ABSTRACT
Creep of narcotized Metridium and Calliactis body-wall at constant tensile stress has been studied quantitatively.
The results can most simply be explained in terms of a cross-linked and a noncross-linked polymeric system, acting in parallel. An explanation in terms of a lattice of inextensible fibres is not satisfactory.
The results are discussed in relation to the behaviour of the animals.
INTRODUCTION
Chapman (1953b) has recently published a qualitative study of the visco-elastic properties of the body-wall in sea anemones. This paper reports quantitative experiments on the same material. Creep, creep recovery and the effect of temperature on creep were investigated, and experiments on isolated mesogloea were carried out as well as ones on intact body-wall. Creep was followed for very much longer times than in Chapman’s experiments. The conclusions reached differ in some important respects from those of Chapman.
MATERIALS AND METHOD
Most of the experiments reported in this paper were carried out on Metridium senile (L.), which is available in abundance locally, but a few experiments on Calliactis parasitica (Couch), obtained from Plymouth, are also described.
The muscles of the specimens were made inactive by narcosis in a mixture of equal parts of 7·5% aqueous MgCl2.6H2O and sea water (Pantin, 1948). In a few experiments menthol was used as the narcotic (Pantin, 1948).
Circumferential strips were cut from the body-wall: in experiments with Metridium the width of these strips was the height of the column from just above the foot to just below the sphincter (about 2 cm. in the narcotized specimens), but in experiments with Calliactis it was only half the height of the column (i.e. about 1 cm.). The primary mesenteries were cut. Silk ligatures were tied round each strip at two points 1 cm. apart (these ligatures were required for attaching it to the apparatus). These preparations were used to determine the properties of the body-wall in circumferential tension.
In a few experiments on Metridium the anemone was divided into two halves by a cut along the axis and a preparation was made of one half. Ligatures were tied on these specimens at two points, one a centimetre above the other on the column. These preparations were used to determine the properties of the body-wall in longitudinal tension. These experiments are reported in a separate section of this paper.
Preliminary experiments showed that the preparations had very long retardation times. It was desirable, to obtain results which were simple to interpret, to start the experiments with preparations whose lengths, before the application of the experimental stress, were constant. In particular, a specimen which had suffered a strong contraction would be unsuitable until elastic recovery was very nearly complete, cutting the body-wall was found to cause marked contraction in non-narcotized animals, and slight contraction even in narcotized ones. The following procedure was adopted. Specimens were allowed to expand, and were then narcotized. At least 2 hr. were allowed for magnesium chloride narcosis, and twelve hours for menthol. The body-wall strip was then cut and the ligatures were tied. The strip was returned to the narcotic solution and kept in it at the temperature at which the experiment was to start for at least 2 hr. The distance between the ligatures was checked immediately before the experiment; on a few occasions it was found to be appreciably greater than i cm., and an adjustment was necessary.
Creep curves at constant stress are easier to interpret than curves at constant load (Ferry, 1961). In simple extension involving large strains, as in this work, the two conditions are very different. Constant stress was obtained by means of a hyper boloid weight sinking into water (Andrade, 1910; Dahlquist, Hendricks & Taylor, 1950). The weight was turned from Perspex, and its dimensions were calculated for a 5 g. initial load on a specimen of initial length 1 cm. Its length (5 cm.) allowed for strains up to 5.
The apparatus was set up as shown in Fig. 1. ABCD is a balsa-wood lever, stiffened from B to D by binding on a piece of umbrella rib, and pivoted at C. AC measures 41·0 cm., while BC and CD each measure 5·2 cm. A fine swinging glass stylus attached at A writes on a tall vertical smoked drum (not shown) which revolves once in 11 min. (in experiments with Calliactis, 21 min.). Suspended by a strong thread from the lever at B is the hyperboloid weight. A wire hook is suspended by a strong silk thread from D, and a lump of Plasticene at this end of the lever is adjusted so that the lever, with the hyperboloid weight out of water and thread E detached, is balanced when 25 g. weight is hung from the hook. The thin silk thread E is attached to the lever and to a retort stand clamp, whose height is adjusted to bring the stylus just below the top of the drum. The water in the beaker F is then adjusted so that its surface is level with the base of the weight.
G is a steel rod with a loop at the end. Its upper end is held by a retort stand. It is raised so that the loop is close to the hook. The ligature at one end of the specimen is tied to the loop, and the other to the hook. The beaker H is filled with the narcotic solution. Just before the experimental stress is to be applied, the rod is moved down till the specimen is just taut, and fixed in this position. The drum is started, and the stress applied by burning the thread E with a match. Ten-second intervals are marked on the drum during one of its revolutions with a time-marker.
Measurements of strain on the completed records were made parallel to the axis of the drum. As the lever was approximately level during the relatively rapid extension in the early part of the experiment, the errors due to ignoring the shift along the time scale as the lever rotated about its pivot were negligible.
In experiments which were carried out above the temperature of the room the beaker H was immersed to just below its brim in a thermostatically-controlled water bath. The temperatures given with the results are those in H; the temperatures of the bath were about one degree higher. When creep recovery was being followed the lever was supported in the horizontal position, so that the specimen was slack, and released only momentarily when readings were taken.
Some experiments are reported on isolated mesogloea of Calliactis. The endoderm and muscles were scraped off and the ectoderm pared off before the ligatures were tied. The completeness of removal of tissues other than mesogloea was subsequently assessed by microscopic examination of about four well-spaced sections of each specimen.
RESULTS
The results reported are for circumferential tension, except those in the separate section devoted to longitudinal tension.
Creep curves
Creep was followed in many specimens of Metridium and a few of Calliactis. Fig. 2 shows the course of creep in two experiments on Metridium. In H14 the specimen stretched over a period of about 12 hr. at a continuously decreasing rate, ultimately reaching a constant length which was about three times its initial length. In H13, however, the rate of stretching, after falling to a low value, started to rise again, and constant length was not achieved in the course of the experiment. Experiments in which the rate of stretching decreased continuously, as in H14, will be referred to as giving type I results, and those in which it showed a minimum, as in H13, as giving type II results. When strain is plotted against the logarithm of time, as in Fig. 3, type I results give a smooth sigmoid curve while type II results show a sudden sharp departure from the sigmoid form.
About 70 % of the experiments gave type I results, and the remainder gave type II results. Type II results must be due to yield or rupture of parts of the specimen. In two experiments an increase in the rate of stretching was followed eventually by breakage of the specimen. Only results of type I are susceptible of precise analysis, and results of type II are ignored in most of this account.
The model represented in Fig. 4 would give creep curves similar to those shown for H14 in Figs. 2 and 3. It consists of a Voigt element (an elastic element, represented by a spring, and a viscous element, represented by a dashpot, in parallel) in series with an elastic element. It would elongate at constant stress according to the equation
The strain 2 sec. after application of the stress in the experiments may be regarded as the instantaneous strain; 2 sec. is long compared to the response time of the apparatus and short compared to the retardation times found. Part of the instantaneous strain was due to strain in the apparatus and inaccuracy in the initial tautening of the specimen. In a series of blank experiments, in which the hook was tied directly to the loop on the rod G (see Fig. 1) with a piece of ligature silk, instantaneous strains equivalent to 0·01 to 0·11 strains of a specimen were found. The values which will be given for ϵ0 (Table 1) are thus too high by significant but indeterminate amounts. The contribution of the apparatus to ϵv was found, however, to be negligible.
Ten experiments with magnesium chloride narcosis were continued until constant length was very nearly achieved. The time course of the slow component of strain (expressed as a proportion of ϵv) in these experiments is compared in Fig. 5 with the time course of strain for a Voigt element. Values of τ have been chosen for the experimental results to make them coincide with the Voigt curve at t/τ = 1. There is some deviation of the experimental points from this curve in the regions of maximum curvature, but their correspondence with it is in general good. It is thus possible to describe these results rather closely in terms of the model represented in Fig. 4. The relevant parameters, which were used in the preparation of Fig. 5, are given in Table 1.
It will be shown in a later section that the course of creep is probably determined by the mesogloea. It is of interest therefore to derive from the values for (ϵ0 + ϵv) values for the equilibrium modulus (Young’s modulus) based on the cross-sectional area of the mesogloea in the specimens. It was hoped to obtain these areas from wax sections of the specimens, taking account of the difference in length of the specimen before the experiment and after fixation. The areas obtained in this way for Calliactis were found, however, to be greatly in excess of the values obtained by rough measurement of the cut end of the mesogloea before stretching, and it was concluded that preparation of sections caused severe swelling. The cut end of the mesogloea of Calliactis specimen H41A measured about 7 mm. × 1 mm., giving a modulus of about 2×104 dynes/cm.2. The dimensions, and so the modulus, of H38B were about the same. The thickness of the mesogloea in unfixed frozen sections of narcotized body-wall of Metridium of about the size used in the creep experiments was found to be about 0·4 mm., indicating a modulus of about 3 × 104 dynes/cm.2.
It had been feared that magnesium chloride might alter the physical properties of the mesogloea, Jones (1956) having shown that 8% aqueous MgCl2.6H2O, undiluted, slowly softens the mesogloea of the sponge Leucosolenia botryoides. The experiments with menthol narcosis were carried out for this reason. The results of those which gave type I creep are listed in Table 2. The results show more variety than those obtained with magnesium chloride, but do not differ from them in any systematic way. Specimen H13, used as an example of type II creep in Figs. 2 and 3, was narcotized with menthol. The general similarity between the results obtained with menthol and with magnesium chloride is evidence that the properties of the body wall were not seriously affected by the narcotics. Magnesium chloride was used exclusively in the experiments reported in the following sections. The extremely low value of ϵv in experiment H18C may perhaps be due to compaction such as seems to have occurred in the isolation of mesogloea (see below).
Creep recovery
Recovery was followed after creep almost to constant length in three experiments on Metridium and one on Calliactis. Fig. 6 shows the result of one of these experiments. The values for creep include the instantaneous component of the strain; those for recovery, however, do not, as the stress was re-imposed momentarily for the taking of each reading. In Table 3 the slow component of the creep, ϵv, is compared with the observed creep recovery in each of the creep recovery experiments carried out. In each case, recovery was at least 80 % ofϵv when the experiment was ended and there was a rough correspondence, as in H 27 (Fig. 6), between the time courses of creep and of recovery. In experiments H29 and H43B, however, recovery was much faster than creep for the first 10 sec.
Effect of temperature
Table 1 shows that the creep properties of Metridium body wall at 15° C. and at 22°C. are very similar. Three experiments were carried out at 29°C. In each case a strain of about 3· 5 was reached (at which strain the stylus ran off the drum) without constant length being achieved.
Fig. 7 shows the result of one of three experiments in which the temperature was raised from room temperature to 22°C. and then 29°C. The other experiments gave results similar to that shown in Fig. 7. A rise from room temperature to 22°C. caused a slight increase in compliance: a rise from 22° C. to 29°C. caused a considerable increase in compliance. The marked extension at 2° C. was, however, preceded by a prolonged contraction.
No experiments at elevated temperatures were carried out on Calliactis.
Isolated mesogloea
Calliactis vias used in the experiments reported in this section, on account of its conveniently thick mesogloea. Microscope sections of the specimens, prepared after the experiments, show that the ectoderm and the bodies of the endoderm cells were completely removed, but in all cases some of the muscle fibres remained. At least 80% of the muscle fibres had been removed from specimen H38A (Fig. 8).
These experiments all gave type II creep, and the initial rate of strain was always much lower than with specimens whose body wall was intact. The result shown in Fig. 8 is typical. The creep of the mesogloea specimen is there compared with that of a strip of equal width of whole body wall from the same animal.
Longitudinal tension
Seven creep experiments with longitudinal tension were carried out, all on Metridium. Five of these gave type II creep, and only two gave type I creep. The course of creep of these latter approximated to that of the model of Fig. 4; ϵ0 was found to be 0·34, 0·33; ϵv 1·3, 2·6; and τ 1300 sec., 3500 sec., respectively. Creep recovery was followed for 1 and 24 hr., respectively, and amounted in those times to 75 and 85% of ϵv.
DISCUSSION
The rheological terms used in this discussion are defined by Leaderman (1957).
Chapman’s creep experiments (1953 b) on the body-walls of Metridium and Calliactis lasted for times of the order of 10 min. He therefore did not find that constant length was eventually reached; for this, times of the order of 24 hr. are required. He found that creep recovery was very incomplete. This result is also to be explained in terms of the shortness of his experiments. As the slow extension of his specimens was so far from complete when the load was removed, the elastic restoring force was very much less than the load and creep recovery was accordingly very slow. Chapman concluded from the failure of his specimens to achieve constant length under stress and from the apparent partial irreversibility of creep that their viscoelastic properties should be represented by a model incorporating a series viscous element. This investigation has shown that a model without such an element (Fig. 4) is more useful.
Cross-linked polymers and cross-linked polymeric gels have high but finite equilibrium compliances. Strains of the magnitude of those reported in Table 1 are possible. But the course of creep in homogeneous polymeric systems cannot be described in terms of the very simple model of Fig. 4. It can only be represented adequately by large numbers of Voigt elements in series, or more usefully by a continuous distribution of retardation times L (log τ). L (log τ) is normally found to be roughly constant over a range of several factors of 10 of retardation time (Tobolsky, Dunnell & Andrews, 1951). In such cases, graphs of strain at constant stress against the logarithm of time have more or less constant gradient over the corresponding range of time (Alfrey & Doty, 1945).
Such wide spectra of retardation times have been found by Buchthal & Kaiser (1951) for striated muscle, by Harkness & Harkness (1959) for the uterine cervix of nonpregnant and early pregnancy rats, and by the writer for the tunica externa of tench swim-bladder (Alexander, 1961) and for human hair (unpublished). These results all resemble those obtained with simple polymeric systems. The results here reported for creep of sea-anemone body-wall are in striking contrast. The retardation spectra are extremely narrow—probably too narrow to be adequately derived by any of the approximations currently available (see Ferry, 1961) for the calculation of retardation spectra from creep results. Fig. 5 shows that the creep behaviour can be closely reproduced by a model with a single retardation time.
Two explanations seem possible. The visco-elastic behaviour observed may be that of a homogeneous polymeric system with a very much narrower retardation spectrum than has hitherto been observed in such systems. Little seems to be known about the factors determining the width of the peaks in retardation spectra. Alternatively, and more probably, the creep properties of sea-anemone body-wall are perhaps to be explained in terms of two polymeric systems acting in parallel, a cross-linked polymeric system contributing the modulus and a non-cross-linked system contributing the viscosity. The retardation spectra of both systems would have to be limited to short times. The steady-state elastic compliance of the non-cross-linked system would appear as the ‘instantaneous’ strain ϵ0. At times larger than the retardation times of its components such a double system would show a very narrow retardation spectrum, approximating to a single retardation time if the two components were uniformly distributed. Such a system would thus behave in creep like the model of Fig. 4— and so like sea-anemone body-wall.
It was hoped that the experiments with isolated mesogloea would provide clear evidence of the location of the viscous and elastic elements in the body-wall. In fact, removal of the other tissues (complete except for a small proportion of the muscle) was found to decrease the rate of stretching. The mechanical properties of the mesogloea were plainly altered by the operation of isolating it. Ferry & Morrison (1947) have shown that compaction under pressure increases the apparent modulus of elasticity of fibrin film in tensile experiments at a fixed rate of loading. They attribute this result to the formation of additional secondary bonds in the more concentrated gel thus produced. The change is only slowly and incompletely reversed when the pressure is removed. It seems likely that similar compaction occurs in mesogloea subjected to the rather rough handling needed to isolate it.
Although the properties of the mesogloea are plainly altered in the process of isolation, there is no reason to believe that the change is enormous. The interpretation even of the altered mechanical properties of the isolated mesogloea is difficult on account of the invariable occurrence of type II creep, but the results show plainly that it has both viscosity and elastic stiffness, and that these are of the same order of magnitude as those of the intact body-wall. It seems probable that the visco-elastic properties of the intact body-wall should be attributed to the mesogloea, as Chapman (1953 b) suggested. It is tempting to identify the mesogloea fibres as the elastic component and the matrix as the viscous component. Chapman (1953a) found very little stainable material in the matrix, but it is possible that fixation caused material from it to associate with the fibres (cf. Jarrett, 1958).
Chapman (1953a) describes the mesogloea of Calliactis as a crossed fibrillar lattice and does not appear to consider that the fibres are stretched when the animal expands. Such a theory cannot explain the complete elastic recovery which occurs after creep. Circumferential and longitudinal strains of the magnitudes found could in any case only be explained in terms of a lattice of inextensible fibres if all the fibres had a very large radial component in their orientation in the unstretched mesogloea. Such an arrangement is not found; indeed, a very large proportion of the fibres lie in the tangential plane (Chapman, 1953 a). Considerable elongation of the fibres must have occurred in the experiments. The usual slight incompleteness of creep recovery (Table 3) may represent the component of the strain due to distortion of the lattice.
There is considerable evidence that the protein of sea-anemone mesogloea is collagen or collagen-like (Chapman, 1953 a; Rudall, 1955). The evidence, however, does not include X-ray studies on this material. Grimstone, Home, Pantin & Robson (1958) found in electron micrographs that the mesogloeal fibres of Metrium senile were banded at intervals of about 260 Å., whereas intervals of 640 Å. are typical of adult collagen. Batham (1960) found the interval to be about 450 Å. in specimens provisionally identified as M. canum. Cowan, North & Randall (1955) have found that the low-angle X-ray diffraction spacing (which corresponds to the electron micrograph banding) of rat-tail tendon collagen increases when the tendon is stretched: a strain of 10% produces an increase in the 640 Å. spacing of about 9%. It would be interesting to know the effect of stretching on the electron micrograph banding of mesogloea. It seems probable that the short period reflects a less extended configuration of the molecules than in tendon collagen, and consequent higher compliance. Periods of about 640 Å. might be expected at large strains.
The isometric tension of stretched tendon decreases with increasing temperature, even when chemical cross-links have been introduced by formalin fixation (Meyer & Ferri, 1937). This indicates that the compliance of tendon is due more to internal energy changes than to entropy changes, and hence that the collagen molecules have a rather highly extended configuration. The large elastic strains of which mesogloea is capable can only be explained in terms of entropy changes (unless a strain amplifier, like a helical spring, be postulated) and require a much less highly extended configuration of the collagen molecules. The observed increase of compliance (equivalent to a decrease of isometric tension) with increasing temperature is not to be attributed to internal energy changes in extension, but to break-down of cross-links. The rigidity of gelatin gels similarly falls as their temperature increases (Ferry, 1948).
It was thought that the initial contraction at 29 °C. might be equivalent to the thermal contraction of tendon collagen, although it occurs at so low a temperature. Contraction of tendon collagen, which can be brought about by heat or certain chemical treatments, is due to disorientation of the collagen molecules, and is accompanied by loss of birefringence (Pryor, 1950). Fragments of Metridium and Calliactis mesogloea were therefore examined with a polarizing microscope after heating for 1 hr. at various temperatures. Considerable loss of birefringence was observed for both genera at 50 ° C., but not at 40 or 30 °C. The mesogloea of Metridium, but not of Calliactis, was almost fluid at 50°C. The observed contraction of Metridium mesogloea at 29 °C. does not seem to be accompanied by very thorough disorientation of the molecules. Chapman (1953b) observed contraction of Calliactis mesogloea at 80 –90 °C.
The finite elastic compliance of the body-wall of sea anemones and the complete reversibility of strains imply the existence for each animal of a unique set of dimensions at which its column can be maintained without the exertion of forces on it by direct or hydrostatic action of the muscles or siphonoglyph. Narcotized unstressed pieces of body-wall will slowly assume their unstrained dimensions. Observation of the specimens used in this investigation indicated that the unstrained dimensions in Calliactis approximated to the normal expanded position, and in Metridium corresponded to a mildly expanded position, intermediate between those positions illustrated by Batham & Pantin (1950a) as their plates 7b and f. The pressures (mean 1·3 cm. water) found by Chapman (1949) in the coelenteron of expanded Calliactis would stress the body-wall, which might be expected therefore to be somewhat strained in the normal expanded position unless the stress was met by muscle tonus.
These pressures would be adequate to cause in time quite considerable strain. There is some doubt, however, as to their magnitude and even as to their existence as Chapman’s technique involved running a small quantity of water into the coelenteron under pressure.
The behaviour of Calliactis does not involve extensive changes in the dimensions of the body-wall. The most important changes are probably those which occur when it closes or opens (see Chapman, 1949). These movements are made in times which are short compared with the extremely long retardation time of the body wall. The non-cross-linked component will be predominant in determining the forces required. In practical discussion of the mechanics of Calliactis movement the model of figure 4 can thus be simplified by omitting the spring in parallel with the dashpot.
The behaviour of Metridium, on the other hand, involves extensive changes of the dimensions of the body-wall. These can most conveniently be discussed by reference to the illustrations in the paper of Batham & Pantin (1950a). The highly expanded condition (their plate 7 a) involves considerable circumferential strain of the bodywall. Hydrostatic pressure will be required not only to inflate the column but also to maintain it in the expanded state. The elongated position (plate 7 e) involves longitudinal strain of the body-wall. Further, the fully contracted position (plate 7d) must involve considerable radial strain of the body-wall, though this is reduced by buckling. Return to the unstrained position from any of these positions should be assisted by the elasticity of the body wall. This may explain the negative pressures found by Batham & Pantin (1950a) in Metridium recovering from extreme contraction.
Reciprocal contractions of the circular and parietal muscles of Metridium occur continually, often with a periodicity of about 10 min. (Batham & Pantin, 1950b). These movements take times much less than the retardation time of the body-wall. If more time was available equal movements could be brought about by smaller forces. These movements involve relatively small strains. Changes of phase, however (Batham & Pantin, 1950c), involve spectacular changes of column dimensions which are accomplished much more slowly. Elongation of the column after feeding, for instance (Batham & Pantin, 1950c, figs. 2 and 4), takes an hour or more. This time is comparable to the retardation time of the body-wall. The forces required to bring about such slow elongation will not greatly exceed those required to maintain the column at its enlarged dimensions. The forces available are probably limited by the maximum pressure the siphonoglyph can produce. In peristalsis and in retraction large strains are achieved relatively rapidly, and correspondingly large forces (which are produced by muscles) will be required.
The elastic properties of the body-wall of Metridium are probably not strictly linear. The strains achieved in my experiments are not, however, grossly different from those occurring naturally in the life of the animal. The results can therefore be used in approximate calculations of the forces developed in the living animal. In the experiments it was found that a strip of body-wall whose width was about 2 cm. was maintained at a tensile strain of about 2 by a force of g., approx. 1·6 g. (the reduction from 5 to g. was due to the hyperboloid weight’s action as a constant stress device). A strain of 2 was thus maintained by a tension of about 0·8 g./cm. A strain of 1 should be maintained by about 0·4 g./cm. The animal from which such a strip was taken would have about 2 cm. diameter in the unstrained state At 4 cm. diameter it would have about 0·4 g./cm. tension in the body-wall. This could be maintained by a pressure of about 0·2 g./cm.2 in the coelenteron. This value is within the range of average pressures (0·07–0·61 g./cm.2) found by Batham & Pantin (1950 a) in long experiments on unstimulated Metridium. These average pressures were probably principally balanced by the elasticity of the mesogloea rather than, as Batham & Pantin suggest, by muscle tonus. A column diameter of double the unstrained value occurs commonly in living Metridium.
A similar rough calculation based on the results of the experiments with longitudinal tension indicates that a Metridium could be maintained with its column at double the unstrained length by a pressure of about 0·5 g./cm.2. Living Metridium are often double the unstrained length.
These calculated pressures will tend to be rather too low owing to their being derived from results of experiments involving simple tension. They cannot in any case be regarded other than as very rough approximations.