On the origin of spontaneous somatic mutations and sectored plaques detected in transgenic mice

Mutation Research 373 Ž1997. 277–284

On the origin of spontaneous somatic mutations and sectored plaques detected in transgenic mice Y. Paashuis-Lew, X.B. Zhang 1, J.A. Heddle

)

Department of Biology, York UniÕersity, Toronto, M3J 1P3, Canada Received 29 November 1995; revised 6 May 1996; accepted 20 August 1996

Abstract The use of transgenic mice with bacterial genes that can be readily recovered and analysed for mutation has made it possible to measure mutant frequencies in many tissues. The mutations are detected by packaging the murine DNA into l phage and then growing these phage on a bacterial lawn under conditions such that the mutants are distinguishable from nonmutants. In the lacI mouse assay, the mutant plaques are blue whereas the nonmutant plaques are clear. The mutations detected in the lacI Big Bluee Mouse are, in principle, a mixture of mutations that arose in the mouse Žin vivo mutations., mutations that arose in the bacterium from lesions pre-existing in the murine DNA Žex vivo mutations., and mutations that arose during growth of the phage on the bacteria Žin vitro mutations.. It has been suggested that plaque morphology can be used to visually distinguish in vivo mutations Žwhich would be seen as wholly blue plaques. from ex vivo mutations Žwhich would produce blue and white sectored plaques. and in vitro mutations Žwhich would produce sectored or pin-point plaques.. We show here that this is not the case: ex vivo mutations produce plaques that are a homogeneous blue. By superinfection of bacteria with mutant and nonmutant phage and by in vitro mutagenesis, we found that blue plaques may contain large proportions of nonmutant phage. None of the mutant plaques seen after in vitro mutagenesis were sectored but most contained nonmutant phage. In addition, we show that most spontaneous mutations from the small intestine, which has a higher than normal mutant frequency, arose in vivo, since 17 of 17 mutants were homogeneous mutants. Sectored plaques must arise in some way other than by ex vivo mutation, like perhaps by the confluence of a mutant and nonmutant plaque. Keywords: Spontaneous mutation; In vivo mutation

1. Introduction Transgenic animals with rescuable genes give researchers the ability to assay for mutants arising in

) Corresponding author. Tel.: 416-736-2100, ext. 33053; Fax: 416-736-5698; E-mail: [email protected] 1 Present address: ViroMed Laboratories Inc., Minneapolis, MN, 55343-9108, USA.

vivo with an in vitro system ŽGossen et al., 1989; Burkhart et al., 1992; Provost et al., 1993.. Potentially mutagenic substances can be administered to the transgenic animal and the resulting mutations can be quantified in vitro. Stratagene has produced a C57BLr6 transgenic mouse with approximately 40 copies of a lambdarlacI shuttle vector containing the lacI repressor and lacZ a gene for mutagenesis testing in vivo ŽProvost et al., 1993.. Mutant frequencies are determined by extracting the genomic

0027-5107r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 2 7 - 5 1 0 7 Ž 9 6 . 0 0 2 1 0 - 2

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DNA, packaging the excised shuttle vectors into phage heads, infecting the SCS-8 E. coli containing the carboxy-terminus of the lacZ gene, and plating on agar containing 5-bromo-4-chloro-3-indolyl-b-Dgalactopyranoside ŽX-gal.. If a mutation occurs in the lacI repressor, transcription can occur in the lacZ a gene, and complementation with the carboxy-terminus of the lacZ protein Žwhich is constitutively produced by the bacteria. occurs. A functional b-galactosidase enzyme is formed, the X-gal is cleaved, and a blue plaque results. Mutant plaques can arise in several ways: Ž1. from in vivo mutations which arise in the animal; Ž2. from ex vivo mutations which arise from in vivo DNA damage but are fixed as a mutation in the bacterium; or Ž3. from mutations arising during phage growth in vitro in the bacterium. There are two potential plaque phenotypes that might be produced by ex vivo and in vitro mutants. The first is a sectored plaque, where one portion of the plaque is blue and the other is colourless. The second is a mosaic plaque, where the plaque is a homogeneous blue and is visually indistinguishable from in vivo mutants. Such mosaic plaques contain both mutant and nonmutant phage. This mosaicism is revealed when the plaque is cored and replated. It should be noted that the term mosaic, as it is used here, is different from that used elsewhere in the literature on transgenic mutation assays ŽProvost et al., 1993; Piegorsch et al., 1995.. While those mosaic plaques do contain both mutant and nonmutant phage, they are sectored and have been postulated to arise from ex vivo mutation. The spontaneous mutant frequency found with these transgenic assays is high in all tissues Žcf. Zhang et al., 1995 for review., which raises issues about the detectability of mutants whether induced or spontaneous, the origin of sectored plaques, and the influence of E. coli replication errors in spontaneous mutant frequencies. One of the major concerns regarding the lacI transgenic mouse assay, as well as other shuttle vector transgenic mutation assays, is the use of an inadequate time for mutation fixation after mutagenic treatment to allow the DNA to replicate at least once so that the adducts can be fixed as mutations or repaired while in the animal ŽInstruction Manual, Big Bluee Transgenic Mouse Mutagenesis

Assay System; Stratagene, 1992; Provost et al., 1993; Provost and Short, 1994.. If the adducts are not repaired in vivo, then they may be fixed in the E. coli to form ex vivo mutations. When a phage containing a mutagenic adduct is plated, one expected result is a mosaic plaque in which there are mutant and nonmutant phage present due to semiconservative replication in the bacterium. Although sectored plaques may indicate the ex vivo origin of the mutations ŽInstruction Manual, Big Bluee Transgenic Mouse Mutagenesis Assay System, 1992, Provost et al., 1993., they may be plaques that overlap sufficiently so that they appear round. In other systems, sectored or mottled phenotypes are not surprising. In tissues where cells are fixed in a specific position, mosaics or patchy tissues with more than one phenotype resulting from mutagen treatment during germinal stages of development, have been well documented ŽFavor et al., 1990; Mohrenweiser and Zingg, 1995.. In mosaic plaques, however, an unsectored morphology may be expected because in a typical burst, where the phage are released from the bacterium, the phage particles are thoroughly intermixed. Indeed, mosaic plaques described in the literature have been unsectored, although mottled in appearance ŽHershey and Rotman, 1948; Loveless and Hampton, 1969; Smith, 1976a,b; Cheng and Smith, 1989.. Cheng and Smith Ž1989. also noted that two different homogeneous plaque morphologies could prove to be mosaic plaques when subsequently analysed. Some plaques contained 100% of a phage genotype, while others contained a mixture of two phage genotypes. First, to determine what plaque morphologies could arise from lesions in the lambdarlacI shuttle vector DNA, lesions were induced in the DNA by treating phage with a mutagen. Second, to determine what percent mutant phage in a mosaic plaque could be detected as blue, mosaics were created by superinfecting the SCS-8 bacteria with a mixture of mutant and nonmutant phage. The mosaicism and sectoring were then quantified in the plaques resulting from the superinfection or mutagen treatment by replating. To see whether mutants arise in vivo or in vitro in untreated animals, DNA from lacI mice, used as untreated controls, was packaged. Isolated mutant plaques were tested for mosaicism, which would be indicative of an in vitro mutant origin.

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2. Materials and methods 2.1. l phage and bacteria All lacI l phage were obtained from packaged phage excised from Big Bluee mice as recommended by Stratagene, or nonmutant lacI plaques replated from an original excision. Plaques were cored from the agar plates, and stored in 900 ml SM buffer with 100 ml chloroform at 48C. The bacteria were the SCS-8 E. coli strain ŽStratagene. grown from an overnight culture in NZY media and 0.2% maltose, and resuspended in 10 mM magnesium sulphate to a concentration of A 600 s 0.5. After the bacteria had been infected by the l phage, they were plated with X-gal ŽAmerican Biorganics Inc., 1.5 mgrml. in NZY top agar and incubated at 378C for 14–16 h as recommended by Stratagene. 2.2. Superinfection of bacteria A mutant phage stock with 1 = 10 5 plaque forming units Žpfu.rml and a nonmutant phage stock with 1.1 = 10 5 pfurml were used. The E. coli were grown from an overnight culture, the cells spun down, the supernatant removed and resuspended in 10 mM magnesium sulphate, and the cells diluted to 2 = 10 3 per ml Žmultiplicity of infection ŽMOI. s 100. and 2 = 10 4 per ml ŽMOI s 10.. 100 ml of each phage stock Ža mutant and a nonmutant. were adsorbed on ice with 100 ml of one of the E. coli dilutions for 15 min. 50 ml of ice-cold 100% ethanol was added and the phagerbacteria mixture which was then incubated in a 378C waterbath for 10 min. This was then mixed with 1.5 ml of a higher concentration E. coli, plated immediately with X-gal in the NZY top agar on 23 cm2 screening plates, and incubated overnight at 378C. Plaques intended for replating were cored and stored as above. One Ž1. ml to 10 ml of phage stock were screened on 10 cm2 plates with X-gal in the top agar. 2.3. ENU treatment of nonmutant l phage A 200 mM stock of 1-ethyl-1-nitrosourea ŽENU. was prepared by dissolving the ENU in 10% of final

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volume dimethyl sulphoxide and adding 100 mM potassium phosphate buffer ŽpH 7.. Approximately 20–25 nonmutant plaques Žapproximately 2 = 10 6 pfu per ml. were cored and suspended together in 1.0 ml of the same phosphate buffer, supplemented with 2% gelatine and 10% chloroform. 10 ml aliquots from this mixture were also used for the controls described below. As the protocol was repeated several times, it was necessary to use several of these concentrated phage mixtures. Equal volumes of ENU and phage were mixed Žfinal concentration 100 mM ENU., and incubated 15 min at 378C. Sodium hydroxide was added to raise the pH to 8 in order to inactivate the ENU, the mixture incubated at 378C for 15 minutes, and the pH was then lowered to 7 with hydrochloric acid to ensure phage and bacterial survival. The treated phage were mixed with 2 ml of E. coli, plated with X-gal in the NZY agar on 23 cm2 screening plates, and incubated at 378C for 16 h. Controls consisted of plates with an aliquot of untreated phage, and plates where the ENU treatment and inactivation was done without the phage and an aliquot of untreated phage added to the mixture just prior to plating. The protocol was repeated several times until sufficient mutant plaques were obtained for analysis. Pin point mutants, where there was a small point of blue at the edge of a nonmutant plaque, were not replated. Mutant plaques were assayed as described above. 2.4. Packaging lacI DNA The DNA used was previously extracted from the small intestine of mice that were either the F1 of SWR = hemizygous Big Bluee mice or the F1 of SWR = homozygous Big Bluee mice, as described elsewhere ŽTao et al., 1993; Shaver-Walker et al., 1995; Zhang et al., 1995, 1996.. Transpack ŽStratagene. packaging extracts were used to package the DNA according to the manufacturer’s recommendations. To ensure fewer than 5000 phage on each 23 cm2 assay tray, several trays were used Žin some cases. for each packaging reaction. Mutant plaques that were at least 1 mm away from the surrounding plaques were cored and stored in 400 ml of SM buffer and 100 ml of chloroform. They were then assayed for mosaicism as above.

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3. Results 3.1. Detection of mutant plaques Since the detectability of a mutation probably depends upon the intensity of its colour, the Big Bluee plaque colour controls of lacI mutants ŽStratagene. were tested on our assay plates. The darkest lacI mutant phage, CM3, was lighter than our darkest mutants, and the lightest, CM0, was darker than our lightest detectable mutants, so we are detecting at least the full range used as standards. Some lacI mutant phage seen in these experiments, including ENU-treated phage, were very light in colour, and while a number were true light coloured mutants, others were mostly nonmutant. For example, for ENU-treated phage, of 19 pale blue plaques 15 were 50% mutant or less, 2 were greater than 85%, and 2 were genuine pale mutants. SCS-8 E. coli were superinfected with equal numbers of a mutant darker than the CM3 colour control and a nonmutant lacI phage, to determine the percent mutant phage required to see the plaque as blue. This test was done to see how many rounds of phage DNA replication were at risk for the production of a visually detectable mutant plaque. By determining the percent mutant phage in both colourless and blue plaques as a result of the superinfection, we could determine the number of rounds of phage DNA replication that were at risk of being detected as a mutant. For instance, if the percent mutant was ; 50% in a blue plaque, then a mutant arising during the first round of phage DNA replication could be detected as a mutant plaque. If the percent mutant was ; 25% in a blue plaque, the

Fig. 1. Percent mutant phage observed in plaques replated from bacteria superinfected with mutant and nonmutant phage. 40 blue plaques and 40 clear plaques were analysed. Plaques were ranked by percent mutant phage in increasing order for clear plaques and decreasing order for blue plaques.

second round of phage DNA replication was also at risk for being counted as a mutant. In order to superinfect the bacteria, several l phage characteristics were used: DNA injection is extremely slow at 08C and instantaneous at 378C; the phage are inactivated and committed to DNA injection in the presence of a solvent like ethanol; and phage movement and attachment can occur at 08C ŽKatsura, 1983.. 40 blue plaques and 40 colourless plaques were analysed ŽFig. 1.. While there were a few ‘outliers’ where the percent mutant was extremely low in blue plaques and extremely high in colourless plaques, generally the plaque would not be seen as blue if the percent mutant phage was much below 40%. This indicates that few ex vivo or in vitro mutations should be detectable unless they arose during the first round of DNA replication. Phage were found to move through the agar over time as shown when agar plugs various distances from plaques were cored, suspended in 400 ml SM buffer and 100 ml chloroform, and were assayed using 100 ml of this stock. In plaques plated within 24 h or less, phage movement was limited to - 1 mm from the plaque. After 1 week, up to 400 pfurml occurred at - 3 mm from the plaque and only a few pfu’s at ) 3 mm. After a month, phage Ž20 pfurml. could be recovered at distances of 4 mm or more. 3.2. Analysis of sectored and mosaic plaques When blue and colourless plaques from the superinfection, and mutant plaques from the ENU experiment were cored and replated, sectored plaques were observed on many of the plaque analysis plates, showing that the original plaques were mosaic. In addition, sectored plaques were also observed on two titre plates during these experiments using a mixture of mutant and nonmutant phage. These plates had mutant and nonmutant phage mixed together, were adsorbed at a low MOI, and plated on 23 cm2 assay trays. 5 out of 650 plaques and 41 out of 2250 plaques from these assay trays were sectored. In an attempt to repeat this phenomenon, a random mutant plaque and a nonmutant plaque were each cored and separately suspended in 1 ml SM buffer Ž10% chloroform.. Equal volumes of the phage were adsorbed into 2 ml bacteria Ž10 8 cells. and plated on 23 cm2

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Table 1 Mutant frequencies of ENU treated lacI lambda phage Treatment

Mutant frequency

Plaques assayed

Žper 100 000 plaques. Untreated control Control Žphage added after ENU treatment. ENU-treated phage Ž100 mM.

Plaques observed Unsectored

Sectored

4.7 6.2

127 000 80 000

6 4

0 1

48.1

237 000

114

0

assay trays. Sectored plaques were observed as follows: 0 out of 25 plaques, 2 out of 175 plaques, and 13 out of 1100 plaques. While the absolute number of sectored plaques increased as plating density increased, the frequency of sectored plaque appearance was essentially the same for all 5 assay trays discussed here. These phage were not treated with any mutagenic substance. Some mutagens such as ENU can produce relatively high mutant frequencies ŽProvost and Short, 1994; Tao et al., 1993; Guttenplan, 1990.. With the large numbers of mutant plaques observed on these assay trays, the occurrence of sectored plaques, while at a much lower frequency, could possibly be due to the confluence of a mutant and nonmutant plaque. The micro-colonies of E. coli at the edge of sectored plaques Ždescribed above. were examined under a dissection microscope. These microcolonies are imbedded evenly throughout the top agar and are the result of colony formation from the original E. coli cell deposited when the agar was poured. At the edge of mutant plaques, the microcolonies are all stained blue, indicating that the bacteria are infected with mutant phage but not lysed. Based on this observation, it was assumed that the microcolonies at the edge of nonmutant plaques were also infected with phage but not lysed. In the clear portion of the sectored plaque the micro-colonies were exclusively a creamy white, while the micro-colonies were exclusively blue in the other part. There were also slight indentations formed by micro-colonies at the colour change border of some plaques. In other more oval bluerclear plaques, the indentation was more pronounced, possibly indicating that there are 2 centres or 2 original phage-infected bacterial cells in close proximity. Indeed, with all round sectored and oval plaques combined, they all could be because of

two overlapping plaques where one was clear and the other blue. Nine of the sectored plaques were analysed and showed that the percent mutant expected occurred 67% of the time based on an estimate made by visual inspection of the plaque. For instance, if the plaque appeared to be ; 75% blue then the percent mutant would be near 75%. Since sectored plaques have been attributed to ex vivo mutations fixed in bacteria ŽProvost et al., 1993., stocks of nonmutant phage were treated with ENU to create lacI phage with DNA adducts. The DNA adducts could then be fixed in the bacteria and scored for sectored and mosaic plaques. Table 1 shows the mutant frequencies observed in this experiment. All but 5 of the 60 replated mutant plaques were mosaic as shown in Fig. 2. Since the treatment increased the mutant frequency about 10-fold, about 1r10th of the plaques could represent pre-existing mutants which should be homogeneous or replication blocks on the nonmutant strand of DNA. Thus all or almost all of the ex vivo mutants were mosaic. The only sectored plaque observed was in a control assay tray. Phage inactivation ranged from 50% to 80%, depending on the assay tray analysed.

Fig. 2. Replated plaques from 60 blue plaques analyzed after ENU treatment of nonmutant lacIrlambda phage in vitro.

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Since in vivo and ex vivo mutants could not be distinguished visually from one another, it was important to know whether mosaic plaques were present on the mutant assay screening plates. The presence of mosaic plaques would be indicative of insufficient time to allow for the repair of DNA adducts or mutant fixation, leading to ex vivo or E. coli derived mutants. In vivo lacI mutants from freshly packaged DNA extracted from mice treated with ENU Ž250 mgrkg. 1 week prior to sacrifice were cored and analysed for mosaics. Fifteen mutants came from the colon and 18 from the small intestine. All but 7 were ) 90% mutant and all but 3 were ) 80% mutant and none were sectored. The remaining 3 plaques were - 50% mutant and all originated in the colon. 3.3. Analysis of mutants arising on the assay trays of DNA packaged from untreated lacI mice Twenty-six DNA samples from untreated mice were packaged for a total of 643 000 plaques. The phage yield varied from 126 000 plaques Žcumulative. from one DNA sample to 240 plaques from another. Animal age ranged from 19 weeks to 68 weeks at the time of sacrifice for an average age of 40 weeks. A total of 47 mutants were observed, including one sectored plaque, for an average mutant frequency of 7.3 = 10y5 mutationsrplaque. Mutant frequencies varied from 0 to 48 = 10 y 5 mutationsrplaque. Of the 47 mutants observed, 17 were isolated sufficiently to ensure minimal crosscontamination from nearby plaques. Seven were 100% mutant, 3 were 99% mutant, 4 were 98% mutant, 1 was 97% mutant, and 2 were 96% mutant. Since all of the isolated mutants analysed were greater than 95% mutant, the majority of spontaneous mutants arose in vivo. The sectored plaque appeared to be about 75% mutant, and when analysed it was found to be 70% mutant, as was expected based on the results reported above.

4. Discussion The contribution to the observed mutant frequencies attributable to ex vivo and in vitro mutations depends upon the number of DNA replications at

risk. We have estimated this by means of two techniques: superinfection with mutant and nonmutant phage and by in vitro mutation. Superinfection showed that phenotypically mutant plaques contained between 10–100% mutants, i.e., as many as 90% nonmutants in one case. More than 85% of the phenotypically mutant plaques contained more mutant than nonmutant phage. After in vitro mutagenesis, the phenotypically mutant plaques contained 10– 100% mutant phage. The completely mutant plaques probably represent pre-existing mutants. The range of mutant: nonmutant mixtures observed was similar to that observed after superinfection, but the majority of the in vitro mutant plaques were less than 50% mutant. This probably reflects the presence of a nonmutant strand in the phage carrying a DNA adduct. Based on these results, it appears that the vast majority of ex vivo and in vitro mutants would only be detectable if fixed in the first 3 rounds of DNA replication. Douglas et al. Ž1995. used a lacZ transgenic mouse under similar assay conditions and observed no sectored morphologies in their plaques after mutagen treatment. The seminiferous tubules and vas deferens were assayed as little as 5 days after treatment when most of the mutants would be expected to arise from unrepaired DNA lesions in nondividing, nonmetabolising spermatozoa. Since distinguishing mutants from nonmutants is somewhat difficult in the nonselective lacZ system, it may be that mosaics are particularly difficult to identify in this system. The lack of mosaics claimed for the selective version of the lacZ transgenic mutation assay is to be expected, since the presence of nonmutant phage in a bacterium under selective conditions could prevent the mutants from surviving. Adequate time for DNA replication and DNA adduct repair or mutant fixation after mutagenic treatments for specific tissues to be assayed might not eliminate the problem of ex vivo mutations ŽProvost and Short, 1994; Provost et al., 1993., because there may be lesions that do not matter to the mouse but do to a bacterium. Tissue turnover is also important if nondividing cells are resistant to mutation. Since it is not always known what the stem cell turnover time for a specific tissue is, this may be established by sampling the tissue at various times after mutagen treatment. Analysing the mutants for

Y. Paashuis-Lew et al.r Mutation Research 373 (1997) 277–284

mosaicism would help to establish the minimum time necessary to allow for DNA replication, the repair of DNA adducts and mutant fixation for that particular tissue. When very few or no mosaics are present, the tissue could be assumed to have repaired any lesions present that could result in ex vivo mutations, and thus that the observed mutants arose in vivo. The phage colour indicator kit is helpful in ensuring that all mutants are being detected. If plaques are to be picked for analysis, it should be done immediately to avoid contamination from other plaques. Phage mobility in the agar will not affect the ability to sequence mutants for the spectra of mutations produced spontaneously or by mutagens, unless there is another mutant nearby. In any case, plaques should be purified by replating prior to lacI sequence analysis. Ex vivo mutants could not be detected by visual analysis in our laboratory because the appearance of the ex vivo mutants was not different from in vivo mutants. No sectored plaques resulted from the presence of a DNA adduct after phage were treated with ENU, but almost all plaques were mosaic in spite of their appearance. In our laboratory, under our assay conditions, sectored plaques are rarely observed. Only by replating the plaque could we differentiate a mosaic from one that is not. Sectored plaques could possibly arise from two E. coli, each infected with a single phage Žwhere one is mutant and the other is not. coming in close proximity such that the resultant plaques overlap, producing what appears to be a single plaque. There may be factors involved in the assay that affect the frequency of sectored plaques, since our experience is that these occur non-randomly. Nevertheless, we feel that such sectored plaques are real mutants and should be counted. When analysing spontaneous mutant frequencies, allowing sufficient time for the repair of DNA adducts is not possible, but ex vivo and in vitro mutations are a factor. Spontaneous mutants are rare ŽLee et al., 1994; Ono et al., 1995. compared to the number produced by mutagens and it is of interest to know what proportion arose in vivo. We observed no mosaic plaques, which would be indicative of in vitro mutants when we packaged DNA from untreated animals and replated isolated mutant plaques. While the number of mutants analysed was not large,

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if in vitro mutants were a significant factor in contributing to spontaneous mutant frequencies, we would have observed at least some mosaic plaques. Zhang et al. Ž1995. cored and replated 18 nonmutant plaques in order to estimate the in vitro mutant frequency. Since some of the mutant phage found in the nonmutant plaques may be clonal, it is necessary to calculate the mutation rate in vitro from the plaques without mutants. This calculation as presented in our previous paper was incorrect. The correct calculation follows. If r is the mutation raterreplication, the probability of no mutant is 1 y r. In the formation of a plaque of n phage, there are at least n y 3 replications at which a mutation can arise. Since n 4 3, the number of replications at risk is essentially equal to the number of phage present. Thus, the probability of no mutants is Ž1 y r . n. Setting n at the observed number of plaques and varying r such that the observed value of 11 of 18 plaques had no mutants gives a value of r s 1.6 = 10y5 mutationsrreplication. This value is much closer to the observed spontaneous frequency than previously calculated. Evidently this calculation over estimates the mutation rate and thus the contribution of in vitro mutation, since the actual proportion of mosaic spontaneous plaques is low. This is probably because there are actually many ineffective replications during phage reproduction. Our results show that most spontaneous mutations observed arose in vivo.

Acknowledgements This research was supported by the National Cancer Institute of Canada with funds from the Canadian Cancer Society and by the Natural Sciences and Engineering Research Council of Canada. We thank Cesare Urlando for his help with the techniques involved and David M. Logan for his advice. We thank John Cairns for pointing out the error in our previous calculation.

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