ON THE MINUTE SIZE OF MITOCHONDRIA

[J. of Exper. Botany, 1959, V 10, N 29, p. 330–336]
Botany Department, Bedford College

D.С. SPANNER

SUMMARY
In very small systems chemical reactions may, it is suggested, take on a periodic or oscillatory character. This would mean that organelles such as mitochondria might become the center of elastic and electromagnetic radiations. This possibility has consequences relevant to the problems of ion uptake, cell microstructure and protein synthesis, amongst other things.

Many years ago the famous physical chemist, G. N. Lewis, speculated on the possibility that bacteria, because of their minute size, might be immune to the implications of the Second Law of Thermodynamics. I am not aware that he carried his speculations very far, but the subject of the possible importance for living things of the very small size of some of their reacting systems has been raised in a new way by the revelations of the electron microscope. Mitochondria, for instance, have been shown to be not merely small in themselves, but also, especially in animals, very highly subdivided by membranes which, so far as one can judge at the moment, would seem to be of a more or less isolating nature. In plants the chloroplasts have an even finer structure; and frequently the cytoplasm itself is intersected by an elaborate membrane reticulum. The ultimate reacting systems which can be considered as at least relatively isolated by membrane barriers may therefore be very small, m mitochondria perhaps about 70 A wide, and in chloroplasts considerably less. Since the diameters of typical metabolic molecules are of the order of 3-10 A (carbon dioxide is about 3-25 A, sucrose about 10 A) it is not possible to pack a very large number of them in at once; and this raises the question as to whether or not the small size of the systems introduces any effects which we shall miss if we confine our attention to macroscopic ones. I should like to put forward the tentative suggestion that it does, and that one at least of the effects is that chemical reactions in mitochondria and chloroplasts take on a periodic or oscillatory nature. Before, however, I discuss the possible consequences I must attempt to justify this suggestion.
 

Periodicity.

Among the processes with which we are familiar periodicity is a very common phenomenon. It is probably best known in vibrating mechanical systems like the clock pendulum; but it is also familiar in electrical circuits and in connection with sound and waves of the sea. But there are some processes in which it rarely, if ever, seems to put in an appearance. Diffusion and thermal conduction never ordinarily show an oscillatory nature, nor does chemical reaction (the Liesegang ring phenomenon represents a periodicity in space rather than in time). Why should this be so, since in the last resort the behavior of all systems depends on the same fundamental properties of the ultimate particles ?

In trying to find an answer to this question it may be helpful to start with some fairly familiar facts. In the first place systems showing oscillatory behavior of a very perfect kind can always have this characteristic quite obliterated by a suitable change in their circumstances. A pendulum, for instance, ceases to show periodicity if it is immersed in thick oil; it simply moves with decreasing speed to its position of rest without overshooting the mark. Similarly the suspended coil of a galvanometer, which normally swings backwards and forwards quite freely, can be made to move quietly to its position of rest without reversal of motion by shorting the terminals with a low enough resistance. What has been done in both these cases is that irreversible processes, of the nature of friction, have been raised to a higher level. As a matter of fact it can be shown that there is a perfectly definite level for these frictional forces such that if they exceed it the motion ceases to be oscillatory; while if they fall below it periodicity is still apparent. This permissible level rises with the mass of the vibrating system, and with the strength of the elastic forces constraining it.

In the second place it is well known that periodicity is commonly most perfect when the system operates with the smallest number of degrees of freedom. That is why the pendulum bob of a clock is carried by a rigid rod, instead of by a flexible cord or chain of links. The latter of course introduce new degrees of freedom, and even if initially the chain swung as a unit sooner or later some of the kinetic energy of the motion would have penetrated these degrees of freedom and the links would be rattling about among themselves. In order further to limit the possibilities the pendulum rod is suspended not by a short cord but by a strip so that it can swing in only one plane.

The implications of these facts would seem to be fairly clear. Systems commonly show periodicity when the number of degrees of freedom called into play is small; and further, when the vibrating part is relatively heavy and stiffly supported. Both of these factors encourage a slowing down of the thermodynamically irreversible processes relative to the reversible ones, and both are relevant to the subject under discussion. Thus, a pendulum and its support can be considered as a single molecule with just one degree of freedom; further, it is designed to be heavy compared with the other molecules, usually those of the air, which react energetically with it. As a result its periodicity is very perfect. On the other hand we have such cases as those presented by diffusion, or by chemically reacting systems. Here, on account of the enormous numbers of molecules involved the number of degrees of freedom is very large and the irreversible dissipation of kinetic energy liable to be correspondingly high; further, there is nothing massive enough to store sufficient kinetic energy to outweigh dissipation.

But in a very minute reacting system the balance might well be different. It is not difficult to envisage diffusion as overshooting the mark, and momentarily building up a concentration gradient in a direction the reverse of the initial one, and the process being repeated a number of times with diminishing amplitude. Nor, I think, is it difficult to think of something similar happening to a chemical reaction. And one would expect the oscillations to be longer sustained and more perfect in character if the molecules or radicals principally concerned were heavier than the majority, such as, for instance, might be the case if a high energy phosphate group was split off, or even if an oxygen molecule was energetically attacked. There is no doubt that this idea needs to be looked into much more thoroughly before it can be finally accepted; but I think it is plausible, and I propose at this point simply to take it for granted and to try to work out its implications.

Figure 1.

The mitochondria are, of course, the seat of numerous and very important biochemical reactions. Let us assume that one or more of such chemical reactions is in progress, pursuing an oscillatory course with the amplitude sustained by a relatively slow overall progress in the reaction (Fig. 1). Then we should have to consider the mitochondrion as the center of two sorts of radiation. In the first place there would be electromagnetic waves. The oscillations would clearly be slower than those giving rise to ordinary thermal radiation which are due to the vibrations of atoms, since larger units would normally be involved. The radiation might be called infra-infra-red waves, and their wavelength would appear to come in a rather empty portion of the spectrum − in fact the mitochondrion might be said to be broadcasting in a vacant channel ! But chemical reactions involve also, in general, a change in shape and volume; and one would expect the mitochondrion therefore to be the center of elastic waves, of an ultra ultrasonic frequency. Both of these types of radiation would possess the same frequency; but whereas the wavelength of the electromagnetic waves would be expected to lie between say 1 м and 1 mm, that of the elastic waves, on account of their far smaller velocity, would be rather of the order of 1/100 to 100 A. Further, the structure of the mitochondria would suggest that the radiation would not be emitted equally in all directions, but would be in the form of beams. It is difficult to say what sort of range would be achieved by the beams, but it will be suggested later that under certain conditions the radiation might be quickly absorbed and the range would be correspondingly short.

Several interesting consequences might follow from such a state of affairs as I have outlined. In fact the interactions of wave systems are so numerous that they cannot be more than touched on and open endless possibilities. In the first place there might be a correlation in the movement of mitochondria and other cell organelles, such as is often observed in cell division. Then again the very short elastic waves might exert an ordering effect on the cell colloids (the dimensions of which would be comparable with their own wavelength), an effect somewhat analogous to the production of sand figures on a vibrating plate. It is not inconceivable that the impact of the radiation on the cell membrane, which it must be remembered has an effective thickness of the order of 50 A, might dynamically, polarize it in the sense that it would actively admit external molecules by a sort of pinocytosis like a not-quite-genuine Maxwell's demon. Alternatively it might increase its permeability as the impact of the waves locally weakened its structure. Permeability change or active uptake or excretion might in some such way be related directly to mitochondrial activity.
 

Ion uptake.

There is, however, another, and I think more interesting, way in which mitochondrial activity might be responsible for active movement, especially of ions. It is a well-known fact that bodies vibrating with the same period can in certain circumstances exert forces on each other, and this principle has been invoked, apparently unsuccessfully, to explain the attractions existing between chromatids and other biological molecules. Here, however, the matter would seem to be somewhat different, since mitochondria are the seat of active metabolic processes releasing energy. If in fact the principle can be applied here it would follow that the mitochondria might exert forces on molecules, among other things, which might be set vibrating at the same frequency by their radiation. It seems to me conceivable that ions might come into that category. Being charged they would of course respond differently from neutral molecules to the electromagnetic waves, and under certain circumstances they might, I think, experience an attraction. One pictures atoms in a solid as vibrating about fixed mean positions, whereas those in a gas possess no such anchorage. In liquids the state of affairs would seem to be somewhat intermediate, so that to some degree ions and other particles in a liquid would possess natural vibratory movements as well as the ability to diffuse fairly freely. Around an ion there is a fairly tight shell of water dipole molecules held electro-statically, and beyond this again further shells held progressively less strongly. This whole structure would possess to some extent at least the elastic properties of a solid, and would therefore be capable of being set in forced or resonant vibrations by either elastic or electromagnetic waves of the right frequency. By some such mechanism as this it is possible that the mitochondria might promote the active uptake of ions into the cell without themselves being in immediate contact with the external solution. In this activity the previously suggested dynamic polarization of the cell membrane might play a part.

In the first place it would satisfy the requirements relevant to the phenomenon of saturation. It is well known that if the rate of active uptake is determined as a function of external concentration a curve rising asymptotically to a limiting value is obtained (Fig. 2). This of course fits in very well with the carrier hypothesis; but it conforms equally well to the present one. Each ion or molecule suitably resonating with the wave field would be absorbing energy from it and so leaving less to promote the movement of other ions. Thus saturation would be reached sooner or later as their concentration was raised.

Figure 2.

Secondly, there is obviously scope here for selectivity and competition. Among the alkali metal ions, for instance, there is a progressive fall in the size of the water shells with rise in atomic weight, and this is accompanied by an increase in mobility. But the differences between lithium and sodium, or sodium and potassium are much greater than those between potassium, rubidium, and cesium. The latter three are fairly alike from this point of view, and rather diverse from the former two; hence it would not be surprising if in active uptake the alkali metal ions fell into two groups which showed competition only between their own members. It has been reported; in confirmation of this that sodium at least in some cases does not compete with potassium, whereas rubidium does. Of course, these facts could equally well fit into the carrier hypothesis.

It is not necessary to assume that an ion which is not being actively absorbed would therefore be without effect. It could, in company with similar ions, act as a reflector for the electromagnetic waves, and by this means it might react to promote the active uptake of other ions. Such a situation has often been observed; the addition of sodium, for instance, raising the uptake of potassium; and calcium that of nitrate. As a matter of fact it is not impossible on some such lines as these to account for even such general phenomena as 'salt respiration', the enhancement of oxygen consumption in the presence of salts. Waves are transmitted, absorbed, or reflected; and in general an atmosphere of ions would behave towards the electromagnetic waves like a metallic conductor towards light − it would be either absorbing or reflecting, or partly both, depending on frequency relationships. Waves absorbed might, on the present suppositions, lead to active uptake; waves reflected would return to the source and might conceivably increase its activity, on the analogy of a fire whose rays were reflected back upon itself.

Vacnolar accumulation.

There is one problem in this connexion which would seem to present rather more difficulty, the problem of accumulation in the vacuole. If the mitochondria do, in fact, attract specific ions then it would, on the surface, appear that they should draw them out of the vacuole rather than push them in; and that accumulation should take place only within the cytoplasm. But this conclusion is, I think, unnecessary. It has to be remembered that ions in the external solution are presented with a unidirectional flux of radiation, whereas those in the vacuole are exposed to it from all sides. It would not be surprising therefore if, like moths surrounded by lights, they hesitated to go anywhere. This way round the difficulty might be harder to apply to the case of a large coenocyte like Valonia, and it might become necessary to invoke other explanations. One such is not difficult to find. As the ions approached a mitochondrion it might be expected that their vibrations would become more intense; intense enough, in fact, to partially disrupt their water shells. This would alter their frequencies, and with it the attractive forces that they experienced. The result would be that they accumulated near but not at the mitochondrion and in the form of particles possessing less water of hydration than usual, but greater kinetic energy than corresponded to the normal energy of thermal agitation. Both these factors would promote passage of the tonoplast membrane if that lay near enough. In view also of the fact that the tonoplast membrane might itself be dynamically polarized I do not think that the phenomenon of vacuolar accumulation presents prima facie any insuperable obstacle to the suggestions. Even if the cell is a very large one, as is the case with Valonia, if the mitochondria are closer to the tonoplast than to the plasma membrane the whole complex might possess a unidirectional pumping action, much as in the presence of luminous energy electrons are passed actively across the rectifying 'membrane' of a selenium photocell.

Protein synthesis.

Another interesting possibility of a quite different kind concerns the mechanism for synthesis of proteins and nucleic acids. The problem here is to account for self-duplication in the case of the nucleic acids, and the production of highly specific molecules in the case of the proteins. Penrose (1957) has suggested a very simple mechanical analogue for the self-duplicating process. In this, specially shaped blocks of wood are confined in a horizontal tray which is agitated lengthwise. A significant point about this model is that the agitation supplied to the blocks has to be confined in direction; were it to be entirely random in direction it would destroy the groupings it produced as fast as it made them. Microscopically speaking, therefore, if the analogue is a valid one, Brownian movement would be useless; some sort of ordered motion is required corresponding to a provision of free energy. It is here that there is a possible role for the radiation fields suggested in this paper; they would be capable, in the thermodynamic sense, of initiating

molecular ordering since, unlike Brownian energy, they themselves possess several degrees of order. The strikingly bipolar properties of amino-acids may also be significant.

Conclusion.

The theory put forward in this paper rests fundamentally on the assumption that in metabolizing systems as small as the compartments of mitochondria and chloroplasts chemical reactions would take on a periodic or oscillatory nature; that is, that they would begin to show one or more definite frequencies instead of a purely random distribution of frequencies such as corresponds to thermal 'noise'. It introduces also as a separate part the idea that hydrated ions possess a natural frequency in the same general range. I must confess that I am not entirely convinced on either of these points, but I think they are as plausible as the suppositions of the carrier hypothesis or the doctrine of anion respiration. Unfortunately the size of the systems concerned falls in a range which is difficult to treat mathematically; it is rather like the calculation of the flow of a gas through pores too small to be treated by Poiseuille's equation but too large for the molecules to be regarded as passing through singly, Nor I think would the frequencies be such as could easily be detected experimentally, at least at the moment. But experimental difficulties of the same order apply to carrier theory. I think the theory possesses, however, several particular attractions; it suggests a direct link between active uptake of ions, and perhaps of other particles, and mitochondrial activity; and it is potentially much wider in its implications than alternative hypotheses. Competition is good; and even if it proves to be wholly untenable, as it may well do, it will have performed a useful function if it merely presents a challenge to the carrier hypothesis which seems for too long to have had matters all its own way.