100 V, 20 mS).
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R. B. HAWKES A N D D. V . HOLBERTON
or In ( h " / T ) us. T-' is plotted, then the relation should be linear and the regression line will give AS: from the intercept and AH: from the slope. Ideally this relation should be determined for the same process in a range of organisms to test the interpretation that isolated pairs of activation enthalpy and entropy values derive from a common isokinetic reaction which is rate-limiting (but see Exner, '64, for a discussion of spurious linear AH: us. AS: relations). In this paper we give the results of applying an elementary analysis to Spirostomum where kinetic events can be followed with some precision, in the hope that alternative techniques will subsequently provide comparable data from myonemal contraction of more or less closely related ciliates. MATERIALS AND METHODS
Rate measurements were taken directly from oscillograph display of contractionrelaxation kinetics from Spirostomum electrically stimulated at different temperatures, using the photometric method described fully in an earlier paper in this series (Hawkes and Holberton, '74). From each oscillograph the intervals (t') and (t") over which a cell contracted and re-extended by one-half cell length (Et = 0.5-Lc) was recorded and the rerespective rate constants k' and h" computed from equations (3) and (4). To compare length change kinetics at different temperatures in a more general way, these measurements were also expressed as simple linear velocities of contraction (U) and relaxation (US over the first part of the response. Temperatures below ambient were obtained at the microscope slide-electrode assembly by heat exchange with a cooling stage. The stage was constructed for this purpose from 1 cm brass stock milled with a convoluted channel, 0.8 cm deep, and closed with a sealing top plate of 1.5 mm brass. A coolant (1:3 v/v commercial antifreeze-water mixture) was carried to and from the stage in thick-walled rubber pressure tubing, and circulation through the stage channel was maintained by a constant velocity water pump. The temperature of the coolant was controlled in two ways. By circulation through glass heatexchange coils in a cryostat cabinet the
temperature was reduced to between - 5 and - 1O"C, and the sub-zero coolant was then brought to final temperature by a variable output heating element. During experiments the temperature was continuously monitored by a thermistor, placed on the glass slide. Thermal contact was improved by a drop of immersion oil on the thermistor tip. There was typically a 5°C difference in temperature between stage and slide, but using this apparatus the temperature at the slide could be varied between 5-19°C and maintained to within 0.5"C. A sufficient number of experiments was carried out to provide rate measurements at each degree interval within this range from at least 2 and up to 11 individual cells. The regression lines plotted in figures 4, 6 and 8 were computed statistically from a total of 72 observations in each case. To extend the observations to temperature effects outside this narrow range, temperatures were raised above ambient from 25°C to 3 5 ° C by an air-curtain incubator (Sage Instruments Ltd.) but were maintained with less accuracy ( 1" C ) . The thermal dependence of viscosity of Chalkley's medium was determined from an Ostwald viscometer in a controlled temperature water bath.
*
RESULTS
A graph of the velocity of contraction
(U) during the apparently constant velocity phase of contraction (Hawkes and Holberton, '74) against temperature is sigmoidal over the temperature range 5-35" C, approaching U = 0 at low temperatures and U = 26 cm (170 cell 1engths)S-1 at high temperatures (fig. 3). Although measurements were not made below 5°C it was clear that contraction still occurred at lower temperatures. While the velocity of contraction shows thermal dependence, the relationship does not necessarily reflect intrinsic reaction rates in a straightforward way since velocity may be affected by other temperature-dependent variables, such as the viscosity of the bathing medium. The force of contraction at different cell lengths may be approximated by Stokes' law for the drag on a body the size and shape of Spirostomum moving in a viscid fluid, and it is probably drag that represents the principal resistance to short-
257
MYONEMAL CONTRACTION OF S P I R O S T O M U M
30
u . uc s-~
cm
15
0
1
I
I
I
I
2 70
280
290
300
310
OK
Fig. 3 Relation between contraction velocity of Spirostomum and thermodynamic temperature. 0- - -0 , measured velocity of shortening ( U cm S - 1 us temperature (K); 0- - - 0, corrected velocity of shortening (U, cm S-1) us. temperature (K). This curve also represents the variation with temperature of the force parameter FL-1 = p U , when the ordinate is in units of N m-1 X 105. The mean sample size is 20.
ening (Hawkes and Holberton, '75). As might be expected, it can be shown experimentally that media of viscosity higher than Chalkley's medium retard contraction velocity considerably while relaxation rates are less affected. For this reason, it is important to allow for the changed viscosity of the bathing medium at each temperature when comparing intrinsic contraction rates, and in figure 3 the curve for corrected rate (UC) is plotted from the expression UC = U p T / p z O ,where p T and pzO represent the dynamic viscosity of Chalkley's medium at temperatures T "C and 20°C. Viscosity may be related to temperature by a number of empirical formulae whose applicability and accuracy depend on the nature of the fluid and on the experimental regime (Dryden et al., '56). Rather than employ one of these, the viscosity of Chalkley's medium at various temperatures was determined experimentally. The behaviour with temperature of the
parameter Uc is essentially a record of the thermal dependence of the product pU which, since temperature does not alter the morphology of Spirostomum, may be taken as a model of the drag (dimensions of force unit length-') experienced by Spirostomum at different temperatures. As the contraction velocity curve flattens at temperatures above 35 C, the greatest load due to drag will be met by Spirostomum shortening at temperatures around 30°C. It is not clear whether above 35°C contraction rate is limited by temperatureindependent factors; cells incubated at 37°C for 30 minutes and then returned to room temperature displayed normal rates of contraction, suggesting that thermal damage is not significant at the higher temperatures. (It may be relevant that Sleigh ('56) found that the maximum beat frequency of the peristomial cilia of Stentor, although not corrected for the small change in viscosity, occurred at 30"C, the rate slowing to zero over the following O
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R. B. HAWKES AND D. V. HOLBERTON
0.0
- 1.0 In ( k ' T-l
)
-2.0 3.5
T-1
(OK-~ x
3.6 103)
Fig. 4 The thermal dependence of contraction rate. The experiments of figure 3 over the temperature range 27tL292 K plotted in the form In (k'T-1) us. T - 1 , where Iz' is the exponential rate constant defined by equation (3). The regression line allows calculation of an activation enthalpy (AH:) and activation entropy (AS:) (see text).
decade.) The temperature coefficient (QlO) for the velocity of contraction (&) was 4.1 over the range 12-22°C. At lower temperatures the exponential form of the plot suggests that the theory of rate kinetics summarized in equation (1) is applicable, and may be used to determine the molar changes in enthalpy and entropy of the reaction that is ratelimiting on contraction. The appropriate rate constant is k' calculated from contraction kinetics, and in figure 4 In (k'T-1) against T-1 is plotted over the temperature range 5 1 9 ° C for which data were TABLE 1
Activation parameters of rate processes in the contraction-relaxation cycle of Spirostomum Process
A H : (kcal mol-1)
Contraction Initiation Relaxation
21.7 -+- 0.74 9.6k0.21 10.4 k 0.38
A ~ : ( e . u .= cal k-1 mol-1)
26.8 % 2.63
- 16.7t0.73
- 23.4 & 1.36
available for every degree interval, and for which the effect of changing viscosity is minimal. Within the limits of experimental error these points lie on a straight line and from equation (3) the slope and intercept of the regression line give AH! and AS: (table 1). Studies of the stimulus requirements for the initiation of contraction (Hawkes and Holberton, '74) indicate that both the stimulus duration and stimulus strength are necessary for definition of the threshold. To investigate the thermal dependence of the initiation of contraction, and hence of stimulus-contraction coupling, it was found most convenient to set the applied voltage at a fixed value and monitor changes in the stimulus duration requirement. The relation between temperature and stimulus duration (fig. 5) shows that the excitability of Spirostomum is temperature dependent, stimulus requirements being significantly reduced by increasing temperature. For the present purpose it is
259
MYONEMAL CONTRACTION OF S P I R O S T O M U M 25
T 20
15
T,,, (mS.1 10
'"'I 1
5
0
2 70
280
1
1
i
2 90
300
310
OK
Fig. 5 Effect of temperature on stimulus duration at contraction threshold. The latent period (Tth) measured between the leading edge of a 50 V square wave stimulus pulse and the beginning of the response is plotted as a function of thermodynamic temperature. The points below 298 K represent the grouped data over a 5 K interval. The mean sample size is 20.
convenient to consider initiation of cell shortening as an endpoint of some chemical reaction, which need not be specified, whose velocity is proportional to the strength of the applied electric field as defined by the stimulus strength-duration relation. In that case it would be expected that the stimulus duration at threshold would be inversely related to the reaction rate and that the reciprocal of duration might be related to thermodynamic temperature by rate kinetics. The relation In ( T t h - I T - ' ) us. T-I where Tth is the duration at threshold, is plotted in figure 6, and the corresponding activation enthalpy and entropy values are given in table 1. The rate of relaxation (Ur) of Spirostomum following a contraction induced by a submaximal stimulus, was determined between 5 3 5 C for the apparently constant velocity phase which accounts for O
the greater part of elongation (fig. 7). Because the relaxation rate is independent of small changes in the viscosity of the bathing medium no correction for the temperature dependence of this quantity is necessary in this case. As for contraction there appears to be an exponential increase in the rate of relaxation between 5-25"C which declines at higher temperatures. The plot of In (k" T - I ) us. T - ' is again linear over the temperature range 5 1 9 ° C (fig. 8) leading to values of AH: and AS: from the slope and intercept of the regression line (table 1). DISCUSSION
The present results cannot easily be interpreted in terms of the rate-limiting step in a reaction series since AH: and AS: values from a single example represent one point of a putative isokinetic correla-
260
R. B. HAWKES AND D. V. HOLBERTON -1
*
1
-1.3
-1.9 3.4
3.5 T-1 ( ' ~ - 1
3.6 x 103
)
Fig. 6 The thermal dependence of stimulus threshold. The data of figure 3 over the temperature range 278-292 K replotted in the form In (T thT)-1 us. '2-1.
2 70
2 80
290
300
310
OK
Fig. 7 The variation of relaxation velocity (U, cm. S-1) of Spirostomzcm with temperature. The points below 298 K represent means of grouped data over 5 K intervals. The mean sample size is 20.
MYONEMAL CONTRACTION OF SPIROSTOMUM
26 1
Fig. 8 The thermal dependence of relaxation rate. The experiments of figure 7 over the temperature range 278-292 K plotted in the form In (k” T-1) us. T-1, where k” is the rate constant of relaxation defined by equation (4).
tion. For instance, similar thermodynamic parameters computed from the variation with temperature of flagellar beat in Strigomonas (Holwill and Silvester, ’65) were subsequently found to be atypical when isolated quantities are compared for cilia and flagella from a number of sources, yet all pairs of values plot as co-ordinates of a probable isokinetic relationship (AS: us. AIi;). The variation may be ascribed to differences in environmental factors, that cannot be controlled in in vivo experiments, and to which the values of AS: and AH: are individually sensitive (Glasstone et al., ’41) but which have much less influence on the free energy of activation. Due to the “compensation effect,” AG: changes little for the same reaction under different conditions. Nevertheless, with these limitations in mind, implications of these parameters measured from Spirostomum may be examined for such models of myonemal mechanism as have been proposed. The activation energy approach cannot satisfactorily distinguish between the two models of spasmoneme contraction proposed by Weis-Fogh and Amos (‘72). In both cases the reaction leading to contraction is that between free Caz+ and ligands
on the contractile apparatus. For a simple reaction between ions in solution (for instance between Caz+ and possible carboxylate ions on the myonemal protein) Glasstone et al. (‘41) predict AS = - 1 O Z C a Z M
(6)
where Z is valency and subscripts Ca and M refer to the calcium ion and the myonemal ligand. In general, for ions of dissimilar sign there is an entropy increase (AS: positive) going from reactants to activated complex, for ions of like sign there is an entropy decrease. The AS: value for a reaction between an ion and a neutral molecule or between two neutral molecules obeys no such simple relation and the magnitude cannot be predicted easily. Superficially there is some agreement between the activation entropy of the reaction governing contraction of Spirostomum (26.8 e.u.) predicted by equation (6) for a reaction between calcium ions and monovalent ligands on the myonemal protein. (In a similar way the values of AS: from glycerol-extracted locust sperm (Hoffman-Berling, ’55) and from cilia of Stentor (Sleigh, ’56) agree closely (-20 e.u., -21 e.u.) and are compatible with the suggestion (Holwill and Silvester, ’65) that the rate-
262
R. B. HAWKES AND D. V. HOLBERTON
limiting reaction is between ions of like sign, yet the result from Strigomonas ( - 1 e.u.) is not compatible, and demonstrates that inference of mechanism from single values of activation energies is inherently unsatisfactory. A negative AS: value appears to be typical of the reaction governing ciliary and flagellar beat rate, and it is possible that the very dissimilar entropy of Spirostomum contraction indicates a rate-limiting step that is different in kind. It is not known whether the rate of contraction of Spirostomum is determined by the rate of the Ca2+-myonemeinteraction or by the velocity of shortening of myonemes in the form of the calcium salt, or indeed by some other rate-limiting process such as diffusion of Ca2+ through the myonemal compartment. The relation between tension and temperature at given extension is unclear for real materials. From the kinetic theory of ideal rubber elasticity, tension is directly proportional to absolute temperature (Treloar, '58). The apparent distinction between Spirostomum contraction and ciliary beat frequency in the nature of the rate-governing reaction finds some confirmation when the AH: values are compared. For myonemal contraction AH: = 21.7 kcal. mol-',, whereas the AH: values for cilia and flagella listed by Holwill and Silvester ('67) from 17 cell types, are scattered, but broadly similar within the range 1.14 kcal mol-1 (boar spermatozoa) to 15.4 kcal mol-1 (Strigomonas). On the other hand AS: and AH: for stimulus duration at threshold do compare with the data from ciliary beat frequency, and the negative AS: value is consistent with a reaction in solution between ions of like sign during excitation-contraction coupling. There is at least one other compatible explanation, the ionization of a neutral molecule. It was suggested in the first paper of this series (Hawkes and Holberton, '74) that stimulus-contraction coupling might be achieved through the stimulus-dependent displacement of Ca2+ from sites on the inner face of the surface membranes which in turn would trigger the regenerative release of Ca2+ from reticular stores. Assuming Ca2+ to be bound to the membrane electrostatically (Dawson and Hauser, '70), displacement would in-
volve ion-pair form$tion which invariably has a,negative A s + (Frost and Pearson, '53). Ettiene ('70) used the photoprotein aequorin to assay free Ca2+ in the cytoplasm of Spirostomum during contractionrelaxation cycles, and the results indicate that relaxation is governed by some intrinsic property of the myoneme and is not synchronised to the fall in free Ca2+ levels. In this case i t is possible that the removal of Ca2+from ligands on the myonemal protein is rate-limiting, and this step may again result in ion pair formation, especially if the charge neutralisation model of myonemal contraction is correct. However, the opposite view, that the rate of relaxation is coupled to the removal of Ca2+from the myonemal compartment, is not excluded by the analysis of its thermal dependence. It is notable that the activation energy values for relaxation (table 1) are close to the AS: vs. AH: relation demonstrated by Holwill and Silvester ('67) for flagellar beat frequency, and to a parallel isokinetic correlation drawn in the same paper through data from isometric tension decay and isotonic elongation of smooth muscle. This relation has been taken to indicate that the rate-limiting reaction of flagellar beat is the breakdown of a n ATP-ATPase complex (AH: = 12.4 kcal mol-l; AS: = -8 e.u., Ouellet et al., '52), since AH: and AS: values from striated muscle relaxation also plot as co-ordinates to this line and the anomalous smooth muscle results can be understood in terms of unusual contractile proteins or differences in cross-bridge behaviour associated with ATP dephosphorylation. It is possible that this reaction may also be rate-limiting on relaxation of Spirostomum at the level of Ca2+ sequestration, since ATP hydrolysis is a known step in Ca2+ transport across muscle sarcoplasmic reticulum (Hasselbach, '64). Alternatively, relaxation of Spirostomum could be driven by a mechanism outside the myoneme since in Stentor extension is thought not to depend on myonemal relaxation, but is probably controlled by intertubule sliding of km microtubules, and this action is believed to be dependent on ATP dephosphorylation (Bannister and Tatchell, '68; Newman, '72; Huang and Pitelka, '73).
MYONEMAL CONTRACTION OF SPIROSTOMUM ACKNOWLEDGMENTS
The authors gratefully acknowledge the technical assistance of Mr. J. Marshall. Dr. R. B. Hawkes was a recipient of a Science Research Council Studentship during the preparation of this work. LITERATURE CITED Bannister, L. H., and E. C. Tatchell 1968 Contractility and fibre systems i n Stentor coerzilazrs. J. Cell. Sci., 3: 295-308. Burge, R. E., and G. F. Elliott 1963 The thermal dependence of (i) the decay of twitch and tetanic tension, and of (ii) elongation after stimulation. J. Physiol., 169: 8 6 4 7 P . Dawson, R. M. C., and H. Hauser 1970 Binding of calcium to phospholipids. In: Symposium on Calcium and Cellular Function. A. W. Cuthbert, ed. Macmillan, London, pp. 1 7 4 1 . Dryden, H. L.,F. D. Murnagham and H. Bateman 1956 Hydrodynamics. Bulletin 84, National Research Council (U.S.A.): report of the Committee on Hydrodynamics, Division of Physical Sciences. Dover Publications Inc, Ettienne, E. M. 1970 Control of contractility of Spirostomum by dissociated calcium ions. J. Gen. Physiol., 56: 168-179. Exner, 0. 1964 Concerning the isokinetic relationship. Nature, 201 : 488490. Frost, A. A,, and R. G. Pearson 1953 Kinetics and Mechanisms. A Study of Homogeneous Chemical Reactions. John Wiley and Sons, Inc., New York. Glasstone, S., K. J. Laidler and H. Eyring 1941 The Theory of Rate Processes. 1st edition. McGraw-Hill, New York and London.
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Hasselbach, W. 1964 ATP-driven active transport of calcium in the membranes of the sarcoplasmic reticulum. Proc. Roy. Sw. B., 160: 501504. Hawkes, R. B. 1974 Myonemal Contraction of Spirostomum. Ph.D. Thesis, University of Hull. Hawkes, R. B., and D. V. Holberton 1974 Myonemal contraction of Spirostomum. I. Kinetics of contraction and relaxation. J. Cell. Physiol., 84: 225236. - 1975 Myonemal contraction of Spirostomum. 11. Some mechanical properties of the contractile apparatus. J. Cell. Physiol., 85: 595602. Hoffman-Berling, H. 1958 Der mechanismus eines neuen, von der muskelkontraktion verschieden kontraktionszyklus. Biochim. Biophys. Acta, 27: 247-255. Holwill, M. E. J., and N. R. Silvester 1965 The thermal dependence of flagellar activity in Strigomonus oncopelti. J. Exp. Biol., 42: 537-544. 1967 Thermodynamic aspects of flagellar activity. J. Exp. Biol., 47: 249-265. Huang, B., and D. R. Pitelka 1973 The contractile process in the ciliate Stentor coeruleus. J. Cell Biol., 57: 704-728. Newman, E. 1972 Contraction in Stentor coerziZeus: acinematic analysis. Science, 177: 447449. Ouellet, L., K. J. Laidler and M. F. Morales 1952 Molecular kineti s of muscle adenosine triphosphate. Arch. Biochem. Biophys., 39: 37-50. Sleigh, M. A. 1956 Metachronism and frequency of beat i n the peristomial cilia of Stentor. J. Exp. Biol., 33: 15-28. Treloar, L. R. G. 1958 The Physics of Rubber Elasticity. 2nd edition. Clarendon Press, Oxford. Weis-Fogh, T., and W. B. Amos 1972 Evidence for a new mechanism of cell motility. Nature, 236: 301-304.
ABSTRACT A microphotometric technique that displays rapid length changes of Spirostomum has been used to follow the variation with temperature of three kinetic parameters of myonemal contraction: contraction rate, relaxation rate and stimulus duration at threshold. In each case the exponential form of the relationship indicated that the gross rate constant might be equated with the limiting rate constant, k, of a driving chemical reaction, and from standard expressions of chemical kinetics the change in activation free energy appropriate to this reaction has been computed. The thermal dependence of contraction is described by an activation enthalpy (AH:) of 21.7 kcal mol-l, and the activation entropy (AS:) of 26.8 e.u. is consistent with a model of contraction requiring neutralization of fixed myonemal charges by divalent cations. The analysis of thermal dependence of relaxation gives a negative activation entropy, a result predicted for a rate-limiting reaction involving dissociation of a neutral molecule. On the other hand, values of AS: and AH: for relaxation fall close to an isokinetic correlation drawn in the literature from analysis of the thermal dependence of ciliary beat frequency in different organisms, and for which breakdown of a n ATP-ATPase complex could be the common ratelimiting reaction. AS for stimulus duration suggests that the rate-limiting step i n excitationcontraction coupling is a reaction between ions of like charge, or ion pair formation from a neutral molecule
From studies of the contraction of the peritrich stalk, both Hoffman-Berling ('58) and Weis-Fogh and Amos ('72) concluded that shortening depends on a mechanism quite distinct from that encountered in muscle. The molecular basis of contraction/relaxation of the spasmoneme is not understood, but evidence from stalk models favours a direct role for free Ca2+. Briefly, it has been proposed that at high Ca2+ concentrations (contracted) the spasmoneme resembles an isotropic rubber, comprising an array of long-chain protein molecules maintained in association by a small number of stable crosslinks. Network extension has been envisaged to occur in one of two ways; either the sequestration of Ca2+ permits the formation of Ca2+-sensitive crosslinks which extend the molecules, or in the absence of CaZ+ negative charge repulsion causes the spasmoneme to expand. In either case the spasmoneme J. CELL. PHYSIOL.,87: 25S264.
becomes anisotropic and birefringent and the decrease in configurational entropy that this implies is the source of energy for subsequent contraction. Some first results from Spirostomum suggest that similar mechano-chemical models may account for the shortening of body myonemes of contractile heterotrichs (Hawkes and Holberton, '75). We have attempted to investigate these models by a thermodynamic analysis of the kinetics of contraction and relaxation. While rigorous analysis is complex for such a gross system, a useful approach is suggested by earlier treatments of the thermal dependence of flagellar beating. Holwill and Silvester ('65) determined the molar changes in entropy (AS:) and enthalpy (AH:) of the reaction which is rate limiting on flagellar beat frequency in Strigomonas, by Received Feb. 4, '75. Accepted June 6, '75.
253
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R. B. HAWKES AND D. V. HOLBERTON
arguing that the theory of rate processes allows activation kinetics to be generally applied to complete systems even when the rate limiting step is not chemical, sensu strictu. The analysis relies on a statistical treatment of first-order reaction kinetics (Glasstone et al., ’41) summarized in the relation : lz
=EL’
(
-AG:/RT)
(1) h in which the k is the Boltzmann constant, h is Plancks constant, R is the gas constant, T is thermodynamic temperature, and k the rate constant of the system. AGT is the molar change in activation free energy and can be written in terms of activation enthalpy and entropy, thus:
AG: = AH: - TAS
(2)
To apply equation (1) to an in vivo biological process requires a suitable parameter for the rate constant k. Sleigh (‘56) successfully applied Arrhenius kinetics to the thermal dependence of peristomial ciliary beat in Stentor by taking k as either beat frequency or wave velocity. Holwill and Silvester (‘65, ’67) also used beat frequency as an indicator of reaction rate, and justified this approach by demonstrating a resemblance between the equation of a first order reaction and the rate of activation of “contractile units” related to the number of such units in the axoneme, if wave propagation is assumed to depend on repeated activation of such units and driven at a rate determined by the slowest reaction in the cycle. Length changes of Spirostomum may also be considered to depend on the activation of microscopic contractile units whose rate of change of configuration follows from the slowest step in the activating reaction sequence. On this view the time course of shortening and elongation will be an image of the kinetics of the driving chemical reaction. At constant temperature Spirostomum shortens with a velocity that is nearly constant for some 4-5 mS before the rate of change of length decays over a much longer interval. In simple terms, the response has two phases (Hawkes and Holberton, ’74), but examined in more detail it can be shown that the decay in shortening rate is of the form,
length beyond contracted length (Lc) at times denoted by the subscripts. Apart from the initial 1-3 mS of the response, shortening, including part of the apparently constant velocity phase, can be accounted for by this exponential decay (fig. 1) and can be assumed to be in phase with a reaction of the first order for which the rate constant k is measured by the shortening constant k‘. Elongation of Spirostomum is much slower, but oscillographs of rate of length change at constant temperature are similar in shape to shortening kinetics (Hawkes and Holberton, ’74; fig. 7 in that paper), and may be approximated by the exponential function (fig. 2), E o - E t = Eoe-k”t
(4)
in which the constant k” may be identified with the rate constant k of the driving first order reaction. Limitations to this argument include the fact that the photometric technique used in these studies measures projected area of a cell and not true length, so there is an inherent small error (of variable magnitude) when oscillographs are used to represent length changes, and that there may be alternative explanations for the particular form of the kinetics of length change. For instance, contraction kinetics have been simulated by determining the velocity at any length from Stokes’ law for the drag on the body of a shape appropriate to that length, assuming that drag is the load in balance with myonemal tension, and tension relates linearly to length (Hawkes, ’74). If this is the case then equation ( 3 ) describes a decay in myonemal tension in phase with a first order reaction. There is a very close parallel between this analysis of length change in Spirostomum and the reasoning applied by Burge and Elliott (‘63) to isometric tension decay following a muscle twitch, or isotonic elongation of some muscles after stimulation, which are also exponential in form. Equations (1) and (2) can now be rewritten
(5)
If the assumption that a first order reE t -- Eoe-k’t (3) action is rate limiting for length change where Et and & are the extensions in is correct, when either In (k‘/T) us. T-’
MYONEMAL CONTRACTION OF SPIROSTOMUM
I
Et cell
0
5
10
15
t i m e (mS) Fig. 1 Shortening kinetics of S p i r o s t o m i i m a t constant temperature. Semi-logarithmic plots of Et, the extension beyond contracted length, against time, to show the exponential form of the kinetics (text, equation 3) following a n early constant velocity phase of shortening. 0-0, averaged time course of contraction in response to electrical stimulation from 20 different cells using the data from an earlier paper (Hawkes and Holberton, '74; fig. 6). The prolonged early phase which is apparently not exponential arises i n part from averaging error a single contraction of Spirostomzim due to incomplete synchrony of the sample. 0-0, in response to electrical stimulation, length changes taken directly from an oscillograph. Shortening is not exponential with respect to time over only the first 1-2 mS.
0.5
0.1 Eo- E t cell lengths
0.01
0.001
time (S) Fig. 2 Relaxation kinetics of S p i r o s t o m z i m a t constant temperature. Semi-logarithmic plots of the extension deficit E,-Et against time. Each plot is the length change of one cell measured from a single relaxation oscillograph (Hawkes and Holberton, '74; fig. 7) and shows that the rate of re-extension becomes exponential as cells return to initial length (defined by equation (4) in text). 0-0, cell extending after a maximal stimulus (50 V, 20 mS). 0 -0 Cell extending after a supramaximal stimulus (100 V, 20 mS).
255
256
R. B. HAWKES A N D D. V . HOLBERTON
or In ( h " / T ) us. T-' is plotted, then the relation should be linear and the regression line will give AS: from the intercept and AH: from the slope. Ideally this relation should be determined for the same process in a range of organisms to test the interpretation that isolated pairs of activation enthalpy and entropy values derive from a common isokinetic reaction which is rate-limiting (but see Exner, '64, for a discussion of spurious linear AH: us. AS: relations). In this paper we give the results of applying an elementary analysis to Spirostomum where kinetic events can be followed with some precision, in the hope that alternative techniques will subsequently provide comparable data from myonemal contraction of more or less closely related ciliates. MATERIALS AND METHODS
Rate measurements were taken directly from oscillograph display of contractionrelaxation kinetics from Spirostomum electrically stimulated at different temperatures, using the photometric method described fully in an earlier paper in this series (Hawkes and Holberton, '74). From each oscillograph the intervals (t') and (t") over which a cell contracted and re-extended by one-half cell length (Et = 0.5-Lc) was recorded and the rerespective rate constants k' and h" computed from equations (3) and (4). To compare length change kinetics at different temperatures in a more general way, these measurements were also expressed as simple linear velocities of contraction (U) and relaxation (US over the first part of the response. Temperatures below ambient were obtained at the microscope slide-electrode assembly by heat exchange with a cooling stage. The stage was constructed for this purpose from 1 cm brass stock milled with a convoluted channel, 0.8 cm deep, and closed with a sealing top plate of 1.5 mm brass. A coolant (1:3 v/v commercial antifreeze-water mixture) was carried to and from the stage in thick-walled rubber pressure tubing, and circulation through the stage channel was maintained by a constant velocity water pump. The temperature of the coolant was controlled in two ways. By circulation through glass heatexchange coils in a cryostat cabinet the
temperature was reduced to between - 5 and - 1O"C, and the sub-zero coolant was then brought to final temperature by a variable output heating element. During experiments the temperature was continuously monitored by a thermistor, placed on the glass slide. Thermal contact was improved by a drop of immersion oil on the thermistor tip. There was typically a 5°C difference in temperature between stage and slide, but using this apparatus the temperature at the slide could be varied between 5-19°C and maintained to within 0.5"C. A sufficient number of experiments was carried out to provide rate measurements at each degree interval within this range from at least 2 and up to 11 individual cells. The regression lines plotted in figures 4, 6 and 8 were computed statistically from a total of 72 observations in each case. To extend the observations to temperature effects outside this narrow range, temperatures were raised above ambient from 25°C to 3 5 ° C by an air-curtain incubator (Sage Instruments Ltd.) but were maintained with less accuracy ( 1" C ) . The thermal dependence of viscosity of Chalkley's medium was determined from an Ostwald viscometer in a controlled temperature water bath.
*
RESULTS
A graph of the velocity of contraction
(U) during the apparently constant velocity phase of contraction (Hawkes and Holberton, '74) against temperature is sigmoidal over the temperature range 5-35" C, approaching U = 0 at low temperatures and U = 26 cm (170 cell 1engths)S-1 at high temperatures (fig. 3). Although measurements were not made below 5°C it was clear that contraction still occurred at lower temperatures. While the velocity of contraction shows thermal dependence, the relationship does not necessarily reflect intrinsic reaction rates in a straightforward way since velocity may be affected by other temperature-dependent variables, such as the viscosity of the bathing medium. The force of contraction at different cell lengths may be approximated by Stokes' law for the drag on a body the size and shape of Spirostomum moving in a viscid fluid, and it is probably drag that represents the principal resistance to short-
257
MYONEMAL CONTRACTION OF S P I R O S T O M U M
30
u . uc s-~
cm
15
0
1
I
I
I
I
2 70
280
290
300
310
OK
Fig. 3 Relation between contraction velocity of Spirostomum and thermodynamic temperature. 0- - -0 , measured velocity of shortening ( U cm S - 1 us temperature (K); 0- - - 0, corrected velocity of shortening (U, cm S-1) us. temperature (K). This curve also represents the variation with temperature of the force parameter FL-1 = p U , when the ordinate is in units of N m-1 X 105. The mean sample size is 20.
ening (Hawkes and Holberton, '75). As might be expected, it can be shown experimentally that media of viscosity higher than Chalkley's medium retard contraction velocity considerably while relaxation rates are less affected. For this reason, it is important to allow for the changed viscosity of the bathing medium at each temperature when comparing intrinsic contraction rates, and in figure 3 the curve for corrected rate (UC) is plotted from the expression UC = U p T / p z O ,where p T and pzO represent the dynamic viscosity of Chalkley's medium at temperatures T "C and 20°C. Viscosity may be related to temperature by a number of empirical formulae whose applicability and accuracy depend on the nature of the fluid and on the experimental regime (Dryden et al., '56). Rather than employ one of these, the viscosity of Chalkley's medium at various temperatures was determined experimentally. The behaviour with temperature of the
parameter Uc is essentially a record of the thermal dependence of the product pU which, since temperature does not alter the morphology of Spirostomum, may be taken as a model of the drag (dimensions of force unit length-') experienced by Spirostomum at different temperatures. As the contraction velocity curve flattens at temperatures above 35 C, the greatest load due to drag will be met by Spirostomum shortening at temperatures around 30°C. It is not clear whether above 35°C contraction rate is limited by temperatureindependent factors; cells incubated at 37°C for 30 minutes and then returned to room temperature displayed normal rates of contraction, suggesting that thermal damage is not significant at the higher temperatures. (It may be relevant that Sleigh ('56) found that the maximum beat frequency of the peristomial cilia of Stentor, although not corrected for the small change in viscosity, occurred at 30"C, the rate slowing to zero over the following O
258
R. B. HAWKES AND D. V. HOLBERTON
0.0
- 1.0 In ( k ' T-l
)
-2.0 3.5
T-1
(OK-~ x
3.6 103)
Fig. 4 The thermal dependence of contraction rate. The experiments of figure 3 over the temperature range 27tL292 K plotted in the form In (k'T-1) us. T - 1 , where Iz' is the exponential rate constant defined by equation (3). The regression line allows calculation of an activation enthalpy (AH:) and activation entropy (AS:) (see text).
decade.) The temperature coefficient (QlO) for the velocity of contraction (&) was 4.1 over the range 12-22°C. At lower temperatures the exponential form of the plot suggests that the theory of rate kinetics summarized in equation (1) is applicable, and may be used to determine the molar changes in enthalpy and entropy of the reaction that is ratelimiting on contraction. The appropriate rate constant is k' calculated from contraction kinetics, and in figure 4 In (k'T-1) against T-1 is plotted over the temperature range 5 1 9 ° C for which data were TABLE 1
Activation parameters of rate processes in the contraction-relaxation cycle of Spirostomum Process
A H : (kcal mol-1)
Contraction Initiation Relaxation
21.7 -+- 0.74 9.6k0.21 10.4 k 0.38
A ~ : ( e . u .= cal k-1 mol-1)
26.8 % 2.63
- 16.7t0.73
- 23.4 & 1.36
available for every degree interval, and for which the effect of changing viscosity is minimal. Within the limits of experimental error these points lie on a straight line and from equation (3) the slope and intercept of the regression line give AH! and AS: (table 1). Studies of the stimulus requirements for the initiation of contraction (Hawkes and Holberton, '74) indicate that both the stimulus duration and stimulus strength are necessary for definition of the threshold. To investigate the thermal dependence of the initiation of contraction, and hence of stimulus-contraction coupling, it was found most convenient to set the applied voltage at a fixed value and monitor changes in the stimulus duration requirement. The relation between temperature and stimulus duration (fig. 5) shows that the excitability of Spirostomum is temperature dependent, stimulus requirements being significantly reduced by increasing temperature. For the present purpose it is
259
MYONEMAL CONTRACTION OF S P I R O S T O M U M 25
T 20
15
T,,, (mS.1 10
'"'I 1
5
0
2 70
280
1
1
i
2 90
300
310
OK
Fig. 5 Effect of temperature on stimulus duration at contraction threshold. The latent period (Tth) measured between the leading edge of a 50 V square wave stimulus pulse and the beginning of the response is plotted as a function of thermodynamic temperature. The points below 298 K represent the grouped data over a 5 K interval. The mean sample size is 20.
convenient to consider initiation of cell shortening as an endpoint of some chemical reaction, which need not be specified, whose velocity is proportional to the strength of the applied electric field as defined by the stimulus strength-duration relation. In that case it would be expected that the stimulus duration at threshold would be inversely related to the reaction rate and that the reciprocal of duration might be related to thermodynamic temperature by rate kinetics. The relation In ( T t h - I T - ' ) us. T-I where Tth is the duration at threshold, is plotted in figure 6, and the corresponding activation enthalpy and entropy values are given in table 1. The rate of relaxation (Ur) of Spirostomum following a contraction induced by a submaximal stimulus, was determined between 5 3 5 C for the apparently constant velocity phase which accounts for O
the greater part of elongation (fig. 7). Because the relaxation rate is independent of small changes in the viscosity of the bathing medium no correction for the temperature dependence of this quantity is necessary in this case. As for contraction there appears to be an exponential increase in the rate of relaxation between 5-25"C which declines at higher temperatures. The plot of In (k" T - I ) us. T - ' is again linear over the temperature range 5 1 9 ° C (fig. 8) leading to values of AH: and AS: from the slope and intercept of the regression line (table 1). DISCUSSION
The present results cannot easily be interpreted in terms of the rate-limiting step in a reaction series since AH: and AS: values from a single example represent one point of a putative isokinetic correla-
260
R. B. HAWKES AND D. V. HOLBERTON -1
*
1
-1.3
-1.9 3.4
3.5 T-1 ( ' ~ - 1
3.6 x 103
)
Fig. 6 The thermal dependence of stimulus threshold. The data of figure 3 over the temperature range 278-292 K replotted in the form In (T thT)-1 us. '2-1.
2 70
2 80
290
300
310
OK
Fig. 7 The variation of relaxation velocity (U, cm. S-1) of Spirostomzcm with temperature. The points below 298 K represent means of grouped data over 5 K intervals. The mean sample size is 20.
MYONEMAL CONTRACTION OF SPIROSTOMUM
26 1
Fig. 8 The thermal dependence of relaxation rate. The experiments of figure 7 over the temperature range 278-292 K plotted in the form In (k” T-1) us. T-1, where k” is the rate constant of relaxation defined by equation (4).
tion. For instance, similar thermodynamic parameters computed from the variation with temperature of flagellar beat in Strigomonas (Holwill and Silvester, ’65) were subsequently found to be atypical when isolated quantities are compared for cilia and flagella from a number of sources, yet all pairs of values plot as co-ordinates of a probable isokinetic relationship (AS: us. AIi;). The variation may be ascribed to differences in environmental factors, that cannot be controlled in in vivo experiments, and to which the values of AS: and AH: are individually sensitive (Glasstone et al., ’41) but which have much less influence on the free energy of activation. Due to the “compensation effect,” AG: changes little for the same reaction under different conditions. Nevertheless, with these limitations in mind, implications of these parameters measured from Spirostomum may be examined for such models of myonemal mechanism as have been proposed. The activation energy approach cannot satisfactorily distinguish between the two models of spasmoneme contraction proposed by Weis-Fogh and Amos (‘72). In both cases the reaction leading to contraction is that between free Caz+ and ligands
on the contractile apparatus. For a simple reaction between ions in solution (for instance between Caz+ and possible carboxylate ions on the myonemal protein) Glasstone et al. (‘41) predict AS = - 1 O Z C a Z M
(6)
where Z is valency and subscripts Ca and M refer to the calcium ion and the myonemal ligand. In general, for ions of dissimilar sign there is an entropy increase (AS: positive) going from reactants to activated complex, for ions of like sign there is an entropy decrease. The AS: value for a reaction between an ion and a neutral molecule or between two neutral molecules obeys no such simple relation and the magnitude cannot be predicted easily. Superficially there is some agreement between the activation entropy of the reaction governing contraction of Spirostomum (26.8 e.u.) predicted by equation (6) for a reaction between calcium ions and monovalent ligands on the myonemal protein. (In a similar way the values of AS: from glycerol-extracted locust sperm (Hoffman-Berling, ’55) and from cilia of Stentor (Sleigh, ’56) agree closely (-20 e.u., -21 e.u.) and are compatible with the suggestion (Holwill and Silvester, ’65) that the rate-
262
R. B. HAWKES AND D. V. HOLBERTON
limiting reaction is between ions of like sign, yet the result from Strigomonas ( - 1 e.u.) is not compatible, and demonstrates that inference of mechanism from single values of activation energies is inherently unsatisfactory. A negative AS: value appears to be typical of the reaction governing ciliary and flagellar beat rate, and it is possible that the very dissimilar entropy of Spirostomum contraction indicates a rate-limiting step that is different in kind. It is not known whether the rate of contraction of Spirostomum is determined by the rate of the Ca2+-myonemeinteraction or by the velocity of shortening of myonemes in the form of the calcium salt, or indeed by some other rate-limiting process such as diffusion of Ca2+ through the myonemal compartment. The relation between tension and temperature at given extension is unclear for real materials. From the kinetic theory of ideal rubber elasticity, tension is directly proportional to absolute temperature (Treloar, '58). The apparent distinction between Spirostomum contraction and ciliary beat frequency in the nature of the rate-governing reaction finds some confirmation when the AH: values are compared. For myonemal contraction AH: = 21.7 kcal. mol-',, whereas the AH: values for cilia and flagella listed by Holwill and Silvester ('67) from 17 cell types, are scattered, but broadly similar within the range 1.14 kcal mol-1 (boar spermatozoa) to 15.4 kcal mol-1 (Strigomonas). On the other hand AS: and AH: for stimulus duration at threshold do compare with the data from ciliary beat frequency, and the negative AS: value is consistent with a reaction in solution between ions of like sign during excitation-contraction coupling. There is at least one other compatible explanation, the ionization of a neutral molecule. It was suggested in the first paper of this series (Hawkes and Holberton, '74) that stimulus-contraction coupling might be achieved through the stimulus-dependent displacement of Ca2+ from sites on the inner face of the surface membranes which in turn would trigger the regenerative release of Ca2+ from reticular stores. Assuming Ca2+ to be bound to the membrane electrostatically (Dawson and Hauser, '70), displacement would in-
volve ion-pair form$tion which invariably has a,negative A s + (Frost and Pearson, '53). Ettiene ('70) used the photoprotein aequorin to assay free Ca2+ in the cytoplasm of Spirostomum during contractionrelaxation cycles, and the results indicate that relaxation is governed by some intrinsic property of the myoneme and is not synchronised to the fall in free Ca2+ levels. In this case i t is possible that the removal of Ca2+from ligands on the myonemal protein is rate-limiting, and this step may again result in ion pair formation, especially if the charge neutralisation model of myonemal contraction is correct. However, the opposite view, that the rate of relaxation is coupled to the removal of Ca2+from the myonemal compartment, is not excluded by the analysis of its thermal dependence. It is notable that the activation energy values for relaxation (table 1) are close to the AS: vs. AH: relation demonstrated by Holwill and Silvester ('67) for flagellar beat frequency, and to a parallel isokinetic correlation drawn in the same paper through data from isometric tension decay and isotonic elongation of smooth muscle. This relation has been taken to indicate that the rate-limiting reaction of flagellar beat is the breakdown of a n ATP-ATPase complex (AH: = 12.4 kcal mol-l; AS: = -8 e.u., Ouellet et al., '52), since AH: and AS: values from striated muscle relaxation also plot as co-ordinates to this line and the anomalous smooth muscle results can be understood in terms of unusual contractile proteins or differences in cross-bridge behaviour associated with ATP dephosphorylation. It is possible that this reaction may also be rate-limiting on relaxation of Spirostomum at the level of Ca2+ sequestration, since ATP hydrolysis is a known step in Ca2+ transport across muscle sarcoplasmic reticulum (Hasselbach, '64). Alternatively, relaxation of Spirostomum could be driven by a mechanism outside the myoneme since in Stentor extension is thought not to depend on myonemal relaxation, but is probably controlled by intertubule sliding of km microtubules, and this action is believed to be dependent on ATP dephosphorylation (Bannister and Tatchell, '68; Newman, '72; Huang and Pitelka, '73).
MYONEMAL CONTRACTION OF SPIROSTOMUM ACKNOWLEDGMENTS
The authors gratefully acknowledge the technical assistance of Mr. J. Marshall. Dr. R. B. Hawkes was a recipient of a Science Research Council Studentship during the preparation of this work. LITERATURE CITED Bannister, L. H., and E. C. Tatchell 1968 Contractility and fibre systems i n Stentor coerzilazrs. J. Cell. Sci., 3: 295-308. Burge, R. E., and G. F. Elliott 1963 The thermal dependence of (i) the decay of twitch and tetanic tension, and of (ii) elongation after stimulation. J. Physiol., 169: 8 6 4 7 P . Dawson, R. M. C., and H. Hauser 1970 Binding of calcium to phospholipids. In: Symposium on Calcium and Cellular Function. A. W. Cuthbert, ed. Macmillan, London, pp. 1 7 4 1 . Dryden, H. L.,F. D. Murnagham and H. Bateman 1956 Hydrodynamics. Bulletin 84, National Research Council (U.S.A.): report of the Committee on Hydrodynamics, Division of Physical Sciences. Dover Publications Inc, Ettienne, E. M. 1970 Control of contractility of Spirostomum by dissociated calcium ions. J. Gen. Physiol., 56: 168-179. Exner, 0. 1964 Concerning the isokinetic relationship. Nature, 201 : 488490. Frost, A. A,, and R. G. Pearson 1953 Kinetics and Mechanisms. A Study of Homogeneous Chemical Reactions. John Wiley and Sons, Inc., New York. Glasstone, S., K. J. Laidler and H. Eyring 1941 The Theory of Rate Processes. 1st edition. McGraw-Hill, New York and London.
263
Hasselbach, W. 1964 ATP-driven active transport of calcium in the membranes of the sarcoplasmic reticulum. Proc. Roy. Sw. B., 160: 501504. Hawkes, R. B. 1974 Myonemal Contraction of Spirostomum. Ph.D. Thesis, University of Hull. Hawkes, R. B., and D. V. Holberton 1974 Myonemal contraction of Spirostomum. I. Kinetics of contraction and relaxation. J. Cell. Physiol., 84: 225236. - 1975 Myonemal contraction of Spirostomum. 11. Some mechanical properties of the contractile apparatus. J. Cell. Physiol., 85: 595602. Hoffman-Berling, H. 1958 Der mechanismus eines neuen, von der muskelkontraktion verschieden kontraktionszyklus. Biochim. Biophys. Acta, 27: 247-255. Holwill, M. E. J., and N. R. Silvester 1965 The thermal dependence of flagellar activity in Strigomonus oncopelti. J. Exp. Biol., 42: 537-544. 1967 Thermodynamic aspects of flagellar activity. J. Exp. Biol., 47: 249-265. Huang, B., and D. R. Pitelka 1973 The contractile process in the ciliate Stentor coeruleus. J. Cell Biol., 57: 704-728. Newman, E. 1972 Contraction in Stentor coerziZeus: acinematic analysis. Science, 177: 447449. Ouellet, L., K. J. Laidler and M. F. Morales 1952 Molecular kineti s of muscle adenosine triphosphate. Arch. Biochem. Biophys., 39: 37-50. Sleigh, M. A. 1956 Metachronism and frequency of beat i n the peristomial cilia of Stentor. J. Exp. Biol., 33: 15-28. Treloar, L. R. G. 1958 The Physics of Rubber Elasticity. 2nd edition. Clarendon Press, Oxford. Weis-Fogh, T., and W. B. Amos 1972 Evidence for a new mechanism of cell motility. Nature, 236: 301-304.
