Lack of polarity of DNA injection by Escherichia coli phage λ

VIROLOGY

43, 1766184 (1971)

Lack of Polarity JOHN Graduate

of DNA

D. SHARPl,

Department

Injection

SAM DONTA2,

of Biochemistry,

Brandeis

by Escher&a AND

DAVID

University,

coli

Phage

x

FREIFELDER3

Waltham,

Massachusetts

O.!?i64

Accepted September 1, 1.~70 The DNA fragments injected by X-irradiated phageX have been isolated from bacteria and analyzed for buoyant density by isopycnic centrifugation in Cs&O4 density gradients containing Hg 2+. The density distribution shows that the amount of material contributed by each of the ends is not significantly different from that obtained for DNA isolated directly from unirradiated phages. Since X-irradiated phage inject only a single fragment-from the end normally injected first up to the first doublestrand break-it can be concluded that the phage population is divided equally between those phages that inject the right end first and those that inject the left end first. Complementation studies with X-irradiated phage showed activity of genes from both the right and left arms of the genetic map, but with different efficiencies. The pattern of these efficiencies suggests, in agreement with the work of others, that the right arm contains the principal promoter for genes R, A, and the rest of the left arm. This pattern also suggests the existence of additional weak promoters between genes A and B, and between H and K.

containing Hg2+ (Skalka, 1971). We have used this technique of density gradient analysis on DNA fragments injected by X-irradiated X phage to show that both left and right ends of the molecule are recovered with equal frequency. Hence we have concluded that a X phage population is divided equally between phages which inject the right end first and those which inject the left end first. In a second series of experiments we have examined the ability of injected fragments derived from each end of the molecule to contribute genetic information in a mixed infection with unirradiated phage. We have found that markers from the right arm of the standard genetic map (i.e., genes N through R) are functional but that most genes on a left arm fragment fail to function, probably because the promot’er for these genes is in the right arm. A similar conclusion has been reached by Herskowitz and Signer (1970).

INTRODUCTION

In the accompanying paper (Sharp and Freifelder, 1971) it was shown that X-irradiated X phage is able to inject only one fragment of DNA-that is, up to the first double-strand break. Using this method of achieving fragmentary injection, it is possible to determine whether Escherichia coli phage x always injects the same end of its DNA first. This is the case both for E. coli phage T5 (Lanni, 1968) and Bacillus subtilis phage SP82G (McAllister, 1970). Skalka et al. (1968) have shown that the x DNA molecule consists of regions of distinct base composition. These regions are distinguishable by isopycnic centrifugation of sheared X DNA in C&O4 gradients 1 Present address: Department of Biological Chemistry, Harvard Medical School, Boston, Massachusetts 02115. 2 Present address: Department of Medicine, Boston University, School of Medicine, Boston, Massachusetts. 8 To whom reprint requests should be sent. Reprints will not be available within the United States.

METHODS

All media, methods for growth of radioactive phage, phage titering, radioactive 176

DNA INJECTION

BY E. COL1 PHAGE h

labeling and counting, X-irradiation and removal of uninjected phage DNA from cells are described in the accompanying paper (Sharp and Freifelder, 1971). The phage mutants are sus mutants described by Campbell (1961). Growth of phage. The X sus mutants were grown by UV induction of C600 lysogens. After lysis the culture was clarified by centrifugation and st.ored over CHC13. These phage lysates were used in the complementation experiments. High-titer preparations of Xhc were obtained by infection of B. coli strain W3350 and purified by banding in CsCl. Analysis of injected DNA in Csd304 density gradients. Cells containing injected X DNA and freed of uninjected DNA (by blending and centrifugation) were brepared as described for the autoradiography experiments in the accompanying paper (Sharp and Freifelder, 1971) and resuspended at 2-3 X log cells/ml in Mg-P. Four milliliters of lysis buffer (0.05 M NaCl, 0.02 M Versene, 0.02 ill: Tris, pH 8.3) were added per milliliter of cell suspension followed by 0.25 ml of lysozyme (10 mg/ml in lysis buffer). After 3 min at room temperature, 0.05 ml of 5% sodium dodecyl sulfate per original ml of cells was added to lyse the cells (2-5 min, room temperature). Lysis was sometimes aided by incubation for a few minutes at 45”. The cell lysates were then vortexed for l-2 min with an equal volume of phenol, previously equilibrated wit.h 0.1 M potassium phosphate buffer, pH 6.S. The aqueous phase was then extracted several times with ether to remove the phenol and dialyzed against three changes of 0.1 M NazSO+ 0.005 M NazB40, buffer, pH 9.0. These DNA extracts were sheared in the presence of at least a 3-fold excess (by absorbance at 260 nm) of Xhc DNA, phenol extracted from CsCl-banded phage in the same manner as the extracts. The shearing was done in a blendor using the same conditions as those used for removing phage from cell walls, yielding heterogeneously sedimenting DNA with a median molecular weight of ca. 13 7% of that of intact X DNA. The sheared extracts were again dialyzed against the sulfateborate buffer to remove any anions that

177

might interfere with binding of Hg2+ to DNA. Equilibrium centrifugation was done in a Spinco 65 angle rotor as described by Nandi et al. (1965), Skalka et al. (1968), and Skalka (1971). For each extract preliminary experiments were found necessary to determine the exact required Hg2+: DNA ratio, as described by Skalka et al. (1968). Care was taken to avoid mixing the DNA with high concentrations of Hg2+ as this causes denaturation of DNA (Nandi et al., 1965). As the Hg2+ concentration was a critical factor in obtaining the desired band positions and separation, solutions were checked for Hg2+ concent’ration with a sensitive spectrophotometric assay which could be carried out in the presence of SOi- ion (Pappas and Powell, 1967). Complementation of X sus mutants by X-irradiated phage. The ability of X-irradiated phage to supply the gene function required for growth of various X sus mutants was tested in two ways. In the infective center assay E. coli strains 594 (SK) and C600 (suII+) were grown in X broth to 5 X lo* cells/ml at 37” with aeration, centrifuged for 5 min at 3000 g and resuspended at log cells/ml in Mg-P. Cells prepared in this way were kept at 0” and used within the next l-2 hr. Strain 594 cells were simultaneously infected with 3 X sus phage per cell carrying the sus mutation in the gene to be tested, and with 0.3 X-irradiated phages per cell. Unirradiated controls and controls with only the sue mutant were always included. The cells were mixed with these phages, usually at a cell concentration of 2 X 108/ml or greater, and incubated for 15 min at 37” for adsorption and injection to occur. Anti-X serum was then added, which reduced the tit.er of a control phage sample lo3 fold or more during a further incubation for 15 min at 37”. The samples were then immediately diluted and plated on C600 bacteria. Controls were always done to assure that the number of infective centers thus obtained was directly proportional to the number of phages added of the type to be irradiated. Thus X-irradiating these phages to 10 % survival would be expected to give 10% as many infective centers as an unir-

178

SHARP,

DONTA,

AND

radiated control if the dead phages could not complement the sus mutant, but more than 10% if they could. The controls omitting the phage t’o be irradiated indicated the amount of “leakiness” of the sus mutant being tested, plus the amount of unadsorbed phage not inactivated by antiserum. This value was subtracted from t’he data before calculating the “complementation survival” (see text). In the data reported, these background values were never greater than one-third of the values from which they were subtracted. In the burst assay the experiment was conducted identically to the above until the point of adding antiserum. The infected cells were then diluted at least IO-fold into x broth and incubated for 90 min for phage growth and cell lysis to occur. The total number of phage produced was then assayed by plating on C600 bacteria. Controls were the same as for the infective center assay. The X-irradiated phage could in principle be any phage known to have a functional gene of the type being tested. In the data presented this irradiated phage is

FREIFELDER

always a X sus phage, although wild type was used in other experiments not present,ed here, with equivalent results. RESULTS

AND

DISCUSSION

Isopycnic Centrifuyation Analysis of Injected DNA. In order to identify the region of the X DNA molecule from which the DNA fragments injected by X-irradiated phages are derived, the buoyant density distribution of this DNA was examined. Xi43414C phages were X-irradiated and allowed to adsorb to CR34(Xi434) bacteria and inject their DNA. The bacteria were freed from uninjected DNA and unadsorbed phage by blending and repeated centrifugation. The DNA was then extracted from the bacteria, mixed with cold carrier DNA, sheared, and centrifuged bo equilibrium in CSZSOJ containing Hg2+. An analysis of the density of the fragments is shown in Figs. l-4. Figure 1 shows the profiles from two separate extracts of DNA from unirradiated phage. It should be noticed that the radioactivity of the injected DNA forms t(wo peaks in the same positions as those formed

0 z Ic 0 c

I

5

9 Fraction

13

17

No. From

Bottom

21

25

FIG. 1. Isopycnic centrifugation of injected A DNA. Phenol extracts of injected hi4s4 DNA, prepared and sheared with carrier Xhc DNA as described in Methods, were centrifuged at 36,000 rpm for 48 hours in a Spinco 65 rotor, with HgClt in sulfate-borate buffer containing 42.7% (w/w) CSZSO~. DNA concentration was initially 40 @g/ml and HgClz was 9.5 Mg/ml. Fractions were collected dropwise from the tube botextract from unirradiated Xi4%-3H; -O-O-, extom after puncture. -O-O--, 01) 2~; -X-X--, tract from unirradiated Xi434-14C.

DNA

INJECTION

5

9

BY E. COLI

PHAGE

179

X

r

2

0 I

17

13

Fraction

No. from

FIG. 2. Isopyenie centrifngation of inject,ed h DNA-X-X-, extract from unirradiated Xi 434-3H; ---O-O-, vival level of 3 X 10p5.

21

25

29

Bottom

Conditions extract

same as Fig. 1. ---m-8--, from Xi434-14CX-irradiated

ODZMI; to a sur-

IO

2

0 Fraction

FIG. 3. Isopycnic centrifugation of injected -X-X-, Xi434-aH total phage DNA; -O--O--,

No. From

Bottom

X DNA. Conditions same as Fig. 1. --e-e-, ext’ract from unirradiated Xi434-14C.

by the added carrier Xhc DNA as indicated by the OD260. As shown by Skalka et al. (196S), t,he lower density peak consists of the high GC left “half” (44% of the mole-

cule); the higher AT right “half” It is curious that the two regions

ODzm;

density peak is the high (56 % of the molecule). the specific activities of appear to be different,

180

SHARP, DONTA,

AND FREIFELDER

2

0 I

5

9 Fraction

13

17

21

25

29

No. From Bottom

FIG. 4. Isopycnic centrifugation of injected x DNA. Conditions same as Fig. 1. -O--O---, ODzw; -X--X, Xi434-3Htotal phage DNA; -O-O-, extract from Xi434-14C, X-irradiated to a survival level of 3 x 10-S.

even when corrections are made for the fact that thymine was used as a label and the thymine content of the two peaks differs. In several runs using different cell extracts it was consistently found that unirradiated, injected DNA shows a stronger bias toward the higher density peak than does added carrier phage DNA. Thus some unknown aspect of the extraction procedure must be responsible for a small but consistent preferential loss of the lower density material. Figures 2 and 4 show the results for DNA from irradiated phages at a survival of 3 X 10-5; the average number of doublestrand breaks at this survival level is 5.2. If there were a unique polarity of injection, the first-piece-only hypothesis confirmed in the accompanying paper (Sharp and Freifelder, 1971) predicts that the injected DNA would be depleted of one of the two density classes seen in these gradients, i.e., that from the last-injected or distal end. The predicted fraction L of the injected DNA falling in this distal density class is shown in the Appendix to be L = ewaz- e-” 1 - e-z ’

where x is the average number of doublestrand breaks per DNA molecule and a = 0.56 or 0.44 for right- or left-end injection, respectively. Hence for x = 5.2 as for Figs. 2 and 4, L would be 0.049 for right-end or 0.097 for left-end injection; since the normal (x = 0) values of L are 0.44 and 0.56 for the two cases, respectively (see Appendix), reductions of l/9.0 or l/5.8 are predicted for the less dense or denser peaks, for rightor left-end injection, respectively. These decreases would result in the virtual absence of one of the peaks. On the other hand, if there were no polarity of injection, neither end would be missing, although DNA recovered from the middle of the molecule would be reduced. It is clear from the figures that both peaks are undiminished when compared to an unirradiated extract or to phage DNA. These results are consistent with lack of polarity of injection. Unfortunately our profiles do not have sufficient resolution to detect loss of middles, but this would be possible with the resolution of Skalka et al. (1968). It should be noticed that the profiles for irradiated DNA are slightly broader than for unirradiated DNA and shifted to a slightly higher density. A possible explanation for this density

DNA INJECTION

BY E. COLI PHAGE x

shift lies in the findings of Skalka et al. (1968) that (1) 32P-labeled X DNA increased in density, in similar gradients with Hg”+, aft’er repeated banding; and (2) on shearing to very small size, the average density of X DNA increased slightly. To explain the latter observation, these authors suggested binding of Hg2+ to molecular ends; the former observation, and our density increase as well, might similarly be explained by binding of Hg2+ to sites of X-ray damage, such as single-strand breaks (Freifelder, 1966). This has not been investigated further. In order to conclude that there is no polarity of injection it is necessary that there be no preferential degradation of injected fragments. In the accompanying paper (Sharp and Freifelder, 1971), it has been shown that little or none of the injected DNA is degraded, so that the DNA seen in the density gradient is a true reflection of the injected DNA. Hence we may conclude from these results that equal amounts of fragments from the right and left ends of the molecule are injected. since an X-irradiated phage Therefore, injects only one fragment of its DNA, half of the phages must inject the right end first and half the left. This probably means that when the DNA is packaged in the phage head, the X system does not possess a mechanism for distinguishing the two ends. Such mechanisms must exist though for other phages since, as mentioned earlier, E. coli phage T5 and B. subtilis phage SP82G both have unique polarity of injection; such a polarity is in fact necessary for T5 infection since genes in one end of the molecule (in the First-Step-Transfer region) must be transcribed prior to further injection. Phage x apparently does not have such a requirement. Genetic function of injected fragments: complementation studies. In this study complementation experiments have been performed to determine whether genes on injected fragments can function. Strain 594 is infected with both an unirradiated sue mutant of X and an X-irradiated phage and it is asked whether the injected fragment can complement the particular sus mutant. This analysis has been carried out by

181

looking at either the total number of phages in a burst following such an infection or at the number of infective centers. In all these experiments the X-irradiation was carried out in a Nz atmosphere since irradiation in air eliminates almost all of the ability to complement. Details concerning this effect of Nz will be reported in a separate communication (Sharp, Donta, and Freifelder, in preparation). In the first series of experiments, complementation has been assayed by measuring infective centers (see Methods). This assay measures the ability of the fragment to contribute enough gene product to make at least one phage, since the infected sucell is plated on a lawn of SZL+cells. Unfortunately, we have not been able to test all known genes with sus mutants since few were found which were sufhciently nonleaky to be usable. Table 1 gives the results of this assay for several mutants. These data are expressed in terms of complementatation survival, the fraction of mixedly infected su- bacteria still capable of making an infective center after a given dose of X-rays to the phage. This figure is directly comparable to the survival of the X-irradiated phage, since this phage is added to the cells at a low multiplicity of infection, whereas the sus mutant in the gene being tested is added at a high multiplicity. Hence if injected fragments could never complement a particular gene, the complementation survival would equal the phage survival. If a fragment could complement, the complementation survival would depend upon (1) the injection of the gene, (2) the presence of its promoter, and (3) the degree of damage to the gene or its promoter. Thus, even complementation by terminally located genes will decrease with X-rays, due to (1) failure of half of the phnges to inject the gene with the first piece W!:IY! ; _’ DNA is broken; (2) some direct damage to the gene or its promoter region or DNA breakage between the gene and its promoter; or (3) damage to adsorption (Sharp and Freifelder, 1970). In the following discussion a gene whose level of complementation survival exceeds the level of phage X-ray survival will be said to show complementation by X-irradiated phage.

182

SHARP,

DONTA,

TABLE 1 COMPLEMENTATION OF VARIOUS LAMBDA PHAGE GENES BY X-IRRADIATED PHAGE: INFECTIVE CENTER ASSAY” X-Irradiated X-Ray Gene tested, m,oip&e, . . = o,3 survival (%) m.0.i. = 3.0 x sus A

13.1

B H J K N P R

Complementation survival (%I 18.1 12.4 25.0 33.2 23.3 28.0 26.8

AND

FREIFELDER

AWBC t

F H

K

J

N

OP Q-S R

TT

FIG. 5. Genetic map for phage X, showing the genes discussed. The dot represents the site proposed by Herskowitz and Signer (1970) for the principal promoter for genes S, R and A to J. The arrows indicate sites of weak promoters proposed in this work (A-W and H-K) and by Herskowitz and Signer (1970) (C-F).

levels of complementation. Hence unless the genes are differentially sensitive to some damaging effect of X-rays (which we believe to be unlikely), it follows that the promoter for the left end gene A must not X sus A 43.5 B 50.0 be in the left arm. This has recently been F 57.7 substantiated by Herskowitz and Signer H 62.9 (1970), who concluded that the main proK 78.5 moter for all the left-end genes A-J lies N 66.4 between genes Q and S in the right arm, 71.6 P with a possible additional weak promoter 72.2 R for genes F and K lying to the right of X sus N 20.9 21.2 A gene C. Thus, transcription of the left arm 22.0 F is seen as occurring principally on DNA J 35.1 molecules whose ends are joined, connecting 28.2 K genes A and R, but occasionally on un48.9 P circularized molecules, beginning at this a Three experiments are shown in which the Xweak promoter. Our data also support irradiated phage was x sus &2 or X sus NT. The X existence of an additional weak promoter, sus mutants used were &z, BI, FBB, H12, Kza, J11, in order to explain transcription of leftN,, Pa and Rs. m.o.i. is multiplicity of infection. arm genes on X-ray-induced fragments, but it should be between A and B to obIn Table 1 are shown the results of infective tain the slight complementation observed center assay experiments. The table indifor B, F and H and not of A; and a second cates that genes in the right arm, i.e., N, P promoter is suggested to the right of gene and R (see Fig. 5) always show a comple- H, to give the rather substantial complementation survival significantly higher than mentation seen for genes K and J. The obphage survival. Complementation of gene A, served polarity of sus mutants in gene W, however, falls off with phage survival, so which extends through genes B and C and that fragments probably cannot complement which is not seen for gene A sus mutants gene A. Gene B shows a small but significant (Parkinson, 1968), may be an indication of complement&ion. Genes F, H, J, and K, a weak promoter site between A and W. all late genes in the left arm, also comple- However, as pointed out by Herskowitz ment above phage survival (F and H being and Signer (1970), it may be a site of mesvariable due to leakiness of these mutants) senger initiation and not a promoter (site but at lower efficiency than the terminal of RNA polymerase binding), or even a right genes P and R. Hence, the pattern consequence of messenger folding (Lodish seen is that left terminal genes lose the and Robertson, 1969). Our results suggest ability to complement more rapidly than it is an additional weak promoter. These right terminal genes, even though they are proposed promoter sites are shown in Fig. 5. injected with equal frequency, and more In 6he second series of experiments, comcentrally located genes show intermediate plementation is assayed by looking at the

DNA TABLE

INJECTION

BY E. COLZ PHAGE

2

COMPLEMENTATION OF VARIOUS LAMBDA PH~GE GENES BY X-IRRADIATED PHAGE: BURST ASSAY”

Irradiated X-Ray survival phase, m.0.i. = 0.3 (%)

Gene tested, m.0.i. = 3.0

Complementation survival (%I

Average burst size before X-rays (phage per cell)

x sus A X sus R

8.7 4.1

R A

30.2 4.5

56 28

x sus A h sus R

7.8 5.9

R A

33.8 3.4

66 27

h sus J x sus R

4.4 5.4

R J

26.4 4.1

68 10.7

h sus A x sus J

6.5 4.4

J A

7.9 4.7

7.9 15.3

h sus A h sus P

10.9 10.7

P A

56.2 4.76

x sus A h sus 0

6.2 6.2

0 A

32.4 5.0

43 12.3

x sus A x sus N

6.1 6.1

N A

14.3 4.0

48 26

X

183

size must be substantially reduced, when this gene is complemented by a fragment, which suggests that when the fragment is transcribed, it is done inefficiently. Since gene J codes for tail components (Buchwald and Siminovitch, 1969) its activity, being stoichiometric rather than catalytic (Thomas, 1966), should be strongly correlated with burst size. Therefore, it is likely that the promoter used in a fragment complementing genes J and K is not the normal promoter. This is in agreement with the conclusion presented above and with those of Herskowitz and Signer (1970), that the left half of the X DNA is not transcribed efficiently unless it is attached to the promoter in the right half. ACKNOWLEDGMENT

a Mutants sus 08.

103 24

used are the same as for Table 1, plus

total burst of phages from cells mixedly infected as above (“burst assay”). In this assay high complementation survival requires that the burst size also remain near normal. The results of these assays are shown in Table 2. The data show that eomplementation survivals for genes N, P, and R are comparable to those found in the infective center assay, relative to the X-ray survivals in each experiment,, and are also high for gene 0. Hence when these genes of the right arm (see Fig. 5) are complemented by fragment,s, there is probably a nearly normal burst size. Also in agreement with the infective center assay, gene A is not complemented by fragments. Gene J is of especial interest since it shows no significant level of complementation in the burst assay as opposed to its behavior in the infective center assay. Hence the burst

This work was supported by contract AT(30-1) 3797 from the Atomic Energy Commission, Grant GM-14358 from the National Institutes of Healt,h, and E-509 from the American Cancer Society. JDS was supported by a predoctoral fellowship (GM-31,266) from the National Institutes of Health; DF by a Career Development Award (GM-7617) from the National Institute of General Medical Science. SD was supported by NIH grant CA5174. This is publication No. 746 of the Graduate Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02154. We thank Atis Folkmanis for performing some of the complementation assays. REFERENCES BUCHWALD, M., and SIMINOVITCH, L. (1969). Production of serum-blocking material by mutant,s of the left arm of the X chromosome. Virology 38, l-7. CAMPBELL, A. (1961). Sensitive mutants of bacteriophage X. Virology 14, 22-32. FREIFELDER, D. (1965). Mechanism of inactivation of coliphage T7 by X-rays. Proc. Nat. Acad. Sci. U. 8. 54, 128-134. FREIFELDER, D. (1966). Lethal changes in bacteriophage DNA produced by X-rays. Radiat. Res. 6, Suppl., 80-90. HERSKOWITZ, I., and SIGNER, E. R. (1970). A site essential for expression of all late genes in bacteriophage X. J. Mol. Biol. 47, 545-556. L.INNI, Y. T. (1968). First-step-transfer deoxyribonucleic acid of bacteriophage T5. Bacterial. Rev. 32, 227-242. LODISH, H. F., and ROBERTSON, H. D. (1969). Regulation of in vitro translation of bacterio-

-184

SHARP, DONTA,

phage f2 RNA. Cold Spring Harbor Symp. Quad. Biol. 34, 655-673. MCALLISTER, W. T. (1970). Bacteriophage infection: which end of the SP82G genome goes in first? J. ViroZ. 5, 194-198. NANDI, U. S., WANG, J. C., and DAVIDSON, N. (1965). Separation of deoxyribonucleic acids by Hg(I1) binding and CszSOa density-gradient centrifugation. Biochemistry 4, 1687-1696. PsPPAS, A. J., and POWELL, H. B. (1967). Spectrophotometric determination of mercury(I1) in aqueous potassium iodide media. Anal. Chem. 39, 579-581. PARKINSON, J. S. (1968). Genetics of the left arm of the chromosome of bacteriophage lambda. Genetics 59, 311-325. SHARP, J. D., and FREIFELDER, D. (1971). Interruption of DNA injection by X-irradiation of phage X. Virology 43, 166-175. SKALK.~, A. (1971). A method for the breakage of DNA and resolution of the fragments. In “Methods in Enzymology” (S. P. Colowick and N. 0. Kaplan, eds.), Vol. 21. Academic Press, New York, in press. SKALKA, A., BURGI, E., and HERSHEY, A. D. (1968). Segmental distribution of nucleotides in the DNA of bacteriophage lambda. J. Mol. Biol. 34, l-16. THOMAS, R. (1966). Control of development in temperate bacteriophages. I. Induction of prophage genes following heteroimmune superinfection. J. Mol. Biol. 22, 79-95. Appendix: CALCULATION CENTRIFUGATION

FOR ISOPYCNIC EXPERIMENT

It is the purpose of this Appendix to show that, assuming the first-piece-only injection hypothesis to be correct, the fraction L of injected DXA arising from the “last-injected

segment” jJa,

is given by -cc --r x) = e-e1 - eez

AND FREIFELDER

In this equation, x is the average number of double-strand breaks per molecule, and a is t,he fraction of the molecule, measured from the “first-injected end,” defined as the “first-injected segment.” This fraction is defined by the natural density discontinuity in the X DNA molecule discovered by Skalka et al. (1968)) located 44 % of the molecular length from the left end. Thus a should be taken as 0.44 or 0.56 for leftor right-end injection, respectively. By definition, L = (total amount of last-injected segment DNA injected)/(total amount of DNA injected). Thus, if dq(x, y) is defined as the fraction of phages injecting a fraction between y and y + dy of their DNA, 1

s

L(U) x) = =

Y>

a> ddx,

1 s0 Y 4dx, Y>

The expression for dq(z, y) is given by Eq. (6) of Appendix 2 of the accompanying paper (Sharp and Freifelder, 1971). Using the property of the delta function given in Eq. (8) of that Appendix, we can derive the results

dq(X, y)=i (e?” -e-“) I’(y-1U) ‘(1 s 0

y @(X, y> = S (1 - e-“)

from which we obtain Eq. (1) above. Note thatj this expression

(1)

(Y -

approaches

1 -

a for

small values of x, this being the required value of L for unirradiated (x = 0) phage.