The Effect of Temperature on Certain Simple Haemolytic Systems

The study of the effect of temperature on simple haemolytic systems has a significance quite apart from any information which it may supply regarding the nature or the kinetics of the haemolytic process, for the system under consideration is one of much less complexity than those usually studied. Most of the recent work on the effect of temperature on biological systems has been devoted to finding the temperature coefficients for such processes as contraction in muscle, conduction in nerve, the movement of whole animals, etc. ; sometimes the effect of temperature on the phenomenon has been found to be in accordance with the Arrhenius equation, sometimes not. It is of considerable interest, accordingly, to find to what extent such an equation describes the effect of temperature on simple systems such as those dealt with in this paper, especially when the effects in such systems can be subjected to a much more detailed analysis than is usually possible in investigations of this kind.

All the data for a study such as this can be obtained from a suitable series of time-dilution curves, i.e. curves showing the relation of the time required to produce complete haemolysis of a certain arbitrary number of red cells to the concentration (or dilution) of lysin producing the haemolysis. Such curves are obtained, at various temperatures, by a technique which has already been fully described (Ponder, 1923 ; Ponder and Yeager, 1929); any one concentration of lysin can then be selected, and the relation between the temperature and the velocity of the haemolytic reaction (reciprocal of the time required for complete lysis) can be plotted in the usual way. The advantage of deriving the data from a complete set of time-dilution curves is that the relation between the temperature and the velocity of the reaction can be found for all concentrations of lysin within the experimental range, instead of for one arbitrarily selected concentration of lysin only.

The time-dilution curves from which the data of this paper are derived were obtained at 5° intervals from 5° to 45°, and show in each case the time required for the complete lysis of 0·4 c.c. of a standard suspension of human erythrocytes by various quantities of saponin at various temperatures. As will be seen from an inspection of these curves in Fig. 1, the observations extend from times of 300 minutes or more at one extreme to times of 0·5 minute or less at the other, i.e. the revised technique recently described by us has been used throughout (Ponder and Yeager, 1929). For reasons of convenience, the observations at 5°, 10° and 15° were made in a refrigerator room containing the water bath and all the apparatus, etc. ; the observations at higher temperatures were made in the usual manner.

The results obtained will be best understood by an inspection of Figs. 1 and 2, the first of which shows the time-dilution curves from which the data are derived, and the second of which shows the logarithm of the velocity of haemolysis plotted against the reciprocal of the absolute temperature for a series of concentrations of lysin ranging from 1 in 6000 to 1 in 45,000. If the effect of temperature is described by the Arrhenius equation, the points obtained at different temperatures for any one concentration of lysin should fall on a straight line, the slope of which gives the temperature coefficient μ ; and further, if the haemolytic process is similar to the simple chemical processes with which it is often compared, the same temperature coefficient should be obtained for all concentrations of lysin, i.e. the lines in Fig. 2 should be parallel.

Inspection of Fig. 2 will show that neither of these conditions is fulfilled. In the first place, the points corresponding to any one concentration of lysin do not fall on a straight line over the entire temperature range, but only over its lower part (from 5° to about 20°) ; above 20° the points deviate considerably from a straight line, the direction of the deviation generally indicating a diminution in velocity at these higher temperatures. This discontinuity in the neighbourhood of 20° is the rule rather than the exception in biological processes, and there are a number of ways of interpreting it. Some observers suppose that one reaction, with a high temperature coefficient, controls the process below I5° –20°, but that above these temperatures the process becomes controlled by another reaction with a lower temperature coefficient than the first (Crozier, 1924; Glaser, 1924). Other investigators ignore the discontinuity altogether, and base their calculations of the temperature coefficient either on the part of the curve below the discontinuity or on the part above it. The simplest method of accounting for the results, however, is to assume that the cells of the tissues examined themselves undergo alteration at high temperatures, the alteration being either of the result of an irreversible “deterioration,” or brought about by obscure changes in the physical, and perhaps in the chemical, properties of the protoplasm, as has been suggested by Heilbrunn and others (Heilbronn, 1925). In the case of cardiac muscle, Brown (1930) has succeeded, in fact, in demonstrating that the “new μ. value” above 20° is the result both of a destructive effect of the heat on the tissue (“deterioration”) and also of obscure intercellular changes, the effect of which remains even after the “deterioration “has been allowed for; in view of the fact that these changes are so conspicuous above 20°, Brown prefers to calculate the temperature coefficient of the process from the points observed below 15°, but at the same time he implies that even these observations are probably affected by obscure changes in the system, these changes occurring at the lower temperatures as well as at the higher, but perhaps being reversible.

In the case of cardiac muscle or of most biological systems, it is almost impossible to decide whether, as the temperature is raised from 10°, say, to 20°, only the velocity of the process under consideration is altered, or whether the system itself undergoes a change, so that the process at 20° is essentially the same process operating in a totally different system and its velocity therefore incapable of being compared with the velocity of the process at 10°. In the case of the haemolytic systems under consideration, however, the question is easy to answer, for if the effect of temperature were merely to alter the velocity of a reaction between the cells and the haemolysin, the time-dilution curves at various temperatures would necessarily all approach the same asymptote. This they show no tendency to do (Fig. 1) ; the position of the asymptote, in fact, becomes first higher and then lower as the temperature increases, thereby indicating first a decrease and then an increase in the resistance of the system with increasing temperature. We shall show below that this change in resistance is reversible at some temperatures and irreversible at others, and that the total change is composed of a change which takes place in the resistance of the cells, together with a change in the properties of the haemolysin ; the essential point in the meantime, however, is that the haemolytic system of cells, NaCl, and saponin at 5° is a different haemolytic system from that produced by the mixing of the same components at 10°, or at any other temperature. It is not permissible, accordingly, to plot three points such as A, B, and C in Fig. 2 with reference to the same coordinate axes, for A is obtained from a cell-lysin system at 5°, while B and C are obtained from different systems ; three such points cannot be properly represented in the same plane and formed by a straight line, nor can a very definite meaning be attached to a “temperature coefficient” obtained from the slope of such a line, for, although the Arrhenius equation may be expected to describe the effect of temperature on the velocity of a process in a particular system, it obviously cannot be expected to describe the effect of temperature on the velocities of processes in several different systems at one and the same time.

Comparatively little regarding the temperature coefficient of the haemolytic process, accordingly, is to be learnt from the conventional graphical representation of the way in which the velocity of the reaction varies with temperature, and it is scarcely more permissible to calculate a μ value from the relatively straight line between 5° and 20°, where the resistance of the system changes, although reversibly, with each change of temperature, than it is to calculate a μ value from the irregular line between 20° and 40°, where the changes in the system are less regular and less reversible. We cannot be satisfied with such a procedure even as a rough approximation, for as soon as we put it into practice we are confronted with a fresh difficulty, in that the various straight lines in Fig. 2 are not parallel. This results in a different μ value being obtained for each concentration of lysin, the value ranging from about 32,000 to about 27,000 ; there is no means of knowing, moreover, which of these values, if any, is the correct one. There is certainly no simple explanation, consistent with what is known regarding the kinetics of haemolytic systems, which can be advanced to reconcile this result with the theory of temperature coefficients, and we are accordingly forced to conclude that the effects of temperature, even in this very simple system, are too complex to be described by such an expression as the Arrhenius equation.

If the findings in the case of saponin are complicated, those in the case in which sodium taurocholate is employed as a haemolysin are far more so. Inspection of the time-dilution curves in Fig. 3 will show that the resistance of the system, as judged by the position of the asymptotes, first increases as temperature rises, and later falls, the system being at its maximum resistance at about 15°. For this reason, among others, the relation between temperature and the velocity of the lytic reaction (Fig. 4) is far from simple, and is represented by a series of curves showing a number of alternating maxima and minima¹.

It is obviously impossible to obtain a value for a temperature coefficient from these curves, especially as their slope may be positive in some parts and negative in others. The curves, however, although of an unfamiliar form, are not in any sense “irregular,” for not only can they be readily reproduced, but they are derived from perfectly smooth and typical time-dilution curves; they differ considerably, at the same time, among themselves, in that the maxima and minima do not always occur at the same temperatures, and in that these maxima and minima are not always equally well marked. Comparison of the curves in Fig. 4 with those in Fig. 3, from which the former are derived, will show that these differences in form are brought about by two separate factors : (a) the variation in the position of the asymptotes of the timedilution curves, and (b) a change in the form of the time-dilution curves themselves with variation in temperature.

(a) The change in the position of the asymptotes is essentially similar to the change observed in the case of saponin, except that in the former case the asymptotic dilutions first decrease and then increase, whereas in the latter case they first increase and later decrease. The variation in the position of the asymptotes, moreover, is to be interpreted in the same way in either case, for it indicates variation in the resistance of the haemolytic system, i.e. in the quantity of lysin imagined to be combined, when lysis is complete, with the particular cell component affected. It is very difficult, however, to find any simple explanation for the occurrence of these changes ; one might, indeed, expect that an increase of temperature would lead to a decrease in resistance, although exactly the opposite is usually the case. We must leave the findings unexplained, accordingly, merely remarking that the increase in resistance with increasing temperatures, unexpected though it is, leads, in increase of saponin at least, to quite a usual result, i.e. the falling away of the curves in Fig. 2 from the linear portion which corresponds to the range of lower temperatures.

Applying this hypothesis to the cases under consideration, it is not surprising to find that different values of n are required to describe the time-dilution curves at various temperatures. In many cases the difference in form between curves at different temperatures is easily seen, e.g. in Fig. 1, the curves at 5·5°, 35° and 45° approach nearly the same asymptote, which enables their very different form to be appreciated at once. A similar instance in the case of Fig. 3 may be found in the curves at 10° and 20°; these approach nearly the same asymptote, but are totally different in form. There is little point in describing the complete analysis of these curves or of tabulating the various values of k, x and n obtained¹; it is sufficient to observe that the effect of temperature is to alter the essential conditions on which the kinetics of the haemolytic systems depend. In scarcely any sense, therefore, is the velocity of the process at 5° comparable with the velocity of the process at 10° or at any other temperature, for the differences in velocity correspond to differences in three quantities, k, x and n; the Arrhenius equation can therefore scarcely be expected to describe the results, since it assumes that changes in temperature affect only the velocity constant.

The curve for the action of sodium taurocholate at 5·5° shows in a peculiar way the effect of temperature on the haemolytic system, for here we see a distinct retardation of lysis in the dilution of 1 in 6000, followed by more rapid lysis by the dilutions of 1 in 7000 and 1 in 8000. This phenomenon (often referred to as a “zone phenomenon”) is quite characteristic of the lysin sodium glycocholate, and is frequently met with in sodium taurocholate systems when sugars are present; in the latter case, at least, it has been shown to be brought about by the activity of the haemolysin itself being depressed, and it is probably permissible in this case also to attribute its appearance to an effect of the low temperature on the physical state of the lysin in the particular dilutions concerned. It is certainly not difficult to imagine that semi-colloidal lysins such as the saponins and the bile salts may undergo quite marked and perhaps abrupt changes in physical state as their temperature is increased ; the fact can, indeed, be demonstrated experimentally, as will be seen below.

The difference between the properties of a haemolytic system at two different temperatures, e.g. 5° and 20°, may be either reversible or irreversible. In order to see how we may distinguish between these two kinds of change, let us examine some specific examples. Suppose that we plot a time-dilution curve for a haemolytic system first at 5°and then at 20° ; call these curves A and B. The fact that these two curves are different indicates that a change in the system has resulted from the increase in temperature. Let us now warm the cell suspension to be added to the haemolytic system by raising it to 20° for a period of, say, 30 minutes, cool it to 5°, add it to various dilutions of lysin at 5°, and so plot a curve at 5° for a system which differs from that used in obtaining curve A only in that the cells have been previously raised to 20°. Call the resulting curve C. Obviously, if A and C coincide, no irreversible change has resulted from warming the cells to 20°, although the fact that A and B differ indicates that a change, which we may call “reversible,” has occurred. If A and C do not coincide, however, the temperature of 20° must have produced a change which persists even after the lower temperature of 5° is again established ; this change we call irreversible.

Continuing, the experiment may be modified by raising the lysin dilutions to 20°for 30 minutes, cooling to 5°, and plotting a curve D by the addition of cells which have not been exposed to the higher temperature. If D and A coincide, no irreversible change has been produced in the lysin at 20° ; if they do not, an irreversible difference has been established. Again, both cells and lysin can be heated to 20° separately, but mixed at 5° to produce curve E ; again this may coincide with A or may not. Yet another modification is to cool (i) cell suspension, (ii) lysin, or (iii) both cells and lysin, to 1°, to warm again to 5°, and then to plot curves F, G and H, which may or may not coincide with A ; in this way it may be discovered whether cooling the components of the haemolytic system results in irreversible changes or not. Finally, there are innumerable modifications of the experiment possible by employing temperatures other than 5° and 20°, e.g. 10° and 20 20° and 40°, etc.

In order to illustrate the type of change met with in the systems under consideration, we shall give a number of experiments in detail.

The first experiment is concerned with the effect of changing the temperature of cells and of saponin within the limits of the range 1° to 22°. The dilution of lysin is represented by δ, and the times in minutes taken for lysis in the standard system at 14° by t₁The column headed t₃ gives the times for complete lysis at 14° in a system composed of lysin together with cells which have been heated to 22° for 3 hours, and then cooled to 14°. Under t₃ are times for lysis of cells at 14° by lysin dilutions which have been warmed to 22° for 3 hours. To obtain the column i₄, the lysin dilutions were placed in the ice-box for 3 hours, and lysis afterwards carried out at 14°, whereas the times for systems at 14° containing cells which had been kept for 3 hours in the ice-box are shown in the column under t₅. In practice, all five timedilution curves were obtained simultaneously.

From these figures we may conclude : (i) that warming either the cells or the lysin to 22° results in a slight increase in resistance, and (ii) that cooling the cells produces a slight increase in resistance, and (iii) that all these changes are very small, and are exhibited principally in connection with the higher dilutions of the lysin.

The second experiment to be recorded concerns the effect of warming cell suspension or saponin dilutions to a temperature of 40°. Here t₁ gives the standard curve at 25°, t₂ the curve for a system composed of lysin plus cells which had been heated to 40°for 3 hours, and t₃ the curve for a system composed of cells plus lysin which had been heated to 40° for 3 hours.

We can conclude from this table that heating the lysin to 40° has very little effect, but that a similar treatment of the cells results in a considerable increase in resistance.

Carrying out similar experiments with sodium taurocholate as the lysin, we obtain the following results: t₁ gives the times for a standard curve at 25°, and t₂ the times for a system in which the cells had been heated to 42° for 3 hours, and t₃ the times for a system in which the cells had been cooled to 10° for 3 hours.

As before, both heating and cooling the cells to 42° and to 10° respectively increases the resistance, but only very slightly. In the last experiment of the four, the effect of warming the dilutions of sodium taurocholate to 42° for 3 hours is investigated ; gives the standard curve at 25°, and t₂ the curve, also at 25°, for the system containing previously warmed lysin.

The effect of temperature on the lysin is quite marked, although perhaps not so marked as we might expect in the case of so unstable a haemolysin. It will be seen that the curve for the second system crosses the curve for the standard system, the times in column t₂ being first shorter than those in t_1, but afterwards longer, i. e. both the asymptote and the value of n are different in the two curves.

These examples, although not individually particularly striking, show quite clearly that changes-in temperature produce irreversible changes both in the red cells and in the haemolysins themselves. In some cases (particularly when high dilutions of lysin are concerned) these changes are sufficiently great to produce a change in the velocity of lysis of as much as too per cent. ; they are almost sufficiently extensive, indeed, to account for the deviations from linearity seen in Fig. 2 in the case of saponin. There is no need, however, to account for such deviations soleley on the grounds that changes in temperature produce irreversible changes in The cells or in the lysins, for they are far more probably due to reversible changes, i.e. to differences which exist in the state of the cells and lysins at different temperatures, but which are not producible at one temperature and detectable at another.

Two varieties of conclusion may be drawn from the foregoing investigation, the first relating to the temperature coefficients of the haemolytic processes studied, and the second relating to temperature coefficients in general.

The most outstanding fact is that both the simple haemolytic systems studied are apparently too complex to be described by the Arrhenius equation. It is impossible, as a consequence, to arrive at a value for the temperature coefficient; the best we can do, in the case of saponin haemolysis, is to say that the value of μ may be between 25,000 and 34,000, while in the case of sodium taurocholate haemolysis we cannot form any idea of the value of the temperature coefficient at all. The principal reason for this failure is that the Arrhenius equation is an expression which describes the effect of temperature on the velocity constant of a system, while, in the cases under consideration, a change of temperature does not change only the velocity constant, but alters the system in other ways; the changes are, in fact, far too complex to allow us to treat the process of haemolysis as if it were a simple chemical reaction. It appears, rather, to be a reaction of quite a complicated kind, for both the cells and the haemolysin, as well as the reaction between them, undergo changes with changes of temperature; a system containing lysin and cells at 20° is, accordingly, by no means the same system, from the point of view of its kinetics, as a system of the same lysin and the same cells at 30°. Such results might be considered as supporting the extreme position of Heilbrunn (1925), who has objected to applying to heterogeneous systems the type of analysis which applies to homogeneous systems and who concludes that it is not only useless to compare temperature coefficients obtained from biological processes with those obtained from chemical reactions, but useless to attempt to invest the former with any significance at all.

It is of considerable interest to compare the above results and the conclusions drawn from them with the results and conclusions of other workers, using other biological material. When we do so, we are at once struck by the fact that most investigations made hitherto have been concerned with much more complex systems than those with which this paper deals, but that, at the same time, the results have been much more simple¹. Temperature coefficients have been obtained, for example, for such processes as the contraction of muscle, the movement of unicellular organisms, and even for certain responses of the whole organism; in many such cases the velocities have proved not so very different from those produced by the Arrhenius equation, and in many cases the more pronounced irregularities associated with the simple systems described in this paper have apparently been absent. It is at first sight a remarkable fact that the reactions of a complex system to temperature should appear simpler than those of a simpler system; such a result, however, is in conformity with a principle which applies to all investigations of this kind.

In the simplest case in which the velocity of a reaction is influenced by temperature, the velocity constant, k, is a particular function of temperature, and the Arrhenius equation is followed. In a more complex case, such as that of either of the haemolytic systems considered above, several independent constants are functions of temperature, i.e. k,x,n=f (t). Unless k, x and n are all similar functions of temperature, and are functions, moreover, of a particular kind, the Arrhenius equation cannot possibly apply, and the result of plotting the logarithm of the velocity against the reciprocal of the temperature will be a curve, the complexity of which will depend on the extent and on the particular way in which x and n vary with temperature. The complex curve may present, indeed, an almost unlimited number of forms, may show maxima and minima, and may show variations in form corresponding to variations in the concentration of the reacting substances, as in the cases referred to in this paper, i.e. if one form of curve is found under a set of conditions A, a different form may arise under a set of conditions B, provided any of the constants are influenced by conditions A or B.

Suppose, however, that we study a very complex system, in which twenty or more constants concerned in the reaction are functions of temperature, i.e. where k, a,b,c,… = f (t), the functions being of different kinds. Under such circumstances, in accordance with well-known statistical rules, the result of plotting the logarithm of the velocity against the reciprocal of the temperature will be, in many cases at least, a smooth curve, devoid of obvious maxima or minima, and often easily mistakable for a straight line. Further, if the curve is obtained under various sets of conditions A, B, C, etc., the form of the curve will tend to be similar under all sets of conditions which do not change a large number of the many constants which are functions of temperature. It is by no means surprising, accordingly, that a complex system (such as an entire cell or an entire organism) should yield an apparently simple “temperature coefficient,” nor that a much simpler system should fail to do so.

This principle, although not usually formulated, can be illustrated by several quite familiar examples¹. The titration curve of a monobasic acid, for instance, is a smooth curve of familiar form. The titration curve of a dibasic acid is more complex, and that of a tribasic acid more complex still; when we consider the curve for a polybasic acid such as a protein, however, we may again revert to the simple form, and the curve can be treated as that of a monobasic acid. Consider, again, the crossing of two organisms of single factor difference. The result is a bimodal curve, but the crossing of two organisms differing by many factors affecting the same characters is a simple frequency curve. The more complicated the state of affairs, indeed, the simpler does the final result seem to be. As a last example, consider the effect of combining waves of various forms, as in harmonic analysis; the result of combining a few waves of different forms is in general to produce an apparently less smooth and simple wave form than is produced by combining many different forms; here, again, an apparent simplicity is effected by an increase in the complexity of the conditions.

The recognition of these facts considerably limits the possibility of determining temperature coefficients in biological processes. Suppose, for example, that we study some reaction of an intact animal (or even of an intact cell) to temperature; provided the system possesses a sufficient degree of complexity, the odds are overwhelmingly in favour of the plotting of the logarithm of the velocity against the reciprocal of the absolute temperature resulting in a smooth curve which may possibly be mistaken for an approximation to a straight line. We shall be unable, however, to investigate any of the intracellular processes involved in the reaction by investigating the slope of such a line, for regarded from the point of view either of the kinetics of the individual intracellular reactions or from the point of view of the Arrhenius equation, the line (or curve) is meaningless for at least two reasons, (i) If there are several reactions involved in bringing about the total response, it is mathematically demonstrable that the slope of the line (or of the curve) is not determined by the temperature coefficient of any one of them alone; a μ value of 10,000, say, derived from the line, does not indicate that any one of the individual reactions has this temperature coefficient, or even that the average μ value of the reactions is 10,000. (ii) The fact that the entire system appears to follow the Arrhenius equation does not even necessarily indicate that any one of the underlying reactions does so; further, if a series of μ values are obtained for various parts of the temperature range, there is no reason to suppose either (a) that each new slope corresponds to a new reaction, or (b) that the μ values obtained for various slopes have any direct relation to the temperature coefficients of the various underlying reactions in the system under consideration.

1. When saponin or sodium taurocholate are used as haemolysins for human red cells, the effect of temperature on the haemolytic process cannot be adequately described by the Arrhenius equation.

2. The failure of this equation to describe the results is due to the fact that changes of temperature affect several constants in the equation for the reaction between the lysin and the cells and not the velocity constant only.

3. It is shown that the changes of temperature produce irreversible changes both in the cells and in the lysin, which fact adds to the difficulty of analysing the results.