the effect of temperature on certain simple … · the effect of temperature on certain simple...

39°

THE EFFECT OF TEMPERATURE ON CERTAINSIMPLE HAEMOLYTIC SYSTEMS

BY ERIC PONDER AND J. FRANKLIN YEAGER.(From Washington Square College, New York University.)

(Received ist May, 1930.)

(With Four Text-figures.)

THIS paper is primarily concerned with an attempt to evaluate the temperaturecoefficients for the velocity of haemolysis in two simple haemolytic systems, thelysin being saponin in the first and sodium taurocholate in the second. There isnothing in the literature to suggest that the problem is one of any complexity, forArrhenius (1915) and his collaborators, by whom most of the existing investigationshave been carried out, find that the effect of temperature is adequately described bythe well-known Arrhenius equation, the values of /n ranging from 26,000 whenacetic, butyric, or proprionic acids are used as lysins to 38,000 when the lysin issodium oleate. Their methods, however, are very unsatisfactory, for either theconcentration of the lysin or the "time of action" (i.e. time required for the pro-duction of a particular degree of haemolysis) is fixed arbitrarily; further, theobservations are made over a short temperature range, and usually between 200 and400. Such experiments are too restricted to show the complete effects of temperatureon the haemolytic systems, and, as will be shown below, lead to quite erroneousresults1.

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

1 In a paper published in 1920, one of us (E. P.) described the effects of temperature as followinga hyperbola approaching the temperature axis as an asymptote. This expression fits the data quite aswell as does the Arrhenius equation, but the present results are considered in terms of h^^equation, purely, as will be seen as a matter of convenience.

The Effect of Temperature on Certain Simple Haemolytic Systems 391

METHODS.

All the data for a study such as this can be obtained from a suitable series oftime-dilution curves, i.e. curves showing the relation of the time required to producecomplete haemolysis of a certain arbitrary number of red cells to the concentration(or dilution) of lysin producing the haemolysis. Such curves are obtained, atvarious temperatures, by a technique which has already been fully described(Ponder, 1923; Ponder and Yeager, 1929); any one concentration of lysin can then

20 «0 60 60 100

Fig. 1. Time-dilution curves for saponin and human red cells at various temperatures. Some curveshave been omitted to avoid overcrowding of the figure. Ordinate: dilution of lysin; abscissa: time inminutes.

be selected, and the relation between the temperature and the velocity of thehaemolytic reaction (reciprocal of the time required for complete lysis) can beplotted in the usual way. The advantage of deriving the data from a complete set oftime-dilution curves is that the relation between the temperature and the velocityof the reaction can be found for all concentrations of lysin within the experimentalrange, instead of for one arbitrarily selected concentration of lysin only.

The time-dilution curves from which the data of this paper are derived wereobtained at 5° intervals from 50 to 450, and show in each case the time required forthe complete lysis of 0-4 c.c. of a standard suspension of human erythrocytes byvs^ns quantities of saponin at various temperatures. As will be seen from aninspection of these curves in Fig. 1, the observations extend from times of 300

392 ERIC PONDER AND J. FRANKLIN YEAGER

minutes or more at one extreme to times of 0-5 minute or less at the other, iAtherevised technique recently described by us has been used throughout (PonderandYeager, 1929). For reasons of convenience, the observations at 50, io° and 150 weremade in a refrigerator room containing the water bath and all the apparatus, etc.;the observations at higher temperatures were made in the usual manner.

RESULTS.

(1) Saponin.

The results obtained will be best understood by an inspection of Figs. 1the first of which shows the time-dilution curvesfrom which the data are derived, and the secondof which shows the logarithm of the velocity ofhaemolysis plotted against the reciprocal of theabsolute temperature for a series of concentra-tions of lysin ranging from 1 in 6000 to 1 in45,000. If the effect of temperature is describedby the Arrhenius equation, the points obtainedat different temperatures for any one concen-tration of lysin should fall on a straight line,the slope of which gives the temperature co-efficient /JL ; and further, if the haemolytic processis similar to the simple chemical processes withwhich it is often compared, the same tempera-ture coefficient should be obtained for all con-centrations of lysin, i.e. the lines in Fig. 2 shouldbe parallel.

Inspection of Fig. 2 will show that neitherof these conditions is fulfilled. In the firstplace, the points corresponding to any oneconcentration of lysin do not fall on a straightline over the entire temperature range, but onlyover its lower part (from 50 to about 200); above200 the points deviate considerably from astraight line, the direction of the deviationgenerally indicating a diminution in velocityat these higher temperatures. This discontinuityin the neighbourhood of 200 is the rule ratherthan the exception in biological processes, andthere are a number of ways of interpreting it.Some observers suppose that one reaction, witha high temperature coefficient, controls theprocess below 15°-2O°, but that above these velocity; abscissa: reciprocal oftemperatures the process becomes controlled

and 2,

15° TO° ii'3f 2f if

0X0)1 040& OjOOU

by another reaction with a lower temperature noted opposite each.


c^fccient than the first (Crozier, 1924; Glaser, 1924). Other investigators ignoretne^liscontinuity altogether, and base their calculations of the temperature coeffi-cient 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 thecells of the tissues examined themselves undergo alteration at high temperatures,the alteration being either of the result of an irreversible "deterioration," or broughtabout by obscure changes in the physical, and perhaps in the chemical, propertiesof the protoplasm, as has been suggested by Heilbrunn and others (Heilbrunn,1925). In the case of cardiac muscle, Brown (1930) has succeeded, in fact, indemonstrating that the "new /x value" above 200 is the result both of a destructiveeffect of the heat on the tissue ("deterioration") and also of obscure intercellularchanges, the effect of which remains even after the " deterioration " has been allowedfor; in view of the fact that these changes are so conspicuous above 200, Brownprefers to calculate the temperature coefficient of the process from the pointsobserved below 150, but at the same time he implies that even these observationsare probably affected by obscure changes in the system, these changes occurringat 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 impossibleto decide whether, as the temperature is raised from 10°, say, to 200, only thevelocity of the process under consideration is altered, or whether the system itselfundergoes a change, so that the process at 20° is essentially the same process operatingin a totally different system and its velocity therefore incapable of being comparedwith the velocity of the process at io°. In the case of the haemolytic systems underconsideration, however, the question is easy to answer, for if the effect of temperaturewere 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 thesame asymptote. This they show no tendency to do (Fig. 1); the position of theasymptote, 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 thesystem with increasing temperature. We shall show below that this change inresistance is reversible at some temperatures and irreversible at others, and that thetotal 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 inthe meantime, however, is that the haemolytic system of cells, NaCl, and saponin at50 is a different haemolytic system from that produced by the mixing of the samecomponents at io°, 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 co-ordinate axes, for A is obtained from a cell-lysin system at 5°, while B and C areobtained from different systems; three such points cannot be properly representedin the same plane and formed by a straight line, nor can a very definite meaningbe 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 tem-{^Bture on the velocity of a process in a particular system, it obviously cannotbe expected to describe the effect of temperature on the velocities of processes inseveral different systems at one and the same time.


Comparatively little regarding the temperature coefficient of the haemolytiacess, accordingly, is to be learnt from the conventional graphical representation ohheway in which the velocity of the reaction varies with temperature, and it is scarcelymore permissible to calculate a n value from the relatively straight line between 50

and 200, where the resistance of the system changes, although reversibly, with eachchange of temperature, than it is to calculate a fi value from the irregular linebetween 200 and 400, where the changes in the system are less regular and lessreversible. We cannot be satisfied with such a procedure even as a rough approxima-tion, 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 differentfj. value being obtained for each concentration of lysin, the value ranging from about

13000

so 100 1*0 ieo iM itt BO i<a 160 ia> 300

Fig. 3. Time-dilution curves for sodium taurocholate and human red cells. Ordinate: dilution oflysin; abscissa: time in minutes.

32,000 to about 27,000; there is no means of knowing, moreover, which of thesevalues, if any, is the correct one. There is certainly no simple explanation, consistentwith what is known regarding the kinetics of haemolytic systems, which can beadvanced to reconcile this result with the theory of temperature coefficients, andwe are accordingly forced to conclude that the effects of temperature, even in thisvery simple system, are too complex to be described by such an expression as theArrhenius equation.

(2) Sodium taurocholate.

If the findings in the case of saponin are complicated, those in the case in \ A hsodium taurocholate is employed as a haemolysin are far more so. Inspection of

1000


th^^ne-dilution curves in Fig. 3 will show that the resistance of the system, asjudged by the position of the asymptotes, first increases as temperature rises, andlater falls, the system being at its maximum resistance at about 150. For this reason,among others, the relation between temperature and the velocity of the lyticreaction (Fig. 4) is far from simple, and is represented by a series of curves showinga number of alternating maxima and minima1.

It is obviously impossible to obtain a value for a temperature coefficient fromthese curves, especially as their slope may bepositive in some parts and negative in others.The curves, however, although of an un-familiar form, are not in any sense " irregular,"for not only can they be readily reproduced,but they are derived from perfectly smooth andtypical time-dilution curves; they differ con-siderably, at the same time, among themselves,in that the maxima and minima do not alwaysoccur at the same temperatures, and in thatthese maxima and minima are not alwaysequally well marked. Comparison of thecurves in Fig. 4 with those in Fig. 3, fromwhich the former are derived, will show that ^these differences in form are brought about by .5two separate factors: (a) the variation in the •*position of the asymptotes of the time- ^dilution curves, and (b) a change in the form -i

of the time-dilution curves themselves with T

.9

variation in temperature. &(a) The change in the position of the -7

asymptotes is essentially similar to the change *observed in the case of saponin, except that in .sthe former case the asymptotic dilutions first 3

decrease and then increase, whereas in the \latter case they first increase and later de- J- o.ooii o.ofe aorta o.<xm ox»is 0.0036crease. T h e variation in the position of the Fig. 4 . Analysis of results for sodium tauro-asymptOtes, moreover, is to be interpreted in cholate and human red cells. Ordinate:, • • v r • • J- logarithm of velocity; abscissa: reciprocal

the same way in either case, for It indicates of absolute temperature. The various curvesvariation in the resistance of the haemolytic correspond to various dilutions of lysin, assystem, i.e. in the quantity of lysin imagined no ted oppos i te each-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 thesechanges; one might, indeed, expect that an increase of temperature would lead to adecrease in resistance, although exactly the opposite is usually the case. We must

•15° if a'

g maxima and minima can also be seen in some of Glaser's curves, their prominencedepending on the scale of plotting.

396 E R I C P O N D E R A N D J . F R A N K L I N Y E A G E R

leave the findings unexplained, accordingly, merely remarking that the incr^fe inresistance with increasing temperatures, unexpected though it is, leads, in m^xaseof saponin at least, to quite a usual result, i.e. the falling away of the curves in Fig. 2from the linear portion which corresponds to the range of lower temperatures.

(b) The change in the form of the time-dilution curves themselves, so wellseen in Fig. 3 and also to a lesser extent in Fig. 1, is perhaps less difficult to accountfor than the changes in the position of the asymptotes, but is nevertheless verydifficult to analyse. The general subject of the form of the time-dilution curves hasbeen fully discussed in another paper (Ponder and Yeager, 1929), and it has beenshown that the curve is best described by the expression

in which c is the initial concentration of lysin producing lysis in time t, x the con-centration corresponding to the asymptotes, k a constant, and p a constant whichdetermines the form of the curve, just as the value of x determines the position of itsasymptote. It is also shown that a special physical significance can be attached to theconstant />, if we imagine that each molecule of the cell component reacts witha number of lysin molecules, and that the latter may exist in groups or aggregatesof varying size. The velocity of a reaction occurring in such a system may then berepresented by dx/dt = k (c - x)" (2),

where n is the value of the ratio (mean number of lysin molecules reacting with eachcell component molecule)/(mean number of lysin molecules in a lysin aggregate);whence, if we write p = ijn, we obtain expression (1).

Applying this hypothesis to the cases under consideration, it'is not surprisingto find that different values of n are required to describe the time-dilution curves atvarious temperatures. In many cases the difference in form between curves atdifferent temperatures is easily seen, e.g. in Fig. 1, the curves at 5-5°, 350 and 450

approach nearly the same asymptote, which enables their very different form to beappreciated at once. A similar instance in the case of Fig. 3 may be found in thecurves at io° and 200; these approach nearly the same asymptote, but are totallydifferent in form. There is little point in describing the complete analysis of thesecurves or of tabulating the various values of k, x and n obtained1; it is sufficient toobserve that the effect of temperature is to alter the essential conditions on which thekinetics of the haemolytic systems depend. In scarcely any sense, therefore, is thevelocity of the process at 50 comparable with the velocity of the process at 10° orat any other temperature, for the differences in velocity correspond to differences

1 Even k, it should be observed, is a complex constant, although in expression (2) it appearssimilar to a velocity constant; further, there is reason to believe that k and n, at least, and perhapsalso x, are functions of each other. If it were possible to isolate a velocity constant for the system,the Arrhenius equation would probably apply to it, although that equation does not apply to thesystem as a whole. It will easily be seen that two criteria can be used to determine the applicabilityof the Arrhenius equation, (i) its applicability to the velocity of the reaction as a whole atucoustemperatures, and (ii) its applicability in describing the magnitude of the velocity con^^B atvarious temperatures; the first criterion, as will be shown below, is ambiguous and is r e a ^ nocriterion at all, and the second can only be used if the reaction is first demonstrated to be of thenecessary simplicity.


quantities, k, x and n; the Arrhenius equation can therefore scarcely beexpected to describe the results, since it assumes that changes in temperature affectonly the velocity constant.

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

(3) Irreversible Effects of Temperature.

The difference between the properties of a haemolytic system at two differenttemperatures, e.g. 50 and 200, may be either reversible or irreversible. In orderto see how we may distinguish between these two kinds of change, let usexamine some specific examples. Suppose that we plot a time-dilution curve for ahaemolytic system first at 50 and then at 200; call these curves A and B. The factthat these two curves are different indicates that a change in the system has resultedfrom the increase in temperature. Let us now warm the cell suspension to be addedto the haemolytic system by raising it to 200 for a period of, say, 30 minutes, cool itto 50, add it to various dilutions of lysin at 50, and so plot a curve at 5° for a systemwhich differs from that used in obtaining curve A only in that the cells have beenpreviously raised to 20°. Call the resulting curve C. Obviously, if A and C coincide,no irreversible change has resulted from warming the cells to 200, although the factthat A and B differ indicates that a change, which we may call "reversible," hasoccurred. If A and C do not coincide, however, the temperature of 200 must haveproduced a change which persists even after the lower temperature of 50 is againestablished; this change we call irreversible.

Continuing, the experiment may be modified by raising the lysin dilutions to200 for 30 minutes, cooling to 50, and plotting a curve D by the addition of cellswhich have not been exposed to the higher temperature. If D and A coincide, noirreversible change has been produced in the lysin at 200; if they do not, an irre-versible difference has been established. Again, both cells and lysin can be heatedto 200 separately, but mixed at 50 to produce curve E; again this may coincide withA or may not. Yet another modification is to cool (i) cell suspension, (ii) lysin, or

cells and lysin, to i°, to warm again to 50, and then to plot curves F, GH, 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 irreversiblechanges or not. Finally, there are innumerable modifications of the experiment

JEB-VIliv 26


possible by employing temperatures other than 50 and 200, e.g. 10° and 2O^pto°and 400, etc.

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

The first experiment is concerned with the effect of changing the temperatureof cells and of saponin within the limits of the range i° to 220. The dilution of lysinis represented by S, and the times in minutes taken for lysis in the standard systemat 140 by /j.The column headed t2 gives the times for complete lysis at 140 in a systemcomposed of lysin together with cells which have been heated to 220 for 3 hours, andthen cooled to 140. Under t3 are times for lysis of cells at 140 by lysin dilutionswhich have been warmed to 22° for 3 hours. To obtain the column t4, the lysindilutions were placed in the ice-box for 3 hours, and lysis afterwards carried out at140, whereas the times for systems at 140 containing cells which had been kept for3 hours in the ice-box are shown in the column under t6. In practice, all five time-dilution curves were obtained simultaneously.

Table I.

s

10,00020,00030,00040,00050,00060,00070,00080,000

h

o-o3 96-8

n - 821-835"557"S

106-0

3-5

I2-I23O

87O150-0

3-8

n - 621-544-09 8 0

170-0

3 9

1 2 720-443 085-5

126-0

h

—3'3—

1 3 81 8 83 8 06 8 0

1080

From these figures we may conclude: (i) that warming either the cells or thelysin to 220 results in a slight increase in resistance, and (ii) that cooling the cellsproduces 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 cellsuspension or saponin dilutions to a temperature of 400. Here ^ gives the standardcurve at 250, t2 the curve for a system composed of lysin plus cells which had beenheated to 400 for 3 hours, and t3 the curve for a system composed of cells plus lysinwhich had been heated to 40° for 3 hours.

Table II.

8

10,00020,00030,00040,00050,00060,00070,00080,00090,000

100,000

'1

O-2

o-SI - I

—

5°—

16-043°95-°

2350

k

O-2

o-SI - I1-94'3

1 3 22 4 S77°

300-0—

h

O-2

o-s1-22-O

4/58-8

i4'54 2 0

I2O-O


can conclude from this table that heating the lysin to 400 has very littlebut 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: tt gives the times for a standard curve at 25°, andt2 the times for a system in which the cells had been heated to 420 for 3 hours, andtz the times for a system in which the cells had been cooled to io° for 3 hours.

Table III.

8

10002000300040005000600070008000

h

osI'O16

3-914-335-590-0140-0

h

OS0 91-74-5iS-S39-0

135°

t,

OS0 91747io-o45 0no-o200-0

As before, both heating and cooling the cells to 42° and to 10° respectivelyincreases the resistance, but only very slightly. In the last experiment of the four,the effect of warming the dilutions of sodium taurocholate to 420 for 3 hours isinvestigated; tx gives the standard curve at 250, and t2 the curve, also at 250, for thesystem containing previously warmed lysin.

Table IV.

8

10002000300040005000600070008000

«i

0 4I'O17308 0

1834101050

U

o-350 7

i-3298-4

35-o70-02IO-O

The effect of temperature on the lysin is quite marked, although perhaps notso marked as we might expect in the case of so unstable a haemolysin. It will beseen 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 t1} 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 quiteclearly that changes-in temperature produce irreversible changes both in the redcells and in the haemolysins themselves. In some cases (particularly when highdilutions of lysin are concerned) these changes are sufficiently great to produce a

^fee in the velocity of lysis of as much as 100 per cent.; they are almost sufficientlye, indeed, to account for the deviations from linearity seen in Fig. 2 in the

400 E R I C PONDER AND J. FRANKLIN YEAGER

case of saponin. There is no need, however, to account for such deviationson the grounds that changes in temperature produce irreversible changescells 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.

CONCLUSIONS.

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

The most outstanding fact is that both the simple haemolytic systems studiedare apparently too complex to be described by the Arrhenius equation. It is impos-sible, as a consequence, to arrive at a value for the temperature coefficient; the bestwe can do, in the case of saponin haemolysis, is to say that the value of /A may bebetween 25,000 and 34,000, while in the case of sodium taurocholate haemolysis wecannot form any idea of the value of the temperature coefficient at all. The principalreason for this failure is that the Arrhenius equation is an expression which describesthe effect of temperature on the velocity constant of a system, while, in the casesunder consideration, a change of temperature does not change only the velocityconstant, but alters the system in other ways; the changes are, in fact, far too complexto 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 cellsand the haemolysin, as well as the reaction between them, undergo changes withchanges of temperature; a system containing lysin and cells at 200 is,, accordingly,by no means the same system, from the point of view of its kinetics, as a system ofthe same lysin and the same cells at 300. Such results might be considered assupporting the extreme position of Heilbrunn (1925), who has objected to applyingto heterogeneous systems the type of analysis which applies to homogeneoussystems and who concludes that it is not only useless to compare temperaturecoefficients obtained from biological processes with those obtained from chemicalreactions, 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 conclusionsdrawn from them with the results and conclusions of other workers, using otherbiological material. When we do so, we are at once struck by the fact that mostinvestigations made hitherto have been concerned with much more complex systemsthan those with which this paper deals, but that, at the same time, the results havebeen much more simple1. Temperature coefficients have been obtained, for example,for such processes as the contraction of muscle, the movement of unicellularorganisms, and even for certain responses of the whole organism; in many such

1 It is true that this simplicity is partly due to the practices of "mass plotting" and of <straight lines through irregularly placed points (see Fulmer and Buchanan, 1928). The probthe apparent simplicity of the results obtained for intact cells and organisms nevertheless relfor, in some cases at least, a relatively simple temperature relation has been obtained by proper means.


velocities have proved not so very different from those produced by thenius equation, and in many cases the more pronounced irregularities associated

with the simple systems described in this paper have apparently been absent. Itis at first sight a remarkable fact that the reactions of a complex system to temperatureshould appear simpler than those of a simpler system; such a result, however, is inconformity 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 tempera-ture, the velocity constant, k, is a particular function of temperature, and theArrhenius equation is followed. In a more complex case, such as that of eitherof the haemolytic systems considered above, several independent constants arefunctions of temperature, i.e. k, x,n = / (t). Unless k, x and n are all similar func-tions of temperature, and are functions, moreover, of a particular kind, the Arrheniusequation cannot possibly apply, and the result of plotting the logarithm of thevelocity against the reciprocal of the temperature will be a curve, the complexity ofwhich will depend on the extent and on the particular way in which x and n varywith temperature. The complex curve may present, indeed, an almost unlimitednumber of forms, may show maxima and minima, and may show variations in formcorresponding to variations in the concentration of the reacting substances, as in thecases referred to in this paper, i.e. if one form of curve is found under a set ofconditions A, a different form may arise under a set of conditions B, provided anyof the constants are influenced by conditions A or B.

Suppose, however, that we study a very complex system, in which twenty ormore 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 logarithmof the velocity against the reciprocal of the temperature will be, in many cases atleast, a smooth curve, devoid of obvious maxima or minima, and often easily mis-takable for a straight line. Further, if the curve is obtained under various sets ofconditions A, B, C, etc., the form of the curve will tend to be similar under all sets ofconditions which do not change a large number of the many constants which arefunctions of temperature. It is by no means surprising, accordingly, that a complexsystem (such as an entire cell or an entire organism) should yield an apparentlysimple " temperature coefficient," nor that a much simpler system should fail to do so.

This principle, although not usually formulated, can be illustrated by severalquite familiar examples1. The titration curve of a monobasic acid, for instance, is asmooth 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 poly-basic acid such as a protein, however, we may again revert to the simple form, andthe curve can be treated as that of a monobasic acid. Consider, again, the crossingof two organisms of single factor difference. The result is a bimodal curve, but thecrossing of two organisms differing by many factors affecting the same characters isa simple frequency curve. The more complicated the state of affairs, indeed, the

^^frhis principle has been remarked upon in a somewhat different connection, as explaining theapparently simple form of growth curves (Plunkett, quoted by Morgan, 1926).


simpler does the final result seem to be. As a last example, consider the j ^combining waves of various forms, as in harmonic analysis; the result of combminga few waves of different forms is in general to produce an apparently less smoothand 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 theconditions.

The recognition of these facts considerably limits the possibility of determiningtemperature coefficients in biological processes. Suppose, for example, that westudy 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 over-whelmingly in favour of the plotting of the logarithm of the velocity against thereciprocal of the absolute temperature resulting in a smooth curve which maypossibly be mistaken for an approximation to a straight line. We shall be unable,however, to investigate any of the intracellular processes involved in the reactionby investigating the slope of such a line, for regarded from the point of view eitherof the kinetics of the individual intracellular reactions or from the point of view ofthe Arrhehius 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 ismathematically demonstrable that the slope of the line (or of the curve) is notdetermined by the temperature coefficient of any one of them alone; a n value of10,000, say, derived from the line, does not indicate that any one of the individualreactions has this temperature coefficient, or even that the average p. value of thereactions is 10,000. (ii) The fact that the entire system appears to follow the Arr-henius equation does not even necessarily indicate that any one of the underlyingreactions does so; further, if a series of /x values are obtained for various parts of thetemperature range, there is no reason to suppose either (a) that each new slopecorresponds to a new reaction, or (b) that the /* values obtained for various slopeshave any direct relation to the temperature coefficients of the various underlyingreactions in the system under consideration.

SUMMARY.

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

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

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


REFERENCES.

AHHHENIUS (1915). Qualitative Laws in Biological Chemistry, p. 65;BROWN (193°)- Joum. Exp. Biol. 7, 373.CROZIER (1924). Journ. Gen. Physiol. 7, 123, 189;FULMER and BUCHANAN (1928). Proc. Soc. Exp. Biol. and Med. 26, 446.GLASER (1924). Journ. Gen. Physiol. 7, 177.HEILBRUNN (1925). Science^ 62, 268.MORGAN (1926). American Naturalist, 60, 506.PONDER (1923). Proc. Royal Soc. B, 95, 42.PONDER and YEAGER (1929). Proc. Royal Soc. B (In the press.)

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