INT. J . RADIAT. BIOL ., 1995, VOL . 67, NO. 4, 453-460

The fi component of human cell survival curves and itsrelationship with split-dose recovery

M. G . A. ALSBEIHt+§, B. FERTIL*, C. BADIEt and E. P. MALAISEt

(Received 13 July 1994 ; revision received 28 .November 1994; accepted 30 .November 1994)

Abstract . In principle, a and /i can be obtained from single-dosesurvival curves using standard linear-quadratic fitting ; however, aand fi being interdependent, it is difficult to evaluate them togetherwith good precision . On the assumption that full recovery from asplit-dose treatment gives a result that is the product of thesingle-dose surviving fraction, it has been suggested that themeasurement of split-dose recovery should provide a method tomeasure f alone using the formula : /iRR = lnRR/2d2 . Most of thestudies published to date have been carried out on cancer cell linesor transformed normal cells. We have systematically tested theabove proposal on two normal human fibroblast cell lines (HF 19 and1BR3) in two different situations : growing cells, and plateau-phasecells. Two different protocols were used to assess both the potentialinfluence of a priming dose on the surviving cells and the extent ofthe split-dose recovery . The survival curves generated after differentpriming doses did not show any significant change in comparisonwith those achieved without previous irradiation . In addition, thesplit-dose survival was not different from the square of thecorresponding single-dose survival (model free) . In these conditions,#RR's obtained by a linear regression of the recovery ratio data werevery similar to the fl's obtained by single doses . However, acurvilinear regression (with a very small negative term at high doses)appears to be more appropriate for cells in plateau phase . This hasthe result that, as the dose increases, the cell survival curves tend tobecome less bending than would be expected from the linear-quadratic model; however, the linear-quadratic fitting is still areasonable characterization of the radiation response since the invitro colony formation method does not allow measurement ofsurvival < 10-4 .

1. Introduction

When a single dose of radiation is replaced with twofractions of this single dose, it is possible to calculate therecovery ratio (RR) by dividing the surviving fractionfrom a split dose by the survival after a single dose .Several studies have suggested that the RR measuredwhen repair is complete may be a radiotherapy

§Author for correspondence at Institut Gustave-Roussy .tLaboratoire de Radiobiologie Cellulaire, Institut Gustave-

Roussy, 94805 Villejuif, France.+Energy Research Group, Damascus University, PO Box 9707,

Damascus, Syria .*Inserm U .66, 91 Boulevard de 1'Hopital, 75634 Paris, France.

0955-3002/95 $10 .00 © 1995 Taylor & Francis Ltd .

resistance factor (Courdi et al. 1992, Pekkola-Heino et al.1992, Taghian et al. 1993). The single-hit, multitargetmodel predicts that RR increases to reach a plateau,depending on the single-dose radiation, with theplateau corresponding to the start of the exponentialpart of the survival curve . For this model, the maximumRR corresponds to the extrapolation number (Elkindand Sutton 1960) .

The linear-quadratic (LQ) fitting of the survivalcurve was developed from two totally different ap-proaches; microdosimetry (Kellerer and Rossi 1972),and molecular biology (Chadwick and Leenhouts1973). Although the hypotheses that led to the LQmodel have not been validated, LQ fitting does haveconsiderable practical importance as it describes thesurvival curves of human cells better than the modelsbased on target theory (Fertil et al. 1980, 1994). Morerecently, this model has provided support to interpretboth sublethal and potentially lethal damage in termsof DNA double-strand breaks (Barendsen 1994). Inaddition, the initial part of the survival curve isaccurately described by the LQmodel, and this initialpart is known to be the region that characterizes theintrinsic radiosensitivity of a cell line (Fertil and Malaise1985). It is also correlated with the tumour response toradiotherapy (Fertil and Malaise 1981, Deacon et al.1984). Unlike the single-hit, multitarget model thatdescribes a curvature in only the initial segment of thesurvival curve, the LQ model describes the survivalcurve as a continuously bending curve . The theorypredicts that the split-dose recovery concerns only thequadratic component of the survival curve (Descha-vanne et al. 1980, Thames 1985) . Thus, the LQ modelpredicts that RR increases indefinitely as a function ofdose according to the formula :

1nRR = 2#d',

where d is the dose per fraction in split treatments .Calculation of the parameters ga and gfJ from

the LQ fit of a single-dose survival curve is

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handicapped by the fact that the value of each of the

2.2. Suroiaal assaysparameters depends on that of the other (Steel et al.1987). Peacock et al. (1988) suggested that /3 could becalculated directly, and thus with greater precision byusing the method of split doses . Provided that RRdepends only on the component $ and as long as repairis complete by the time of the second irradiaiton, andthat radiosensitivity has not changed since the first dose,/3 can be measured using the relationship :

#RR =1nRR/2d 2 .

Peacock et al. (1992) used this method to measure /3 forseveral cell lines and concluded that it varied from onecell line to another . Most of the experiments designedto measure /3 using the split-dose method wereperformed on exponentially growing cancer cell lines ortransformed normal cells (McMillan et al. 1989, Peacocket al. 1989, Holmes et al. 1990, Yang et al. 1990, 1991,McMillan et al. 1992). Van Der Maazen et al. (1993) arethe only group who, to our knowledge, has applied thisconcept of the recovery ratio linked to /3 to untrans-formed normal (glial) cells. In log-phase populations,the survival curve is known to reflect a heterogeneouscell cycle-related intrinsic radiosensitivity and hence thefitting of such curves has suggested the existence of atleast two /3 and two a components (Skarsgaard et al.1991, Skwarchuk. et al. 1993). Therefore, fitting ofsurvival curves for growing cells with a two-parametermodel provides rather imprecise values of a and /3 . Wehave studied /3 by the split-dose method using untrans-formed human fibroblast cell lines . We selected two celllines having different fl's for irradiated, exponentiallygrowing cells. The experiments were carried out onplateau-phase cells and on exponentially growing cells .

2. Materials and methods

2 . 1 . Cell lines

Two cell lines of untransformed fibroblasts, HF19and 1 BR3, were used . Neither cell line is associated withany known disease . HF19 cells were derived from afoetal lung (Cox et al. 1977) and 1BR3 cells originatedfrom a healthy adult donor (Arlett et al. 1988) . Both celllines were kept in monolayer culture in MEM (Earle'ssalts) supplemented with 10% foetal calf serum (FCS) ina 5% C02/95% air atmosphere . HF19 cells were usedfrom passages 16 to 24, and 1 BR3 from passages 10 to22. The plating efficiency for HF19 was 20-35% forplateau-phase cells and 12-21 o/ for growing cells ; theequivalent efficiencies for 1BR3 were 30-44 and17-35%. Suspensions of cells were prepared bytrypsinization (0-1% trypsin, 0 . 04% EDTA in acalcium-free salt solution) .

Three protocols were used: the usual single-dosesurvival curves, survival curves preceded by differentpriming doses, and multiple split doses (1 + 1, 2 + 2 Gy,etc) . The interval between two successive doses in thelast two protocols was selected to allow completesplit-dose recovery and to avoid any proliferation ofsurviving cells . The kinetics of split dose recovery forexponentially growing cells was determined with two4-Gy doses separated by an interval of 0-12 h . Thesurvival level for both cell lines increased up to 6 h, andno significant change occurred between 6 and 12 h(Figure 1). An interval of 12 h was therefore used for thesplit-dose protocol for growing cells, while the intervalwas 24 h for plateau-phase cells . The experiments ongrowing cells were performed on cells taken from agrowing cell stock culture . The first irradiation wasgiven 12 h after plating out. The plateau-phase cellswere obtained by plating out 5 X 10 5 cells in 25-cm2plastic flasks ; the cells were confluent 3 days later andremained in plateau phase for 7 more days beforeirradiation. The irradiated cells were kept in plateauphase for a further 24 h to allow a full delayed platingrecovery. Feeder cells at a concentration of 600cells cm - 2 were used for both the growing-phase cellsand plateau-phase cells of both lines . The maximumnumber of cells plated out per flask (feeder cells plus thecells whose radiosensitivity was to be tested) neverexceeded 2500 cells cm -2 . The irradiated cells werethen kept in a medium supplemented with 20% FCSand incubated for 2-3, weeks . This time is long enoughfor all the surviving cells to give rise to colonies of at least50 cells .

2.4. Irradiation

Cells were irradiated at room temperature with a137Cs beam, giving a dose-rate of 1 .8 Gy/min .

HF19 (exponential growing phase) 1BR3 (exponential growing phase)

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Figure 1 . Survival as a function of incubation time (37 °C) betweentwo doses of 4 Gy . Each data point represents the mean ofthe data from three-to-five replicate experiments . Barsrepresent the 95% confidence limits around the mean .

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2.5 . Curve fitting

The non-linear, curve-fitting platform ofJMP statis-tical software (SAS, INDt Inc .) was used to fit all data.The best fit was obtained by minimizing a custom lossfunction by the Newton-Raphson method. Whencomparing the effect of split dose and of the correspond-ing single dose, it was essential to check beforehand thatthe second dose survival curve did not differ from thefirst . If this is so, the effect of the second fraction of thesplit dose will be the same as that of the first . Under theseconditions, the survival after the split doses should beequal to the square of the survival after one of thefractions ; this last survival level was already determinedby the single-dose survival curves . The overall relation-ship between the survival after split doses and the squareof the survival after one fraction should be a linearfunction with a slope of 1 . The advantage of thisapproach is that it involves no prediction as to the shapeof the survival curve itself (model free). We also analysedall the data (single-dose curves, split-dose survival, andsurvival curves after different priming doses, pooled alltogether) using the LQmodel. A four-parameter modelwas developed. In this, the first curve (C i) is character-ized by the parameters of a l and /31, the second curveby the parameters a2 and /32 . With Do being the primingdose, the formula is :

S= exp (- a1Do - /3 1Do 2 ) exp (- a2D -12D2 ) .This approach allows all the data to be used to obtainthe best fit for curve C l , and thus obtain the best originfor curve . C 2. If C 2 = Cl , then a2 = a l and /32 = /3 i .Lastly, the relationship between RR and dose wasanalysed using two different formulae, one linear andone non-linear :

InRR = 2/d21nRR = 2/3d 2 - Ed' .

The quality of the fitting was assessed by plotting theresidual error ( = fitted InRR - experimental 1nRR)versus the fitted InRR.

3. Results

The survival curves for the two cell lines were fairlysimilar (Figure 2). HF19 cells appeared to be a littlemore radiosensitive than 1BR3 cells when tested asplateau-phase cells with immediate plating, or asexponentially growing cells (Table 1) . The situation wasreversed when the irradiated plateau-phase cellswere plated out 24 h later; in this case the HF19cells were a little less radiosensitive than the 1 BR3cells. The mean inactivation dose (D), which isequal to the area under the survival curve when

l3 component and split-dose recoveryW19 (plot- phau) I BR3 (platau phase)

455

Figure 2. Survival curves of the two cell lines in three differentsituations (growing cells, plateau phase cells with immediateor with delayed plating) . Solid lines represent the LQfittingto the data . Symbols show individual data points of fiveindependent experiments .

the latter is plotted arithmetically, is known to bean appropriate parameter for describing intrinsicradiosensitivity of human cell lines and for comparingdifferent cell lines (Fertil et al. 1984, Malaise et al. 1989) .The delayed plating recovery, as indicated by the Dratios (Fertil et al. 1988), was higher for HF19 (2 . 02) thanfor 1 BR3 cells (1 .65). Analysis of the survival curves withthe LQ model showed that the exponentially growingHF19 cells had a smaller /3 than did the 1BR3 cells(Table 1) .

The three experimental protocols described abovewere used in a single experimental design for atotal of five replicate experiments . First, the split-dose survival rates were compared with the squaresof the single-dose survival rates . They showed alinear relationship with a slope close to 1 for bothgrowing and plateau-phase cells of both cell lines(Figure 3) . Second, the single-dose survival ratesand those obtained after an initial irradiation werecompared using two priming doses, 2 and 4 Gyfor growing-phase cells, and 2 and 6 Gy for plateau-phase cells . The radiosensitivity of the cells irradiatedfor the first time and those irradiated after a primingdose were essentially the same, both for the twocell lines and for cells in growing and plateau phases(Table 1) . Third, all the results obtained by comparingthe effect of split and single doses were used to examinethe correlation between InRR and 2d 2 (Figures 4-6) . We

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(Single dose surviving traction)'

HF19 (exponential growing Plume)

also evaluated the quality of the regression by compar-ing the residual 1nRR to the fitted 1nRR. The linearregression was satisfactory for exponentially growingHF19 and 1BR3 cells (Figure 4) . Interestingly, thelinear regression remained satisfacory up to a dose of10 Gy for single doses, i .e. doses corresponding to asurvival of about 3-4 X 10-4

. The linear regression fitwas also used for plateau-phase cells given singledoses up to 14 Gy, corresponding to survival ratesof 1-4 X 10-4

. This linear regression may appearto be satisfactory, especially for 1BR3 cells (Figure 5),but, in fact, a curvilinear regression gives a betterfit, especially for the HF19 cells (Figure 6) . Last, #RR'swere calculated using the relationship InRR = 2/3d 2 .

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Figure 3 . Relationship between the split-dose survivingfractions and the square of the single dosesurviving fractions (solid lines) ; this single dosecorresponds to one fraction of the split-dose .Dotted lines represent a one-to-one relationship .

gfiR did not differ significantly from /3 obtained forsingle doses for either of the cell lines, in growing orplateau phase (Table 2) .

4. Discussion

The intrinsic radiosensitivity of the two fibroblast celllines is very like that obtained previously for these cells .First, the intrinsic radiosensitivity of exponentiallygrowing cells is similar to that of plateau-phase cells withimmediate plating out. Second, delayed plating resultsin a much greater survival, and it is a that is reduced(Malaise et al. 1989). Last, the size of the delayed plating

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Figure 4. Relationship between lnRR and 2d 2 (upper) forexponentially growing cells of the two cell lines . Solidlines represent the linear regression of the data . Thequality of the fitting was assessed by studying the residualerror ( = fitted 1nRR - experimental lnRR) as a functionof the fitted InRR (lower) . Symbols show individual datapoints from five independent experiments .

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recovery is cell line dependent and is higher for HF 19than for 1 BR3 cells .

Both methods used to compare the radiosensitivityto an initial dose and that to a second dose led to thesame conclusion : SF for a given dose does not vary,whether or not the cells are irradiated 12 or 24 hpreviously . This holds for both cell lines in eithergrowing or plateau phase (Table 1) . However, /32tended to increase for 1 BR3 cells in growing phase, butthis was offset by a smaller a2 resulting in similar SF2and D. In addition, the split-dose survival did not differsignificantly from the square of the singledose survival (Figure 3) . This lack of difference inradiosensitivity may initially appear paradoxical, but isexplained by the interdependence of a and fl, as wasdescribed by Steel et al. (1989) . The comparison of thesurvival levels for split-doses to the square of thesingle-dose survival levels suggest that the results are notbiased by using a statistical model to analyse the survivalcurves . This prerequisite is essential for the remainderof the analyses .

Analysis of the relationship between InRR and 2d2 forgrowing cells strongly suggests that this parameterincreases indefinitely over the range of doses studied .This seems to be an important conclusion if wetake into account the fact that the correspondingsurvival curve spans almost 4 decades . This constitutesa major reason for using the LQ fit to analyse thesurvival curves for human fibroblast cell lines . This isparticularly important, as it is often believed thatanalysis of this type of curve by a multi-target expres-sion (n, Do) would be just as valid because theshoulder is small, and thus we could say that thefibroblast survival curves are to all intents and purposeslike an exponential preceded by a small shoulder .

M. G. A. Alsbeih et al.

so 100

3

Figure 5 . Relationship between InRR and 2d2 (upper) forplateau-phase cells of the two cell lines . Solid linesrepresent the linear regression of the data . The qualityof the fitting was assessed by studying the residual error(= fitted InRR - experimental 1nRR) as a function of thefitted InRR (lower) . Symbols show individual data pointsfrom five independent experiments .

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Detailed analysis of these curves shows that thecurvature really continues right up to the fourthdecade, as already suggested by analysis of single-dosecurves (Figure 2) . It therefore appears that /3 may becalculated by the method advocated by Peacock et al .(1988) under these satisfactory conditions for growingcells, provided it has been previously shown that apriming dose does not change the intrinsic radiosensi-tivity. JI obtained by the single-dose method do notdiffer from those obtained by the split-dose method,given the size of the confidence intervals (Table 2) .These results agree well with those of Peacock et al .(1992) for cells of intermediate or low sensitivity . Thesimilar confidence intervals are not, however, anindication that the split dose method gives a moreprecise f .

Linear regression gives /3RR's for plateau-phasecells that are very similar to those obtained for singledoses (Table 2) . This should be interpreted as yetanother confirmation of Peacock's hypothesis, thistime under conditions that exclude any bias dueto a cell cycle-related phenomenon . The curvilinearregression does not fundamentally change the aboveconclusion, because an average /3 is calculated fromall the values for either split doses or single doses .However, a more detailed analysis of the split-doserecovery data suggests that the curvature is greater(and thus #RR is higher) for the initial part of the survivalcurve. Thus, the curvilinear regression gives an initial#RR that is higher than that obtained by a linearregression for the two cell lines (Table 2) . The verysmall negative term results at higher doses in a smaller/3RR, suggesting that the curvature gradually gets smallertowards the distal part of the curve . This is similar tothe conclusion of Fertil et al. (1994), who suggested that

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In conclusion, the results indicate that the LQ fitprovides a satisfactory description of the survivalcurves down to a survival level of almost 10-4 .They confirm the proposal of Peacock et al. (1988),that f3 can be calculated independently of a usingthe split-dose method, for both exponentially growingand plateau-phase cells . However, for the twocell lines described here, analysis of survival curvesfor plateau-phase cells with a single fl appears tobe a compromise ; it is probably a satisfactory com-promise, nevertheless, since the technique doesnot allow measurement of survival < 10 -4. It shouldbe noted that this method would not be applicablewhen radiosensitivity is modified after a primingdose, as has been sometimes reported to be the case(Lehnert et al. 1986, Ngo et al. 1986, Alsbeih et al.unpublished data) .

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Figure 6 . Data from figure 5 fitted by a curvilinear regression .

Acknowledgements

We wish to thank Dr Colin Arlett for generouslyproviding the human fibroblast cell line 1BR3 . Thiswork was supported by the Institut National de la Santeet de la Recherche Medicale, la Ligue NationaleFrancaise Contre le Cancer (Comite des Hauts-deSeine) and by the Energy Research Group of theUniversity of Damascus .

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459

Table 2 . fl's (Gy-2 ) obtained from the single-dose survival curve and from the split-dose experiments

I'RR

flee

included in the formulalinear regression

of the curvilinear regression

•

0

0-031

0-038(2d2) - 1 .045 X 10-4 (2d 2)2(0 .029 - 0.033)

(0.034 - 0 .042)0-034

(0 .030 - 0-038)

0.028

0 .037(2d 2) - 1 . 119 X 10 -4 (2d2)2(0 .026 - 0 .030)

(0 .029 - 0 .044)0.041

(0-038 - 0 .045)

Residuals vs. FittedA

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00 00

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3

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