Mulalion Research
Elsevier Publishing C o m p a n y , A m s t e r d a m
505
Printed in The Netherlands
RECOMBINATION IN ESCHERICHIA COLI
III. MAPPING BY T H E G R A D I E N T OF TRANSMISSION*
P. G. DE H A A N , V¢. P. M. H O E K S T R A , C. V E R H O E F AND I-t. S. F E L I X
Laboratory for ~1licrobiology, Stale Universily, Utrecht (The Netherlands)
(Received S e p t e m b e r ist, 1969)
SUMMARY
Mapping of markers on the Escherichia coli chromosome by the gradient of
transmission is presented. The method appeared to be useful and accurate if chromosome withdrawal is prevented and if the viability of the zygotes is assured.
The guaC was mapped by this method in the 89-90 min region of the chromosome map of TAYLOR AND TROTTER.
I. INTRODUCTION
The first step in bacterial conjugation is the random collision of cells of opposite mating type and the formation of a conjugation bridge between them 5. This step
is followed by the transfer of genetic material from donor to recipient cell. In Hfr × F crosses, it starts from the same point in all cells of a given Hfr type and proceeds in a
pre-determined sequence6, le. The transfer of the whole chromosome is completed 14
in about 9° min.
Spontaneous interruption of conjugation by breakage of the conjugation bridge
usually occurs before the entire donor chromosome has been transferred. Thus zygotes
generally receive only a fragment of the donor chromosome, the size of the fragment
differing from zygote to zygote. The further a given marker is from the origin, the
lower is the probability that it is transferred to the zygotes (gradient of transfer).
The transfer process has been studied experimentally by stopping conjugation at
intervals by shaking to break up the conjugation bridge 16 or by killinge, 1'~ the donor
with phage T6.
It was found that each genetic marker in a given Hfr × F - cross begins to enter
the zygotes at a different and specific time after the beginning of mating. Thereafter
the nmnber of zygotes, and consequently the number of recombinants which inherit
the donor marker, rises until a plateau level is reached. The time interval between the
curves for various donor markers can be translated into a time scale which is a function of the physical distance between these markers.
* For p a r t s I and I I of this series see refs. 15 and 2.
3Iutation Res., 8 (1969) 5o5-512
500
P. (,. 1)I: HA.\.x, ~'[ it,/
T h e t r a n s f e r t i m e ()f a g i v e n m a r k e r is defined as the tirol: at wlfich the first
r e c o m b i n a n t s are found, i.e. t h e i n t e r s e c t i o n p o i n t of t h e c u r v e a ith t h e tim(~ axis.
T h e s h a p e of t h e t r a n s f e r c u r v e is a v e r y c o m p l e x one a n d is d e p e n d e n t (m a YlUlllber
of factors, such as c o n t a c t f o r m a t i o n a n d t r a n s f e r d e / a r k T h e i n t e r s c c t i o n p o i n t witl~
t h e t i m e axis is t h e r e f o r e difficult to d e t e r m i n e , a l t h o u g h good r e s u l t s h a v e be~,n
obtained with this method.
T h e s p o n t a n e o u s b r e a k a g e of t h e b r i d g e d u r i n g t h e t r a n s f e r process causes an
e x p o n e n t i a l g r a d i e n t of transfer1% As a n y d o n o r m a r k e r has t h e s a m e p r o b a b i l i t y
of b e i n g i n c o r p o r a t e d i n t o a r e c o m b i n a n t o n c e it has e n t e r e d t h e z y g o t e ~, t h e r e is a
g r a d i e n t of t r a n s m i s s i o n for t h e v a r i o u s H f r m a r k e r s . M a p p i n g b y t h e g r a d i e n t of
t r a n s m i s s i o n is in p r i n c i p l e possible as has b e e n s u g g e s t e d b y HAVI.:s 7 a n d r e c e n t h '
b y WOOD 17. AS far as we k n o w , h o w e v e r , this m e t h o d has n e v e r been used. In this
p a p e r a m e t h o d for m a p p i n g b y t h e g r a d i e n t of t r a n s m i s s i o n is p r e s e n t e d .
II.
MATERIALS AND METHODS
Bacterial strains
B a c t e r i a l s t r a i n s e m p l o y e d are l i s t e d in T a b l e I. All d o n o r s t r a i n s are Str~; all
r e c i p i e n t s t r a i n s a r e Str ~.
TABLE I
BACTERIAL STRAINS
Strain n
Hfr H (ref. 5)
0020 Hfr R 4 (ref. 12)
oo2I Hfr R 4
Hfr KL 160
o172 F KI2
020.5 F KI2
0206 F KI2
0207 F Ki2e
0009
A uxotrophic markers
his
ilv
leu
met
+
~-.
+
:
~
i
q
!
+
+
!
--
~
~
]
~
+
~-
pro
put
pyr
t
1
"
~
~
+
~-
t
~
]
+
-
i
i
~
~
;
proA
proB
proA
-
}
proA
o212 F-b2I 2c
purH
[
guaB
purA
purA
purH
guaC
purH
guaC
thi
lhr
trp
tyr
i
l
pyrA
•
i
,
I
!
t
;
:
!
i
a Cultures of these strains are present in the phabagen collection, Laboratory for Microbiology,
Utrecht.
b Obtained by the courtesy of Dr. B. Low.
e ()btained by the courtesy of Dr. H. J. J. NIJKAMP.
B a c t e r i a l crosses
O v e r n i g h t c u l t u r e s of d o n o r a n d a c c e p t o r s t r a i n s in n u t r i e n t b r o t h w e r e
d i l u t e d I o - f o l d in p r e - w a r m e d b r o t h a n d i n c u b a t e d at 37 ° for 9 ° m i n on an i n c l i n e d
t u r n t a b l e (cell d e n s i t y 2 .Io8/ml). M a t i n g m i x t u r e s w e r e o b t a i n e d b y m i x i n g I v o l u m e
of d o n o r w i t h IO v o l u m e s of r e c i p i e n t c u l t u r e . 5 m i n a f t e r m i x i n g , t h e n o n r o t a t e d susp e n s i o n was d i l u t e d i o o o - f o l d in p r e - w a r m e d b r o t h , a n d a s u i t a b l e t r a n s f e r p e r i o d
was a l l o w e d . D u r i n g t r a n s f e r , t h e m a t i n g m i x t u r e was g e n e r a l l y i n c u b a t e d w i t h o u t
s h a k i n g , b u t in s o m e e x p e r i m e n t s t h e m i x t u r e was g e n t l y s h a k e n . M a t i n g was i n t e r r u p t e d b y v i g o r o u s l y s h a k i n g on a m i c r o i d flask s h a k e r . T h e z y g o t e s w e r e i n c u b a t e d
:?,Iu/ation lees., 8 (1969) 5o5 512
MAPPING BY THE GRADIENT OF TRANSMISSION
507
in broth for 75 rain before plating. Donor cells were killed by streptomycin in the
selection plates or by addition of excess phage T6 to the blended suspension.
Recombinants were selected on appropriate selection plates. The number of
recombinants was determined by counting 5 plates, each with a suitable number of
recombinants (3o-3oo).
The necessary growth factors were added at the following concentrations:
adenine 2o/:g/ml, guanine 2o Fg/ml, d/-histidine 2o E,~g/ml, d/-isoleucine 2o/~g/ml,
dl-leucine 4 °/:g/ml, dl-methionine 2o/:g/ml, dl-proline 6o/:g/ml, thiamine IO/:g/ml,
d/-threonine Ioo /.,g/ml, d/-tyrosine 2o Fg/nll, dl-tryptophane 2o /~g/ml, dl-valine
2o/:g/ml.
Streptomycin was added at a concentration of IOO Fg/ml.
III. E X P E R I M E N T A L
PLAN AND RESULTS
Let us consider a hypothetical cross in which each Hfr cell transfers its chromosome in the order: o r i g i n - - A - - B - - C ...... T. Hfr and F - cells are mixed and, after a
short period necessary for contact formation, the mixture is diluted to stop the formation of new contacts. Transfer begins after the formation of contacts although
the initiation of transfer in the population is not synchronized 1. The number of
mating pairs decreases with time due to the spontaneous breakage of the conjugation
bridge, and in some systems the breakage is accompanied by withdrawal of the
transferred donor fragment from a fraction of the mating acceptor cells. We will
assume that chromosome withdrawal is absent and that each mating pair has the
same constant probability (k) per unit time for spontaneous separation. The probability that the two cells of a mating pair are not separated in a time interval t is then :
exp (--kt).
The rate of transfer is constant in all mating pairs, which means that the interval in transfer time between two markers is constant in all mating pairs. Based upon
these considerations we may state that after the completion of transfer of a given
marker T, transferred t rain after a more proximal marker A, the number of F - cells
which contain the T marker is:
F(T) = F(A) exp
(--kt)
(I)
where F(A) represents the number of F- cells which contain the A marker.
The number of recombinants (R) which may be recovered from the (blended)
suspension depends on the number of F - cells which contain the marker and on the
probability that the transferred marker is incorporated in the acceptor chromosome.
As stated before, the incorporation probability is assumed to be equal for all markers.
Thus
R(T) = R(A) exp
(--kt)
or
lOglo R(T) = log10 R(A) -- 0.43
kt
(2)
This equation predicts a straight line when the lOglo of the number of T +, C+, B +
and A + recombinants is plotted against the transfer intervals between the involved
marker and the marker A.
Mutation Res., 8 (1969) 5 o 5 - 5 1 2
5o8
P. ~;. I)1': ]-l.\,\N c'[ ~t/.
thr
i~v
~
W
t~#
guaB
F i g . I. P o s i t i o n of r e l e v a n t m a r k e r s a n d o r i g i n s o f t h e H f r s t r a i n s .
3.5
3,C
CI
b
c
c
c
~3
E
o
E
8
8
P
3,c
L 2.5
L
E
E
0
ff
o
O
2,5
0
I
thr teu
i
I
I
J____.l
2
4
6 I
Transfer
2.C
8
proA
I
2
0
proB
I
4
Tr,Jnsfer
intervals (mln)
/
I
6
I le
teu thr
I
10
I
~2
pur4
intervclls (m[n)
I
3.C
C
c
E
o
o 2.c
s
.
o
~
b
2
1.0
.
5
~
c
o
°o . . . . . .
pro,4
thr
Transfer
''''o'i,
intervals
2'001
itv
(rain)
tyrAguaB
101
20
his
Transfer
intervals
I
tpp
(rain)
F i g . 2. R e s u l t s of b a c t e r i a l c r o s s e s . (a) H f r H × o 2 o 5 ;
(b) H f r I 5 4 × o 2 o 6 ; (c) H f r R 4 X o 2 t 2 ;
(d) H f r K L I 6 x o 1 7 2 . T r a n s f e r i n t e r v a l s f o r t h e p u r A . . . . . . p r o B r e g i o n a r e d e r i v e d f r o m VERHOEF
AND D E HAAN15; t h e o t h e r i n t e r v a l s a r e d e r i v e d f r o m t h e TAYLOR AND TROTTER 1~ m a p .
Mutation
Res., 8 (i969) 505 512
MAPPING BY THE GRADIENT OF TRANSMISSION
509
Tile v a l i d i t y of eqn. (2) was t e s t e d in a series of crosses (see Fig. i for m a r k e r
p o s i t i o n a n d H f r types). I n t h e crosses with H f r H or Hfr K L 16 as donor, the m a t i n g
m i x t u r e was n o t s h a k e n a n d the donor cells were killed b y s t r e p t o m y c i n . I n the two
crosses w i t h Hfr R 4 as donor, the m a t i n g m i x t u r e s were g e n t l y , s h a k e n in a s h a k i n g
machine (12o strokes per rain) to minimize t h e interference b y c h r o m o s o m e withd r a w a l which is o b s e r v e d in crosses w i t h this Hfr. U n s h a k e n crosses w i t h Hfr R 4 as
donor always gave s l i g h t l y b e n t curves. The results of the crosses are p r e s e n t e d in
Fig. 2. I t m a y be seen from Fig. 2 t h a t a s t r a i g h t line was o b t a i n e d from all crosses,
p r o v i n g t h a t eqn. 2 is valid for the first I 5 - m i n transfer b y H f r H a n d for the first
3o-min t r a n s f e r b y H f r R4 or H f r K L I 6 .
IV. CALCULATION OF TRANSFER INTERVALS
R e l a t i o n 2 m a y be used for the m a p p i n g of a m a r k e r with u n k n o w n t r a n s f e r
t i m e if t w o or more m a r k e r s w i t h k n o w n t r a n s f e r i n t e r v a l s are available. The first s t e p
is the calculation b y the m e t h o d of least squares of the p a r a m e t e r s of the regression
line :
( Y x -- Y)
b(X - - X )
(3)
where" Y~ is t h e l o g a r i t h m of t h e n u m b e r of r e c o m b i n a n t s of a m a r k e r t r a n s f e r r e d
X min after t h e first reference m a r k e r . Y is the m e a n of the l o g a r i t h m s of the n u m b e r
of r e c o m b i n a n t s i n h e r i t i n g t h e reference markers, b is the slope of the curve. -~ is
t h e m e a n of the t r a n s f e r i n t e r v a l s of the reference markers.
The I O O ( I - - ~ ) % confidence limits for t h e transfer t i m e X of t h e u n k n o w n
m a r k e r is t h e n c a l c u l a t e d from t h e m e a n of the l o g a r i t h m s of the n u m b e r of recomb i n a n t s (Y,) with the aid of eqn. (4) (see DIXON AND MASSEY3).
-
-
Y~ = Y + b(X -- -X) m t ~ Syx £ + -- -¢-
- O ~,(~-i)S;J
m
[
or from its e q u i v a l e n t f o r m :
[Yx--T--b(X--X)'
k
], = ts~S~[ I-+! + (x-x)'1
(n--I)S2]
tn
m
where n is the t o t a l n u m b e r of o b s e r v a t i o n s from which the regression coefficients
are calculated, m is the n u m b e r of o b s e r v a t i o n s on which Y~ is based, a n d t½~ represents the percentile of the t - d i s t r i b u t i o n for (n--2) degrees of freedom (see ref. 3,
T a b l e A-5).
The results of t h e H f r R 4 × F-- p u r A lhr leu proB cross (Fig. 2b) will serve as an
e x a m p l e for the calculation of t h e transfer i n t e r v a l proB-thr. The d a t a of this cross
are given in T a b l e I I , a n d the regression line b a s e d on the o b s e r v e d n u m b e r s of
proB +, leu + a n d p u r A + r e c o m b i n a n t s is:
(Y~ - - 2.38) = - - o.o576(X - - 6.5)
The 95% confidence limits for the t r a n s f e r i n t e r v a l p r o B - t h r are o b t a i n e d b y
s t r a i g h t f o r w a r d solution of:
31utation Res., 8 (1969) 505 512
5 IO
I'. (~. I)E HAAN t'[ Ct/.
[
¸
-- ( ) . I J
" °'('576(X
(i5)
' " ° ° 4 0 ~5
367.5
J
from which it follows that" X ..... 8 rain 43 sec ~ 37 sec. The transfer interval proH
thr, d e t e r m i n e d from time of e n t r y experiments and from r e c o m b i n a n t analysis is
8 rain 3o sec.
TABLI£
[1
DATA
A
oF
lift R 4 × 0200
CROSS
Geno@pe o¢
recombina~t
X." t r a n s f e r inter~.'al
from proB
lcu +
purA ~
thr ~
7.5
i 2.o
X
~ L" Io~, n ~ m b e r o f r : c o m b i n a n t s
2.74;
2.34 ;
2.o 3:
2.25:
-'.78;
2.28;
2.o2;
2.2~;
The table gives the data of the experiment diagrammed
F o r e x p e r i m e n t a l d e t a i l s , see t e x t .
T h e p a r a m e t e r s of t h e r e g r e s s i o n line a r e ,\" : ~L5 ~-" :
2.78:
2.3: ;
2.o 9;
2.24;
2.7~:
2.33 ;
2.0 4;
2.23;
2.75
2.3o
2.I3
2.20
in F i g . 2 b.
-'.3 s a n d b
o.o507,
The guaC marker, t e n t a t i v e l y localized b y NIJKAMP AND I)E HAANt° was also
m a p p e d with this method. The Hfr R 4 as well as the acceptor strain o2o 7 K I 2 F
c o n t a i n e d a purH marker which allows the selection of guaC+ r e c o m b i n a n t s on a
m e d i u m with g u a n i n e as purine source. I n the first cross proA a n d thr were used as
reference inarkers. The calculated i n t e r v a l / ) r o A - g u a C was 7 rain 12 sec ; 24 sec.
I n a second cross, the same Hfr was crossed with an ih, derivative of the o2o 7 acceptor
strain. Here ih,., thr a n d proA were used as reference markers a n d the i n t e r v a l proA
guaC was 6 rain 42 sec ~ I6 sec. The m e a n of the two d e t e r m i n a t i o n s is 6 min 57 sec.
The guaC is thus transferred b y Hfr R 4 a b o u t 3 ° sec later t h a n the lhr marker.
V. D I S C U S S I O N
I n the present s t u d y a m e t h o d for the calculation of intervals in transfer time
is presented. The m e t h o d is based on the e x p o n e n t i a l g r a d i e n t of transmission which
manifests itself as a consequence of the r a n d o m breakage of the conjugation bridge.
I n the example given in this paper, the transfer i n t e r v a l proB-thr was calculated from
a cross in which the proB, leu a n d purA markers were used as reference markers. The
i n t e r v a l proB-thr was calculated as 8 m i n 43 sec which is in good agreement with an
i n t e r v a l of 8 m i n 3o sec, o b t a i n e d from transfer curves or calculated from r e c o m b i n a n t
analysis. The i n t e r v a l was d e t e r m i n e d with a n error of + 7%" the calculation of the
confidence limits being based on the a s s u m p t i o n t h a t the transfer intervals between
the reference markers are a c c u r a t e l y known.
The m e t h o d is more accurate t h a n the t i m e - o f - e n t r y method, a n d its accuracy
can be e n h a n c e d b y increasing the p r o b a b i l i t y of breakage of the bridge (shaking).
T h e easiest method, however, for the d e t e r m i n a t i o n of the order of closely linked
m a r k e r s is t r a n s d u c t i o n , in spite of the fact t h a t a m a p p i n g function based u p o n
t r a n s d u c t i o n frequencies is n o t available.
A n u m b e r of e x p e r i m e n t a l conditions are i m p o r t a n t in m a p p i n g b y the gradient
Mutation
Res., 8 ( I 9 6 9 ) 5 o 5 - 5 1 2
MAPPING BY THE GRADIENT OF TRANSMISSION
51I
of transmission. A differential viability of certain recombinant classes was observed
in some crosses if zygotes were plated immediately after the interruption of transfer.
Good results were obtained when the zygotes were incubated for about two generations in broth before plating. This is in agreement with observations that the recovery
of recombinants from zygotes is sensitive to a metabolic shift-down I and with the
observation that the mathematical analysis of recombination data is useful only if
zygotes are incubated in broth before plating 2.
A second factor is the chromosome withdrawal which is observed in crosses
with certain Hfr strains as donors. The effect of withdrawal decreases the number of
zygotes which receive a given donor marker and this effect is greater for proximal
than for distal markers, due to the limitation of the transfer period. Experimental
conditions which prevented withdrawal, such as gently shaking of the mating mixture,
again gave an exponential gradient of transmission.
The random breakage of the conjugation bridge predicts an exponential
gradient of transfer of donor markers to the zygotes. The number of recombinants
which may be obtained from a zygote suspension depends on the number of zygotes
which received that particular marker and on its incorporation frequency in the
zygotes. The exponential gradient observed in the number of recombinants shows
that the incorporation frequencies of the markers in each cross presented in this
paper are equal.
The experiment with Hfr R4 as donor shows that the incorporation frequency of
the proB marker, which may be regarded as an early marker (o. 5 min from the origin),
was normal.
More proximal markers than proB, however, may be incorporated with a lower
p r o b a b i l i t y . GLANSDORFF4, as well as PITTARD AND WALKER 11, have shown that
certain markers near to the origin are incorporated at a lower frequency than other
markers. Experiments of Low ~ point in the same direction. The low incorporation
of early markers would make mapping of these markers by the gradient of transmission impossible.
REFERENCES
I DE HAAN, P. G., AND J. D. GROSS, T r a n s f e r delay and c h r o m o s o m e w i t h d r a w a l during conjugation in Escherichia coli, Genet. Res., 3 (1962) 251-272.
2 DE HAAN, P. G., AND C. VERHOEF, Genetic recombination in Escherichia coli, II. Calculation
of incorporation frequency and relative m a p distance b y r e c o m b i n a n t analysis, Mutation Res.,
3 (1966) 111-117 .
3 DIXON, \¥. J., AND F. J. MASSEY, Introduction to Statistical Analysis, 2nd ed., McGraw-Hill,
New York, 1957, p. 192.
4 GLANSDORFF, N., Pseudo inversion in the c h r o m o s o m e of Escherichia coli KI2, Genetics, 55
(1966) 49 61.
5 HAYES, W., The m e c h a n i s m of genetic recombination in Escherichia coli, Cold Spring Harbor
Syrup. Quant. Biol., 18 (1953) 75-93.
6 HAYES, SV., The kinetics of the m a t i n g process in Escherichia coli, J. Gen. Microbiol., 16 (1957)
97-119.
7 HAYES, W., The Genetics of Bacteria and Their Viruses, Blackwell, Oxford, 1964, p. 584 .
8 JACOB, F., AND E. g. WOLLMAN, Sexuality and the Genetics of Bacteria, Academic Press, New
York, 1961, p. 152.
9 L o w , B., Low r e c o m b i n a t i o n frequency for m a r k e r s very near to the origin in conjugation in
Eseherichia eoli, Genet. Res., 2 (1965) 4o6-413 .
io NIJKAMP, M. J. J., AND P. G. DE HAAN, Genetic and biochemical studies of the guanosine 5'n l o n o p h o s p h a t e p a t h w a y in Escherichia coli, Biochim. Biophys. Acta, 145 (1967) 31-4 o.
,VIutation Res., 8 (1969) 5o5-512
512
P. (',. I~1". HAAN ~[ rl/,
i 1 PITTARD, J., AND ['~. ~I. \~'ALKKR, ( ' o n j u ~ a t i ( m m hschm'ichia coli, l ~ e c o m b m a t i ( m c v e n t ~ ~H
t e r m i n a l r e g i o n s of t r a n s f e r r e d d c s o x y r i b o n u c l c i c acid, .]. Haclcri+d., 94 (I()67) l(}5ti l(ff)3"
I2 RFEVI~ZS, H., Role of H f r m u t a n t s in 1:" l: c r o s s e s in 1:'. toli I(12, .\'alurv, I,%5 (I0()O) 2() 5 2()(L
I 3 SKAAR, I ). ])., AND A. (;AP.FN, T h e o r i e n t a t i o n a l l d e x t e n t of gone t r a n s f e r in [:.schcrivhta ¢.[~,
Pro& Natl. ,qcad. ,qci. (1LS".), 42 (I956) 019 624.
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