Equations for the Incorporation of Radioactivity Due to the Linear Growth of Tobacco MosaicVirusAuthor(s): Jonathan TownsendSource: Proceedings of the National Academy of Sciences of the United States of America,Vol. 48, No. 12 (Dec. 15, 1962), pp. 2083-2087Published by: National Academy of SciencesStable URL: http://www.jstor.org/stable/71563 .

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VOL. 48, 1962 BIOCHEMISTRY: J. TOWNSEND 2083

accomplishing such synchronous synthesis other than coordinate linear extension of both structures. This suggests that the RNA fiber, like the array of protein sub- units, is extended linearly as it is synthesized.

Direct experimental support for this conclusion can be derived from the data summarized in Table 3 of reference 5, which show that the ratios between the C14- specific activities in virus protein and RNA found in 1,000 A and 3,000 A rods differ by no more than 30 per cent. This suggests that within this limit of accuracy the systematic change in specific activity associated with the linear extension of the protein component of the rod also occurs in its RNA fiber. Hence, it would appear that within an experimental limit of about 300 A (30 per cent of 1,000 A), the available data indicate that the linear extension of the RNA fiber and of the helical array of protein subunits are coordinate, synchronous processes.

In sum, the experimental results show that TMV is synthesized by a process which, within a time that is at most quite short compared to the time required for the formation of a full-length rod (about 2-3 min compared to 15-20 min), accom- plishes the incorporation of C14 from C1402 into both the RNA and the protein actually present in the extractable virus ribonucleoprotein rods. The experimental results are consistent with a biosynthetic process which involves the coordinate linear extension of the virus' RNA fiber and of its helical array of protein subunits.8 If the time between biosynthesis and incorporation into the rod is actually zero, then each protein subunit is synthesized in situ at its locus in the virus rod and each ribonucleotide residue is added terminally to the RNA fiber, the latter being at all times embedded in its final position in the growing ribonucleoprotein rod.

* The work reported in this paper was aided by grants from the National Foundation and from the National Science Foundation.

1 Commoner, B., J. A. Lippincott, and J. Symington, Nature, 184, 1992 (1959). 2Symington, J., B. Commoner, and M. Yamada, these PROCEEDINGS, 48, 1675 (1962). 3 Commoner, B., and G. B. Shearer, Nature (in press, 1962). 4 Commoner, B., G. B. Shearer, and M. Yamada, these PROCEEDINGS, 48, 1788 (1962). 5 Commoner, B., and J. Symington, these PROCEEDINGS, 48, 1984 (1962). 6 Commoner, B., D. L. Schieber, and P. M. Dietz, J. Gen. Physiology, 36, 807 (1953). 7 Townsend, J., these PROCEEDINGS, 48, 2083 (1962). 8 Commoner, B., Nature, 184, 1998 (1959).

EQUATIONS FOR THE INCORPORATION OF RADIOACTIVITY DUE TO THE LINEAR GROWTH OF TOBACCO MOSAIC VIRUS

BY JONATHAN TOWNSEND

DEPARTMENT OF PHYSICS AND COMMITTEE ON MOLECULAR BIOLOGY,

WASHINGTON UNIVERSITY, ST. LOUIS

Communicated by Frits W. Went, October 17, 1962

In previous papers,' Commoner et al. have demonstrated several interesting aspects of the growth of tobacco mosaic virus (TMV), using measurements of C14 in virus particles resulting from a controlled exposure of TMV-infected leaves to C1402. It is the purpose of this paper to present a quantitative analysis of the

VOL. 48, 1962 BIOCHEMISTRY: J. TOWNSEND 2083

accomplishing such synchronous synthesis other than coordinate linear extension of both structures. This suggests that the RNA fiber, like the array of protein sub- units, is extended linearly as it is synthesized.

Direct experimental support for this conclusion can be derived from the data summarized in Table 3 of reference 5, which show that the ratios between the C14- specific activities in virus protein and RNA found in 1,000 A and 3,000 A rods differ by no more than 30 per cent. This suggests that within this limit of accuracy the systematic change in specific activity associated with the linear extension of the protein component of the rod also occurs in its RNA fiber. Hence, it would appear that within an experimental limit of about 300 A (30 per cent of 1,000 A), the available data indicate that the linear extension of the RNA fiber and of the helical array of protein subunits are coordinate, synchronous processes.

In sum, the experimental results show that TMV is synthesized by a process which, within a time that is at most quite short compared to the time required for the formation of a full-length rod (about 2-3 min compared to 15-20 min), accom- plishes the incorporation of C14 from C1402 into both the RNA and the protein actually present in the extractable virus ribonucleoprotein rods. The experimental results are consistent with a biosynthetic process which involves the coordinate linear extension of the virus' RNA fiber and of its helical array of protein subunits.8 If the time between biosynthesis and incorporation into the rod is actually zero, then each protein subunit is synthesized in situ at its locus in the virus rod and each ribonucleotide residue is added terminally to the RNA fiber, the latter being at all times embedded in its final position in the growing ribonucleoprotein rod.

* The work reported in this paper was aided by grants from the National Foundation and from the National Science Foundation.

1 Commoner, B., J. A. Lippincott, and J. Symington, Nature, 184, 1992 (1959). 2Symington, J., B. Commoner, and M. Yamada, these PROCEEDINGS, 48, 1675 (1962). 3 Commoner, B., and G. B. Shearer, Nature (in press, 1962). 4 Commoner, B., G. B. Shearer, and M. Yamada, these PROCEEDINGS, 48, 1788 (1962). 5 Commoner, B., and J. Symington, these PROCEEDINGS, 48, 1984 (1962). 6 Commoner, B., D. L. Schieber, and P. M. Dietz, J. Gen. Physiology, 36, 807 (1953). 7 Townsend, J., these PROCEEDINGS, 48, 2083 (1962). 8 Commoner, B., Nature, 184, 1998 (1959).

EQUATIONS FOR THE INCORPORATION OF RADIOACTIVITY DUE TO THE LINEAR GROWTH OF TOBACCO MOSAIC VIRUS

BY JONATHAN TOWNSEND

DEPARTMENT OF PHYSICS AND COMMITTEE ON MOLECULAR BIOLOGY,

WASHINGTON UNIVERSITY, ST. LOUIS

Communicated by Frits W. Went, October 17, 1962

In previous papers,' Commoner et al. have demonstrated several interesting aspects of the growth of tobacco mosaic virus (TMV), using measurements of C14 in virus particles resulting from a controlled exposure of TMV-infected leaves to C1402. It is the purpose of this paper to present a quantitative analysis of the

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2084 BIOCHEMIS'IRY: J. TO WNSEND PRoc. N. A. S.

mechanism of linear growth of TMV proposed by these authors, to account for their results, and to derive some equations relevant to that model. This analysis is based on the assumptions implicit in the model of linear growth described by Commoner et al. and on several explicit assumptions to be discussed below. The chief attribute of the model to be considered is that the incorporation of C14 by the substance of the virus is due to the linear extension of the virus rod.

Assumptions.-The first assumption arises from a lack of detailed knowledge about the precursor pool for virus synthesis and the way C14 enters this pool. Pre- liminary experiments' indicate that a lag of only several minutes occurs between exposure of the leaf to the radioactive C02 and the appearance of C14 in the amino acids and ribonucleotides in the cell fluids. Since the shortest time involved in the experiments is several times longer, this lag will be taken as zero.

Secondly, the build-up of C14 in the precursor pool will be taken as a linearly increasing function of time. The best justification for this is that it is the only function requiring only one adjustable parameter (the rate of increase). It is desirable, of course, to minimize the number of independent adjustable parameters involved so as to show more conclusively that the data fit the predicted equation.

The third assumption is that all virus rods grow at the same rate, and that this rate is constant, i.e., independent of time and of rod. length.

Finally, it is assumed that the rate of production (birth rate) is independent of time during the experiment.

Analysis.-Time is the central variable in the analysis, and a time scale is taken with t = 0 at the time the leaf is inoculated. Several days later, at t = ts, the leaf

is exposed to C1402. The exposure is continued until t = tS + At, when the leaf cells are broken and the virus is extracted. The interval At ranges from 5 to 25

minutes. During this time, the specific activity of the virus precursor pool (cpm/ unit mass) taken as a weighted average, with each chemical species weighted in

proportion to its weight fraction in the virus, will be P = R(t - ts). The growth of a virus rod may start at any time to, and will continue until l(, +

LT, where L is the length of the virus rod expressed as a fraction of the length of a

fully grown virus (3,000 A) and T is the time required to grow 3,000 A. During time dt, the growing rod will increase in mass by (M/T)dt, where AJ is the mass of a

fully grown rod, and it will increase in radioactivity by (MJ/T)Pdt. The activity of a rod is then

a = (M/T) + Pdt. (1)

Here, the rods are divided into three classes, depending on their to's and L's.

Class A rods are defined by the relation to + LT < ts and are nonradioactive.

Class B rods are defined by to < tS < to + LT and are radioactive along parts of their

lengths, and Class C rods, defined by to > ts, are radioactive along their entire

lengths. For these classes, the indicated integration gives:

aA = 0, (2a)

a1, (J1R/T) ft,) + 'LT (t -

t)dt (- ('R/T)(to + LT - t.)'/2, (2b)

ac (-A R/') f/) o + L'' (t - t,)dt = (AIR/T) LT'(to- + '/,T). (2c)

The experiment is stopped at time ts + At, and the rods are extracted and frac-

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VOL. 48, 1.962 BIOCHEMISTRY: J. TOWNSEND 2085

tionated according to length. A fract,ion having a length L is selected. These will include, in general, all three c{lasses of rods, except in the case of At < LT, in which case Class C will be absent. This will be called Case I, and the case of At > LT, involving all three classes, will be called Case II.

The specific activities of fractions of various lengths are the measured quantities. In general, the specific activity of a fraction of length L is

ftsL +

At - LT b(L,to)a(L,to)dto ML fot + At -- L b(L,to)dto (3)

where b(L,to) is a function which gives the number of rods per unit time beginning their growth at time to and growing to length L. It is the "birth rate" of rods of length L. The numerator represents the radioactivity of the fraction, which comes from Class B and Class C (if any) rods. The denominator is the mass of the fraction and is very nearly all due to Class A rods. It is to be noted that the numerator is an integral over a period At, of the order of minutes, and the denomina- tor is an integral over a period of days. (The term, -LT, in the upper limit of each integration, expresses the observed fact that the extracted virus fraction does not contain rods started too late to complete their growth to length L before the end of the experiment at t, + At.)

The birth rate b(L,to) can be expressed as the product of a function b'(L), ex- pressing the "spectrum of rod length," and a function b"(to) which increases gradu- ally over the course of the infection of the leaf. This factorization is justified by the observed fact that the distribution of L is the same both early and late in the infection. Now evidently b'(L) can be cancelled from equation (3). Further- more, we are justified in factoring b"(to) out of the integral in the numerator and setting it equal to b"(tf), where tf stands for t, + At - LT.

A = b"(tf) fts + t - L' a(L,to)dto ML ff b"(to)dto

'

The experiments were carried out in such a way that b"(to) varied in a reproducible manner, and we may write

b"(tf) _ b"(t) K ( fot b"(to)dto <b"(to)> tf tf

where the angular brackets denote an average birth rate from to = 0 to to = tf and K is a constant. Equation (4) then reduces to

A = (K/MLtf) fts +At - LI a(L,to)dto. (6)

This expression may now be evaluated for Case I, using only aB as the integrand, which gives

AI - (KR/6tf) At3/LT (for At < LT), (7a)

while for Case II, aB is integrated from ts -- LT to ts, and ac is integrated from ts to ts + At - LT, which gives

AiI = (KR/6tf) [(LT) - 3LTAt + 3At2] (for At> LT). (7b)

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2086 BIOCHEMISTRY: J. TOWNSEND PROC. N. A. S.

1.0- l -.....- In other words, the specific activity of a fraction of length

.8 , L is expected to increase as the \\ '~,cube of the time interval At

> .6 iA until the interval equals the growth time LT, and from then

^< \ X on the increase is a quadratic ", .'\ \^ function, which, for large At,

\'\ \^'^^ approaches a simple propor- '.2 '\ ^_____

' tionality to the square of At.

. , '\ . . ,. . . Graphical Method of Deter-

Co?) . .8 2 6 2.0 24 mining T.-The experimental

L/m^ data are in the form of values

FIG. 1.-?A plot of A/At2 versus L/At. The scale of of the specific activities of vari- ordinates is in units of KR/2tf. The scale of abscissae ous length fractions obtained is in units of 1/T. The straight line is tangent to the curve at the point where the curve intersects the vertical after various values of At. axis, and this line cuts the horizontal axis at 1/T, giving Little is known about the an empirical value of T.

quantities K and R, but this does not prevent a determination of T if the data are taken with At values both

larger and smaller than T. Equations (7a) and (7b) can be put into the forms

A/At2 = (KR/2tf)(1/3)(At/LT) (for LT/At> 1), (8a)

A,i/At2 = (KR/2tf) [1- LT/At + '.. 'T (1/3)(LT/At)2] (for LT/At < 1), (8b)

an examination of which will verify that if one makes a plot of the observed values of A/At2 versus L/At, all the points should lie

2'/ +^.:1 5 along a single curve, if this model is correct.

2/ This curve is shown in Figure 1. The curve intercepts the vertical axis at KR/2tf and is,

\ / y/ at the intercept, tangent to a line of slope ~< / / -KRT/2tf. This tangent intersects the

horizontal axis at 1/T, thus providing a basis 1 / / * ^ ~?~UT for a graphical determination of T.

// / ^

/' Average Activity per Virus Particle.-The

// • /^ ?..' 751 average activity per particle, Cr, of the Class

1/ //-^ ̂' - I ? B and C rods (excluding the inactive Class /, T:50___T A rods from the average) is of interest.

This can be calculated by averaging the o .2 .4 .6 .8 1o0 aA and aB over the particles produced.

*L Since the rate of production is constant, a FIG. 2.-A plot of AL/t, which is pro- time average gives the same result, which is, portional to the average activity per par-

ticle of the radioactive virus particles in for the two cases, a fraction of length L versus L for various values of At. The scale of ordinates is in CrjII = AI,II(MLtf/KAt). (9) units of KRT/6tf. The dotted curve separates Case I from Case II. Since M, t!, and K are constants, one may

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VOL. 48, 1962 BIOCHEMISTRY: GARDNER ET AL. 2087

say that the quantity AL/At is proportional to Cr. This quantity is given by

AIL/At = (KRT/6tf)(At/T)2 (for At < LT), (lOa)

AIIL/At = (KRT/6tf) [3L(At/T) - 3L2 + L3(T/At) ]

(for At> LT). (10b)

These equations are plotted in Figure 2, with L as the abscissa. It is evident that for Case I, Cr is independent of L and varies as the square of At, while for the extreme Case II, or large At/T, Cr becomes nearly proportional to L. These rela- tionships are the same as those proposed by Commoner et al. from a more qualita- tive analysis of the model.

In the previous paper, Commoner et al. demonstrate that the relationship among the values of A, L, and At determined by experiments with TMV is in reasonably good agreement with equations (8) and (10) and leads to the calculation of the value of T for the growth of the TMV rod, 15 min. It is to be expected that better data will require refinements such as changes in the description of the in- crease of the pool activity P and perhaps the introduction of a growth rate which is a function of rod length. However, it is difficult to see how these possible changes could invalidate the main conclusion, i.e., TMV particles grow linearly with one process taking about 15-20 min per 3,000 A rod, and all other processes taking much less time.

The model under discussion is unusual in that it relates isotope data descriptive of a chemical process, biosynthesis, to the geometry of the particle being syn- thesized and in particular to its length. If it proves possible to obtain correspond- ing geometrical data for other chemical and biochemical processes, the foregoing mathematical treatment may be applicable to them.

' Commoner, B., and J. Symington, these PROCEEDINGS, 48, 1984 (1962); Commoner, B., these

PROCEEDINGS, 48, 2076 (1962). 2Lucas, Z. J., unpublished experiments.

SYNTHETIC POLYNUCLEOTIDES AND THE AMINO ACID CODE, VII*

BY ROBERT S. GARDNER, ALBERT J. WAHBA,t CARLOS BASILIO,T

ROBERT S. MILLER, PETER LENGYEL, AND JOSEPH F. SPEYER

DEPARTMENT OF BIOCHEMISTRY, NEW YORK UNIVERSITY SCHOOL OF MEDICINE

Communicated by Severo Ochoa, November 2, 1962

Previous papers of this series' have dealt with the effect of uracil-containing synthetic polyribonucleotides on amino acid incorporation in a cell-free system of Escherichia coli. The present paper deals mainly with the effect of polynucleotides which do not contain uracil. It was found that poly A stimulates the incorporation of lysine, and of no other amino acid, by the E. coli system. Poly-L-lysine appears to be the product of this reaction. This observation made it possible to use

VOL. 48, 1962 BIOCHEMISTRY: GARDNER ET AL. 2087

say that the quantity AL/At is proportional to Cr. This quantity is given by

AIL/At = (KRT/6tf)(At/T)2 (for At < LT), (lOa)

AIIL/At = (KRT/6tf) [3L(At/T) - 3L2 + L3(T/At) ]

(for At> LT). (10b)

These equations are plotted in Figure 2, with L as the abscissa. It is evident that for Case I, Cr is independent of L and varies as the square of At, while for the extreme Case II, or large At/T, Cr becomes nearly proportional to L. These rela- tionships are the same as those proposed by Commoner et al. from a more qualita- tive analysis of the model.

In the previous paper, Commoner et al. demonstrate that the relationship among the values of A, L, and At determined by experiments with TMV is in reasonably good agreement with equations (8) and (10) and leads to the calculation of the value of T for the growth of the TMV rod, 15 min. It is to be expected that better data will require refinements such as changes in the description of the in- crease of the pool activity P and perhaps the introduction of a growth rate which is a function of rod length. However, it is difficult to see how these possible changes could invalidate the main conclusion, i.e., TMV particles grow linearly with one process taking about 15-20 min per 3,000 A rod, and all other processes taking much less time.

The model under discussion is unusual in that it relates isotope data descriptive of a chemical process, biosynthesis, to the geometry of the particle being syn- thesized and in particular to its length. If it proves possible to obtain correspond- ing geometrical data for other chemical and biochemical processes, the foregoing mathematical treatment may be applicable to them.

' Commoner, B., and J. Symington, these PROCEEDINGS, 48, 1984 (1962); Commoner, B., these

PROCEEDINGS, 48, 2076 (1962). 2Lucas, Z. J., unpublished experiments.

SYNTHETIC POLYNUCLEOTIDES AND THE AMINO ACID CODE, VII*

BY ROBERT S. GARDNER, ALBERT J. WAHBA,t CARLOS BASILIO,T

ROBERT S. MILLER, PETER LENGYEL, AND JOSEPH F. SPEYER

DEPARTMENT OF BIOCHEMISTRY, NEW YORK UNIVERSITY SCHOOL OF MEDICINE

Communicated by Severo Ochoa, November 2, 1962

Previous papers of this series' have dealt with the effect of uracil-containing synthetic polyribonucleotides on amino acid incorporation in a cell-free system of Escherichia coli. The present paper deals mainly with the effect of polynucleotides which do not contain uracil. It was found that poly A stimulates the incorporation of lysine, and of no other amino acid, by the E. coli system. Poly-L-lysine appears to be the product of this reaction. This observation made it possible to use

This content downloaded from 169.229.32.136 on Wed, 7 May 2014 19:31:50 PMAll use subject to JSTOR Terms and Conditions