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Conjugational chromosome transfer—Complete or partial? Kinetics of chromosome transfer in bacterial conjugation
I. theor. Biol. (1981) 90,283-291
Conjugational Chromosome Transfer-Complete or Partial? Kinetics of Chromosome Transfer in Bacterial Conjugation N. A. TROITSKY AND S. E. DROMASHKO Institute (Received
of Genetics
and Cytology, Academy B.S.S.R., Minsk, U.S.S.R.
of Sciences of the
1980 and in revised form 6 January
14 January
1981)
A mathematical model is proposed which describes the kinetics of chromosome transfer during conjugation of bacteriaEscherichia coli K- 12. The kinetics of pairing and the appearance of individual recombinants is expressed quantitatively, and on this basis the quantity of donor genetic material transferred to the recipient cell during crossing is considered. Predictions of the theoretical model are compared with experiments on transfer of radioactive label. This comparison indicates that the whole donor chromosome is transferred during conjugation. 1. Introduction
The commonly-held view of position-dependent decline in donor marker expression during bacterial conjugation is that this decline is due to spontaneous breakage of transferred DNA (Jacob & Wollman, 1961). One way of checking this hypothesis would be to investigate simultaneously the kinetics of recombinant formation and DNA transfer. 2. Kinetics of Conjugation
The initial ascending phase of recombinant curves (Fig. 2) expresses the kinetics of conjugation-asynchrony of pairing, mobilisation of the chromosome and its transfer in the cells of crossed populations. For a description of how the number of recombinants formed varies as a function of time, a system of two differential equations was used (Dromashko & Troitsky, 1977):
dp 0) -=a[1 dt
-pO)l,
dp 0, xl) = cx[p(t -x, dt
(la) - 7-O) -P(t,
X,)1,
(lb)
2x3
0022-5193/81/100283+09$02.00/0
@ 1981 Academic Press
Inc. (London)
Ltd.
284
N
A
TROITSKY
AND
S. E. IIROMASHKO
where p (t ) and P( t, X, ) designate the fraction of bacteria forming pairs and transferring a given marker (a) (located at X,, ) during the time t; T,, is the minimum time necessary for the pairing of bacteria of opposite mating types and mobilisation of the chromosome; u and a represent the probability of formation of pairs and transfer of a given gene in a unit of time. In equation (la) the maximum number of pairs formed was taken as unity. In equation (1 b) the delay in transfer of a given gene is taken into account. Thus, the maximum quantity of the genes a (in fractions of unity) which can be present in F cells at the moment f is equal to p (t -X, T,,). The initial conditions for equations (1) take the form p(O) = 0. P(X, The solutions of system parameters v and (Y :
(2)
+ T,,, x, ) = 0.
(1) depend substantially p(t) = 1 -e
on the ratio between
I”,
Figures 1 and 2 give a graphic expression of the dependences described by equalities (3). The biological significance of the parameter u becomes clear
1 (mln)
FIG. 1. Kinetics c7 = 0.02 min-‘.
of pairing.
Curve
1. rr = 0.2 min
‘; curve
2. (r = 0.05 min
‘; curve
3,
CONJUGATIONAL
CHROMOSOME
TRANSFER
245
FIG. 2. Kinetics of recombinant appearance. Curve 1, a = 0.2 min-‘, 0 = O-4 min-‘, To = 5 min; curve 2, a = 0.09 min-‘, cr = O-4 min-‘, To = 20 min; curve 3, Q = 0.09 min-*, g = 0.07 min-‘, To = 20 min; curve 4, o = 0.2 min-‘, u = O-01 min-‘, To = 5 min.
from the first expression of (3). l/a is the mean pairing time, i.e. the time interval during which the quantity of bacteria which has still not paired decreases e times. The biological significance of the parameter LYcan be explained by the second equality (3). Actually, where a CCu formula (4) is true for recombinant frequency: p(t, X,) = 1 -e-acr-xa-TO). (4) Hence it is clear that the reciprocal of parameter (Y represents the average dispersion in the duration of transfer of a given gene in different pairs. The value u may change depending on experimental conditions (nutrient medium etc.). In particular, experimental data of Jacob & Wollman on crossing in a liquid medium (Jacob & Wollman, 1961, fig. 23) are in good agreement with curves given by equation (3) when o = O-07 mm-‘. Pairing on membrane filters takes place practically instantaneously, corresponding to the values o >>1 (Troitsky, Dromashko & Yakovenko, 1978). Experiments have revealed that the dispersion of the transfer time interval increases with distance from the origin (see, for example, Taylor & Adelberg, 1960), so that each transferred marker has its own value of a. A similar conclusion follows from an analysis of the kinetics of unselective marker transfer (Wollman & Jacob, 1955). This phenomenon may be explained by the existence in the population of crossed bacteria of a certain
286
N.
/\\.
TKOITSKY
ANI)
S
F..
l>KOMAStlh~,
variability in the rate of chromosome transfer. In this case IO0 min (Bachmann, Low&Taylor, 1976) is only the minimum transfer interval. This time applies to only the “fastest” bacteria: the population as a whole is described by a mean transfer interval. Mathematically this is expressed by the formula a-
I
T,,+X
T,,+T
I.-;!
T-T
where T is the average transfer interval, T is the minimum interval equal to 100 min. On the basisof formulae (4) and (5) we can calculate the parameters T,, and T. In particular, for the experiments of Wollman & Jacob (1955) where T = 100 min we obtain T,, = 2.9~ 0.6 min and T = 150* 1 min. 3. Chromosome Transfer Having in hand a mathematical model of the first stagesof conjugation, we can consider the kinetics of DNA transfer, in particular the time during which a certain fraction of the chromosome is transferred to the zygote: (6) Another formula for the calculation of the fraction R of transferred DNA proves more convenient for comparison with experimental data (Dromashko & Troitsky. 1977): I
R(t)=
t c- T,,
0,
I
1 l-T,, P(t,X)P,(X)dX. T I ()
T,,stsT<,+T
1 lP(t, X)Pt(X) T I ,I
t > T,, + T.
dx.
Here Z’,(X) represents the probability transferred (Jacob & Wollman, 1961): Pt(X)=epk”
(7)
of donor genetic markers being (8)
where k gives the frequency of spontaneous breakage of the Hfr chromosome. Figure 3 shows chromosome transfer curves calculated from formula (7) for different values of parameters included in it. It is obvious that the kinetics of transfer depend substantially on the value of k. In particular, for the
CONJUGATIONAL
CHROMOSOME
TRANSFER
287
0
FIG. 3. Fraction of chromosome-R transferred during conjugation as a function of crossing interval. T,,= 3 min, T = lOOmin, T = 150 min. Curve 1.0 >>1,/c =O;curve2,(~ = 0.07 min- . k =O; curve 3.0 ,> 1, k = 0.02 min-‘; curve 4,~ = 0.07 min-‘. k = 0.02 mine’; curve 5.~ x 1. k = 0.06 min-‘; curve 6. CT= 0.07 min-‘, k = 0.06 min-‘.
generally accepted value of k = 0.06 mini I the kinetics of transfer is represented by curves 5 and 6 and for k = 0 (complete transfer) by curves 1 and 2. In conjugation experiments with labelled donor DNA, parameters u and F can be determined from experimental results giving the kinetics of recombinant formation (Troitsky et al., 1978), and then from formula (7) the kinetics of chromosome transfer can be calculated for comparison with label transfer kinetics. Figure 4 shows the results of such calculations, carried out on the basis of the data of Wilkins, Hollom & Rupp (197 1). The same calculations were made on the basis of other data (Greenberg, Green & Bar-Nun, 1970; Siddiqi & Fox, 1973; Sarathy & Siddiqi, 1973; Popowski & KunickiGoldfinger, 1974; Troitsky, 1978). It can be seen from Fig. 4 that experimental data are in good agreement with predictions of the model, where k = 0. This result gives evidence in favour of the absence of spontaneous DNA breakage during conjugation. The curves represent the kinetics of DNA transfer, and in this way it is possible to avoid a whole series of corrections and assumptions mentioned below, some of which were used by Jacob and Wollman in the evaluation of the portion of chromosome transferred. For a comparison of the predictions of the model with experimental data on the final relative quantity of transferred donor DNA the following observations must be taken into account: (a) In conjugation only one previously existing DNA strand is transferred to the recipient. (b) The
288
N.
A.
TROITSKY
0
20
AND
S. E.
40
60
DROhdASHKO
80
100
/bmn)
FIG. 4. Comparison with the experimental data of Wilkins, Hollom & Rupp (1071). v =0.056*0.014 min -‘, -i; = 141 ~t21 min. Curve 1, k = 0.06 min ‘: curve 2. k = 0; curve 3. experimental data.
number of nucleoids per cell in log phase can be taken as equal to 3. (c) Due to constant vegetative replication one nucleoide contains an average of 1.5 chromosomes. (d) Furthermore, all donor cells in a crossing population do not necessarily take part in conjugation. In early studies of tracer DNA transfer, frequencies of proximal recombinants were about 25%, so that only one-half of the donor cells transferred DNA. (e) Asynchrony of conjugation must be taken into account. Thus, to make the transition from fraction of transferred radioactivity to fraction of transferred chromsome a correction coefficient is necessary, 2 x 3 x 1.5 x 2 = 18. The area under the exponent Pt = emkrat k = 0.06 mini’ is equal to - 17% of the area of a square limited by Pt = 1 and t = 120. Therefore, by using the correction coefficient it can be estimated that with spontaneous interruption of transfer not more than 1% (N = 17/18 = 1) of donor radioactivity (DNA) can be transferred to the recipient in 120 min. In caseof complete transfer we can expect 5.5% donor activity in the zygote (N = 100/18 = 5.5). Earlier experiments given a value of 7-12% of the activity of the donor cells in crossing for 60 min (Garen & Skaar, 1958) and 120 min (Stent & Wollman; see Jacob & Wollman, 1961), and 9% for 90 min crossing time (Silver, 1963). This is even more than expected for complete transfer. In later works, where only the acid-insoluble fraction of zygotes was measured. the percent of transferred label is lower: in 90 min crossesdifferent authors
CONJUGATIONAL
CHROMOSOME
TRANSFER
289
obtained 2.1% (Siddiqi & Fox, 1973); 4.2% (Popowski & KunickiGoldfinger, 1974); 6.5% (Troitsky et al., 1978). These results are also in agreement with the assumption that chromosome transfer is uninterrupted. 4. Discussion
Using the model presented in this paper it is possible to describe chromosome transfer quantitatively on the basis of data on the kinetics of recombinant formation. This enables us to reinforce with calculations the suggestion made earlier (Troitsky & Dromashko, 1977) on complete chromosome transfer from Hfr to F- cells during conjugation. This hypothesis of complete transfer is in contrast with the commonly accepted hypothesis of partial transfer (Jacob & Wollman, 1961). The latter is based on two groups of experimental results: (1) The amount of labelled DNA transferred to zygotes in conjugation is not more than one-eighth of the donor activity. (2) There is a position-dependent gradient of zygotic induction. However, as shown above, the evaluation of transferred label gives evidence of complete transfer. Applicability of zygotic induction data is based on the assumption of prompt induction of transferred prophage in the recipient cells. The necessity of previous joint molecule formation was deemed remote because of assymetry in reciprocal crosses (Hfr x F-A ) when zygotic induction does not occur. However, in these crosses only the lytic cycle is not observed, while prophage exclusion occurs. Therefore it seems opportune to admit the necessity of the formation of molecular hybrid structures before zygotic induction. In case of interference in synapsis formation, the frequency of zygotic induction is lower than in the wild type due to inactivation of transferred prophage (Iton & Tomizawa, 1971). In this case prophage DNA in the distal region of linear transferred structure is subjected to exonuclease action, like any late transferred gene. The drastic decrease in frequencies of distal unselected markers in zygotic induction experiments may be easily explained by complete chromosome transfer. This gradient is due to prophage transfer, which is not induced but interferes with proximal gene integration. On the other hand, if the prophage has not entered the zygote as the partial transfer hypothesis predicts, the gradient of distal unselected markers must be unchanged. It does not seem obvious that zygotic induction in Hfr and F- mating may serve as a measure of prophage transfer, or that the existence of its position-dependent gradient would support the partial transfer hypothesis. Achtman, Morelli & Schwuchow (1978) who, on the basis of the stability of crossing aggegates in Hfr x F- crosses have shown that no pair separation
290
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occurs, at least in 60 min mating, mention the necessity of searching for ,i hypothesis other than pair separation to explain the gene transmission gradient. In our opinion (Troitsky & Dromashko, I Y77) chromosome transfer from Hfr to F- cells is complete, i.e. without spontaneous interruption. In the zygote, transferred DNA becomes an object of competition between enzymes for degradation and integration. Because of immediate synapsisof the proximal end of the transferred chromosome with a recipient one (Curtiss. 1969; Bergmans. Hoekstra & Zuidweg. I975 J, fermentative breakdown in DNA destroys the link between proximal and distal markers which leads to their less frequent participation in recombination. It is just this effect which is described quantitatively by the function P,(X 1introduced by Jacob & Wollman (1961) [see formula (8)] and simulates the gene transmission gradient. An appealing candidate for an enzyme which fixes the transmission gradient is endonuclease II, because in its absence recipient cells (xth A) show marked enhancement of the number of distal recombinants (Zieg, Maples 6t Kushner, 1Y78). The complete transfer hypothesis ought to be testable by treating the zygotes or by using as recipients mutants with defects in endonucleases. In the experiments of Ou & Wood (1973’1 on inhibition of protein synthesis within 50-80 min after mixing mating cultures, the frequency of Lac’ recombinants increased. The sameeffect for distal markers is shown by us (Troitsky et al. 1979). Goldfarb et al. (197.3 i detect a threefold increase in the number of recombinants after treatment of the zygotes with culture medium filtrate. Zieg et al. (lY78) show that mutation in gene x th A of recipient cells increased the frequency of distal Lac’ recombinants to 13-fold, although the proximal ones were not affected. This is possible for a distal-located lac gene separated by 37 and 23 min on the map from the origin (for E. coli Hfr kL96 and Hfr Ra-2. respectively) only when such a mutation prevents DNA breakage and excludes the position-dependent transmission gradient.
REFERENCES ACHTMAN.M..MORELLI. G. & SCHWUCHOW,S. (1978). J.Bacreriol. 135, 1053. BACHMANN. B.J., Low.K. B.& TAYL.OR, A. L. (1976LBacreriol. Rea.40, 116. BERGMANS. H. E.N.,HOEKSTRA, W.P. M.& Z~~1~~~~,E.M.~1Y7S).Molec.gen.Gene~. 137, 1. CLJRTISS, R. (1969). Ann. Rev. Microbial. 23, 69. DROMASHKO. S. E. & TROITSKY, N. A. (1977). Proc. B.S.S.R. Acad. Sci.. biol. ser. 4, h6. GAREN, A. & SKAAR. P. D. (1958). Biochim. biophys. Acra 27, 457. GOLDFARB.D.M..GOLDBERG.G.I..CHERNIN,L.S..GUK~VA,L.A..AVDIENKO.I.D.. KUZNETSOVA,B.N.& KusHNER.I.CH.(~Y~~). Molec.gen. Genet. 120,211. GREENBERG,J.,GREEN,M.H.L.& BAR-N~~.N.(1970). Mok. gen. Gener. 107.209.
CONJUGATIONAL
CHROMOSOME
TRANSFER
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ITON, T. & TOMIZAWA, J. (1971). Genetics 68,l. JACOB, F. & WOLLMAN, E. L. (1961). Sex&@ and he Genetics of Bacretia. New York: Academic Press. Ou, J. T. &WOOD, T. H. (1973). Genetics 75,579. POPOWSKI, J. & KUNICKI-GOLDFINGER, W. J. H. (1974). Acta Microbial. Polon., ser. A 6,
205. SARATHY, P. V. & SIDDIQI, 0. (1973). J. mol. Biol. 78,443. SIDDIQI, 0. & Fox, M. (1973). J. mol. Biol. 77, 101. SILVER, S. D. (1963). J. mol. Biol. 6, 349. TAYLOR, A. L. & ADELBERG, E. A. (1960). Genetics 45,1233. TROITSKY, N. A. & DROMASHKO, S. E. (1977). Proc. B.S.S.R. Acad. Sci., biol. ser. 2, 67. TROITSKY. N. A., DROMASHKO, S. E. & YAKOVENKO, K. N. (1978). BacterialConjugution. Minsk: Nauka i Tekhnika. TROITSKY, N. A., NOVITSKAYA, M. A., YAKOVENKO, K. N., OKULICH, L. A. & DROMASHKO, S. E. (1979). Proe. B.S.S.R. Acad. Sci., biol. ser. 3,56. WILKINS, B. M., HOLLOM, S. E. & RUPP, W. D. (1971). J. Bacterial. 107, 505. WOLLMAN, E. L. & JACOB, F. (1955). C.R. Hebd. Seonc. Acad. Sci., Paris 240,2449. ZIEG. J., MAPLES, V. F. & KUSHNER, S. R. (1978). J. Bacterial. 134, 958.
Conjugational Chromosome Transfer-Complete or Partial? Kinetics of Chromosome Transfer in Bacterial Conjugation N. A. TROITSKY AND S. E. DROMASHKO Institute (Received
of Genetics
and Cytology, Academy B.S.S.R., Minsk, U.S.S.R.
of Sciences of the
1980 and in revised form 6 January
14 January
1981)
A mathematical model is proposed which describes the kinetics of chromosome transfer during conjugation of bacteriaEscherichia coli K- 12. The kinetics of pairing and the appearance of individual recombinants is expressed quantitatively, and on this basis the quantity of donor genetic material transferred to the recipient cell during crossing is considered. Predictions of the theoretical model are compared with experiments on transfer of radioactive label. This comparison indicates that the whole donor chromosome is transferred during conjugation. 1. Introduction
The commonly-held view of position-dependent decline in donor marker expression during bacterial conjugation is that this decline is due to spontaneous breakage of transferred DNA (Jacob & Wollman, 1961). One way of checking this hypothesis would be to investigate simultaneously the kinetics of recombinant formation and DNA transfer. 2. Kinetics of Conjugation
The initial ascending phase of recombinant curves (Fig. 2) expresses the kinetics of conjugation-asynchrony of pairing, mobilisation of the chromosome and its transfer in the cells of crossed populations. For a description of how the number of recombinants formed varies as a function of time, a system of two differential equations was used (Dromashko & Troitsky, 1977):
dp 0) -=a[1 dt
-pO)l,
dp 0, xl) = cx[p(t -x, dt
(la) - 7-O) -P(t,
X,)1,
(lb)
2x3
0022-5193/81/100283+09$02.00/0
@ 1981 Academic Press
Inc. (London)
Ltd.
284
N
A
TROITSKY
AND
S. E. IIROMASHKO
where p (t ) and P( t, X, ) designate the fraction of bacteria forming pairs and transferring a given marker (a) (located at X,, ) during the time t; T,, is the minimum time necessary for the pairing of bacteria of opposite mating types and mobilisation of the chromosome; u and a represent the probability of formation of pairs and transfer of a given gene in a unit of time. In equation (la) the maximum number of pairs formed was taken as unity. In equation (1 b) the delay in transfer of a given gene is taken into account. Thus, the maximum quantity of the genes a (in fractions of unity) which can be present in F cells at the moment f is equal to p (t -X, T,,). The initial conditions for equations (1) take the form p(O) = 0. P(X, The solutions of system parameters v and (Y :
(2)
+ T,,, x, ) = 0.
(1) depend substantially p(t) = 1 -e
on the ratio between
I”,
Figures 1 and 2 give a graphic expression of the dependences described by equalities (3). The biological significance of the parameter u becomes clear
1 (mln)
FIG. 1. Kinetics c7 = 0.02 min-‘.
of pairing.
Curve
1. rr = 0.2 min
‘; curve
2. (r = 0.05 min
‘; curve
3,
CONJUGATIONAL
CHROMOSOME
TRANSFER
245
FIG. 2. Kinetics of recombinant appearance. Curve 1, a = 0.2 min-‘, 0 = O-4 min-‘, To = 5 min; curve 2, a = 0.09 min-‘, cr = O-4 min-‘, To = 20 min; curve 3, Q = 0.09 min-*, g = 0.07 min-‘, To = 20 min; curve 4, o = 0.2 min-‘, u = O-01 min-‘, To = 5 min.
from the first expression of (3). l/a is the mean pairing time, i.e. the time interval during which the quantity of bacteria which has still not paired decreases e times. The biological significance of the parameter LYcan be explained by the second equality (3). Actually, where a CCu formula (4) is true for recombinant frequency: p(t, X,) = 1 -e-acr-xa-TO). (4) Hence it is clear that the reciprocal of parameter (Y represents the average dispersion in the duration of transfer of a given gene in different pairs. The value u may change depending on experimental conditions (nutrient medium etc.). In particular, experimental data of Jacob & Wollman on crossing in a liquid medium (Jacob & Wollman, 1961, fig. 23) are in good agreement with curves given by equation (3) when o = O-07 mm-‘. Pairing on membrane filters takes place practically instantaneously, corresponding to the values o >>1 (Troitsky, Dromashko & Yakovenko, 1978). Experiments have revealed that the dispersion of the transfer time interval increases with distance from the origin (see, for example, Taylor & Adelberg, 1960), so that each transferred marker has its own value of a. A similar conclusion follows from an analysis of the kinetics of unselective marker transfer (Wollman & Jacob, 1955). This phenomenon may be explained by the existence in the population of crossed bacteria of a certain
286
N.
/\\.
TKOITSKY
ANI)
S
F..
l>KOMAStlh~,
variability in the rate of chromosome transfer. In this case IO0 min (Bachmann, Low&Taylor, 1976) is only the minimum transfer interval. This time applies to only the “fastest” bacteria: the population as a whole is described by a mean transfer interval. Mathematically this is expressed by the formula a-
I
T,,+X
T,,+T
I.-;!
T-T
where T is the average transfer interval, T is the minimum interval equal to 100 min. On the basisof formulae (4) and (5) we can calculate the parameters T,, and T. In particular, for the experiments of Wollman & Jacob (1955) where T = 100 min we obtain T,, = 2.9~ 0.6 min and T = 150* 1 min. 3. Chromosome Transfer Having in hand a mathematical model of the first stagesof conjugation, we can consider the kinetics of DNA transfer, in particular the time during which a certain fraction of the chromosome is transferred to the zygote: (6) Another formula for the calculation of the fraction R of transferred DNA proves more convenient for comparison with experimental data (Dromashko & Troitsky. 1977): I
R(t)=
t c- T,,
0,
I
1 l-T,, P(t,X)P,(X)dX. T I ()
T,,stsT<,+T
1 lP(t, X)Pt(X) T I ,I
t > T,, + T.
dx.
Here Z’,(X) represents the probability transferred (Jacob & Wollman, 1961): Pt(X)=epk”
(7)
of donor genetic markers being (8)
where k gives the frequency of spontaneous breakage of the Hfr chromosome. Figure 3 shows chromosome transfer curves calculated from formula (7) for different values of parameters included in it. It is obvious that the kinetics of transfer depend substantially on the value of k. In particular, for the
CONJUGATIONAL
CHROMOSOME
TRANSFER
287
0
FIG. 3. Fraction of chromosome-R transferred during conjugation as a function of crossing interval. T,,= 3 min, T = lOOmin, T = 150 min. Curve 1.0 >>1,/c =O;curve2,(~ = 0.07 min- . k =O; curve 3.0 ,> 1, k = 0.02 min-‘; curve 4,~ = 0.07 min-‘. k = 0.02 mine’; curve 5.~ x 1. k = 0.06 min-‘; curve 6. CT= 0.07 min-‘, k = 0.06 min-‘.
generally accepted value of k = 0.06 mini I the kinetics of transfer is represented by curves 5 and 6 and for k = 0 (complete transfer) by curves 1 and 2. In conjugation experiments with labelled donor DNA, parameters u and F can be determined from experimental results giving the kinetics of recombinant formation (Troitsky et al., 1978), and then from formula (7) the kinetics of chromosome transfer can be calculated for comparison with label transfer kinetics. Figure 4 shows the results of such calculations, carried out on the basis of the data of Wilkins, Hollom & Rupp (197 1). The same calculations were made on the basis of other data (Greenberg, Green & Bar-Nun, 1970; Siddiqi & Fox, 1973; Sarathy & Siddiqi, 1973; Popowski & KunickiGoldfinger, 1974; Troitsky, 1978). It can be seen from Fig. 4 that experimental data are in good agreement with predictions of the model, where k = 0. This result gives evidence in favour of the absence of spontaneous DNA breakage during conjugation. The curves represent the kinetics of DNA transfer, and in this way it is possible to avoid a whole series of corrections and assumptions mentioned below, some of which were used by Jacob and Wollman in the evaluation of the portion of chromosome transferred. For a comparison of the predictions of the model with experimental data on the final relative quantity of transferred donor DNA the following observations must be taken into account: (a) In conjugation only one previously existing DNA strand is transferred to the recipient. (b) The
288
N.
A.
TROITSKY
0
20
AND
S. E.
40
60
DROhdASHKO
80
100
/bmn)
FIG. 4. Comparison with the experimental data of Wilkins, Hollom & Rupp (1071). v =0.056*0.014 min -‘, -i; = 141 ~t21 min. Curve 1, k = 0.06 min ‘: curve 2. k = 0; curve 3. experimental data.
number of nucleoids per cell in log phase can be taken as equal to 3. (c) Due to constant vegetative replication one nucleoide contains an average of 1.5 chromosomes. (d) Furthermore, all donor cells in a crossing population do not necessarily take part in conjugation. In early studies of tracer DNA transfer, frequencies of proximal recombinants were about 25%, so that only one-half of the donor cells transferred DNA. (e) Asynchrony of conjugation must be taken into account. Thus, to make the transition from fraction of transferred radioactivity to fraction of transferred chromsome a correction coefficient is necessary, 2 x 3 x 1.5 x 2 = 18. The area under the exponent Pt = emkrat k = 0.06 mini’ is equal to - 17% of the area of a square limited by Pt = 1 and t = 120. Therefore, by using the correction coefficient it can be estimated that with spontaneous interruption of transfer not more than 1% (N = 17/18 = 1) of donor radioactivity (DNA) can be transferred to the recipient in 120 min. In caseof complete transfer we can expect 5.5% donor activity in the zygote (N = 100/18 = 5.5). Earlier experiments given a value of 7-12% of the activity of the donor cells in crossing for 60 min (Garen & Skaar, 1958) and 120 min (Stent & Wollman; see Jacob & Wollman, 1961), and 9% for 90 min crossing time (Silver, 1963). This is even more than expected for complete transfer. In later works, where only the acid-insoluble fraction of zygotes was measured. the percent of transferred label is lower: in 90 min crossesdifferent authors
CONJUGATIONAL
CHROMOSOME
TRANSFER
289
obtained 2.1% (Siddiqi & Fox, 1973); 4.2% (Popowski & KunickiGoldfinger, 1974); 6.5% (Troitsky et al., 1978). These results are also in agreement with the assumption that chromosome transfer is uninterrupted. 4. Discussion
Using the model presented in this paper it is possible to describe chromosome transfer quantitatively on the basis of data on the kinetics of recombinant formation. This enables us to reinforce with calculations the suggestion made earlier (Troitsky & Dromashko, 1977) on complete chromosome transfer from Hfr to F- cells during conjugation. This hypothesis of complete transfer is in contrast with the commonly accepted hypothesis of partial transfer (Jacob & Wollman, 1961). The latter is based on two groups of experimental results: (1) The amount of labelled DNA transferred to zygotes in conjugation is not more than one-eighth of the donor activity. (2) There is a position-dependent gradient of zygotic induction. However, as shown above, the evaluation of transferred label gives evidence of complete transfer. Applicability of zygotic induction data is based on the assumption of prompt induction of transferred prophage in the recipient cells. The necessity of previous joint molecule formation was deemed remote because of assymetry in reciprocal crosses (Hfr x F-A ) when zygotic induction does not occur. However, in these crosses only the lytic cycle is not observed, while prophage exclusion occurs. Therefore it seems opportune to admit the necessity of the formation of molecular hybrid structures before zygotic induction. In case of interference in synapsis formation, the frequency of zygotic induction is lower than in the wild type due to inactivation of transferred prophage (Iton & Tomizawa, 1971). In this case prophage DNA in the distal region of linear transferred structure is subjected to exonuclease action, like any late transferred gene. The drastic decrease in frequencies of distal unselected markers in zygotic induction experiments may be easily explained by complete chromosome transfer. This gradient is due to prophage transfer, which is not induced but interferes with proximal gene integration. On the other hand, if the prophage has not entered the zygote as the partial transfer hypothesis predicts, the gradient of distal unselected markers must be unchanged. It does not seem obvious that zygotic induction in Hfr and F- mating may serve as a measure of prophage transfer, or that the existence of its position-dependent gradient would support the partial transfer hypothesis. Achtman, Morelli & Schwuchow (1978) who, on the basis of the stability of crossing aggegates in Hfr x F- crosses have shown that no pair separation
290
N. ,\ 'TKOITSK\r'
.,\NI)
S. 11. I>KOhl~\?,~lh(,
occurs, at least in 60 min mating, mention the necessity of searching for ,i hypothesis other than pair separation to explain the gene transmission gradient. In our opinion (Troitsky & Dromashko, I Y77) chromosome transfer from Hfr to F- cells is complete, i.e. without spontaneous interruption. In the zygote, transferred DNA becomes an object of competition between enzymes for degradation and integration. Because of immediate synapsisof the proximal end of the transferred chromosome with a recipient one (Curtiss. 1969; Bergmans. Hoekstra & Zuidweg. I975 J, fermentative breakdown in DNA destroys the link between proximal and distal markers which leads to their less frequent participation in recombination. It is just this effect which is described quantitatively by the function P,(X 1introduced by Jacob & Wollman (1961) [see formula (8)] and simulates the gene transmission gradient. An appealing candidate for an enzyme which fixes the transmission gradient is endonuclease II, because in its absence recipient cells (xth A) show marked enhancement of the number of distal recombinants (Zieg, Maples 6t Kushner, 1Y78). The complete transfer hypothesis ought to be testable by treating the zygotes or by using as recipients mutants with defects in endonucleases. In the experiments of Ou & Wood (1973’1 on inhibition of protein synthesis within 50-80 min after mixing mating cultures, the frequency of Lac’ recombinants increased. The sameeffect for distal markers is shown by us (Troitsky et al. 1979). Goldfarb et al. (197.3 i detect a threefold increase in the number of recombinants after treatment of the zygotes with culture medium filtrate. Zieg et al. (lY78) show that mutation in gene x th A of recipient cells increased the frequency of distal Lac’ recombinants to 13-fold, although the proximal ones were not affected. This is possible for a distal-located lac gene separated by 37 and 23 min on the map from the origin (for E. coli Hfr kL96 and Hfr Ra-2. respectively) only when such a mutation prevents DNA breakage and excludes the position-dependent transmission gradient.
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