Oxidation, utilization, and incorporation into protein of alanine and lysine during metamorphosis of the blowfly Phormia regina (Meigen)

ARCHIVES

OF

BIOCHEMISTRY

Oxidation, and

AND

BIOPHYSICS

Utilization,

and

Lysine

during

137,

Incorporation

Metamorphosis regina

MARIA

National

Institute

of Arthritis Department

(1966)

110-119

into

Protein

of the Blowfly

of Aianine Phormia

(Meigen)

LUISA DINARIARCA1 AND L. LEVENBOOK (With an appendix by John Z. Hearon) and Metabolic

Diseases, National a?bd Welfare,

of Health, Education

Received

March

Institutes Bethesda,

of Health, Public Health Service, Maryland

20014

2, 1966

The extent of alanine and lysine oxidation by various developmental stages of the blowfly Phormia regina is stage specific. Both amino acids are most slowly oxidized at about half way along adult development, but alanine is most rapidly oxidized by the adult fly, and lysine by the white pupa at the commencement of pupation. The rate of utilization (K,) for free pool alanine is at all corresponding stages higher than for lysine. Variations in K,-alanine during metamorphosis are far more pronounced than for K,-lysine, K,-alanine being particularly high in the white pupa. Alanine and lysine were incorporated into total protein at identical rates (K,) during metamorphosis except in the mature fly, where K,-lysine was higher than K,-alanine. The Kp values, at all times low, decreased markedly during adult development. It is suggested that protein synthesis during blowfly metamorphosis is less extensive than had previously been assumed.

Insects as a class are characterized by relatively high levels of free amino acids (FAA) (cf. (l)), but despite extensive analytical studies no general explanation for the physiological significance of these high concentrations has yet been proposed. Virtually nothing is known regarding the dynamic state of insect FAA in vivo, even though such information is an obvious prerequisite for any rational hypothesis relating their biochemical role to the various stages of insect development. In particular, an understanding of the extent to which the FAA participate in protein synthesis during insect metamorphosis is clearly of interest. Several investigators have measured the rate at which radioactivity appears in protein after injection of tagged amino acids into various insects (2, 3), but a meaningful kinetic study in vivo has not heretofore been made. 1 Present address: Department of Parasitology, Biochemistry Section, School of Medicine, University of Chile, Santiago, Chile.

In an attempt to answer some of the questions indicated above, the present work is concerned with t.he dynamic state of free alanine and lysine during metamorphosis of the blowfly Phormia regina. These two amino acids were selected because of their very different metabolic pathways (4), and the fact that lysine is a dietary essential whereas alanine is not (5). Thus, the kinetic behavior of alanine and lysine may be considered, in a broad sense, representative of the wider variety of FAA occurring in this insect (1). METHODS Phormia regina raised on chopped horse meat was maintained at 28-29” and about 80% relative humidity. Fully grown larvae which had reached the “wandering stage” and had purged their guts were selected for larval experiments. The time for adult development, from the so-called “white pupa” (O-time) to adult emergence is about 100 hours under the above conditions, and this time fpan has been denoted as 100% pupal develop110

A~IIXO

ACIDS

DURING

BLOWFLY

ment* (P.11.) in the figures. Experiments on adults were performed on flies 6-7 days old which were fed on sucrose and water but no meat; in the absence so a protein meal ovarian development does not, occur in these blowflies. 12eogent.s. L-Alanine-IJ-14C (123 mC per millimole and L-lysine-U-l% (223 mC per millimole) were purcha,sed from New England Nuclear Corporation. Each amino acid yielded only a single radioactive spot on paper ionophoresis (6). lhperimental procedure. Blowflies at the desired stage of development were injected quantitatively with 1.Opl of isot,ope, employing a calibrated glass needle and an “i\gla” (Burroughs Wellcome Company) injection apparatus. In the case of pllpae, the hard external puparium wyasfirst pierced with a fine needle in the abdominal region lateral t.o the hearf,, the glass needle was inserted into the aperiurc for the injection, and the small wound was sealed with a drop of paraffin wax. Adults were rolitinely injected in the thorax, since initial trial tsxperiments revealed that injections into the abdomen produced somewhat lower metabolic rates. The accuracy of the injected volumes was f 510’>;, and in all experiments the 0.6-0.9 pC of injected isotope was negligible in amount relative to tho free pool alanine or lysine content of the insects (1). Measurement of expired ‘*CO2 . 14C0 production was measured by the vibrating-reed electrometer procedure of Levenbook and Dinamarca (7). Rerliocherr~ical methods. FAA were extracted by homogenizing individual insects in 1.0 ml of 80% (v/v) ethanol, and heating the homogenate to boiling and then centrifuging it. The insoluble precipitatewaswashedthreetimeswithhot80%ethanal, which in pilot experiments sufficed to extract essentiallyalltheradioactivityfrominsectsinjected with either of the tagged amino acids and analyzed immediately after injection. The combined supernatant fractions were desalted according to Dreze et al. (8) and evaporated to dryness. The FAA were then dissolved in a minimal volume of distilled water. The protein residlle was dissolved in 1.5 ml of 1 Y NaOH, and re-precipitated with trichloroacetic acid. Lipids and nucleic acids were removed according to Schneider (Q), and the purified protein was dried with ether and dissolved in concentrated formic acid. Portions of this solution were taken for analysis of prot.ein content (biuret), for radioactivity by infinitely thin plating, and for acid hydrolysis with constant boiling HCl (I) aft,cr first, evaporating off the formic acid. 2 The term pupal development is employed loosely to denote development of a quiescent, resting stage enclosed by a hard puparium which includes the true pupa and the developing adult.

METAMOI~PHOSIS

111

iZlanine and lysine from both the FAA pool :LII~ protein hydrolyzates were isolated by high vctli age electrophoresis in 8::; iv/v) formic acid pH 2.0 (ii;, and their concentrations were determined by the cadmium-ninhydrin procedure (10). The red spots were extracted with methanol, attd aliqltots of the met,hanolie solutions were counted (infitiitel~~ thin) with a gas-flow windowless COIIII~PI.~~ptlatrtl it( thi: proportional range. Correction for fzperi7vwrztal /owes. :212uritlcBat111 lysine standards raarried throllgh I he cut ire isol;ltion procedure were c~,nsisletltly recuvc~r~~dI o I he extent of ‘305,. AccordiliglJ~, a correction f:lrtor ~)f 1.10 was applied in calculating the cotlcent r:ttic)rls of these amino acids back to the original flee :mli~lr, acid pool. No correction m-as reqrlirrtl for t ho ~“‘$1. tein amino acids since IIO desalting ;rtcp was itIvoIved. Measurement, of radioactivity Ir~q[~irtrtl a11 additional correction for loss of ‘“CO, clue t I) dr?carboxylntion of the radioactive amino a(sids tl>ninhydrin during color development. I:ndet 0111 experimental condit,ions 3656 of the alallille COIIIII:: (theor: 33.35;) and 179; of the lysine (:(J(I~I~ 5 (theor: IM.7y0) were lost, by decarbosylal ioll, ‘1’1111s. in computing the t.otal alanine and lysinca radio activity, correction factors of 1.5(i :1r11l1.20, I’(‘spectivrly, were employed.

Free a,rGno acid orGlutio~~. 11s :\, c’ritcriorl of alanine and lysine oxidat,ion w havc~ MWured 14C02 production after the injec&tiorl of the labeled amino ac%ls int,o blowflks ;II; various stages of development. Typic*;ll (lxperiments are shown in I:igs. 1 :md 2. It. is evident, that at c*orresponding st agt~ OI development alanine is more rapidly :ttlcl extensively oxidized than lysinc. HOWWT, there is a marked difference in thr ext,c~i, ot’ oxidation relative to t,hc life cycle. Thq the pattern of alanine oxidation is knilnr to thta charact’eristic C-shaped rcspirat,ion t*urvt’ fol insects during mcttamorphosis (cJ’, I’:& :brld Bu& (11)) ; the rate is high during I tlcl l:~rval and adult st,ages, and lowest at about halfway along adult duvelopmrnt. But, while adult flies arc that most, a(tiv(~ st,:~gr?in oxidizing &nine, they oxidized Iysi~~c?rclxtively poorly. By c*ontrast, the newly fornlcltl (O-time) pupa, which is hy far the most :ICtive sbage in oxidizing lysinr, oxidizes al:~nirlc: at only an inkrmediatct rat,c. Progress turves of the type depicted in Figs. 1 and 2 obeyed neither first nor sc~ontl order kinetics; a simpk tlc:rivatioIl of the

112

DINAMARCA

AND LEVENBOOK

/M-c /

r’ 2

/--

#---

I

I I

I 2

L

TIME

I AFTER

75%PD ---

I 3

$

INJECTION

I 4

,

_.--/

0 T!me

..’

/” /”

ii ,”

/.’

I 5

1

L-L I

2

I

1

I

I

I

3 4 5 6 7 TIME AFTER INJECTION(hrs)

I 8

FIG. 2. Oxidation of lysine-U-14C by various developmental stages 3f P. regim. Zero-time and P.D. are defined in the text (see Methods).

I 6

stages of P. regina. Zero-

rate constants for oxidation of the two amino acids was therefore difficult. As might be expected, the highest oxidation rates were found very shortly after injection of the isotope. Unfortunately these early time measurements were the least reliable because of the time period required for the injected isotope to equilibrate with the amino acid pool throughout the insect, and for stabilization of the electrometer after insertion of the specimen into the ionization chamber. In generaI, it would appear that the extent of 14C02 production was proportional to the early oxidation rates during the first l-2 hours. Rate of free alanine

0

1

(hrs.1

FIG. 1. Oxidation of alanine-UJ4C by various developmental time and P.D. are defined in the text (see Methods).

20

Lowa ____e----

0 Time

,’ .’

0

----

and lysine utilization.

To assess the dynamic state of the pool alanine and lysine, we have measured the individual rates of utilization of t,he two amino acids. Clearly, if the pool size remains constant, the rate of utilization equals the rate of synthesis which by definition is the turnover rate (12). It should be noted that we deal with the entire free pool, as opposed to specific activity measurements of pool samples. For the present purpose we assume the simplest possible model, i.e., a single

SMINO

ACIDS

DURING

BLOWFLY

METAMOI~PHOSIS

113

.I0 -

.08 -

,006

.06 aIS 5 X

cl ( .04-

TIME AFTER INJECTION

(hrs.)

FIG. 3. Derivation of the rate constants for free lysine utilization (0, left-hand ordinate), and incorporation into protein (A, right-hand ordinate) in P. rqinu pupae ha1fwa.v along adult development. For further details, see text.

homogeneous amino acid pool of constant size during t,he period of isotopic sampling, first order kinetics (an assumpt’ion which can be t#ested), and complete mixing of the t,agged amino acid with the measured pool. The small size of the blowfly, which precludes successive sampling from a single individual, and t’he wide variat#ion in pool size possible among different individuals at identical stages of development presentted special difficulties. These were overcome as follows: Several insects at the same stage of development were separately injected with the same accurately measured “pulse” of labeled alanine or lysine. Individual insects were analyzed at progressive intervals, each yielding a value on a time curve. Correction for different pool sizes was achieved by measuring the total free alanine or lysine content of each insect, and calculating the turnover rate K, (see .4ppendix for derivation) from

the equation

K, t = --a .Irl qli’~

(1)

where K, = pmolcs amino acid turned over;’ insect/hour; a = pool size, in kmolcs “ins&; yo = radioac%ivity of injected &nine (or lysine) in (‘pm; ql = radioactivity remaining in alanine (or lysine) pool at time t in cpm. A plot’ of the right-hand side as :t function of time yields a linear cuwc \vhost> slope is -K,, as shown for :L typical espcriment in Fig. 3. Thus t,he assumption of first,-order kinetics appears t,o be justified. Two such plots were made for each of :I rlumber of development~al st’ages, and t hc mean K=‘s were computed. The results, shower in Fig. 1, indicsabe t,hat, t,hc turnover rates for &nine and lysine during metnmoryhosis are markedly different. Thus, although the larval rate for both amino acids increaseti about) 2.5 t.imcs to a maximum at t hc onset, of

114

DINAMARCA

AND LEVENBOOK

.25-

.20-

5

.15-

: s I 2% g

.lO-

.05 -

01

I

I

I

I

I

I

L

0

25

50

75

A

PERCENT

PUPAL

DURATION

during metamorphosis of P. regina. L = larva; A = adult fly 6-7 days after emergence from puparium. FIG. 4. Rates of free alanine and lysine utilization

TABLE KINETICS

OF THE FREE ALANINE

1

AND LYSINE POOLS DURING METAMORPHOSIS OF THE BLOWFLY -

Lysine stage

Larva White pupa (= O-time) 25% P.D. 50% P.D. 757, P.D. Adult

I

-

.38 .30 .16 .ll .lO .20

.096 .260 .llR .034 .04f .090

2.8 0.8 1.0 2.2 1.7 1.5

pupation (white pupa stage), the absolute rate for alanine is about 5 times that for lysine. Further, the subsequent rate of alanine turnover decreases sharply to a minimum at about halfway along develop-

25 87 70 31 41 45

.16 .15 .16 .19 .lO .07

.027 .050 .040 .02.4 .029 .020

4.1 2.1 2.8 5.5 3.0 2.4

17 33 25 13 23 29

-

ment and then increases, whereas that for lysine shows a slight but progressive decline. The above changes can be also described in terms of half-life and pool turnover (Table I). These calculations further underscore the

AMINO

ACIDS

0

I

DURING

BLOWFLY

2 TIME

4

3 AFTER

11r,

METAMORPHOSIS

5

6

INJECTION(hrs.)

FIG. 5. Changes in protein specific activity with time after injection of alanine-U-l% lysine-U-l”C into larval and adult P. regina.

high met,abolic activity of the white pupa, and the relatively sluggish amino acid turnover of mnt,ure larvae and pupae more than 25 % along adult development. Rate of amino acid incorporation into protein. The ext,ent to which insect proteins become labelled after injection of a tagged amino acid depends, inter alia, on the particular tissue prot’eins, the species, and its stage of development (13, 14). Such incorporation has loosely been assumed to be a manifestat’ion of protein synthesis, but, except, under certain fortuit,ous circumstances, the time course of the increase in protein specific act,ivity is not in itself a true measure of the rate of amino acid incorporation. This fact is illustrated by the following experiment. Two series of P. q&a larvae and adults were injected with alanine and lysine, re-

or

spectively. At successive time intervals t,hc protein of individual ir1sect.swas purified and its specific activity was determined, as shown in E’ig. 5. Such progress curves denotfcl merely the rate of labelling of the protein pool. However, by taking into account individual quantitative differences in t]otnl protein and amino acid pool sizes, the tIotal radioactivity of t,he incorporat,ed amino arid and its over-all utilization rate from the fret: pool, a true estimate of the rate of amino acid incorporation may be obtained. The above parameters were used in the determination of K,the rate of amino acid incorporat,ion into blowfly protein-from t’he equat’ion (cJ Appendix) : cprn in total

K, r

_-_

protein

ala&e or lvrine -‘x K,,, !qo - qJ

(2)

116

DINAMARCA

AND LEVENBOOK

.012c:

.OIOC

E ,007s \ 2 z -3 y” .005c

.oo 2f

I L

I 0

I 50

I 25 PERCENT

I 75

I A

PUPAL DURATION

FIG. 6. Rates of incorporation of alanine and lysine into protein during metamorphosis of P. regina. L = larva; A = adult flies. In each of the three series of experiments with adult flies the rate for lysine was higher than for alanine.

where K, = pmoles amino acid incorporated/insect/hour and the remaining symbols are as defined in Eq. 1. K, was actually determined from the slope of the linear curve resulting from a plot of the right hand side of Eq. 2 X t, as shown in Fig. 3. Correction for differences in protein pool size was achieved by determining the total protein of each insect prior to hydrolysis. The rates of alanine and lysine incorporation into protein during metamorphosis are shown in Fig. 6. It is apparent that both amino acids are incorporated at essentially identical rates at all stages of development except for the adult, where the rate for lysine is some 2.5 times that for alanine. The incorporation rate is highest in the mature larva; it declines in an almost linear fashion

during metamorphosis to less than 10 per cent of the larval value at about halfway along adult development, and remains at this low level until after eclosion of the adult. DISCUSSION

The production of 14C02 by P. regina injected with a labelled amino acid is clearly the end result of a sequence of metabolic reactions depending upon the particular amino acid and the stage of insect development. Changes in the rate of 14C02 formation during metamorphosis therefore reflect variations in any one of a number of possible rate-limiting reactions. Thus, our finding that the blowfly oxidizes alanine more rapidly and extensively than lysine undoubtedly results from the fact that transaminases converting alanine to pyruvate,

ARZIKO ACIDS

DURING

BLOWFLk-

and t,he oxidative citric acid cycle, are highly active in insects (2). By contrast, Sedee et al. (15) and Sedee (16) fed two types of tagged amino acid precursors t’o larvae of the related blowfly Calliphora erythrocephala and showed that, whereas the protein and pool alanine attained a. remarkably high specific activity, the labelling in lysine was negligible. This result confirms that lysine is I‘ ‘metabolically inert’ in animals as compared to most of the other amino acids” (4). Extensive 14CO~ production from lysine-14C injected blowflies would not, therefore, be expected. Iinst~ings and McGinnis (5) reported t,hat injected glutamate-U-14C was oxidized to the extent of some 50 % by P. ~eyina larvae; we have confirmed t,his observation and find th:lt, the time course of 14C02formation from glutamat,eJ4C is about the same as for a1anine-“4C‘. The similarity bet,ween the rates of alanine oxidation and 02 uptake during metamorphosis (11) suggests a possible metabolic relationship. Lysine oxidation, however, followsa differentpattern characterized by highest oxidative activity in the larva and early pupa. Our tre:itment of the total free alanine and lysinr of the blowfly as components of a single pool is obviously a gross oversimplification. The insect, like the mammalian organism ilij, cannot be considered as a homogrnou~ medium wit’h regard to the distribut.ion of labelled amino acids, and there is probably :i funct~ional heterogeneity, either st,ructural or chemical, among amino acids even within the cell (IS). In this connection some 60 ‘7 of the l:AA of the mature larva is concent8rwted in the blood (19) where they appear t’o be merely stored, while utilization and nyrnhc.+ occur in the tissues. Thus t’he blood l’A;1 serve to dilute the true metabolic pool5, mtl hence our measured turnover rates are undoubtedly too low by an amount which could be as much as an order of magnitude. Non-ever, cvcn despite this error, the calcul:tt,ed percent’age pool t,urnover per hour can be very substantial, varying from 87 % (white pupa,) to 25 C/; (larva) for alanine, and 33 % (white pupa) to 13 70 (at middle metamorphosis’) for lysine. The values for lysine in particula,r are unexpectedly high in view of Sedee’s isotopic precursor experiments mentioned abovr.

ME;TAMOIIPHOSIS

117

Except for the mature fly, where the rate for lysine is considerably greater than for alanine, lysine and alanine are incorporated into protein at essentially identical rates in the fully grown larva and during metamorphosis. Since the molar concentrations of these two amino acids in the bulk protein arc about the same (20), it appears that our findings fulfill one criterion for net protein synthesis, namely, that the relative incorporation rates of different amino acids should bc proportional to their relative molar CO~WII~ trations in the final protein structure. The absolute amount of protein synthesized during metamorphosis can be calculated from the alanine and lysine content. of the bulk protein, and measurement of the area under the rate curves in Fig. 6. This value, computed from either alanine or lysine, is of the order of 0.16 mg protein per individual. The total protein content of the blowfly remains surprisingly constant at, 8.1 mg per insect during metamorphosis, although the amount decreases to about 5.2 mg in the adults. From this it appears that only some 2 % of the entire protein pool of the insect is replaced during adult development. As already indicated, the true intracellular alanine and lysine turnover rates are undoubtedly higher than our experimentally determined values for the entire insect; since: this discrepancy is reflected in the calculated rate of protein synthesis (Eq. 2), the computed amount of protein synthesized is correspondingly too low. Additional cornplexities relating to the interpretation of ~TL vivo protein biosynthesis data are discussed by Eagle et ul. (21); these are difficult to evaluate, and parbicularly so in organisms such as metamorphosing insects where protein brcakdon-n and synthesis may be proceeding concurrently. Nevertheless, the possibilities of localized preferential utilia:ltion of protein breakdown products for rcsynthesis, or of incomplete or negligible mixing of the tagged amino acid wit,h the intracellular precursor free pool, etc., would result in our c&mates of the true rabrs of protein synthesis being too low. Metamorphosis of the blowfly, like that of many holometubolic insects, is associated with extensive morphological reconstruction (22), and it is generally believed that sub-

118

DINAMARCA

AND LEVENBOOK

stantial amounts of new, adult-type proteins must perforce be formed. In the light of this assumption the first quantitative estimation-our value of 2% new protein-seems inordinately low. However, there is no biochemical or experimental evidence to support the notion of extensive protein breakdown and resynthesis during insect metamorphosis, while, to the contrary, there is some indication that such reactions could be of less importance than had previously been assumed. Thus the findings that during metamorphosis the FAA pool scarcely changes in size (23), and there is relatively little breakdown of larval blood proteins (Chen and Levenbook, unpublished data), that homologous larval and adult muscIe proteins are very similar (24) and that certain proteins during insect oogenesis(25) and vertebrate embryogenesis (26, 27) can be transferred intact from the mother to the egg or embryo all support the speculation that during insect adult development some larval proteins could be carried over intact into the adult form without prior breakdown and resynthesis. Techniques and mathematical models more sophisticated than those employed in the present work wiIl obviously be required to test this hypothesis. REFERENCES L., AND DINAMARCA, M. L., J. Insect Physiol. 18, 341 (1966). CHEFURKA, W., in “The Physiology of Insecta” (M. Rockstein, ed.), Vol. 2, p. 669. Academic Press, New York (1965). SKINNER, D. M., Biol. Bull. 126, 165 (1963). MEISTER, A., “Biochemistry of the Amino Acids,” Vol. 2,2nd edition. Academic Press, New York (1965). KASTING, R., AND MCGINNIS, A. J., &an. J. Biochem. Physiol. 38, 1229 (1960). KATZ, A. M., DREYER, W. J., AND ANFINSEN, C. B., J. Biol. Chem. 234, 2897 (1959). LEVENBOOK, L., AND DINAMARCA, M. L., Anal. Biochem. 11, 391 (1965). DR~~zE, A., MOORE, S., AND BIGWOOD, E. J., Anal. Chim. Acta 11, 554 (1954). SCHNEIDER, W. C., J. Biol. Chem. 161, 293 (1945). ATFIELD, G. N., AND MORRIS, C. J. R., Biohem. J. 81, 606 (1961).

1. LEVENBOOK,

2.

3. 4.

5. 6.

7. 8.

9. 10.

11. PARK, H. D., AND BUCK, J., J. Insect Physiol. 4, 220 (1960). 12. JEFFAY, H., J. Biol. Chem. 236, 2352 (1960).

13. DEMYANOVSKY, S. Y.4., VASILYEVA, AND KONEKOVA, A. S., Biokhimiya

N. V., 17, 529

(1952). 14. WEINMANN, H. P., Z. verg. Physiol. 48, 429 (1964). 15. SEDEE, P. D. J. W., AALBERS, J. G., VAN STRATUM, P. G. C., VONK, H. J., DEN BOER, D. H. W., BORG, W. A. J., AND GIESBERTS, M. A. H., Arch. Intern. Physiol. Biochem. 67, 384 (1959). 16. SEDEE, P. D. J. W., Arch. Intern. Physiol. BioBiochem. 69, 295 (1961). 17. HENRIQUES, 0. B., HENRIQUES, S. B., AND NEUBERGER, A., Biochem. J. 60, 409 (1955). 18. KIPNIS, D. M., REISS, E., AND HELMREICH, E., Biochim. Biophys. Acta 61, 519 (1961). 19. LEVENBOOK, L., Comp. Biochem. Biophys. In press. 20. HENRY, S. M., AND COOK, T. W., Contrib. Boyce Thompson Inst. 22, 133 (1963). 21. EAGLE, H., PIEZ, K. A., AND FLEISCHMAN, R., J. Biol. Chem. 228, 847 (1957). 22. P&REZ, C., Arch. Zool. Ezptl. Gen. 4, 1 (1910). 23. LEVENBOOK, L., AND DINAMARCA, M. L., J. Insect Physiol. In press. 24. KOMINZ, D. R., MARUYAMA, K., LEVENBOOK, L., AND LEWIS, M., Biochim. Biophys. Acta 63, 106 (1962). 25. TELFER, W. H., BioZ. Bull. 118, 338 (1960). 26. WARREN, L. G., AND BORSOS, T., J. Immunol. 82, 585 (1959) 27. COHEN, S., AND PORTER, R. R., Advan. Immunol. 4, 287 (1964). 28. HEARON, J. Z., Ann. N.Y. Acad. Sci. 108, 36 (1963). APPENDIX JOHN

2.

HEARON

Although the equations used here can be deduced as a special case of more general formulations in tracer kinetics (28), in the present case direct derivation is just as simple and renders somewhat clearer the assumptions involved. Let a be the size of the amino acid pool, 51 the amount of labeled ammo acid in the pool at any time, and K, the total rate at which amino acid leaves the pool over all pathways (oxidation, protein synthesis, etc.). Assuming complete mixing in the pool and assuming further that over the times considered recycling or return of label to the pool is negligible, we have dq -= dt

-K

=a’ 0

!?

(1)

AMINO

ACIDS

DUI:ING

BLOWFLY

LetK1,Kq, ... , K, be the rates at which amino acid is incorporated into the first, second, . . . , nth protein and let pl , p2 , . . . , p, be the amount of labeled amino acid in the first, second . . . , nth protein. Assuming that over the times considered, the subsequent loss of 1:&x1 from protein is negligible we have

(lpn -= dt

K,

If K, has been determined from Eq. 4, values of K, cm be calculated, over SW cessivc time intervals from successi\- valuc~. of p alltl y, from K,

K, = fln’$$!

Iv-hen a, g(O), and n(t) are known. From Eqs. 1 and 3, it follows that Ka

dp

-KJi-

and for any time interval (tl , tz) over which is essentially constant, we have

KG/K,

-4

= q(h) - q(h)

= -$@

[p(tz)

-

(7)

9 0 a

Provided K,/a is constant over the interval (O,t), K, is determined from Eq. 1, by

dt

= K,~p/Acl.

It is worth noting that li;q. 3, and tirrlccl 5 and 7, is valid under more general c&onditiorr:: than assumed irl writing Eq. t’: 11’ t,h(l proteins are interconverted among thcmsclvc+ but no one of them is appreciably c*onvcrtotl to a nonprotein sl)ccjcs, then 2 is replacctl I)y

Denote by p = pl + p2 . . . + p. the amount of labeled amino acid in total protein and by K, = KI + Kz + . . . + K, the total rate of incorporation of amino acid into protein. Then by simply adding Eq. 2 we have

dq -z.z

1 I!,

~ll;IETAMOILI’HOSIS

p(tl)]

= -2

P

Ap.

(6)

(2’)

ClYn -(It

K” R

0a

+ ?‘, )

where ri is the rate of change of pi due to the conversion of the ith protein to, or its formation from, other proteins. But under the assumption that no label is leaving any protein due to conversion to non-protein substance, ~1 + 1.2+ . . ’ + rIL = 0, i.e., any redistribution of the label among the protein species contributes nothing to the rate of change of the amount of label found in the aggregate of these species.* By adding Eqs. 2’ we again obtain 3 and the arguments leading to Eq. 7 are unchanged. * Actudls, F: = Cj (ri,sj - TENSE),where 7%)is the rate of formation of the ith from the jth protein and sI is the specifics activity of lhe jlh protein (28). Clearly then cf = 0, since if T;>s, = cj - b,,j :tntl~,~ = rj+si = 6fi then pi = $:rj

(bij - bi<) = 0.