JOURNAL OF BACTERIOLOGY, JUlY 1975, p 7-19 Vol. 123, No. 1Copyright 0 1975 American Society for Microbiology Printed in U.S.A.

Control of Cell Length in Bacillus subtilisMICHAEL G. SARGENT

National Institute for Medical Research, Mill Hill, LondonNW7 1AA, United Kingdom

Received for publication 24 March 1975

During inhibition of deoxyribonucleic acid synthesis in Bacillus subtilis 168Thy- Tryp-, the rate of length extension is constant. A nutritional shift-upduring thymine starvation causes an acceleration in the linear rate of lengthextension. During a nutritional shift-up in the presence of thymine, the rate oflength extension gradually increases, reaching a new steady state at about 50 minbefore the new steady-state rate of cell division is reached. The steady-staterates of nuclear division and length extension are reached at approximatelythe same time. The ratio of average cell length to numbers of nuclei per cellin exponential cultures is constant over a fourfold range of growth rates. Theseobservations are consistent with: (i) surface growth zones which operate at aconstant rate of length extension under any one growth condition, but whichoperate at an absolute rate proportional to the growth rate of the culture, (ii)a doubling in number of growth zones at nuclear segregation, and (iii) a require-ment for deoxyribonucleic acid replication for the doubling in a number of sites.

The shape and dimensions of a bacteriummust reflect the processes by which the externallayers or shape-determining structures grow.Rod-shaped bacteria, such as Bacillus, proba-bly grow only in length, as there is very littlevariation in width among cells of different ageunder any one growth condition (22). This couldbe achieved by large numbers of growth zonesoperating all over the surface or by a fewannular zones. Studies of surface labeling ofrod-shaped bacteria have provided evidence infavor of both views (11, 23-25, 32). The recentstudies of Kepes and Autissier (14) in Esche-richia coli have suggested that some membraneproteins may be the only surface componentsthat exhibit conservation during growth andthat lipid and mucopeptide are either random-ized during growth or are inserted over theentire surface. In corroboration of this conclu-sion, Ryter et al. (33) have shown localizedincorporation of diaminopimelic acid in veryshort pulses in E. coli. Probably the mostsatisfactory synthesis of the data available isthat in rod-shaped organisms there are a limitednumber of growth zones but that certain compo-nents of the surface may appear not to beconserved, either because they are randomizedafter synthesis, or they are indeed synthesizedall over the surface, or there is turnover ofsurface components.The time course of length extension in rod-

shaped organisms has been studied on individ-ual growing cells (17), on populations of syn-

7

chronous cells (41), and by inference from thelength distribution of exponential-phase cul-tures (3). Such results show that length exten-sion is undoubtedly continuous throughout thecell cycle but do not distinguish between expo-nential and linear growth models with certainty.Biochemical evidence that indirectly favorslinear growth has been obtained by showingthat mucopeptide in E. coli (10) and membraneprotein in Bacillus subtilis (35) are synthesizedat a constant rate with doublings in rate atparticular points in each cycle. The pattern ofsynthesis of these components during the cellcycle might be expected to correspond with thatof growth in length of the bacterium.The suggestion of Jacob et al. (12) that

chromosome segregation is achieved by surfacegrowth between attached chromosomes imposescertain limitations on possible models of sur-face growth (36). An important conclusion fromattempts to devise schemes of chromosomesegregation depending solely on surface growthis that segregation can only be achieved withone or two growth zones per chromosome(36). The strongest support for the repliconhypothesis (12) remains the observation ofLark and co-workers (on B. subtilis [7], E. coli[21], and Lactobacillus acidophilus [1 ]) thatlabeled deoxyribonucleic acid (DNA) strandsare not segregated randomly and that pulse-labeled chromosomes are inherited with thecell envelope to which it was attached whenfirst used as a template. Pierucci and Zuchow-

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

8 SARGENT

ski (28) have confirmed these observations forE. coli and satisfactorily explained conflictingdata. If chromosomes are segregated by sur-face growth, then temporal control of theappearance of surface growth zones should becoupled to chromosome replication (18, 29, 30,43). In support of this, Kubitschek (18) hasshown that volume increase in E. coli is linearin the absence of DNA synthesis, suggestingthat the appearance of new growth zones isdependent on DNA replication.There is strong evidence in E. coli that the

chromosome cycle has a strict temporal rela-tionship with cell separation (8). If the appear-ance of surface growth zones is coupled to aparticular point in the chromosome cycle, thenthe length of a rod-shaped bacterium will be anexponential function of growth rate. Evidencefor this has been obtained in a number of cases(37, 40, 43). Zaritsky and Pritchard (43) havesuggested that the variation in average celllength with growth rate in E. coli is consistentwith the appearance of growth zones at termina-tion of replication and with the rate of extensionper growth zone being proportional to growthrate. In this communication, three models arediscussed for the control of cell length, whichprovides a reasonable fit to the observed varia-tion in cell length with growth rate. Experi-ments have been devised that test the assump-tions underlying the derivation of these models.

MATERIALS AND METHODS

Organism. B. subtilis 168/S, an asporogenic vari-ant of 168 Thy- Tryp-, able to grow on succinate asthe sole carbon source, was maintained in a freeze-dried state. B. subtilis 168 Nil, a PBSX- mutant of168 Thy- Tryp-, was kindly supplied by D. Karamataand was maintained as spores.Growth conditions. The basal medium (34) used

contains phosphate buffer (7.1 g of disodium hydrogenphosphate and 1.3 g of potassium dihydrogen phos-phate [anhydrous] per liter, pH 7.3), magnesiumsulfate (0.25 mg/ml), ferrous sulfate (.7H20) (1 jig/ml), and manganese sulfate (.4H20) (0.1 jg/ml).Thymine (10 gg/ml unless otherwise stated) andtryptophan (5 ug/ml) were subsequently added asep-tically to give the final concentrations shown. Carbonand nitrogen sources were added as shown in Table 1.The amino acid mixture shown contains L-arginine,L-alanine, L-glutamic acid, glycine, L-histidine, L-isoleucine, L-leucine, L-lysine, L-proline, L-serine, L-threonine, and L-valine. The final concentration ofeach amino acid was 100 gg/ml (in media 7 through13). In media 4 and 5, proline and arginine werepresent at 4 mg/ml. In media 1 through 3, theconcentration of ammonium sulfate was 2 mg/ml andthat of carbon sources was 4 mg/ml.

Inocula were grown in medium 3 and subsequentlysubcultured into the media described below, with

inocula chosen to give cultures in the exponentialphase of growth after overnight incubation. Thus, allmeasurements by the criteria of a constant ratio ofoptical density at 540 nm (OD,40) to particle numberand DNA to OD.40 (data to be given separately) overat least three generations have been made on bacteriathat have been grown in the exponential phase formore than 15 generations and were in balancedgrowth. All steady-state measurements shown inTable 1 were obtained after the overnight culture (stillgrowing exponentially) was subcultured into freshprewarmed media to give an OD of 0.02, and measure-ments were made on cultures having OD valuesbetween 0.1 and 1.0. All cultures were grown at 35 Cwith vigorous aeration.Measurement of growth. The mass of bacteria per

milliliter of culture was expressed as OD,40. TheOD540 is proportional to dry weight over the range of 0to 1.0 for a culture in balanced growth. For culturesgrown on succinate, glucose and glucose plus caseinhydrolysate, the dry weight per unit of OD540 = 200ug. Although OD measurements represent a measureof cell volume, a constant ratio of OD to dry weightunder a wide range of conditions has commonly beenobserved (16).

Coulter counting. Particle counting was as de-scribed previously (34). All references to cell numberrepresent the number of Coulter units.Length measurements. Cell length was measured

by using a Watson image-splitting eyepiece on heat-fixed cells stained with 0.01% crystal violet. Averagelengths obtained, with unstained cells under phaseoptics and stained cells under normal optics, did notdiffer significantly. Measurements were made on 40 to50 cells of two preparations from each sample. Thestandard error of the mean for each set of measure-ments was usually less than 5% of the mean.

Septa. Septa were counted on heat-fixed prepara-tions of bacteria stained with 0.01% crystal violet (34).At least 200 cells were counted on two preparations ofeach sample. The frequency of septa (S) was ex-pressed as a fraction of cells counted. The timeelapsing between appearance of septa and cell separa-tion is given by (S + 1) = 2s'/g, where St is theseparation time and g is the generation time (seeAppendix).

Nuclear staining. Heat-fixed specimens were hy-drolyzed with 1 N HCI for 7 min at 60 C, washed inphosphate buffer (0.1 M, pH 7.3), stained with freshlyprepared Giemsa stain (B.D.H.) (diluted 1:10 withphosphate buffer [0.1 M, pH 7.3] and filtered) for 5min, and examined while they were still immersed inthe stain. The nuclei in 200 cells in two preparationsof each sample were counted and expressed as afraction of the cells counted (i.e., Nu). The timeelapsing between nuclear division and cell separationis given by (Nu) = 2y/g, where y is time elapsingbetween nuclear division and cell separation (seebelow).

RESULTSModels for length growth. The length of a

rod-shaped organism that grows only in length

J. BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS 9

is determined by: (i) the number of growthzones, (ii) the rate of length extension pergrowth zone, and (iii) the time in each cycleover which length extension occurs. Expressionsfor the average length of cells in an exponential-phase population of bacteria have been derivedby using the age distribution theorem (31),assuming either linear or exponential growth inlength during the cell cycle (see Appendix). Ineach of the three models considered, the rate oflength extension has been considered independ-ently of the cell width. Models based on the rateof increase in surface area can be derived (30).However, in the case of the strain of B. subtilisused for the experimental tests described below,there is no detectable variation in cell widthwith growth rate. Therefore, any conclusionspertaining to cell length extension apply equallyto surface area increase.Linear growth models. Linear growth would

occur during a period in which the number ofgrowth zones did not change and the rate oflength extension per site remained constant.Thus, in the cell cycle, if the number of growthzones doubled at time t (Fig. la) and the rate oflength extension per site was constant, then thelength of the cell would increase linearly with adoubling in rate at t. Two alternative models oflinear growth have been considered.

(i) Model A. The rate of linear extension persite is constant at all growth rates. The averagelength (l) is given by:

l = (nl'/loge2) g 2x/g

where 1' is a constant with dimensions of lengthper minute, x is the time elapsing between thedoubling in number of growth zones and cellseparation, g is generation time in minutes, andn is the number of growth zones present in acell before the doubling in rate (i.e., cell ageinterval 0 - t, Fig. 1A) when x < g.

(ii) Model B. The rate of length extensionper site is proportional to growth rate, i.e.,

E = (nlAoge2) 2x/g

where 1 is a constant with dimensions of length.Exponential growth model. (iii) Model C.

The number of sites increase exponentially, butthe rate of length extension per site is constantunder any one growth condition and varies inproportion to growth rate, i.e., E = nl 2,/g,where 1 is a constant with dimensions of lengthand n is the number of sites of length extensionat x minutes before cell separation. This modelis formally indistinguishable from model B,although the constants in each formula differ insignificance. A number of alternative models

2 Lo

I

A

UB

2

O r% t

2LorLi-Lol

(0 10OCELL AGE (a)

FIG. 1. Relationship between cell length, relativecell age, and age distribution. (A) Linear growth inlength with doubling in rate at relative cell age (t). (B)Age distribution given by N(a) = No 2-a (31). (C)Exponential growth in length. Length at t (Lt) = Lo21. Vertical axis is on arithmetic scale.

have been considered (see Appendix). As withlinear models, the r'elationship between the rateof extension per site and growth rate has thebiggest effect on the form of the equation. Thesymbols 1' and 1 have been used to distinguishconstants with different dimension.Calculation of nuclear segregation time,

septal separation time, and time of commit-ment to division. If an event occurs at aspecific cell age in the cell cycle (i.e., t, Fig.1B), the proportion of cells (p) in the popula-tion that have passed this point can be cal-culated from the age distribution theorem (31)by the formula p = 2 t") (where t is expressedin fractions of a generation time). Proofs ofthis relationship have been given by others(13, 20, 27).The nuclear segragation time, septal separa-

tion time, and time of commitment to divisioncan be determined by using this relationship asfollows.

(i) The time elapsing between nuclear divi-sion and cell separation (y) is given by Nu =

2y/g, where Nu is the average number ofnuclei per cell. Note, y is expressed in real time.

(ii) The time between appearance of septaand cell separation (St) is given by (1 + S) =

VOL. 123, 1975

u

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

10 SARGENT

2st/g, where S is the average number of septaper growth unit and (1 + S) is the averagenumber of cells separated by a septum (i.e., ifthere is an average 0.1 septum per cell, theaverage number of separate cells is 1.1 perCoulter unit).

(iii) When DNA synthesis is inhibited (i.e., bythymine starvation in a thymine-requiringstrain), only those cells that have completedtheir chromosomes are able to divide (4). Thetime elapsing between commitment to division(z) and cell separation is given by Nd = 2z/g x100, where Nd is the percent increase in cellnumber over those present at zero time duringthymine starvation. The time of commitment todivision is defined as that time in the cell cycleat which cells proceed to division in the absenceof DNA synthesis.

Effect of growth conditions on length, nu-

cleation, and septation. The variation in aver-age length, number of nuclei, and number ofsepta in B. subtilis 168/S grown under a widevariety of conditions is shown in Table 1. Ifammonium sulfate is the sole nitrogen source

and the carbon source is varied, growth ratesbetween 0.5 and 1.0 generations per h areobtained. Arginine, proline, and glutamate willact as the sole carbon and nitrogen sourceswithin the range of growth rates. Mixtures ofamino acids in the presence of glucose allowgrowth rates of up to 2 generations per h.

The figures shown represent the average of atleast two estimates of the parameters shown,made with bacteria from cultures in whichgrowth rate and cell mass were very similar, ifnot identical. Many other experiments withthese media have indicated that the growthrates are typical of the media, although largevariations in generation time (120 to 105 min)were encountered with different batches of suc-cinate-containing media.

All calculations have been based on numbersof particles per milliliter of culture (measuredby a Coulter counter), since this is operationallyconvenient, although septum formation occurssubstantially before cell separation.

Septa. The time elapsing between the ap-pearance of the septum and cell separation canbe calculated from the average number of septaper cell (Table 1). The average number of septavaries between 0.1 per average cell in slow-grow-ing cells and 0.6 per cell in fast-growing cells.The calculated separation time is about 20 minunder most conditions but is marginally longerin media 7 and 8. A separation time of 138 min(which is unaffected by growth rate) has beendemonstrated in another strain of B. subtilis(27) under slightly different growth conditions. Ihave also shown that separation time can bevaried by alteration in the ionic composition ofthe growth medium (34).

Nuclei. The appearance of Giemsa-stained

TABLE 1. Nuclei, septa, and cell length in B. subtilis in relation to growth rate

IGrowth rate 4Nuclei/cell | Segregation SeptumMedium" Grwt rae ule/cl time" Septa/cell separation Cell length EN(divisions/h) (Nu) |(y,min) (S) timec(Cn| m) C(St, min)

1 0.53 1.37 52 0.12 20 2.46 1.942 0.87 1.71 53 0.20 19 2.9 1.73 1.03 1.8 49 0.24 18 3.46 1.924 0.62 1.72 76 0.18 23 2.95 1.715 0.88 1.87 63 0.24 21 3.38 1.816 1.2 3.15 81 0.27 17 5.69 1.87 1.09 3.0 87 0.38 26 5.43 1.828 1.18 2.8 76 0.58 29 5.02 1.799 1.5 3.08 65 0.47 18 5.52 1.7810 1.54 3.07 63 0.4 19 5.53 1.8111 1.88 3.53 58 0.58 21 6.52 1.8412 1.91 3.4 55 0.45 17 6.12 1.813 2.0 3.25 51 0.52 18 5.8 1.7814 2.18 3.3 47 0.58 18 5.35 1.62

a Media: (1) Succinate-ammonia, (2) glycerol-ammonia, (3) glucose-ammonia, (4) proline, (5) arginine, (6)glucose-arginine, (7) glucose-amino acid mix minus valine, (8) glucose-amino acid mix minus methionine, (9)glucose-amino acid mix minus glutamate, (10) glucose-amino acid mix minus proline, (11) glucose-amino acidmix minus histidine, (12) glucose-amino acid mix minus lysine, (13) glucose plus complete amino acid mix, (14)glucose plus casein hydrolysate.

b Segregation time (y) calculated from Nu = 2y1g.cSeptum separation time calculated from (1 + S) = 2stlg.

J.- BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS

nuclei in heat-fixed preparations is shown inFig. 2. Nuclei are seen either in the center ofcells or at 25% from either end (36) and can,therefore, be scored quite unambiguously sincethere are very few intermediate forms. For-malin-fixed nuclei, on the other hand, mayappear as lobed structures and, in some prepa-rations at high growth rates, these appear as

separate nuclei, with the result that largernumbers of nuclei per cell are recorded. Neitherimage can be regarded as corresponding to thenuclear form in living bacteria, but there isevidence that nuclear division, as scored opera-tionally with heat-fixed preparations, occurs ator close to the time of commitment to division(see Fig. 4a). Table 1 shows the number ofnuclei per cell and the time between nucleardivision and cell separation (y) as calculatedabove. Under most conditions, values for y of 45to 65 min were obtained, although with organicnitrogen sources at lower growth rates thevalues of y were 60% longer than this.

Cell length. Each of the formulas for thetheoretical mnodels discussed above can be rear-

ranged to give straight-line relationships of theform a = mb + c, as shown in Table 2 [models Athrough C (i) ]. In each case, log2 L or log2 l/g isproportional to divisions per hour, and theslopes of the lines would then have values of x.

The variation in average cell length with growthrate is shown in Fig. 3a and b, plotted as (a) log2L/g and (b) log2 against generations per hour.Both plots provide moderately good fits to a

straight line (determined by least-squaresregression analysis). However, in Fig. 3a x has a

value of 118 i 12 min and in Fig. 3b it has a

value of 46 10 min (Table 2).The variation from a straight line seen in Fig.

3 indicates that x cannot be constant under allthe growth conditions. This is probably ac-

counted for by the variation in the time betweennuclear division and cell separation (y) (Table1), which would therefore alter x. The equationsfor each model can be modified to take this into

*.g *

0*

.. ,..

..

:: :: :: .: :.

:..: .: .... :..:*.. .: .:.. : :..: .:

.:

.: .: .:

:.::

eF

*:: .: ::... :. ... : :.:*.. :: .:: .... .. : . : :.*.: ::

:: . ;.w:.: . .*:

... {

::: ::

:

:t

Ss ef::S.;.....

*.o

:e. .::w.^*g *.

,^ e.. .... ' .. '..:* : . : .

:: :.: :.

,. ...

* ':

:' *..

!JF .*

:..#

FIG. 2. Giemsa-stained nuclei of B. subtilis 168/Sgrown in glucose-ammonium medium no. 3.

TABLE 2. Graphical analysis of three models of cell length extension.

Model Formula Rearrangement x r Best fit for Constant Ca(min)

A (i) E = gnl'/log.2.2x/g LogJ(E/g) = x (1)(g) + log2(nl'/log.2) 118 ± 12.5 Log2(1.55 nl' = 1.07 x 10-2X 10-2) pm/min

B (i) l = ni/log.2.2x/g Log,E = x (1)/(g) + log4(nl/og.2) 46 ± 10 Log 2 (2.3) nl = 1.59 um

C (i) l = nl.2x/g Log2E = x(1)/(g) + log2nl 46 4 10 Log2(2.3) nl = 2.3,um

A (ii) lINu = gnlI'log.2-2xYIg Logfl/gNu) = (x - y) (M)/(g) + 67 ± 5 Log2(1.93 nl' = 1.33 x 10-2

log2(nl'/log.2) X 10-2) Am/min

B (ii) l/Nu = nA/log.2.22-Y/g Log 2 (EINu) = (x - y) (1)/(g) + -3 2 Log2(1.875) ni = 1.29pimlog4(nl/loge2)

C (ii) Li/Nu - nl .2x-Y/g Log2( /Nu) = (x - y) (M1)(g) + 1og2 nI -3 ± 2 Log2 (1.875) nl = 1.875 Am

a Formula rearranged to form a = mb + C. Left-hand side = a; m = x for models A (i), B (i), and C (i); m = (x - y) for modelsA (ii), B (ii), and C (ii); b = llg; and second term on the right = C.

b Standard error (SE) of regression coefficient.

11VOL. 123, 1975

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

12 SARGENT

0

I

0i)

L 6 CNug 4

x 1022 i,

rMnin

U1tH i

r'~ 10 2:0DIVISIONS PER HOUR

FIG. 3. Relationship between cell length andgrowth rate. (A) Log2 l/g plotted against growth rate(divisions per hour), where E is the cell length(micrometers). (B) Log2 l plotted against growthrate. (C) Log, LiNug plotted against growth rate. (D)Log2 l/Nu plotted against growth rate.

account by dividing each equation by that forthe numbers of nuclei, i.e., Nu = 2Y/g. Theserelationships are shown in Table 2, togetherwith the transformations for graphical analysis[models A through C (ii)]. Figure 3c and dshows log2 E/gNu or log2 E/Nu plotted againstgenerations per hour. Model A gives a value of(x - y) (the slope) of 67 t 5 min, whereasmodesl B and C give values of -3 2 min. Thelatter is not significantly different from zero byStudent's t test. In both cases, the fit to astraight line is substantially better than whenplotted as in Fig. 3a and b. The fit to models Band C (Fig. 3d) is probably marginally betterthan for A. Thus, on the basis of model A,growth zones double in number 67 min beforenuclear segregation, but, according to models Bor C, x is reached at or close to nuclearsegregation.

Effect of thymine starvation on length ex-tension and cell division. In deriving themodels of length extension suggested above, aspecific temporal relationship between the timeat which growth zones double in number andthe time of cell separation has been proposed.The most tangible physical basis for such arelationship is that certain parts of the chromo-some have to be replicated to generate new sitesof length extension. If so, then during inhibitionof DNA synthesis the rate of extension shouldremain constant at the rate determined by thenumber of preexisting sites. For an exponentialculture, the rate of length extension at anylength (l) is E/g. Log.2 and would be equal tothe initial rate of extension on any model ofgrowth. The constant-rate model A suggeststhat in a nutritional shift-up during thyminestarvation the rate of length extension willremain unchanged, whereas model B suggeststhere should be an increased rate of lengthextension. DNA synthesis was inhibited bythymine starvation of strain Nil of B. subtilis168, which lacks the defective phage PBSX andtherefore does not lyse during this treatment.Also, Nil differs from 168/S (but is similar to168 Thy- Tryp-) in that it grows more slowly inglucose minimal medium and has slightly largercells (20% greater than 168/S). The average celllength per nucleus was not significantly differ-ent for the two strains. Prior to thymine starva-tion, the strain was grown on glucose-ammon-ium medium (3) (Table 2) with a generationtime of 76 min and was then collected on amembrane filter (Millipore Corp.), washed freeof thymine, and suspended in medium lackingthymine. Half of the resuspended culture wastransferred to a flask containing casein hydroly-sate to give a final concentration of 0.5%.During thymine starvation, the OD,40 contin-ued to increase exponentially for 2 h and thenslowed quite markedly, finally giving a 2.5-foldincrease over the initial value (Fig. 4a). Cellnumbers increased to 160% (Fig. 4a), and thenno further cell division occurred. At this stage,20% of these cells contained septa so that thetotal increment in cells that formed septa overthe initial concentration of cells (Coulter units)was 192%, which was reproducible to within10%, although the proportion of septate cellsremaining was lower in some experiments.Under these conditions, production of anucleatecells has not been seen (6). The point of com-mitment at which completely separate bac-terial units are produced is, therefore, 54 minbefore cell separation, and that to produce aseptum is about 70 min before cell separation

J. BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS 13

(calculated as shown above). The nuclearsegregation time in this strain is also 70 min;therefore, commitment to septum formationoccurs almost simultaneously with nuclearsegregation.The average length changes very little for 80

min after starvation but, thereafter, starts toincrease considerably as the division rate falls(Fig. 4b). The rate of length extension can beconsidered independently of cell numbers byfollowing the sum of cell lengths (i.e., averagecell length x cell number). This is approxi-mately linear for 4 h and gives a total increase of2.5-fold (Fig. 4c).A nutritional shift-up during thymine starva-

tion has very little effect on the extent or rate ofresidual cell division (Fig. 4a). The mass growthrate is initially marginally higher and ultimatelyincreases threefold before stopping. Cell lengthincreases rapidly and, when plotted as the sumof cell lengths, is approximately linear for 4 hwith a 4.5-fold increase in total length (Fig. 4c).The rate of length extension with glucose as

carbon source was 0.77 x 108 Mm/h and duringthe shift-up was 1.72 x 108,Mm/h. This is clearlynot consistent with constant-rate model A. Therate of length extension predicted by model Bcan be calculated as follows:

rate of length extension per cell

= nl/g x 2x/g x 60,um/hThe value of 2x/g was shown above to be equalto the number of nuclei per cell, and a value ofnl of 1.29 ,m was obtained from length pernucleus (Table 2). For strain Nil grown onglucose the generation time was 76 min. Theexpected rate of extension per cell was therefore0.8 Mm/h and for 1.25 x 108 cells per ml wouldbe 1.0 x 108 im/ml of culture. The observedvalue was about 20% lower than this.The typical postshift mass doubling time of

exponential-phase cells for Nil was 40 min.During thymine starvation, the mass growthrate apparently did not reach this rate during ashift-up. However, the theoretical rate of lengthextension, calculated as above, using 40 min asa value of g, was 1.88 x 108 um/h, and theobserved rate was 10% lower than this.Length extension during a nutritional shift

in unstarved exponential-phase cells. Whenexponentially growing cells are shifted-up nutri-tionally, the mass growth rate accelerates to anew rate almost immediately (15, 37), whereasother processes, such as cell division or DNAsynthesis, show a lag before reaching the newrate. For each process the time elapsing be-

Oa~~~~~~~~~~c0A0x

06 A3,oO4 -10 1U-) z

Y2Y -05,

10 B

6-z

-J

X C'C -.w 31 ~ -

__JoCD6

0 1 2 3 4TIME HOURS

FIG. 4. Effect of nutritional shift on growth in celllength during thymine starvation of B. subtilis Nil.Nil was grown on glucose-ammonium medium no. 3,collected on a Millipore filter, and washed with freshmedium lacking thymine. This was divided into twoportions. Casein hydrolysate was added to one ofthese (final concentration 0.5%). (A) 0 andO*, 0D540for glucose and glucose plus casein hydrolysate, re-spectively; 0 and *, cell number per milliliter(Coulters units) for glucose and glucose plus caseinhydrolysate. (B) 0 and@*, Cell length (micrometer)for glucose and glucose plus casein hydrolysate. (C) 0and@*, Total cell length (i.e., cell number x averagecell lenth) for glucose and glucose plus casein hydroly-sate. ( ) and (---) Theoretical rates for glucoseand glucose plus casein hydrolysate, respectively.

tween the shift and attainment of the newsteady state is equal to the length of timerequired from initiation of the process tocompletion (e.g., a new rate of chromosomeinitiation is reached C + D minutes beforecell division, where C is the chromosomalreplication time and D is the time elapsingbetween termination and cell division) (8).

This priciple can be used to distinguishbetween model A and the other two. For thedata shown above (Fig. 3, Table 2) to fit modelA, the doubling in rate must occur approxi-mately 70 min before nuclear segregation. In thetransition from succinate to glucose (Table 1),this is about 120 min before the rate of celldivision reaches a steady state. On the basis of

VOL. 123, 1975

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

14 SARGENT

model B, x is equal to the time elapsing betweennuclear segregation and cell division, which inthe case of glucose-grown cells will be about 50min before cell separation. In a nutritionaltransition, therefore, length extension shouldreach a steady state only 50 min before celldivision. Clear-cut evidence against model Ahas been obtained in the transition from succi-nate to glucose medium.

Bacteria growing on succinate with a dou-bling time of 115 min were diluted with fresh,prewarmed medium containing 0.4% glucose.The mass growth rate accelerated almost in-stantaneously to a doubling time of 60 min,whereas cell numbers increased only gradually,reaching a new steady state after about 130 min(Fig. 5b). Figure 5a shows cell mass (OD per 109cells), plotted on an arithmetic scale, togetherwith cell length and numbers of nuclei duringthe transition. The latter two parameterschanged most sharply in the interval 80 to 120min. This could be explained as follows. If anyevent is controlled by a specific part of thechromosome, the product (on a per cell basis)will increase during the interval between thiselement reaching a new steady state of replica-tion and the time at which the new steady stateof cell division is reached. The sharp changes innumbers of nuclei and cell length between 80and 120 min represent the time between thedoubling in rate of length extension and celldivision. The time of the transition can be seenmore clearly, in this case, by plotting the timecourses of total length increase and increase innumbers of nuclei per milliliter (Fig. 5b). Bothnuclei and cell length reach steady states atabout 80 min and not immediately after theshift-up. Model A is therefore most unlikely onthis analysis.The effect of the variable rate element on the

time course of the transition is shown in Fig. 6,where the data for total length per milliliter ofculture is shown, plotted on an arithmetic scale,relative to the theoretical initial rates of lengthextension calculated for values ofg of 60 and 120min. The initial rate of length extension fallsabout the rate to be expected for a culture witha generation time of 60 min, but over the firsthour the difference between this and the rate fora generation time of 120 min is small and barelysignificant statistically. However, the overalltrend appears consistent with model B.

DISCUSSIONThe time taken to reach a new steady state of

total length extension during a nutritional shift(from succinate to glucose) provides a critical

4-

Ir 3-CDzJ--J

C0)2

A

B

04

TIME HOURSFIG. 5. Effect of nutritional shift up on cell length

and nucleation in B. subtilis 168/S. At zero time,glucose was added (final concentration 4 mg/ml) to anexponential-phase culture of B. subtilis 168/S growingon succinate-ammonium medium no. 1. Culture wasdiluted 1:1 with fresh medium after 90 min. Allconcentration figures after the dilution were multi-plied by 2. (A) 0, Average cell length (micrometers);*, average cell mass, i.e., OD,,, per 109 Coulter units;O, average number of nuclei per cell. All figuresplotted on an arithmetic scale. (B) 0, Cell number(Coulter units) per milliliter; O, total cell length perml, i.e., cell number x average cell length; 0, total

J. BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS 15

difference between models A and B. The newrate is reached after about 80 min, as predictedby model B, whereas model A predicts that anew rate would be reached soon after thetransition. Sud and Schaecter (40) have alsoobserved a lag in the rate of increase in totallength during nutritional transition experi-ments in Bacillus megaterium.A second difference between models A and B

is that the rate of length extension per site isconstant at all growth rates in the former caseand variable in the latter. Strong support for thevariable-rate model (B) has been obtained bydemonstrating an acceleration in rate of lengthextension during a nutritional shift-up of bacte-ria starved of thymine. This experiment isbased on the assumption that inhibition ofDNA synthesis (by thymine starvation) pre-vents the appearance of new sites of lengthextension but allows length extension frompreexisting sites and, indeed, during thyminestarvation the rate of total length extension islinear, both during a nutritional shift-up and inunshifted cultures. Kubitschek (18), using E.coli, has shown a linear increase in volume overtwo generations during thymine starvation.Although exponential models cannot be elim-

inated by this analysis, a small amount ofindirect evidence against them is available.Thus, synthesis of mucopeptide in E. coli (10)and membrane protein in B. subtilis (35) occurlinearly with doublings in rate at specific timesin each cycle, and these might be expected tocorrespond to the pattern of length growthshown by the organism. If there are indeedsmall numbers of growth zones (11, 14, 32, 33) inrod-shaped bacteria, to sustain linear growtheach site would have to extend at an exponen-tially increasing rate. The thymine starvationexperiments suggest this is unlikely.On the basis of either model B or C, the cell

length at nuclear division is a constant ormultiple thereof at all growth rates (see Appen-dix) and, furthermore, nuclear segregation in168/S occurs in cells of the same range oflengths (2.5 to 3.0 um) in both succinate- andglucose-grown bacteria in which the average celllengths are 2.4 and 3.5 um, respectively (36).Nuclei in mononucleate cells are found in thecenter of cells, and at nuclear division thedaughter nuclei appear to move abruptly to asite 25% from either end of the cell (36). Thus,

TIME HOURSFIG. 6. Comparison of rate of length extension with

theoretical rates during shift-up. (0) Total cell lengthper milliliter (cell length x cell number per milliliter)plotted on arithmetic scale. Data from Fig. 5B. (---)Theoretical rate of length extension at zero time forpreshift culture grown at generation time of 120 min.( ~) Theoretical rate of length extension at zerotime for culture grown at generation time of 60 min.

during nuclear division the distance moved bynuclei on either side of the center is the same atall growth rates.

If, as Jacob et al. (12) have suggested, chro-mosome segregation is achieved only by surfacegrowth between attached chromosomes, therecan be only one or two growth zones perchromosome (36). Thus, either there is onegrowth zone, generating surface symmetricallyon either side (36), or there are two asym-metric growth zones flanking the newly syn-thesized part of the surface (as suggested byDonachie and Begg [5]). Ryter and colleagues(32, 33) have provided evidence for symmetricalgrowth zones in B. subtilis and E. coli.The apparent "jump" in the position of the

nuclei appears superficially to be incompatible(36) with the idea that surface growth betweenchromosomal attachment sites achieves segre-gation (12). However, this observation can bereconciled with the theory as shown in Fig. 7.The chromosome is shown attached to the cellsurface by the terminus at a growth zone(symmetrical) and at the next potential growthzone by the origin, with the bulk of the nucleuslocated at the terminus attachment site. As

number of nuclei per milliliter (cell number per ml xaverage number of nuclei per cell). (---) OD..40 inpost-shift culture. ( ) Preshift growth rate(OD5,40). All figures plotted on log scale.

VOL. 123, 1975

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

16 SARGENT

A

G

B

G

C

GD

G S GFIG. 7. Relationship between surface growth and

chromosome replication. (A-D) Stages in chromo-some replication. (A) Immediately after establish-ment of new growth zone (G), chromosome-initiatedorigins (0) and terminus (0); (B) 0.2 generationsater segregation (note origins moving apart butterminus at growth zone); (C) 0.8 generations aftersegregation; (D) Termination. Terminus detachesfrom growth zone and moves to junction of old andnew wall formed one generation previously. Oldgrowth zone committed to septum formation (S).Junction of oblique dotted lines represents junctionof old and new cell surface.

length extension proceeds, the origin is movedaway from the bulk of the nucleus, and oncompletion of the chromosome the nucleusmoves to the site at which the origin wasattached and then attaches strongly by theterminus. There is biochemical evidence thatthe chromosome is more strongly attached bythe terminus than by the origin (42). If nuclearsegregation is achieved by a single symmetricalgrowth zone, then n, in the formula for model B,would have a value of 1.0 and cells at the pointof nuclear division would be 2 1 long. At thistime, the length of surface synthesized is equalto 0.5 1 on either side of the nucleus. Afternuclear division, the daughter nuclei move topositions 25% from either end of the cell, and,

therefore, to the junction of old and new surfaceformed one generation previously. The origin ofthe surface of such a cell on the point of divisionis shown in Fig. 8. If n is greater than 2 andgrowth zones operate symmetrically, surfacegrowth cannot be the sole mechanism of chro-mosome segregation, and the site to whichnuclei move would not be identifiable in thismanner.Although the average length at nuclear segre-

gation is constant over a range of growth rates,studies of the frequency of nuclear divisionrelative to cell length (36) indicate that nucleardivision occurs over a range of cell lengths(coefficient of variation of mean length at nu-clear division is about 0.14 on glucose andsuccinate [unpublished data]). Furthermore,length extension studies during thymine starva-tion, described above, indicate that cells areable to exceed the normal cell length at nucleardivision. Schaecter et al. (38) showed that inseveral enteric bacteria the variation in celllength at division was less than the variation ingeneration time, and from this concluded thatattainment of a certain length at division wasan important element in commitment to divi-sion.Experiments showing that growth occurs

symmetrically around nuclei (32, 36) indicatethat at about the time of nuclear division theold growth zone must cease length extension.Presumably this site is then committed to adevelopmental sequence, culminating in sep-tum formation, which does not involve lengthextension. The observation that the rate ofresidual division during thymine starvation isnot significantly affected by a nutritional shiftwhereas the rate of cell extension doubles can be

Al

A2

B2 1IB.ID. .FIG. 8. Pattern of surface growth assuming linear

growth from sites of nuclear attachment. The origin ofcell surface in a cell at the moment of separation isshown in B2. Bl represents this cell at the point ofsegregation in the same cycle. Al and A2 representcells at segregation and separation, respectively, inthe previous cycle. Sites of nuclear attachment, 0.Sites to which nuclei move at segregation, 0.

J. BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS 17

regarded as evidence that the rate of septumformation is controlled independently of periph-eral wall extension.The dependence of the rate of linear extension

on growth rate is similar to the general responseof bacterial cells to a nutritional shift-up. Thus,during a shift-up, there is a rapid increase inrate of protein synthesis as a result of anincrease in ribosome synthesis (15). Cell lengthextension is presumably dependent on mem-brane protein synthesis and can be expected toshow the same response as cytoplasmic proteinsynthesis. Regulation of surface-synthesizingcomponents must, therefore, be visualised attwo levels: (i) a regulation of rate per site that isaffected by the nutritional status of the growthmedium; (ii) a regulation at individual sitesthat, when a new growth zone forms, inducesformation of the necessary length-extendingmachinery (ribosomes for synthesis of mem-brane proteins, etc.).The model for Bacillus growth and division,

described above, has strong similarities to themodel for the division of Streptococcus faecalispresented by Higgins et al. (9, 39). In thisorganism, there is evidence that (i) surfacegrowth zones develop to become septa, i.e.,septum formation occurs at a site in the newestwall; (ii) new growth zones are formed at thejunction of old and new wall; (iii) growthzones operate symmetrically; (iv) there areindications that the nucleus is attached onlyat growth zones; (v) formation of the septumcan be regarded as a developmental processto which the growth zone is committed onceperipheral wall extension at that site has ceased.The essential difference between the coccaland bacillary growth forms, on this analysis,seems to be the angle at which new peripheralwall is inserted relative to old peripheral walland the angle at which cross walls are insertedrelative to the peripheral wall.

APPENDIXModels for the determination of average cell

length. The average length (l) of an exponentiallygrowing culture is given by

Linear growth. Linear growth would occur duringa period in which there was no change in the numberof sites of length extension. Thus, in an exponentiallygrowing culture, if the number of sites double innumber at time t (a fraction of generation time), therate of length extension doubles (Fig. la).The time elapsing (in generation times) between t

and cell separation equals (m - t), where m is thenumber of cycles of cell division over which the periodbetween t and cell separation extends. In which case,the total number of growth zones before and after twould be n.2 ( -l1) and 2 * n 2 (m-1), respectively, i.e.,during the interval 0 - t, in a cell in which m = 1, thenumber of growth zones equals n. A cell of this kindmay be regarded as one growth unit.

During the intervals of cell age a, 0 - t, and (t -

1.0), the cell length would be:

L = Lo + n-2m.l-Ka, where o <a <t (3)

and

L = Lo + [n-2m-l-K(t)] + [2n.2m-l(a - t)K], (4)where t < a< 1.0

where Lo is the length of a newborn cell and K is rateof length extension relative to cell age and a is relativecell age.The length of a newborn cell is equal to the total

length synthesised during one cycle, i.e.,Lo = n.2(m-1).K.(2 - t) (5)

Substituting equation 5 in equation 3

(6)L = n-2(m-l)-K(a - t + 2)

and in equation 4

L = 2n.2(m-l').K.(a - t + 1)

Since L is a discontinuous function, equation 1 issolved in the form

fa tf: N(a) L(a) da + a =N(a) L(a) da (8)fa l N(a)

substituting equations 2, 6, and 7 in equation 8

l = n *2m- I *(K/Iog.2) *22-'t (9)This can be expressed in real time (in contrast torelative cell age). Thus, K = Ig, where I is the rate oflength extension per site in real time and has thedimensions length per minute and t = [(mg - x)Ig],where x is the time (in real time) elapsing between t(in relative cell age) and cell separation. Therefore,

l = fJ o °L(a) N(a) dafaa=1N(a) da

(1)

where L is the cell length at relative cell age (a) and Nis the cell number at cell age a given by the agedistribution theorem (31) (Fig. lb), i.e.,

N(a) = No 2-a (2)Expressions for average length can be obtained bysubstituting a term for L as a function of cell age inequation 1. Linear and exponential functions havebeen considered.

l = (n * lg)/(log. 2) 2x/g (10)

Two alternatives of this model have been consid-ered: model A, in which I is a rate and is a constant atall growth rates (i.e., equation 10); model B, in which Iis proportional to growth rate, which gives the rela-tionship:

l = (nl/log.2) 2x/g (11)

in which case I has dimensions of length.The cell length x minutes before cell separation

(Lx) can be calculated as follows: Lx equals the length

VOL..123, 1975

(7)

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

18 SARGENT

of newborn cell plus length of cell synthesized be-tween cell age 0 and (g - x). In the case of model A, Lx= 2n-I-g; In the case of model B, Lx = 2n-1. Thus,cell length at x would be a constant.

Exponential growth. Exponential growth in lengthwould occur if: (i) new sites of length extensionappeared at an exponential rate during the cell cy-cle, or (ii) if each site operated at an exponentiallyincreasing rate of length extension. An expression forthe time course of length extension in terms of thenumber of sites and rate per site can be obtained asfollows. The rate of length extension per cell

dL/da = n(a) K

where n is the number of sites per cell at a cell age aand K is the rate of linear extension per site.The cell length at cell age a

L(a) = Jn(a)K-da

If the rate of length extension per site is constant(under any one growth condition) and n(a) = n0 2a,where n0 is the number of sites in a newborn cell

(12)L(a) = (nO K 2a/log02)

substituting in equation 1

l = 2nO K

An expression for n0 can be obtained by postulatingthat at a time x minutes before cell separation thecell contains a constant number of growth zones (n)or multiples thereof. The number of growth zonesat cell separation, i.e., (2n0) = n 2x/g, substitutingin equation 13

l=Kn2x/g (14)

As with linear models, the constant K is ex-pressed in terms of relative cell age and can be ex-pressed in real time as Ig,

i.e., l = nlg2x/g (15)

This is formally identical to model A.If I is proportional to growth rate

E = nl.2x/g (16)

This is formally identical to model B above and hasbeen investigated as model C above. As with model B,it can be shown that the cell length at x is a con-stant, i.e., from equation 12.

Lx = (n0 K/log.2) 29-x/g

substituting n0 as for equation 14

Lx = nK/log.2

Thus, if K is a constant, (i.e., I is proportional togrowth rate), Lx is a constant at all growth rates.

Terms used.a: Cell age (as a fraction of generation time)g: Generation time (minutes)K: Rate of length extension per site (micrometers

per unit of cell age).

l: Average cell length (micrometers)Lo: Length of newborn cell (micrometers)1': Constant of proportionality (micrometers per

minute, model A)l: Constant of proportionality (micrometers, model

B)m: Number of cell cycles over which time be-

tween t and cell separation extendsN(a), No: Number of cells in age distribution at

cell ages a and o, respectively.Nu: Average number of nuclei per celln: Number of growth zones per growth unitS: Average number of septa per cellSt: Time elapsing between appearance of septum

and cell separation (minutes)t: Time at which number of sites of length ex-

tension double in number (as a fraction of genera-tion time)

x: Time elapsing between doubling in number ofgrowth zones and cell separation (minutes)

y: Time elapsing between nuclear division and cellseparation (minutes)

z: Time elapsing between commitment to divisionand cell division

ACKNOWLEDGMENTSValuable discussions with Howard J. Rogers and R. F.

(13) Rosenberger are gratefully acknowledged.

LITERATURE CITED1. Chai, N. C., and K. G. Lark. 1967. Segregation of

deoxyribonucleic acid in bacteria: association of thesegregating unit with the cell envelope. J. Bacteriol.94:415-421.

2. Cole, R. M. 1965. Symposium on the fine structure andreplication of bacteria and their parts. m. Bacterial cellwall replication followed by immunofluorescence. Bac-teriol. Rev. 29:326-344.

3. Collins, J. F., and M. H. Richmond. 1962. Rate of growthof Bacillus cereus between divisions. J. Gen. Microbiol.28:15-33.

4. Dix, D. E., and C. E. Helmstetter. 1973. Couplingbetween chromosome completion and cell division inEscherichia coli. J. Bacteriol. 115:786-795.

5. Donachie, W. D., and K. J. Begg. 1970. Growth of thebacterial cell. Nature (London) 227:1220-1225.

6. Donachie, W. D., D. T. M. Martin, and K. J. Begg. 1971.Independence of cell division and DNA replication inBacillus subtilis. Nature (London) New Biol.231:274-276.

7. Eberle, H., and K. G. Lark. 1966. Chromosome segrega-tion in Bacillus subtilis. J. Mol. Biol. 22:183-186.

8. Helmstetter, C. E., S. Cooper, 0. Pierucci, and E.Revelos. 1968. On the bacterial life sequence. ColdSpring Harbor Symp. Quant. Biol. 33:809-822.

9. Higgins, M. L., and G. D. Shockman. 1970. Model for cellwall growth in Streptococcus faecalis. J. Bacteriol.101:643-648.

10. Hoffman, B., W. Messer, and U. Schwarz. 1972. Regula-tion of polar cap formation in the life cycle of Esche-richia coli. J. Supramol. Struct. 1:29-37.

11. Hughes, R. C., and E. Stokes. 1971. Cell wall growth inBacillus licheniformis followed by immunofluorescencewith mucopeptic specific antiserum. J. Bacteriol.106:694-696.

12. Jacob, F., S. Brenner, and F. Cuzin. 1963. On theregulation of DNA replication in bacteria. Cold SpringHarbor Symp. Quant. Bioi. 28:329-347.

13. James, T. W. 1960. Controlled division synchrony and

J. BACTERIOL.

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from

CELL LENGTH IN B. SUBTILIS 19

growth in Protozoan micro-organisms. Ann. N.Y. Acad.Sci. 90:550-564.

14. Kepes, A., and F. Autissier. 1972. Topology of membranegrowth in bacteria. Biochim. Biophys. Acta265:443-469.

15. Kjeldgaard, N. O., 0. Maal0e, and M. Schaecter. 1958.The transition between different physiological statesduring balanced growth of S. typhimurium. J. Gen.Microbiol. 19:607-616.

16. Koch, A. L. 1970. Turbidity measurements of bacterialcultures in some commercial instruments. Anal. Bio-chem. 38:252-259.

17. Kubitschek, H. E. 1970. Evidence for the generality oflinear cell growth. J. Theoret. Biol. 28:15-29.

18. Kubitschek, H. E. 1971. Control of cell growth in bacteriaexperiments with thymine starvation. J. Bacteriol.105:472-476.

19. Kubitschek, H. E., M. L. Freedman, and S. Silver. 1971.Potassium uptake in synchronous and synchronisedcultures of Escherichia coli. Biophys. J. 11:787-797.

20. Lapidus, J. R. 1971. Analysis of a model for multisepta-tion in bacteria. J. Bacteriol. 108:607-608.

21. Lark, K. G., H. Eberle, R. A. Consigli, H. C. Minorko,N. Chai, and C. Lark. 1967. Chromosome segregationand the regulation of DNA replication, p. 63-89. InH. J. Vogel, J. 0. Lampen, and V. Bryson (ed.),Organizational biosynthesis. Academic Press Inc., NewYork.

22. Marr, A. G., R. J. Harvey, and W. C. Trentini. 1966.Growth and division of Escherichia coli. J. Bacteriol.91:2388-2389.

23. Mauck, J., L. Chan, and L. Glaser. 1972. Model of cellwall growth of Bacillus megaterium. J. Bacteriol.109:373-378.

24. Mindich, L., and S. Dales. 1972. Membrane synthesis inBacillus subtilis. III. Morphological localisation of sitesof membrane synthesis. J. Cell Biol. 55:32-41.

25. Morrison, D. C., and H. J. Morowitz. 1970. Studies onmembrane synthesis in Bacillus megaterium, K. M. J.Mol. Biol. 49:441-459.

26. Ohki, M. 1972. Correlation between metabolism of phos-phatidyl glycerol and membrane synthesis in Esche-richia coli. J. Mol. Biol. 68:249-264.

27. Paulton, R. J. L. 1970. Analysis of the multiseptatepotential of Bacillus subtilis. J. Bacteriol. 104:762-767.

28. Pierucci, O., and C. Zuchowski. 1973. Non-random segre-gation of DNA strands in Escherichia coli B/r. J. Mol.Biol. 80:477-503.

29. Previc, E. P. 1970. Biochemical determination of bacte-rial morpology and the geometry of cell division. J.Theoret. Biol. 27:471-497.

30. Pritchard, R. H. 1974. On the growth and form of abacterial cell. Philos. Trans. R. Soc. London267:303-336.

31. Powell, E. 0. 1956. Growth rate and generation time ofbacteria with special reference to continuous culture. J.Gen. Microbiol. 15:492-511.

32. Ryter, A. 1971. Etude de la croissance de la membranechez Bacillus subtilis au moyen de la distribution desflagelles. Ann. Inst. Pasteur Paris. 121:271-288.

33. Ryter, A., Y. Hirota, and U. Schwarz. 1973. Process ofcellular division in Escherichia coli. Growth pattern ofEscherichia coli murein. J. Mol. Biol. 78:185-195.

34. Sargent, M. G. 1973. Synchronous cultures of Bacillussubtilis obtained by filtration with glass fiber filters. J.Bacteriol. 116:736-740.

35. Sargent, M. G. 1973. Membrane synthesis in synchronouscultures of Bacillus subtilis 168. J. Bacteriol.116:397-409.

36. Sargent, M. G. (1974). Nuclear segregation in Bacillussubtilis. Nature (London). 250:252-254.

37. Schaecter, M., 0. Maaloe, and N. 0. Kjeldgaard. 1958.Dependency on medium and temperature of cell sizeand chemical composition during balanced growth of S.typhimurium. J. Gen. Microbiol. 19:592-606.

38. Schaecter, M., J. P. Williamson, J. R. Wood, and A. L.Koch. 1962. Growth, cell and nuclear divisions in somebacteria. J. Gen. Microbiol. 29:421-434.

39. Shockman, G. D., L. Daneo-Moore, and M. L. Higgins.1974. Problems of cell wall and membrane growth,enlargment and division. Ann. N.Y. Acad. Sci.235:161-197.

40. Sud, I. J., and M. Schaecter. 1964. Dependence on thecontent of cell envelope on the growth rate of Bacillusmegaterium. J. Bacteriol. 88:1612-1617.

41. Ward, C. B., and D. A. Glaser. 1971. Correlation betweenrate of cell growth and rate of DNA synthesis inEscherichia coli B/r. Proc. Natl. Acad. Sci. U.S.A.68:1061-1064.

42. Yamaguchi, K., and H. Yoshikawa. 1973. Topography ofchromosome membrane function in Bacillus subtilis.Nature (London) New Biol. 244:204-206.

43. Zaritsky, A., and R. H. Pritchard. 1973. Changes in cellsize and shape associated with changes in the replica-tion time of the chromosome of Escherichia coli. J.Bacteriol. 114:824-837.

VOL. 123, 1975

on June 23, 2018 by guesthttp://jb.asm

.org/D

ownloaded from