Replication in Bacteria After a Stepwise Increase in the Velocity of Replication

JOURNAL OF BACTrMOLOGY,Apr. 1977, p. 92-99 CopyrightC 1977 American Society for Microbiology

Vol. 130, No.1 Printed inU.S.A.

Initiation and Termination of Deoxyribonucleic Acid

Replication in Bacteria After a Stepwise Increase in the

Velocity of Replication

H. BREMER, R. YOUNG,1 AND G. CHURCHWARD TheUniversity of Texas at Dallas,Richardson,Texas 75080

Received for publication 21 October 1976

The theoretical relations between replication, initiation, termination, and

deoxyribonucleic acid (DNA) accumulation were derived for experiments in

which the length of the time required for the replication of the bacterial

chromosome (C period) can be varied. This theory enables

one to

determine

absolute values of the C period from kinetics of DNA accumulation after

a

"step-

up" with thymine-requiring bacteria that are subjected

to a

sudden increase in

the exogenous thymine concentration. Application of this method of data evalua-

tion to an observed step-up experiment with a thy- derivative ofEscherichia coli

B/r (ATCC 12407) indicates that the theory describes the observed post-step

accumulation of DNA accurately within experimental

errors.

It is also concluded

that changes

in

the replication velocity (C) do

not

measurably affect the timing

of initiation

events in a

culture.

Pritchard and Zaritsky (6) showed that

in

certain thymine-requiring bacteria the velocity

of the chromosome replication fork

can

be

var-

ied by changing the concentration of the thy-

mine supplied

in

the growth medium. In the

experiment they called

a

"step-up," they

trans-

ferred bacteria from low

to

high thymine

con-

centrations and observed that accumulation of

deoxyribonucleic acid (DNA) immediately

ac-

celerated, although the

mass

doubling time

was not affected. Later after the step-up, DNA

accumulation returned

to

the doubling time of

the mass, but the DNA mass ratio remained

at

the new, higher steady

state.

The "step-up"

is

then distinct from and complementary

to

the

nutritional "shift-up" (5). In the nutritional

shift-up, the

mass

doubling time (T) decreases

but the time required for chromosome replica-

tion (the "C" period as defined by Cooper and

Helmstetter [31) remains constant. In the Prit-

chard and Zaritsky step-up, the C period de-

creases

(since the replication fork velocity is

increased

in

the higher thymine concentra-

tion), but T is constant. Just as analysis of the

nutritional shift-up has proven to be important

in

investigating the control of ribonucleic acid

(RNA) and protein synthesis (5), analysis of the

step-up experiment is important in studying

the regulation of DNA replication. In addition,

since

the step-up results in an altered DNA/

1Presentaddress:DepartmentofMicrobiology, Harvard MedicalSchool, Boston, MA.02115.

mass ratio but the net synthesis of RNA and

protein is unaffected, there must be changes

in

the rate of transcription per DNA

or

per

aver-

age gene. Thus

an

understanding of the step-up

is also important for the problem of regulation

of gene transcription.

Pritchard and Zaritsky used an evaluation of

their step-up experiments that enabled them

to

calculate

a

relative post-step value of the C

period compared with

an

assumed pre-step

value (or vice versa). In the present study we

have extended Pritchard and Zaritsky's analy-

sis of the step-up experiment and have derived

the theoretical relation between replication

ini-

tiation, termination, and DNA accumulation

after

a

step-up. With this theory

it

is possible

to

determine absolute values of the replication

times before and after the step-up rather than

relative values. The theory also suggests a

method to answer the question of whether the

cell mass per replication origin at the time of

initiation varies with the length of the C pe-

riod. For a 2.5-fold change in C, our data do not

show

a

measurable change

in

the initiation

mass per origin.

The purpose of this paper is to present the

theory on which the new method of evaluation

is based and to give an example of its applica-

bility by showing an actually observed step-up

with a newly isolated thy- derivative of the

Escherichia coli B/r strain (ATCC 12407) used

by Helmstetter and Cooper (3). The results ob-

tained are essentially the same as those ob-

92

served previously

with

thy-

derivatives of

other

E. coli strains

(6).

We will

present

elsewhere

(manuscripts

in preparation) detailed experi-

mental

results

for

the

C period

in

E.. coli

B/r

using

various

conditions of growth (thymine

concentrations, doubling times) and

using

both

this and another method.

MATERIALS AND METHODS

Bacterial strain and growth conditions. The bac- terialstrainused in this study wasTJK16,a sponta- neous derivative of E. coli B/r ATCC 12407 (the strainusedbyCooper andHelmstetter [3]),isolated andkindly made availableby T. J. Kwoh. It is F- thyA drm,obtainedby trimethoprim selection, and islessthan 2%leakyasmeasuredby incorporation ofradioactive uridineintoalkali-insoluble, trichlo- roacetic acid-precipitable material in the absence of exogenousthymine (datanotshown).Cultureswere grown at 37°C in C medium (4) supplemented with 0.2%(wt/vol)glucose,anartificialmixtureof all 20 aminoacids, eachto afinal concentration of 0.05%

(wt/vol) (50 jug/ml),and anappropriate concentra- tion of thymine. Aerationwas performed by vigor- ous bubbling. Allcultures were inoculated with a 1:1,000dilutionof afreshovernightculturecontain- ing 20

Ag

of thymine per ml. Under these conditions, a constantdoublingtime of 29 min wasmaintained for at least one generation before and after the ex- perimentalperiod.

Measurementof DNA synthesis before and after achange inthymine concentration. Medium con- taining 1 ,ag of

[2-'4C]thymine

per ml (Schwarz/

Mann; final specific activity, 0.01

juCi/,ug)

^{was inoc-}

ulated,and theabsorbancyat460 nm and accumula- tion of DNA were monitored. Optical density was followedbyusing a Zeiss PMQII spectrophotometer.

For estimation ofDNA, samples (0.5 ml) were re- moved atintervals into 1.0 ml of a solution of 1 M trichloroacetic acidcontaining 2 M NaCl and kept onice.After at least 30 min, the precipitates were collected on Schleicher andSchuell membrane fil- ters (0.45-j,m pore size), washed withcold0.01 M trichloroacetic acid, dried, andplacedinvials with 5.0 mloftoluene-basedscintillation fluid. Radioac- tivitywasdetermined by using a Beckman LS-100 scintillation counter.

At anabsorbancyat 460 nmof 0.4, the culture was dilutedtwofold into fresh, prewarmed, aerated me- dium to give a final thymine concentration of 20,ug/

ml.The specificactivityremainedconstant. Optical densityand DNA accumulation were followed for 1 h afterthe changeinconcentrationof exogenousthy- mine. The doubling time was unaffected by this treatment.

THEORY

Principle of approach. Thefollowingtheoryhas several sections. At first [section (i), below], we describethe relation between the number of chro- mosome origins forreplication initiation, termini, replication forks, replication time (C), DNA con- tent, and doublingtime ofanexponentially grow-

ing, steady-state culture. The doubling time and DNA content are easily observable, and itrequires measurement ofonly one additional parameter to determine allremainingparameters. Forexample, the equations derived in this section can be used to find C from the number of origins measured by hybridization techniques (1). We have chosenan- other approach, based on an evaluation of step-up experiments (fordefinitionof step-upexperiments, seeintroduction).

In the following section (ii), we extend the theo- retical analysis to the time after a step-up. It turns out that the more complex shape of the DNA accu- mulation curve during the transition period be- tween the twosteady states (i.e.,immediatelyafter the step-up) containsinformation about all the pa- rameters listed above. In fact, there are now two replicationtimes, Cl before and C2 after the step-up;

both can be determined from the kinetics of DNA accumulation. In this section, the effect of the step- up onthe rate of DNA synthesis (number of replica- tionforks)isderived.

The next three sections (iii, iv, v) deal with the accumulation of DNA and the evaluation of its ki- netics, mainlytofind Cl and C2.

The final section (vi) deals with a particular as- pect of theevaluation, the question of whether the cell massper replication origin is affected by the step-up.

Definitions. I is the number of chromosome origins (i.e., initiation sites for DNAreplication)per milliliter of culture. T is the number of chromosome termini permilliliter of culture. F is the number of replication forks per milliliter of culture. G is the amount of DNA in genome equivalents (8.2 x 106 nucleotides for E.coli)permilliliter ofculture.Cl is the time (in minutes) to replicate a chromosome beforethe step-up (t < 0). C2 is the time (in minutes) toreplicate a chromosome after the step-up (t>0).T

isthedoublingtime (inminutes) of cell mass, pro- tein, andRNA before and after the step-up. Io,

To,

Fo,

and

Go

areI, T, F,andG, respectively, at t =0 (step-uptime).

(i) Initiation,termination, and DNAreplication forks during steady-state growth. During the steady-state exponential growth, the number of chromosome origins per milliliter of culture in- creasesexponentially (likeany other component of theculture)accordingtothegrowthequation:

I =Jo*t/7) (1) Anychromosomeinitiated isterminatedC min later (definitionofC); hence,the number of chromosome termini is:

T =Io.2(t-c)/7 Settingt = 0 inequation2agives:

To= IO.2-C/T

andsubstituting equation2b into 2agives:

T = To *2t"T analogoustoequation1.

(2a)

(2b)

(2c)

94

BREMER, YOUNG, AND CHURCHWARD Thedifference "chromosome origins minus chro- mosome termini" is equal to the number of replica- tionforks if replication is unidirectional; for bidirec- tional replication, two replication forks are created for every initiation and disappear again after termi- nation, such that

F=2(I- T) (3a)

or,substituting equations 1 and 2a:

F= 2I(1 -2-C/T) (3b) Eachreplicationfork"synthesizes" DNA at a rate of (1/2)/C,i.e.,one-half genomeequivalentperreplica- tiontimeC. Thus, the rate of DNA synthesis in a culture is:

dG

dt

⁼

F*

1¹

(4)

dt 2C

The rate of DNA

synthesis

^canalso befound from the

exponentially increasing

amountof DNA

(see section iii, below) and hence is described by equation 1,thenthe terminationaftert=C2reflects initiations that haveoccurredafter t=0, i.e., for t >

C2 (seeequation 2a,above):

T=

Io.2(t-C2)ft

^{for t 2 C2 (2b)} According to equations 10 and 2b, the curvelog T versus time shows twodiscontinuities (breaks);the first one at t= 0and asecondone at t = C2(Fig. 1).

Substituting equation 1 forI andequation10 or 2b for T into equation 3a gives the number of replica- tion forks after a step-up.

F= 2[Io2t/T To2(c,Ic2)

(t2)]

for0 < tt C2 F⁼

21o[2t.

2(t-c2)IT] for C2 <T

(11) (12) Inequations 11 and 12,I0 and

To

areconstants that canbe found from the amount of DNA (per milliliter ofculture) at t = 0,

Go,

using equations 8 and 9, respectively. For t = C2, both equations 11 and 12 give:

G=

Go

2IT (5)

bydifferentiation

dG ln2

dt=

G-

dt Xr

(6)

Combining equations4and6andsolvingforFgives:

2C ln2

F= *G

T (7)

Substituting equation7intoequation3bandsolving for I gives the number ofreplication origins as a function ofthe amount of DNA (G), the doubling time (r),and thereplicationtime (C):

I⁼ (1^-2-CIT)-l.G

1r

(8)

Similarly, the number of termini is obtained by combining equations 8,2a, and1:

T=C

ln2 (2C/T-1)-l.

G

Tr (9)

Theserelationships areillustratedintheexample of Fig. 1 for

Go

= 1 (relative amount of DNA per milliliter ofculturevolume at t = 0); C= C1 = 80 minand r= 30min.

(ii) Effect of a step-up on the rateof DNA syn- thesis. At a step-up (at zero time), the pre-step replication time C1 shortens suddenly to the post- stepreplication time C2; hence all terminations that wouldnormally (without step-up) occur during the timeinterval between zero and Cl will now occur during the shorter interval between zero and C2.

This is illustrated in Fig. 1 for anexample in which it isassumed thatCl =80 min,C2=40min, and T= 30 min. The acceleration factor is equal to the ratio C1/C2,such that the terminations between zeroand t = C2 are given by:

T= To-2(C )A(C2,)for 0S t<C2 (10) Ifthe rateofinitiation is not affected by the step-up

Timeafter step-up(min)

FIG. 1. Theoretical relationship between the num- ber of chromosome origins (equation 8), termini (equations 9 and 10), and replication forks (equa- tions11 and 12) before andafter a step-up (pre-step replication time Cl = 80 min; post-step replication timeC2 = 40min; doubling time of culture T =30 min). The ordinate values are normalized for a DNA content of the culture of1 genome equivalent per (arbitrary) unit ofculture volume at zero time (=step- up time. The numberof replication forks is set equal tothedifference of origins minus termini (unidirec- tional replication); for bidirectional replication the numberofforks is twice as large (equation 3a; i.e., the curve is to beshifted upward corresponding to a factorof 2).

J. BACTERIOL.

F =2J0[2C21T - 1] for t = C2 (11,12) Thekinetics of thechangeinthenumber of replica- tionforksafter a step-updescribedby equations 11 and 12 areillustrated in Fig. 1.

(iii) Effect of a step-up on theaccumulation of DNA. The DNA accumulation between zero time (step-up) and t = C2 (in genome equivalents per minute permilliliter ofculture) is found from equa- tion 4:

dG F (4)

dt

=2C

by substituting equation 11 for F, setting C = C2, integrating from zero to t, and furthersubstituting equations 8 and 9for

Io

and To, respectively. The resulting equationdescribes the DNA accumulation inthe stepped-up culture in genome equivalents per unit of culturevolume:

G=

GO[a(2IT-1)

-

b(2(CiIc2) (t/T)

^-

1)

+

1]

(13a)

for 0<t<C2 where

a =Cl(1 -2-Cl/7)-l C2

b= (2C1/T - j)-I

After t=C2,the amountof DNA is obtainedby an analogousoperation exceptusingequation12for F:

G=G(C2) *2(1-C,)iT (14) whereG(C2), the amount of DNA permilliliter at t=

C2, isobtainedbysettingt= C2inequation13a:

(13b) G(C2) =- C

GC)=C2(1-2 __2cz,

^-

IT,) ))

^Go

These kinetics are illustrated in Fig. 2.

(iv) Change inDNA/mass ratio. The amount of DNA ina stepped-up culture increasesfaster than theDNA in anunstepped-up control culture (Fig. 2).

The ratio of the amount of DNA in the stepped-up culture at time t (given by equations 13 and 14) overthe DNA in the control (=

Go2"r)

willbe desig- natedas

AG(

(Fig. 2, lower curve). Since the accu- mulation of mass is not affected by the step-up (i.e., mass increases in both cultures according to the function

Mo21lT), AG,

also representsthe changein theDNA/massratio,GIM,aftertminatthehigher thymine concentration. The final change in this ratio isdesignated

AG.,,

givenby:

AG. = AG(t a C2)

G(t> C2) G(C2) 2c,IT

Go-

2TIT

Go

Substitutingequation 13b forG(C2) gives:

AG.

=G0/M(step-up) C1(1-2-C2IT)

A

C/M(control)

-C2(1 -2-CI/T) (15a)

Accordingtoequation15b,theDNA/massratio fora

givendoubling time, ^T,isproportionalto(1-2-CIT)/

C, inagreement with equation 3 of Pritchard and Zaritsky (6).

(v) Determination of C from the step-up kinetics.

Both Cl and C2, i.e., the replication times of the chromosome before and after the step,canbe deter- mined from the post-stepkinetics of DNA accumula- tion.The ratio

C1/C2

is given by thechange in the slope of thekinetics at t = 0, sinceimmediately after the step-up it is justthe acceleration of the preexist- ingforks thatdetermines the change in DNA accu- mulation. The absolute value of C2 is given bythe timeat whichthe kineticsinthesemilog plot(Fig.

2) become linear.

Forthe accuratedetermination of C2, the square rootof thedifferenceAG. -

AG,

isplottedversust;

the intercept of this function with the time axis is C2 (Fig. 3).

For amathematicaldescription,thesymbolFwill beused,definedby:

F =AG.-

AGt

=lim [G(t)]

Gt)

⁽¹⁶⁾

For t = 0, F represents the (final) increase in the DNA/mass ratio caused by the step-up (equation 15).For any t >C2, r = 0. BetweenzeroandC2, F decreasesnearlyparabolicallytozerosuch that JR decreases nearly linearly (Fig. 3). Substituting equation13afor

Gt

gives:

r =[2(cit/C2T)+a]b . 2-t/T-c

(17)

where

zE

a

(C1/C2) - 1

%.-1

^-2-c,/T

0 20 40 60 80

Time after

step-up(min)

FIG. 2. Theoretical kineticsofDNA accumulation afterastep-up[G(step-up)], calculatedfromtheex-

ample in Fig. 1 by using equation 13a. Symbols:

)accumulationofDNA inanunstepped-upcon- trolculture;(---)AG1 =ratioofthetwouppercurves.

96

BREMER, YOUNG, AND CHURCHWARD

,_v.

o lo 20 30 40

Time after step-u p ( min )

FIG. 3. Determination

of

the post-step C

period

(C2)

from

theobservedaccumulation

of

DNA

after

a

step-up. Illustratedarethreetheoretical

exalmples for

T =

30,'

calculatedby using

equation

17. Givenare

thevalues

of C,

andC2,indicatedas

fraction C,IC,.

For example, the curve O ~O

designated

80140

means: C1 = 80 min, C2 = 40 min. The curves

intersectthe time axisatC2.

2-C

IT

~ b

1-2-c,/r

(ClIC2)

*2-C2/T

10-1 2-cl0

Thismethodpresupposesthatthe initiationmass peroriginisnotaffected

by

the shift. Whetherthis isthecasecanbetestedasdescribedinthe

following

section.

(vi) Change in initiation mass per origin. A

change

inthe value of the cellmassperchromosome originatthetime ofreplicationinitiationduetothe step-upmustcause atemporaryincreaseordecrease in the

slope

of the kinetics of chromosome origin accumulation. This results in a (downward or up- ward)

parallel

shift of the latepost-step sectionof the Icurve inFig. 1

(parallel

because

during

final

steady-state

growth in the post-step medium the slopesof allcurvesinFig.1 mustbe

equal

^tothepre- step slopes,

corresponding

to the

unchanged

dou-

bling

time ofthe culture). A downward (or

right-

ward) shiftmeans a reductioninthe origins/mass ratioand hencean increase inthe initiationmass perorigin; an

upward

(or leftward) shiftmeans a

decreaseintheinitiationmassperorigin.

This consideration suggests a direct method to determine whether the initiation mass depends on C: one mayfollow the accumulation of chromosome origins after astep-up. Forexample, with a trans- duction assay (2)orwith a hybridizationassay(1), anunchanged exponential increaseinthe number of origins after the step-up indicates an unchanged initiation mass. However, it isalso possibleto an- swer thisquestion fromanevaluation of the kinetics of DNA accumulation after the step-up, which can bemeasuredmoreeasily.

Any changes (i.e., horizontal parallel shifts) in the origin kinetics (origin curve in Fig. 1) cause corresponding changes in the terminus kinetics, only with adelayof C2 min (equation 2a).Hence, the late sections of the kinetics of replication forks (equation3a)and of DNA accumulationareshifted similarly as in the I curve. Immediatelyafter the step-up,however, thekinetics of DNA accumulation reflectonly theacceleration of thereplicationforks;

i.e., the kinetics arecompletelydeterminedby the

(C1/C2)-fold

increase in the slope and are not af- fected by changes in the initiation mass. Thus, changesinthe initiation mass causedistortions in the kinetics of DNA accumulation such that they can no longerbe described by equation 13a or 17.

These distortions areevaluatedfrom the

v/Pr

curve asfollows.

Figure 3shows, as anexample, three

/PF

curves calculated from equation 17, i.e., assuming no change in the initiation mass. For all curves, the doubling time of the culturewasassumedtobe 30 min. Intwocurvesthe ratioC1/C2isthesame(4:1), but the valuesof C2 (andthusalso

Cj)

aredifferent (C2=20andC2=40). In anotherpairofcultures the C2valuesarethesame(C2=40),butthe ratioC1/C2 isdifferent (2:1and 4:1).

Let usassumethe ratioC1/C2 has beenobserved in aparticularstep-up experimenttobe4:1 (r = 30 min). If there were nochangeininitiationmassper origin, thenaninfinite number ofroughlyparallel /Fcurves would be consistent with this4:1 ratio, twoof which areillustrated in Fig. 3.

Now assume that thefinal part of the

v'Vcurve

intersectsthe time axisat t = 40. Thiscouldmean either that the initiation mass has in fact not changed, asassumedinFig. 3,and therefore C2 =

40, orthat the initiation mass may havechanged and therefore C2 *40. Any shift of the origin curve (Fig. 1) to the right (= increase in themass/origin ratio; seeabove) would delay the time at which the DNAaccumulation becomes exponential, and hence itwould delay the time at whichr' =0and atwhich the /F curve intersects the time axis. Thus, if the mass/origin ratio had increased, C2 would actually be smaller than the observed t = 0intercept of the

v curve (in this example, C2 < 40); correspond-

ingly,

a decrease in the mass/origin ratio means thatC2 is actually greater than theobserved inter- sectionvalue. To see whethersuch a change in the mass/origin value has occurred or not, we observe the intersection of the

\/i-

curve with the ordinate (reflecting the final change in the DNA/mass ratio).

Ifthere was no change in the mass/origin ratio, then v'T should be equal to 1.21 (Fig. 3, value of top J. BACTERIOL.

curve at t = 0; i.e., forC1/C2= 4and

VTF

=Oatt = 40). If this isfoundand,further, if the observed vY values fall on the theoretical curve, then one can conclude that the initiation mass/origin value has not changed.

In contrast, one may find that v/i' is 0.65 and that the observed

V/Pcurve

corresponds to the curve calculated for a

C1/C2

ratio= 2(Fig. 3). Thiswould indicate an increase in the origin/mass ratio and hence a smaller C2 (see above). For example, ifC2 were equal to 20 min, then without a change in the initiation mass/origin the curve indicated by trian- gular symbols might have been observed, but the right (or downward) shift of the originkineticspro- duces arightwardshift of the intersection withthe time axis (i.e., from 20 to 40 min) and simultane- ouslyadownward shift (equivalent to arightward shift)of the final DNA accumulation curve and thus areduction ofvI's(i.e., from 0.87 to 0.65).As Fig. 3 shows, this curve is inconsistent with an initial slopeincrease

(Cl/C2)

= 4:1.

Inconclusion, any change in the initiation mass/

origin ratioafter a step-up results in

\/R

kinetics that are not consistent with the observable(C,/C2) ratio.

EXPERIMENTAL

Figure 4a shows the results of a step-up experi- ment from 1 to 20 ,ug of thymine perml. Although there is no detectable change in the mass doubling time, there is an immediate change in the kinetics of DNA accumulation similar to that predicted in Fig. 2 and observed previously by Pritchard andZaritsky (6). After normalization of the data to

Go

= 1 (Fig.

4c),thefunction

\-G7

^-

AGi

(Fig. 4b) was calcu- latedas follows.

AG,

was calculated as the quotient

G(t)/2"1T.

The average of the final sixvalues of

AG,

wastaken as

AG..

Thus the final values of

V`G-

AG,

must have an average value of zero, which defines the height of the abscissa in Fig. 4b. The best-fit straight line extrapolated to a value of 33 min onthe abscissa, indicating that C2 is equal to 33 min under these conditions. In the calculation of

AG,.

(as an average from six values), it was implied that the scatter in the final points was random. This means that the final values of

/Go -3-Gt-

in Fig.

4bshould cluster around zero with a Gaussian dis- tribution. It is possible that this condition is not met:for example, the positive values of

VA'G&

-

AG(

amongthe finalsamplesinFig. 4bcouldbe due to spillage rather than random sampling error such that the true values are those clustering around -0.2 (corresponding to a 3% higher final curve in Fig. 4a). Inthis case,

AG,.

has beenunderestimated bytheaveragingprocedure and C2would beequalto 39 min. On the other hand, if the values of

VA'_

-

AGt

clustering around 0.2 were correct, AG. would havebeen overestimated and the value of C2 would be nearer to 28 min. For a more accuratedetermina- tion ofC, this uncertainty can be minimized by increasing the number of final samples.

Fromthe (2.3-fold)changeininitialslope ofthe kinetics,avalue of 76 min wasobtained forCl (i.e., 2.3 x 33 = 76). From the finalchangeintheDNA/

mass ratio(Fig. 4c; 1.55-fold) andC2 = 33 min, Cl

wascalculated to be 80 min by equation 15b. These values of ClandC2 weresubstitutedinequation 13a, and the accumulation of DNA after the step-up was calculated (curve inFig. 4c). This curve is seen to describe the observed data points very accurately (+3%). In a repeat of this experiment for a step-up from1.3 to 20 ,ug of thymine per ml, we foundC,to be 66 min and C2 to be 35 min.

The effect of the step-up is assumed to be brought aboutby anincreasedsize of theintracellularpoolof thymidine 5'-triphosphate (TTP), which is limited by the (thymine concentration-dependent) rate of thymine uptake and which itself limits the rate of DNA chain growth. Since the cells cannot synthe- size thymine and thespecific radioactivity ofthy- mine was kept constant during the experiment, there could not have been any effect of poolequili- bration on the kinetics of incorporation ofradioac- tivity into DNA. The only conceivable effectwould be a slow rather than a stepwise increase in the TTP concentration, but the observed stepwise increase in the rate of DNA accumulation (Fig. 4a) indicates that the increase inTTP is not measurablydelayed.

DISCUSSION

The

kinetics of DNA accumulation

after

the

step-up in Fig. 4a are similar to those found in

previously published experiments

(6).

Using

the

method of evaluation described

in

the first

part

of the

paper, we

have determined that for

this

particular

strain growing in 20

,ug of thy-

mine

per

ml the C period has

an average

value

of 34 min

(two experiments) for glucose amino

acid

cultures. This is somewhat shorter than

the values obtained for the wild-type

parent

of

this strain by Helmstetter and Cooper, and also

shorter than

our

estimates using

an

independ-

ent

method (manuscript

in

preparation).

The average

of all

our

experimental results

is 37 min.

Presumably the difference between this

and

Helmstetter and Cooper's value of

41min is

mainly due to variability of growth and experi-

mental

errors

involved

in

the different

meth- ods.

More importantly for the

present

discussion,

tha, theory developed

in

the first

part

of this

paper enables

us to

accurately describe the

ki-

netics of DNA accumulation after

a

step-up

on

the basis of

two

assumptions (illustrated

in

Fig.

1): (i) that

a step-up

produces

an

immediate

stepwise change

inthe

replication velocity;

and

(ii) that initiation

is not

affected by changes

in the

replication velocity.

The

agreement

of the

observed

and

theoretically predicted

kinetics

indicates that these assumptions

are essen-

tially correct.

It is

true, though, that

thesame

DNA accumulation

could be derived from other

assumptions,

for

example by assuming

addi-

tional

initiations

compensated by premature

terminations. However, underlying

such adhoc

assumptions

arefurther restrictions thatmake

7E

0~~~~

1000 o 3 6 .0 4.

800 / 0.8 a 7/

E600

-I06p

~~~~~~/0.60_

I0

X2.0 .

400 0.4

/V ~~~~~~~~~.5

004

200 0.2

100~~~~~~~~~~*

I I I

.

° I I

-30 0 30 60 0 15 30 45 60

Time after step-up(min) Time after

step-up(min)

0.9 0.6 0

0.40

* ~~~C233 min

0~~~~

[20.2~~~~~~~~~~~~~

0~~~~~~~~~~~~~~

-0.2.

0

-0.4

0

0 9 Is 27 36 45 54

Time after step-up ( m i)

FIG. 4.

98

them untenable. In this example, these addi-

tional replication forks must also prematurely

terminate; moreover, this must occur at exactly

the time when those other prematurely termi-

nated forks would normally (without step-up)

have completed their replication. As far as we

can detect, therefore, there is no change in the

initiation mass per origin after the step-up.

This means the theory is an accurate represen-

tation of the events occurring in cultures dur-

ing a transition between different replication

velocities, and therefore it enables us to esti-

mate replication velocities from measurements

on exponentially growing cultures, after a dilu-

tion into fresh medium containing a different

concentration of thymine. This procedure re-

sults

in

very little, if any, disturbance to the

cells since the rate of mass increase is un-

changed by the step-up (see also reference 6).

This compares with the membrane elution

technique, where the cells apparently have a

shorter doubling time when grown on the mem-

brane (4).

ACKNOWLEDGEMENT

Thisworkwassupported by Public Health Service gen- eral medicalscience grant15412 from the National Insti- tutes ofHealth.

LITERATURE CITED

1. Bird, R. E., J. Louarn, J. Martuscelli, and L. Caro.

1972. Origin andsequence of chromosome replication inEscherichia coli. J. Mol. Biol. 70:549-566.

2. Caro, L., and C. M. Berg. 1969. Chromosome replica- tion inEscherichiacoli.H.Origin of replication in F- andF+strains. J.Mol. Biol. 45:325-336.

3. Cooper, S., andC. E. Helmstetter. 1968. Chromosome replication and thedivision cycle of E. coli B/r. J.

Mol. Biol. 31:519-540.

4. Helmstetter,C. E. 1967. Rateof DNA synthesisduring the division cycle of E.coli B/r. J.Mol. Biol.24:417- 427.

5. Maaloe, O., and N. 0. Kjeldgaard. 1966. Control of macromolecular synthesis. W. A. Benjamin, Inc., New York and Amsterdam.

6. Pritchard,R.H., and A. Zaritsky.1970. Effect ofthy- mine concentration on the replication velocity of DNA in a thymineless mutant of E. coli. Nature (London)226:126-131.

FIG. 4. Analysisofastep-upexperiment.(a)AccumulationofDNAand culturegrowthbeforeandaftera step-up.Atzerotime,aculture growing with 1 pgof

["'Cithymine

permlwasdiluted into mediumcontaining ['4C]thymine ofthesamespecificactivity, buthigher concentration such that thefinalconcentrationwas20 pg/ml.Forfurtherdetailssee text.Thedashedline represents DNA accumulation inanunstepped culture. (b) EstimationofC2(

1)

fromthe datain(a). Fordefinition oftheordinate,seeequation17.Thenegativevalues representthe square rootsofthe modulus ofnegativedifferences. Thelargescatterafter 36minreflectsthefact thatthese valuesarederived fromdifferencesoftwolargenumbers;theexperimentalaccuracyis +3%[see (a)]. The open circlesarethetwoexperimentalpoints thatcanbeseenin(a)tobe

clearly

outside the normal range ofvariation. They have not been included in the least-square fit. (c) Calculated kinetics

of

DNA accumulation ( ), usingequation13a and C1 = 80 min, C2 = 33 min, and T =29 min. Symbols: (0) Observed data pointsfrom (a) after normalizationto1.0at t= 0;( )initial

slope, corresponding

toa2.3- foldincreaseintherateofaccumulation; (..* )DNAaccumulation in

unstepped-up

controlculture;(-- -) extrapolationofthefinalsectionofthekinetics intersectingthe ordinate-at1.55, which is

equal

tothe

final

increase inthe DNA permassratioduetothe step-up =

AG,.