56o 



NA TURE 



[October i, 1908 



the seedlings and determining the increase of the essential 

 (non-digestible) proteids day by day. The amount of these 

 proteids he regards as a measure of the amount of actual 

 protoplasm present. Assuming this to be so, he finds an 

 approximately constant ratio between the amount of proto- 

 plasm at any stage and the respiration. 



As germination progresses in the dark the supplies of 

 reserve carbohydrate presently fail, and then the respiration 

 no longer increases in spite of the abundant protoplasm. 

 According to our thesis the catalyst is now in excess and 

 the CO, production is limited by the shortage of respirable 

 material. 



This second type of case was more completely investigated 

 by Miss Matthaji and myself in working on the respiration 

 of cut leaves of cherry-laurel kept starved in the dark, i'or 

 a time the CO, production of these non-growing structures 

 remains uniform, and then it begins to fall off in a 

 logarithmic curve, so that the course of respiration is just 

 like c in Fig. i. We interpret both phenomena in the 

 same way : in the initial level phase the respirable material 

 in the leaf is in excess, and the amount of catalytic pro- 

 toplasm limits the respiration to the normal biological 

 level ; in the second falling phase some supply of material 

 is being exhausted, and we get a logarithmic curve con- 

 trolled by the law of mass, as much, it would seem, as 

 when cane-sugar is hydrolysed in aqueous solution. 



After these two illustrations of the action of the law of 

 mass from the more simple case of respiration we return 

 to the consideration of the totality of metabolic reactions 

 as exemplified in growth. 



What should we expect to be the ideal course of growth, 

 that is, the increase of the mass of the plant regarded as 

 a complex of reactions catalysed by protoplasm? Let us 

 consider, first, the simplest possible case, that of a bac- 

 terium growing normally in a rich culture solution. When 

 its mass has increased by anabolism of the food material 

 of the culture medium to a certain amount it divides into 

 two. As all the individuals are alike, counting them would 

 take the place of weighing their mass. The simplest expecta- 

 tion would be that, under uniform conditions, growth and 

 division would succeed each other with monotonous regularitv, 

 and so the number or mass of bacteria present would double 

 itself every n minutes. This may be accepted as the ideal 

 condition. 



The following actual experiment mav be quoted to 

 show that for a time the ideal rate of growth 

 is maintained, and that at the end of every n 

 minutes there is a doubled amount of protoplasm 

 capable of catalysing a doubled amount of chemical 

 change and carrying on a doubled growth and development. 



From a culture of liacillus typhosus in broth at 37° C. 

 five small samples were withdrawn at intervals of an hour, 

 and the number of bacteria per unit volume determined bv 

 the usual procedure. The number of organisms per drop 

 increased in the following series : 6-7, 14-4, 33-1, 70-1, i6i-o.' 

 This shows a doubling of the mass of bacteria in every 

 fifty-four minutes and is the case actually represented in 

 the strictly logarithmic curve of Fig. 2. 



We may quote some observations made by E. Buchner - 

 of the rate at which bacteria increase in culture media. 

 Bacillus coU communis was grown at 37° C. for two to 

 five hours, and by comparison of the initial and final 

 numbers of bacteria the time required for doubling the 

 mass was calculated. Out of twenty-seven similar experi- 

 ments a few were erratic, but in twenty cases the time 

 for doubling was between 19-4 and 24-8 minutes, giving a 

 mean of 22 minutes. This produces an increase from 170 

 to 288,000 in four hours. No possible culture medium will 

 provide for prolonged multiplication of bacteria at these 

 rates. 



Cohn ' states that if division takes place everv sixteen 

 minutes, then in twenty-four hours a single bacterium i^ 

 long_ will be represented by a multitude "so large that it 

 requires twenty-eight figures to express it. and placed end 

 to end they would stretch so far that a ray of light to 

 travel from one end to the other would take 100,000 years. 



' For this unpublished experiment on bacterbl growth I am indebted to 

 Miss LaneClaypon, of the Lister Institute of Preventive Medicine. 

 .- Buchner, " Zuwachsgrossen u. Wachsthumsgeschwindigkeiten " (Leip- 

 zig, 1901). ^ ^ ' 

 '•> Cohn, "Die Pflanze," p. 438 (Breslau, 1882). 



NO. 2031, VOL. 78] 



The potentialities of protoplasmic catalysis are thus made 

 clear, but the actualities are speedily cut short by limiting 

 factors. 



For a while, however, this ideal rate of growth is main- 

 tained, ."^t the end of every u minutes there is a doubled 

 amount of protoplasm present, and this will be capable 

 of catalysing twice the amount of chemical change and 

 carrying on a doubled amount of growth and development. 

 This is what common sense and the law of mass alike 

 indicate, and is exactly what this logarithmic curve in 

 Fig. 2 expresses. 



This increase of the amount of catalytic protoplasm by 

 its own catalytic activity is an interesting phenomenon. 

 In Section K we call it growth, attribute it to a specific 

 power of protoplasm for assimilation (in the strict sense), 

 and leave it alone as a fundamental phenomenon, but are 

 much concerned as to the distribution of the new growth 

 in innumerable specifically distinct forms. In the Chemical 

 Section they call this class of phenomenon " autocatalysis," 

 and a number of cases of it are known. In these a chemical 

 reaction gives rise to some substance which happens to 

 catalyse the particular reaction itself, so that it goes on and 

 on with ever-increas- 

 ing velocity. Thus, 

 we said that free acid 

 was a catalyst to the 

 hydrolysis of cane- 

 sugar ; suppose now 

 that free acid were 

 one of the products of 

 the hydrolysis of sugar, 

 then the catalyst would 

 continually increase in 

 amount in the test- 

 tube, and the reaction 

 would go faster and 

 faster. L'nder certain 

 conditions this actually 

 happens. .Again, when 

 methyl acetate is 

 hydrolysed we normally 

 get methyl alcohol and 

 free acetic acid. This 

 free acid acts as a 

 catalyst to the hydro- 

 lysis, and the rate of 

 change continually 

 accelerates. Here, if 

 the supply of methyl 

 acetate ■ were kept up 

 by constant addition.-., 

 the reaction would go 

 faster and faster with 

 a logarithmic accelera- 

 tion, giving a curve of 

 velocity identical with 

 Fig. 2,' A. 



For a clear mani- 

 festation of this auto- 

 catalytic increase in the plant it is, of course, essential 

 that the supply of food materials to the protoplasm be 

 adequate. 



Another case where we might look for a simple form 

 of this autocatalytic increase in the rate of conversion of 

 food materials to anabolites would he in the growth of a 

 filamentous alga, like Spirogyra. Here, as in the bac- 

 terium, all the cells are still capable of growth. In this 

 case the food-material needed in greatest bulk is carbon, 

 which has to be obtained by photosynthesis. Some experi- 

 ments have been started in the Cambridge Laboratory on 

 the rate of growth of Spirogyra in large tubs of water 

 kept at different temperatures and with varying facilities 

 for photosynthesis and metabolism. Under rather depres- 

 sing conditions the Spirogyra took several days to double 

 its weight — a rate of metabolism out of all comparison 

 slower than that of bacteria. Experiments on these lines, 

 with the different food materials as limiting factors, should 

 give instructive results. 



We turn now lo consider the growth of a flowering plant. 

 Here conditions an' more complex, and we know that at 

 the flowering stage or end of the season the growth 



\X 1 



Fig. 2. 



