Gene Transfer by Means of Cell Fusion

J. Cell Sci. 25, 17-37 (i977) 17 Printed in Great Britain

GENE TRANSFER BY MEANS OF CELL FUSION

I. STATISTICAL MAPPING OF THE HUMAN X-CHROMOSOME BY ANALYSIS OF RADIATION- INDUCED GENE SEGREGATION

S. J. GOSS AND H. HARRIS The Sir William Dunn School of Pathology, University of Oxford, South Parks Road, Oxford OXi 3RE, England

SUMMARY Hybrid cells were obtained by virus-induced fusion of hamster cells with irradiated human cells. The analysis of such hybrids permits a study of the effects of lethal doses of radiation on human cells and provides a method of sub-chromosomal genetic mapping that is independent of karyological analysis. Radiation-induced chromosome exchanges are shown to be extremely localized, and a map of 4 X-linked genes is presented.

INTRODUCTION Methods have recently been developed that have led to rapid progress in the assignment of genes to specific human chromosomes. Cell fusion induced by Sendai virus is used to make hybrids between human and rodent cells (Harris & Watkins, 1965); from such hybrids human chromosomes are preferentially eliminated (Weiss & Green, 1967). Since specific human chromosomes can be recognized by their banding patterns after appropriate staining procedures (Caspersson, Lomakka & Zech, 1971), it is possible to search for a correlation between the expression of a chosen human gene in the hybrid cell and the retention of a particular human chromosome. By means of such cor- relations approximately 100 genes have been assigned to specific human chromosomes (McKusick, Klinger, Bootsma & Ruddle, 1976). Regional assignment of genes within a chromosome can subsequently be achieved by examining a second set of hybrids, in which the chromosome of interest is translocated or otherwise rearranged in some identifiable way. The expression of the human gene can then be correlated with the presence of a section of the chromosome in question. Progress in regional mapping is being made by this approach (Burgerhout & Jongsma, 1976), but it is limited, to some extent by the availability of suitable translocations, and more seriously by the difficulty of identifying the exact nature of the chromosome rearrangements observed. Thus, despite extensive studies, there are still inconsistent regional assignments for genes on the X-chromosome, most probably because of incorrect determination of the chromosome break-points (Brown et al. 1976). Karyological mapping is, moreover, limited in resolution, in that it can only localize genes to a segment of chromosome large enough to be identified by light microscopy. Much smaller chromosomal fragments may, however, be retained in hybrid cells (Schwartz, Cook & Harris, 1971; Boyd & Harris, 1973; McBride & Ozer, 1973); so that the full potential of gene 18 S.J.Goss and H.Harris mapping by the techniques of somatic cell genetics has clearly not yet been rea- lized. The present paper describes a new approach to the problem, which relies on a study of the retention of human genes in hybrids made by fusing hamster fibroblasts with human lymphocytes given different doses of ionizing radiation. By using a hamster cell line, Wg3-h, that lacks the enzyme hypoxanthine phosphoribosyl transferase (HPRT), and isolating the hybrids in 'HAT' medium (Littlefield, 1964), we could ensure the selective retention, in all hybrids, of the human X-linked gene for HPRT. It is known from the cytological studies of Westerveld, Visser, Meera Khan & Bootsma (1971) that human chromosomes not selected for are rapidly lost from Wg3-h/ human lymphocyte hybrids. In the first part of this paper, we show that unselected X-linked genes are, in general, retained in the hybrids only if their linkage to HPRT has not been disrupted by radiation damage. We describe such genes as having been 'co-transferred' with HPRT. Autosomal genes, and those X-linked genes whose linkage with HPRT has been disrupted by the radiation, are rapidly eliminated. By analysing the co-transfer of X-linked genes, we can derive a map of the human X- chromosome. Preliminary reports of this work have appeared elsewhere (Goss & Harris, 1975; Goss, 1976).

MATERIALS AND METHODS Cell culture The Chinese hamster cell lines, Wg3-h and a-23, were kindly supplied by Dr A. Westerveld (Westerveld et al. 1971), Wg3-h is deficient in the enzyme hypoxanthine phosphoribosyl transferase (HPRT, E.C. No. 2.4.2.8.) and a-23 exhibits a greatly reduced level of thymidine kinase (TK, E.C. No. 2.7.1.75). All cells were grown in monolayers in medium based on Eagle's minimal essential medium (MEM), supplemented with 10 % foetal calf serum. To keep Wg3-h stocks free from HPRT+ revertants, 6-thioguanine was added to the MEM to a final concentration of 6 /tg/ml. Medium containing 6-thioguanine was also used for the back-selection of hybrids. HAT medium (Littlefield, 1964) was used for the isolation and propagation of the man-hamster hybrid cells. Our formulation of HAT is MEM containing hypoxanthine (6 x 10" 5M), thymidine (1 x IO~5M), aminopterin (4-5 x IO"'M) and glycine (4 x IO"4M). Prior to back-selection, cells were withdrawn from HAT by 2 passages in HAT without aminopterin. This avoids the massive cell death due to the persistent effects of aminopterin. Human peripheral blood lymphocytes were prepared essentially according to the method of Boyum (1968). The same male donor (SJG) was used throughout, in order to reduce as much as possible any variation between batches of cells. Cells prepared in this way showed no DNA synthesis, as detected by the incorporation of radioactivity into acid-insoluble material, after culture of the cells for 1 h in MEM containing tritiated thymidine. We therefore assumed that most of these cells were non-dividing, and that each contained one complete copy of the human X-chromosome. No abnormalities could be detected in the G-banded X-chromosome of these cells (E. P. Evans and M. Burtenshaw, personal communication).

Irradiation of the lymphocytes The cells were irradiated in a Gammacell 40 (Atomic Energy of Canada Ltd, Ottawa.). This equipment contained two 137Cs sources and delivered gamma-rays at a fixed rate of 1-2 J kg"1 min"1. The lymphocytes were suspended in ice-cold MEM without serum for the period of irradiation. Cold medium was used to minimize repair of the radiation damage (Kleijer, Hoek- sema, Sluyter & Bootsma, 1973), since repair would be expected to diminish the total effect of the irradiation (Dewey, Miller & Leeper, 1971). Statistical mapping of the human X-chromosome 19

Cell fusion Three million hamster cells were fused with approximately io7 lymphocytes by the technique of Harris & Watkins (1965). To facilitate fusion, the lymphocytes were first trypsinized lightly by the method of Sun, Chang & Chu (1974), and then suspended together with the hamster cells. Each fusion was done in a total volume of 05 ml, 5000 haemagglutinating units of ultraviolet-inactivated Sendai virus being added. Cytological examination of the cell suspen- sion immediately after cell fusion by the method of Obara, Chai, Weinfeld & Sandberg (1974) showed that the majority of heterokaryons contained a single lymphocyte nucleus. The fusion was thus likely to produce hybrid cells containing, at least initially, a single human X-chromosome. The fused cells were plated in 20 srrall.plastic tissue culture flasks (Falcon Plastics) and cultured for 1 day in MEM. The medium was then changed to HAT, which was renewed after 1 week. A week after that, the hybrid clones were isolated and grown up. Only one clone from each flask was analysed, so we can be certain of the independent origin of all the clones studied.

Chromosome spreads The karyotypes of parental cells and hybrids were studied in chromosome spreads prepared according to Miller et al. (19716). The chromosomes were sometimes banded by the method of Kao (i973)-

Identification of human enzymes in the hybrids Human enzymes were detected in lysates of hybrid cells by Cellogel electrophoresis. The enzymes studied are listed in Table 1. The basic procedure is that of Meera Khan (1971). All electrophoresis was done in a Shandon U77 tank in the cold room at 4 °C. Buffer I of Meera Khan (1971) was used for G6PD, PGK and IPO, and his buffer V for HPRT and aGAL. Table 2 shows the running conditions for the electrophoresis. The lysates (approx. 2 fd of each sample) were applied 1 cm from the cathodal bridge in all cases.

Table 1. Human enzymes analysed in the hybrid cells

Gene Chromo- catalogue some as- Enzyme (trivial name) Abbreviation E.C. no. no.* signmentf Hypoxanthine phosphoribosyl transfers se HPRT 2.4. 2.8 30800 X Glucose-6-phosphate dehydrogenase G6PD 1.1. 1.49 30590 X 3-phosphoglycerate kinase PGK 2.7. 2-3 31180 X a-galactosidase A aGAL 3.2. I .22 30150 X Indophenol oxidase A IPO-A 1. iS;. 1.1 14745 21 Indophenol oxidase B IPO-B 1.15;. 1.1 14746 6 * McKusick (1975). f Chromosome assignments are taken from McKusick, Klinger, Bootsma & Ruddle (1976).

The method for developing bands of enzyme activity on the gels after electrophoresis is described for HPRT, G6PD, PGK and IPO, by Meera Khan (1971), and for aGAL by Grzeschik (Grzeschik et al. 1972). The HPRT gels were incubated in the appropriate reaction mixture and then soaked for 15 min in a buffered lanthanum chloride solution (Nichols & Ruddle, 1974) to precipitate radiolabelled inosinic acid on the gel. Unincorporated radioactive hypoxanthine was 20 S. J. Goss and H. Harris removed from the gel by washing with fast-running tap water for 15 min. Each track on the gel was sliced into 5-mm strips and the radioactivity of the strips measured by scintillation counting. The site of HPRT activity on the gel was thus located. To facilitate the resolution of human and hamster aGAL, the lysates were pretreated with neuraminidase before electrophoresis (Meera Khan, Westerveld, Wurzer-Figurelli & Bootsma, J97S)- The lysates were incubated at 37 °C for 45 min with an equal volume of neuraminidase from Vibrio cholerae (B.D.H. 500 U./ml.).

Table 2. Electrophoresis conditions

Gap width Initial current (across which Constant vpltage (through a gel voltage is (power-pack 8 cm in width), Duration of run, Enzyme applied), cm ouput), V mA h

HPRT 8 300 3'5 2 G6PD 8 200 7 i-7S PGK 8 200 7 2-S aGAL 12 500 4'5 2 IPO 8 200 7 1-25

RESULTS Radiation-induced segregation of X-linked genes Initially the species of origin of HPRT was checked in all clones isolated. In every case the HPRT was found to be human, indicating that the clones were hybrids and not revertant hamster cells. Later, HPRT assays were only done on hybrids expressing no other human X-linked genes. In no case was reversion of the hamster HPRT gene detected. We may assume that all hybrids contain human HPRT. All hybrid clones were screened for the expression of the three human X-linked genes specifying the enzymes PGK, aGAL and G6PD. As there is no evidence to suggest that the expression of these genes is modulated by cell fusion, we adopt the usual convention of somatic cell genetics and assume that the absence of any of these enzymes indicates the loss, from the hybrid cell, of the gene specifying that enzyme. We can thus tabulate the frequencies with which the three X-linked genes are retained in the hybrids (Table 3, p. 34). These retention frequencies are greatly reduced by irradi- ating the human cells before fusion. This effect is clearly dependent on the dose of y-rays administered, and is greater for some genes (e.g. for PGK) than for others (e.g. for G6PD). Since all the hybrids have retained the HPRT gene, this effect can be described as a radiation-induced segregation of syntenic genetic loci. It might be suggested that this effect is simply a manifestation of radiation-induced gene mutation. However, a typical estimate of the rate of radiation-induced gene mutation is of the order io~5/J kg^/locus (Albertini & DeMars, 1973; Russell et al. 1976), and this is clearly too infrequent to explain the large effect of radiation in the present experiment. It would seem more likely that the segregation of the X-linked genes from HPRT is due to the induction of rearrangements of the X-chromosome with subsequent loss from the hybrids of genes no longer linked to HPRT. This hypothesis is tested in the following experiments. Statistical mapping of the human X-chromosome 21

Retention in the hybrids of unselected chromosome fragments Unselected autosomal genes, not being linked to the selected locus, HPRT, will serve us as models for X-linked genes whose linkage with HPRT has been disrupted. It follows from our argument in the previous section that autosomal genes should rarely be retained in the hybrids. Table 4 records the expression in the hybrids of the human indophenol oxidase isozymes, IPO-A and IPO-B, whose genetic loci are on chromosomes 21 and 6 respectively. The retention frequency per locus has been calculated for both of these genes, taking into account the fact that each hybrid initially receives two copies of each autosomal gene at fusion. It will be seen from Table 4, that the retention of loci independent of the HPRT locus is low compared with the retention frequencies of X-linked loci shown in Table 3. The retention frequency of IPO-A is considerably greater than that of IPO-B, indicating some non-randomness of gene retention. The following experiment was done to study the retention of unselected fragments of the X-chromosome more closely. A small series of hybrids was made between the thymidine kinase-deficient hamster cell line, a-23 and irradiated human lymphocytes, a-23 is derived from the same wild type cell line as Wg3-h (Westerveld et al. 1971), and it closely resembles Wg3-h in its growth properties, a-23/lymphocyte hybrids isolated in HAT medium retain the human gene for TK, which is on chromosome 17 (Miller et al. 1971a), but there is no selection in this case for the retention of human HPRT. Thus all fragments of the X-chromosome in these hybrids might be expected to behave like unselected fragments of the X-chromosome in Wg3-h hybrids. In 15 clones of hybrids between a-23 and lymphocytes previously irradiated with 20 J kg"1 of y-rays, no case of PGK or G6PD retention was found; and in 18 similar hybrid clones in which the lymphocytes had received 40 J kg"1 of radiation there were only 2 clones retaining G6PD, and none retaining PGK. It thus appears that unselected fragments of the X-chromosome are only rarely retained in the Wg3-h hybrids.

Back-selection experiments It is possible to back-select for hybrids that have lost human HPRT, by cloning in medium containing 6-thioguanine. Because the loss of human chromosomes from hybrids between rodent and human cells is relatively frequent, the loss of HPRT in back- selection experiments will most often be due to chromosome loss, rather than mutation of the HPRT gene. If an unselected X-linked gene is retained in a hybrid only by virtue of its linkage with HPRT, it should also be lost from the hybrid during back- selection. Table 5 shows the result of back-selecting 10 hybrid clones. Of the 16 unselected X-linked genes originally present in these hybrids, only 1 was retained after back- selection. All 16 genes were retained in control cultures grown in HAT for the 3-week period of the back selection. That the loss of the unselected X-linked genes in thioguanine-containing medium was not induced by some non-specific trauma involved in back-selection, is shown by the persistence of the 4 IPO genes that were present in 3 22 5. J. Goss and H. Harris fr c? (;i u ')i ii (•' 11 5 6 7 HUMAN II SI 44* 10

•fi ii (i

I ft I « 8 9 10 * Statistical mapping of the human X-chromosome 23 of the hybrids. These results thus confirm that the retention of unselected X-linked genes is dependent mainly on their linkage with HPRT.

Correlation between hybrid karyotypes and retention of human genes A limited karyological study was made of the hybrids. Figures 1 and 2 show karyotypes of two typical hybrids. The first of these was produced from unirradiated human lymphocytes. It retained all 3 unselected X-linked genes and contains an intact human X-chromosome. No other human chromosome was identified in this hybrid. The hybrid shown in Fig. 2 was produced by fusion of \Vg3-h with lymphocytes given 40 J kg"1 of irradiation. No human chromosome can be detected in this clone, but it is possible that the small dot chromosome, which is not present in Wg3-h, may be a fragment of a human chromosome. This hybrid clone did not retain any X-linked markers other than HPRT. The massive elimination of human chromosomal material from these hybrids and the fragmentation of the X-chromosome in the hybrid made with irradiated lymphocytes are in obvious agreement with our proposed mechanism of gene segregation. Of 28 hybrid clones examined karyotypically, 25 contained one Wg3-h chromosome set and a small number of human chromosomes. Most viable hybrids in these experiments thus appear to be derived from the fusion of one lymphocyte with one hamster cell. Our subsequent analysis of gene segregation assumes that each hybrid cell initially received a single copy of the human X-chromosome.

Interdependent segregation of the X-linked genes: the derivation of gene order The final test of our argument that the radiation-induced segregation of X-linked genes is due to chromosome rearrangement is a test for interdependent gene segregation. Consider 4 syntenic genes, in linear order A.B.C.D, where C is the selected gene. A chromosome break between B and C will then segregate both A and B from C, that is to say, the segregation of A is in part dependent on the segregation of B. In contrast, the segregation of D from C would be independent of the segregation of either A or B from C. Gene segregation due to chromosome rearrangment must show patterns of interdependence which reflect linear gene order. It is possible to demonstrate such interdependence in the following way. One con- siders a pair of genes, say A and B for which there will be 4 segregant classes (A+B+, A~B~, A+B~, A~B+). The number of clones to be expected in each class can then be calculated on the assumption that A and B segregate independently of one another. If

Fig. 1. The trypsin-banded karyotype of a hybrid clone derived from the fusion of \Vg3-h cells with unirradiated human lymphocytes. The only chromosome that is clearly not derived from the Chinese hamster parent is the human X-chromosome. The Chinese hamster chromosomes are numbered according to Ray & Mohondas (1976). Fig. 2. The karyotype of a \Vg3-h x human lymphocyte hybrid. The lymphocyte was exposed to 40 J kg"1 y-rays before fusion. There are no recognizable human chromosomes in this karyotype, but the dot chromosome (asterisked), which is not normally seen in \Vg3-h karyotypes, may be a fragment of human chromosome material. 24 S. J. Goss and H. Harris this is so, the observed distribution of segregant classes should agree with the calculated distribution. However, if, as described above, the segregation of B involves the simultaneous segregation of A, we should observe an excess, relative to expectation, of clones in the concordant classes, A+B+ and A~B~, and a deficiency of the discordant classes, A+B~ and A~B+. Table 6 shows the results of such a test of the independence of segregation of PGK and G6PD, and Table 7 shows the results of the same test applied to PGK and aGAL. Comparison of these two Tables shows that the segregation of PGK is largely independent of that of G6PD, but markedly dependent on that of aGAL. This implies that PGK and aGAL are on one side of HPRT, and that G6PD is on the other side. As expected from this gene order, the segregation of aGAL is found to be largely independent of the segregation of G6PD (not shown). The slight degree of interdependence of segregation of loci apparently situated on opposite sides of HPRT is significant at the 5% level; this is explained below by reference to the effect of interstitial deletions.

Deduction of the complete gene order We have now discussed 4 lines of evidence which indicate that the retention of X- linked genes in our hybrids is almost entirely dependent on their co-transfer with HPRT. The radiation-induced segregation of such genes from HPRT is due to chromosome rearrangement. Table 3 can then be interpreted as showing that chromosome rearrangement was induced more often between PGK and HPRT, than between aGAL and HPRT which implies that PGK is situated further from HPRT than aGAL. Combining this result with the partial gene order derived in the preceding paragraph, we can deduce the complete gene order: PGK - aGAL - HPRT - G6PD. This gene order is consistent with the majority of regional assignments for these genes based on cytological mapping experiments (Brown et al. 1976).

Rapid determination of the position of further X-linked genes The hybrids produced in this experiment can be grouped according to the length of intact X-chromosome retained. These groups can be screened for the retention of other X-linked loci for which no regional assignment is available. Using this approach, Buck, Goss & Bodmer (1976) were able to map the X-linked gene determining a surface antigen.

Estimation of the relative distances between loci The relative distances between loci may be estimated by the application of a simple target theory. We define a segregational event as any event that disrupts the linkage of two loci. These events may be considered as occurring in a target delimited by the two loci, the target for the segregation of two widely spaced loci being larger than that for two loci close together. The mean number of events, St, induced by radiation in any such target, will obviously depend on the size of the target and on some function of the Statistical mapping of the human X-chromosome 25 dose of radiation administered, t(D). Our measure of target size, t, is chosen so that the mean number of events induced in the target is proportional to t. We may therefore write:

St= U{D).

The actual number of events occurring in this target will be scattered around the mean value of St with a Poisson frequency distribution. We can therefore predict the probability that the linkage will not be disrupted by radiation. In the absence of significant spontaneous breakage, this probability is equal to the frequency of co-transfer, Po, for the two loci. We may write:

P0 = exp(-*.f(Z>)).

We have shown that the retention of X-linked loci is dependent on their co-transfer with HPRT. Provided that the viability of the hybrid cell is not significantly affected by the segregation of any particular unselected marker, we can therefore equate the co-transfer frequency, Po, of any two markers with the frequency, F, of hybrid clones expressing both markers. For example, the frequencies in Table 3 will be our estimates of the frequency of co-transfer of each unselected marker with HPRT. Hence,

F = exp(-*.f(Z>)) and -inF = t.f(D).

This relationship predicts that if the logarithm of the estimated co-transfer frequency of two loci is plotted against an appropriate function of radiation dose, a straight line should be defined with a slope proportional to the size of the target for the segregation of the two loci. Such plots have been made in Fig. 3 for 3 targets. The function of dose that approximately linearizes all three plots is found to be (dose)1'7. A similar dose dependence has been found for the induction of cytologically detectable chromosome aberrations by y-rays (reviewed by Evans, 1974). This further corroborates our thesis that the gene segregation seen in these experiments is the result of chromosome rearrangement. Until we know more about the factors determining the sensitivity of our cells to y-rays we propose to measure the target sizes relative to some biological standard. For this reason, we have expressed all targets as a fraction of the target for the segregation of PGK from HPRT ('target PGK/HPRT'). As there is very little spontaneous segregation in our experiments, the plots in Fig. 3 very nearly pass through the origin, so that the ratio of any target, A/B, to the target PGK/HPRT can be most simply calculated by taking each dose, the value of log Po for the loci A and B and dividing it by the value of log Po for PGK and HPRT. A weighted average can then be taken of the ratios obtained at different doses, allowance being made for the smaller variance of the results at higher values of Po. This procedure can be summarized as follows: + If nA clones are assayed for locus A, and a clones are found to have retained this locus, we have: a+ Po(A) = —' and a+ + a~~ = nA- 26 5. J. Goss and H. Harris

1-5

10 20 40

1 5 r-

10 20 40 Dose. J kg-'

Fig. 3. The logarithms of the frequencies of co-transfer of PGK with HPRT (A), of aGAL with HPRT (O), and of G6PD with HPRT (•) are plotted against the dose of radiation administered to the human lymphocytes before fusion. The dose axis has been expanded as (dose)1'7, an empirically determined function which converts the plots to linearity. The slopes of the lines are proportional to the targets for the segregation of each pair of loci (see text). The target aGAL/HPRT is compared with the target PGK/HPRT in (A), and target G6PD/HPRT is compared with the target PGK/ HPRT in B. Statistical mapping of the human X-chromosome 27 + Likewise, if nP clones are assayed for PGK, and p clones are found to have retained PGK, we have:

and + -fV) =— p +p~ = nP. nP The target ratio, Ra, is calculated at each dose, d. » _l0gfi)(A) log P0(P)

An estimate of the error variance of Ra (which ignores the covariance of P0(A) is var *,, = [, "A JT^-" +

A weighted mean target ratio, R, is calculated using the values Ra obtained at different doses:

S(i/vari?d) * Then var R = .^7 . /var^d) The resulting target sizes are set out in Table 8.

Gene segregation by interstitial deletion Table 7 reveals the existence of a small number of clones that have segregated aGAL but retained PGK. These clones were used in the back-selection experiment summarized in Table 5. Back-selection indicated that, in 6 clones out of 7, PGK was still linked to HPRT, although aGAL which lies between these two loci had been eliminated. aGAL has therefore been segregated in these clones by some localized event which, unlike a simple break or translocation, has not segregated the loci on one side of it from those on the other side. The two types of event that could produce such a localized effect are gene mutation and interstitial deletion, both of which are known to be induced by ionizing radiation. We have already discussed the rarity with which induced mutation might be expected to occur so that interstitial deletion would seem a priori to be the more probable cause of this effect. Fortunately, we can dis- tinguish between these two possibilities by further examination of our results. There is no reason to believe that such localized segregational events would be limited to the aGAL locus. Let us consider the effects of mutation and interstitial deletion at the HPRT locus. Mutation at this locus would merely reduce the yield of clones but would not otherwise affect the data. But interstitial deletion of HPRT should be reflected in the results, because, in this case, the deleted fragment bearing HPRT would be selectively retained in the hybrid. All other fragments of the X-chromosome would tend to be eliminated, so that the net result of the interstitial deletion of HPRT would be the simultaneous segregation of genes on opposite sides of that locus. 28 S. J. Goss and H. Harris This, we suggest, is the explanation of the slight degree of interdependent segregation of PGK and G6PD, and of aGAL and G6PD (see, for example, Table 6). Such interdependent segregation of loci on opposite sides of the selected locus would not be expected if chromosome breaks and translocations were the only segregational events.

Calculation of the effective target sizes for interstitial deletions The target for the interstitial deletion of aGAL can be calculated directly by the method used for calculating the targets shown in Table 8. The probability that aGAL is not deleted is: _ _ No. of clones retaining both aGAL and PGK 0 No. of clones retaining PGK

The target for the interstitial deletion of HPRT can be estimated by either of two indirect approaches: (i) It will be noted that a locus could be segregated from another, syntenic, locus, by translocation or breakage of the chromosome at any site between the two loci or by deletion of either locus from the chromosome. Thus the target PGK/HPRT will include a target for chromosome translocation at sites between these loci, a target for the deletion of PGK, and a target for the deletion of HPRT. The target G6PD/ HPRT will likewise include two deletion targets. The sum of the targets PGK/HPRT and G6PD/HPRT will therefore consist of the target for chromosome translocation at sites between PGK and G6PD, plus 4 deletion targets. But the target for the segregation of PGK from G6PD, measured directly using

Po = co-transfer frequency of PGK with G6PD will include only 3 deletion targets, one each for PGK, G6PD and HPRT: it will therefore be less than the sum of the targets PGK/HPRT and G6PD/HPRT by an amount equal to the target for the deletion of HPRT. (ii) Alternatively, the target for the segregation of PGK from HPRT, excluding the deletion of HPRT, can be calculated by measuring the co-transfer of PGK with HPRT in clones that have retained G6PD. Since the interstitial deletion of HPRT would cause the segregation of G6PD, we can be certain that HPRT has not been deleted in these clones. The target for the deletion of HPRT is then the difference between this newly calculated target, PGK/HPRT(G6PD)+, and the target PGK/ HPRT calculated for all clones. The data used to estimate the targets for the deletion of aGAL and of HPRT are set out in Table 9. It will be seen that the target for the interstitial deletion of aGAL is significantly different from zero. Although none of the estimates of the target for the deletion of HPRT is significantly different from zero it is clear that our various estimates of this target are similar, being of the order 0-17 of the target PGK/HPRT. Statistical mapping of the human X-chromosome 29

Map distances between loci We define the map distance between two loci, A and B (distance A-B), as having the property of additivity: Distance A-B + distance B-C = distance A-C, where A, B, and C are syntenic genes in the order A-B-C. The target for the segregation of one gene from another as a result of chromosome breakage or translocation at sites between the two genes should have this property of additivity and will thus serve as a measure of map distance. The true map distance between two genes can therefore be estimated by subtracting from the overall target for the segregation of the genes that part of the target due to deletion of the genes. A list of such map distances, and the methods used in their calculation, are set out in Table 10.

A model of gene segregation by chromosome exchange: estimation of the 'rejoining distance' and ratio of exchanges between and within chromosomes In estimating the map distances in Table 10, we have assumed that the targets for the deletion of any of the loci under discussion are equal to the target for the deletion of aGAL (i.e. 0-18 of the target PGK/HPRT). This was suggested by the similarity of the deletion targets at HPRT and at aGAL. This simplification may be adequate for widely spaced loci, but it could not justifiably be applied to closely linked loci. Consider 3 loci in the order A-B-C. According to the exchange hypothesis of chromosome aberration (Revell, 1959), the interstitial deletion of locus B from the group is due to the occurrence of an intrachange between segments A-B and B-C. Because the ' rejoining' of y-ray induced lesions can only occur if the lesions are closely situated in the nucleus (Lea, 1955; Neary, Savage & Evans, 1964a), the frequency of deletion of locus B would be independent of the distances A-B and B-C if these distances were large compared with the rejoining distance. However, if A-B and B-C were small compared with the rejoining distance, the frequency of deletion of B would be reduced and would then depend in some way on the magnitude of the distances A-B and B-C. On these assumptions we can make a model relating the target for the segregation of two genes to the map distance between them. Consider two genes, A and B, separated by distance d in which d lesions are induced by the radiation. Any of these d lesions may interact with any of x lesions in the immediate neighbourhood. The value x then represents that part of the genome within rejoining distance of the lesions in d. The mean number of chromosome exchanges occurring at sites between A and B will be proportional to the product, dx. However, if a number, i, of the x lesions is on the same chromosome as genes A and B, some of the exchanges, di, will be intrachanges. If the distance d is large relative to i, all the intrachanges will occur within the distance d, and hence will not contribute to the segregation of A from B. The mean number of segregational events between A and B will be proportional to S where S = dx-di

3 C ILL 25 30 S. J. Goss and H. Harris S is, of course, proportional to the target for the segregation of A from B. If d is very small relative to i, the number of intrachanges occurring within the distance d, and so producing no segregation, becomes proportional to d2. This leaves a number of intrachanges, d(i—d), due to the interaction of lesions in d with lesions situated elsewhere on the same chromosome. Of these, approximately one half will result in the inversion rather than the deletion of A or B, and so, when d is small, we may write: S = dx-d*-o-sd(i-d). The function, 5 = dx-di{i-o-s&-dli), (i) varies continuously with d between these two limiting cases; and we have found that it adequately describes the experimental data. In deriving this simple model, we have ignored the occurrence of incomplete exchanges. It is apparent from the data of Revell (1959), and also from the data reviewed by Neary et al. (19646), that approximately 90% of exchanges are typically complete both proximally and distally. The remaining 10% show single incompleteness; double incompleteness is only very rarely seen. Since it is only certain subclasses of incomplete exchange that affect our model, incompleteness can only have a small effect on its formulation. Values of x and i that gave a good fit for the experimental results were found by successive approximation. To illustrate how well the model fits the data we have used equation 1 to compute the map distances between pairs of loci from the targets for the segregation of those loci. The computed map distances are compared in Table 11 with the map distances deduced from consideration of interstitial deletion targets (i.e. those presented in Table 10). The satisfactory value of x was found to be 0-5, which is 0-78 of the map distance PGK-HPRT. Taking this latter distance as approximately 0-008 of the diploid genome (by consideration of the total length of the diploid metaphase chromosome set), we have that a y-ray induced lesion may interact with lesions in the neighbouring six thousandths of the total genome. Assuming that chromatin is uniformly dispersed in a lymphocyte nucleus of radius 3 /tm, we estimate a rejoining radius of 0-55 /im. This should be regarded as an upper limit, since the chromatin is probably condensed in an uneven pattern in the nucleus. The approximate agreement between this very crude estimate of the rejoining radius and the estimate of Neary, Preston & Savage (1967) lends some plausibility to the model. The satisfactory value of i is 0-4, giving a ratio of intrachanges to interchanges i:{x-i) = 4:1. Very similar values have been obtained for this ratio from cytogenetic studies (Evans, 1962). The high value of the ratio is generally taken to indicate the extremely localized nature of chromosome exchange. Our model of gene segregation thus adequately describes our experimental results and is in agreement with other radiobiological studies. The model should be of value in converting segregation targets to map distances in cases where interstitial deletion cannot be so easily detected as in the present experiments (Goss & Harris, 1977). Statistical mapping of the human X-chromosome 31

DISCUSSION We have shown that it is possible to obtain viable hybrid cells from fusions between hamster cells and lethally irradiated human cells. Large numbers of hybrid clones have been isolated in this laboratory even after the administration of 800 J kg"1 to one of the parent cells. It may therefore be expected that cell fusion will be of use in studying the genetic effects of high doses of radiation in mammalian cells.

PGK aGAL HPRT G6PD 1 1 1 1

0-33 ,, 0-30 ,, 0-23 , 0-52 0-64 .

088

Fig. 4. A diagrammatic representation of 4 X-linked loci, showing the order of the loci and the approximate relative distances between them.

The work described in the present paper shows that y-radiation induces the segregation of syntenic genes by a mechanism that can be understood in terms of the classi- cal forms of radiation-induced chromosome rearrangement. Events equivalent to simple translocations and to interstitial deletions can be recognized, and the dependence of these events on radiation dose is similar to that observed for cytologically detectable aberrations induced by much lower radiation doses. It is possible to describe the induced gene segregation by a model based on the exchange hypothesis of chromosome aberration. A statistical analysis of gene segregation permits one to derive a chromosome map, which shows the order of the genes on the chromosome and the approximate distances between them (Fig. 4). This approach to gene mapping has the advantage that it is not limited in resolution by karyological analysis. The relationship between the map distances derived by this form of analysis and the structure of the metaphase chromosome is discussed in the accompanying paper (Goss & Harris, 1977). Our approach should be applicable to any chromosome bearing a gene whose retention can be ensured by the use of an appropriate selective system. Selectable loci have now been assigned to several autosomes (Ruddle, 1973), and cells bearing X-autosome translocations can be used to study chromosomes for which no selective system is known. Thus the approach should be widely applicable throughout the human genome. One would, however, anticipate some difficulty in resolving the gene order in a tightly linked group of genes situated at a distance from the selected locus. The accompanying paper (Goss & Harris, 1977) describes how this difficulty may be overcome by a method of analysis that does not depend on selectable genes.

We thank Dr F. H. C. Marriott for advice on the statistical analysis of our results and Mrs Jean Kerr-Harnott for technical assistance. S.J.G. is a Junior Research Fellow of Lincoln College, Oxford. The work was supported by the Cancer Research Campaign.

3-2 32 S. J. Goss and H. Harris

REFERENCES

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(Received 29 November 1976) 34 S. J. Goss and H. Harris

Table 3. The frequency of retention of the human genes PGK, OLGAL and G6PD in hybrids between Wgyh and human lymphocytes

Frequency of the X-linked gene A No. of clones Dose, J kg"1 PGK aGAL G6PD examined

0 o-9S o'95 o-95 46 10 0-82 0-91 o-88 74 20 o-S4 068 o-75 79 40 0-22 o-34 0-41 88

Table 4. The frequency of retention of the human genes IPO-A and IPO-B in hybrids between Wgyh and irradiated human lymphocytes

Frequency of clones (E) Calculated retention expressing the isozyme frequency per locus (r)* A No. of clones Dose, J kg""1 IPO-A IPO-B IPO-A IPO-B examined

0 Q'55 0-30 o-33 0-16 44 10 o-S7 O-2O O'35 o-io 61 20 0-40 017 022 0-09 58 40 0-16 OO8 008 0-04 62 * r = 1 - Vd ~E).

Table 5. The effect of back-selection in 6-thioguanine on the retention of human genes in a set of 10 hybrid clones

No. of clones expressing the named human gene

(i) (ii) (iii) 1 month after fusion After a further 3 After back-selection weeks' growth in in medium contain- HAT medium ing 6-thioguanine Human gene HPRT 10 10 0 PGK 9 9 1 aGAL 2 2 0 G6PD 5 5 0 IPO-A 2 2 2 IPO-B 2 2 2 PGK in aGAL" 7 7 1 clones Statistical mapping of the human X-chromosome 35

Table 6. A test of the independence of segregation of PGK and G6PD

No. of hybrid clones in each class at each dose A Class of segregant 10 J kg"1 20 J kg"1 40 J kg-1 Total PGK+G6PD+ expected 53-6 318 7-8 93-2 observed 56 34 11 101 PGK-G6PD- expected 16 8-8 40-8 512 observed 4 11 44 59 PGK+G6PD- expected 7-4 102 112 28-8 observed 5 8 8 21 PGK-G6PD+ expected n-4 27-2 28-2 66-8 observed 9 25 25 59 The number of clones observed in each of the possible classes of segregant for the two markers PGK and G6PD is compared with that expected* if the segregation of PGK from HPRTwas independent of the segregation of G6PD from HPRT. %2 = 4-86 (calculated from the totals with 1 degree of freedom). * If the overall frequency, at any one dose, for the segregation of PGK is p~, and of G6PD is g~, the number of clones expected in each class, will be: for PGK+G6PD+, n(i —p~). (1 —g~); for PGK-G6PD-, np~.g~; for PGK+G6PD", «(i -p~).g-\ and for PGK-G6PD+, np-(i -g), where n is the number of clones examined at each dose.

Table 7. To show the interdependent segregation of PGK and aGAL

No. of hybrid clones in each class at each dose

Class of segregant 10 J kg"1 20 J kg-1 40 J kg"1 Total

PGK+aGAL+ expected 55-2 29-4 6-5 QI-I observed 61 39 14 114 PGK-aGAL- expected 1-2 n-4 45'5 58-1 observed 7 21 53 81 PGK+aGAL- expected 5-8 136 12-5 3i-9 observed 0 4 5 9 PGK-aGAL+ expected n-8 24-6 23-5 59'9 observed 6 15 16 37 This table is analogous to Table 6. The difference between the observed and expected numbers of clones in each class is highly significant. X" — 4° (calculated from the totals, with 1 degree of freedom). 36 S. J. Goss and H. Harris

Table 8. The sizes of targets for the segregation of pairs of X-linked loci, expressed as fractions of the target for the segregation of PGK and HPRT

Relative size of Target target ( ± 1 s.E.) PGK/HPRT (i) 1 aGAL/HPRT (ii) 0-65 ±0095 G6PD/HPRT (iii) 0-55 ± 0-08

Table 9. Estimation of the interstitial deletion targets at aGAL and HPRT

Target as a fraction of Target and means of calculation PGK/HPRT 1 s.E. PGK/HPRT(G6PD+) (iv) 0-82 0-14 aGAL/HPRT(G6PD+) (v) 0-49 0-09 G6PD/HPRT(aGAL+) («) 0-42 009 PGK/G6PD (vii) i-38 0-17 aGAL/G6PD (viii) i'O7 0-15 Deletion of HPRT (i)-(iv) 018 014 Deletion of HPRT (ii)-(v) 0-16 013 Deletion of HPRT (iii)-(vi) 013 0-12 Deletion of HPRT (i) + (iii) — (vii) 0-17 019 Deletion of HPRT (ii) +(iii)-(viii) 013 0-19 Deletion of aGAL (ix) 0-18 006

Table 10. Map distances between loci on the X-chromosome

Relative distance Loci Calculation between loci PGK-HPRT (iv)-o-i8 0-64 aGAL-HPRT (v) -0-18 031 G6PD-HPRT (vi)-o-i8 0-24 PGK-aGAL Target aGAL/PGK-018 i.e. 0-51 —018 o-33 PGK-G6PD (vii) -3 x (018) 0-84 aGAL-G6PD (viii) —3 x (0-18) °S3 Statistical mapping of the human X-chromosome 37

Table 11. Computed map distances, obtained by applying the model of gene segregation by chromosome exchange, are compared with those derived from direct correction of segregation targets for interstitial deletion

Map distance from consideration of Experimentally determined* target Computed map interstitial for segregation of loci, distance, deletion Loci t d (as in Table 10)

PGK-HPRT 1 (i) 064 064 aGAL-HPRT 0-65 (ii) 030 031 G6PD-HPRT °-55 ("0 0-23 0-24 PGK-aGAL 069 aGAL/PGK + 018 033 o-33 PGK-G6PD i-2 (vii) —o-18 088 084 aGAL-G6PD 089 (viii) — 018 0-52 °-53 * The origin of the value, t, is indicated. In some cases it is necessary to make the indicated adjustment to ensure that the target used includes two deletion targets. The value, d, satisfies the equation: dx-di(i-o-se-dli)-kt = o = f(d) where x = 05, i = 0-4 and k = 00898. The constant, k, merely adjusts the solutions, d, by a constant factor, to make them directly comparable with the map distances obtained from consideration of interstitial deletion. The solution, d, was obtained by repeatedly computing

d* - d- ^ i\d) using successive values of d* in place of d, until the series converged.