analysis of deletions induced in the genome of mammalian cells by ionizing radiation

J. Mol. Biol. (1995) 254, 372–380

Analysis of Deletions Induced in the Genome ofMammalian Cells by Ionizing Radiation

Franklin Hutchinson

Radiobiology Laboratory A theory is presented for the distribution in size of deletions induced byDepartment of Therapeutic ionizing radiation, based on three assumptions: (1) deletions that are

observed delete part or all of a gene to make a mutation, but not adjacentRadiology, and Department ofMolecular Biophysics and DNA sequences essential for survival of the mutant; (2) deletions are

distributed at random along the DNA; (3) the probability of formation isBiochemistry, Yale Universityproportional to the rate at which the two endpoints, which must meet333 Cedar St., New Havento form the deletion, collide with each other. Experimental data forCT 06520-8040, USAradiation-induced deletions in human and hamster hprt genes are in goodagreement with calculations that assume the inducing lesion does not breakthe intracellular chromatin fiber; calculations assuming the inducing lesionis a break are not a good fit to the data. The low frequency of deletionsobserved in the hamster aprt gene is shown to be a consequence of the smallgene size and the presence of a nearby essential DNA sequence, ensuringthat most deletions affecting the gene also delete the essential sequence andare thus not observed.

7 1995 Academic Press Limited

Keywords: DNA deletions; mutation; ionizing radiation; mammaliancells; DNA double-strand breaks

Introduction

This paper analyzes deletions of kilobase toseveral megabase size that typically form asubstantial fraction of the mutations induced inmammalian cells by ionizing radiation. In earlystudies, large deletions were detected by loss ofcontiguous genes assayed by genetic methods(Hartman et al., 1971; Webber & de Serres, 1965);later experiments utilized Southern blots of theDNA after digestion with restriction endonucleases(Breimer et al., 1986). More recently, deletions havebeen identified by the absence of marker sequences,by failure of labelled probes to hybridize to cellDNA or of polymerase chain reaction (PCR) toamplify the sequences. The deletions analyzed herewere induced by ionizing radiation in the humanhprt gene (Bao et al., 1995; Denault & Liber, 1993;Morris et al., 1993; Nelson et al., 1994, 1995), thehamster hprt gene (Morgan et al., 1990; Thackeret al., 1990), and the hamster aprt gene (Grosovskyet al., 1986; Miles et al., 1990).

Agents such as ionizing radiation that frequentlyinduce deletions also make DNA double-strandbreaks, which has led to a general supposition thatlarge deletions are mainly the result of misjoiningof broken ends. However, genomic DNA is not inthe form of free intracellular molecules, butpackaged with protein in highly structured chro-

matin fibers (van Holde, 1989), and the relationbetween DNA double-strand breaks and interrup-tions in the chromatin is unknown. It is shown herethat expressions for the distribution in size ofdeletions induced by breaks in the chromatin are inpoor agreement with experiment. Equations derivedon the assumption that the inducing lesion does notbreak the chromatin are, however, in excellentagreement with the data.

Theory

A deletion in genomic DNA is nearly alwaysdetected as a mutation that deletes part or all ofthe gene. As shown in Figure 1(a), a deletion oflength m affects a gene of length M whenever anypart of the deletion overlaps the gene. The mutantcell must survive, so an observable deletioncannot delete essential DNA sequences flanking thegene. A deletion large enough to affect both geneand the nearest essential sequence a distance R fromthe gene, m > R, is limited to a region (M + R) asshown in Figure 1(b). For m > L, the distance to thenearest essential sequence on the other side of thegene, the locations of an observable deletion arerestricted to a region (L + M + R) − m (Figure 1(c)).The largest deletion detectable as a mutation ism = L + M + R.

0022–2836/95/480372–09 $12.00/0 7 1995 Academic Press Limited

Deletions Induced by Ionizing Radiation 373

Figure 1. Diagram showing limits of the location of anobservable deletion of length m affecting a gene of lengthM. The bar at the top represents a linear genome with acoordinate origin at O and the gene stretching from O toM. The nearest essential DNA sequence is a distance Rfrom the gene, or M + R from the origin. The nearestessential sequence on the other side is a distance L fromthe closest part of the gene at O. L' and M + R' arelocations of markers used in particular experiments.

Figure 2. The function p(m), the relative probability ofobserving a deletion of length m, as a function of m(equation (1)). Note that p(m) is not normalized;calculated numbers of deletions are normalized with theconstant K in equations (2) and (7).

size distribution function f(m) dm, the number ofdeletions of size between m and m + dm, is:

f(m) dm = K dm/m3/2 (2)

where K is a constant.Equations (1) and (2) can be used to calculate

numbers to compare with experimental results. Onequantity is the cumulative number N(<m) ofdeletions of size less than m:

N(<m) = Kfp(m)f(m) dm (3a)

Z < m < R, N(<m) = Kf(M + m) dm/m3/2

= 2K4M(Z−1/2 − m−1/2) + (m1/2 − Z1/2)5 (3b)

Z is the smallest value of m for equation (2) to bevalid, and is discussed below:

R < m < L, N(<m) = N(<R)

+ 2K(M + R)(R−1/2 − m−1/2) (3c)

L < m < L + M + R, N(<m) =N(<L)

+ 2K4(L + M + R)(L−1/2 − m−1/2)

− (m1/2 − L1/2)5 (3d)

The total number of deletions that include M and lieentirely within (L and R > Z) is:

N([L + M + R]) = 2K4(M − Z)/Z1/2

+ 2(L1/2 + R1/2 − (L + M + R)1/2)5 (4)

Many experiments describe deletions by report-ing the presence or absence of specific DNAsequences, determined by hybridizing probes or byPCR: e.g. if marker L is present but not L' (Fig-ure 3), and R but not R ', there is a deletion with oneend between L and L' and the other end betweenR ' and R. To calculate the probability of such a

It is assumed that a deletion is equally likely tobe formed at any location, a reasonable assumptionsince, on a scale measured in kb, ionizing radiationforms damage sites randomly in the DNA.Therefore, a suitable weighting function p(m),proportional to the probability a deletion will bedetected, is a length equal to the possible locationsof the deletion, and is graphed in Figure 2:

p(m) = M + m for m < R

= M + R for R < m < L

= L + M + R − m

for L < m < L + M + R (1)

One factor that could determine the distributionin length of deletions is the spacing s betweenlesions in the DNA, which varies as exp(−s/b) forrandom lesions of mean spacing b. In most cases themean spacing is very large compared with thelargest observable deletion in a viable cell; form/b�1, exp(−m/b)11. By this criterion, deletionsof various lengths occur with approximately equalprobability.

A second determinant of deletion size is therequirement that the two parts of the DNA to bejoined must collide with each other. Two possibili-ties are considered: (1) the lesion initiating thedeletion process does not break the chromatin fiber;(2) the initiating lesion breaks the chromatin.

Deletions induced by lesions that do notbreak the chromatin

An intracellular chromatin fiber of sufficientlength acts like a random-coil polymer in that themean-square distance �r2� between two pointsseparated by m kb along the DNA is proportionalto m, �r2� = h2m (van den Engh et al., 1992), whereh is a constant. It may be shown that the two pointswill collide with each other at a rate proportional to�r2�−3/2, and therefore to m−3/2 (Doi & Edwards,1986). Thus, for sufficiently large values of m, the

Figure 3. Diagram for equations (5) and (10), for thenumber of deletions with one end between markers L andL' (separated by distance A), and the other between R'and R (separated by B); see the text.

Deletions Induced by Ionizing Radiation374

deletion, let one endpoint be between x and x + dx(Figure 3): the probability that its endpoint is in Bis given by the expression in brackets 45 in equation(5), and integrating over x, the number N(A, B, C)of deletions with endpoints in regions A and B thatare a distance C apart is:

N(A, B, C) = gA

0 6dxgA + B + C − x

A + C − x

f(m) dm7 (5)

With f(m) as in equation (2), this is readilyevaluated:

N(A, B, C) = 4K4(A + C)1/2 − C1/2 + (B + C)1/2

− (A + B + C)1/25 (6)

here C must be greater than Z, the minimum sizedeletion.

Deletions formed by a break in the chromatin

If the initiating lesion results in a break in thechromatin, the two points on the DNA that mustcollide to make a deletion are no longer tetheredtogether. The deletion can be between an end fromone break misjoining with an end from anotherbreak a distance m down the DNA, or one brokenend can diffuse to join, by some unspecifiedprocess, with DNA a distance m along the polymerchain. The rate at which two diffusing endpoints,initially a distance r apart, will collide with eachother is proportional to (1/r)exp(−r/a) (Hutchin-son, 1957; Wijsman, 1952). Without loss ofgenerality, it may be assumed that one endpoint isstationary and ascribe all motion to the other; thena is the mean distance the diffusing structure movesfrom its initial position before it is no longeravailable to form the deletion; e.g. a diffusing endmay join with some other DNA.

For deletion endpoints initially separated byr = �r2�1/2 = hm1/2:

f(m) dm = K(1/m1/2)exp(−m1/2/q) dm, q = a/h (7)

For M, Z, R and L defined as before, the cumulativenumber of deletions smaller than m is, for Z < m < R(as in equation (3b)):

N(<m) = Kf(M + m)m−1/2 exp(−m1/2/q) dm

= 2qK4(M + Z)exp(−Z1/2/q)

− (M + m)exp(−m1/2/q)

+ U(Z) − U(R)5 (8)

where U(Y) = (2Y1/2q + 2q2)exp(−Y1/2/q). Equiva-lents of equations (3c) and (3d), for R < m < L andL < m < L + M + R, are readily derived (not given).The number of detectable deletions confinedentirely within (L and R > Z) is:

N(<[L + M + R]) = 2qK4(M + Z)exp(−Z1/2/q)

+U(Z) + U(L + M + R) − U(R) − U(L)5 (9)

The number of deletions with one end in A and theother in B, which are separated by C (Figure 3) is,from equations (5) and (7):

N(A, B, C) = 2qK4U(C) + U(A + B + C)

−U(A + B) − U(A + C)5 (10)

Limits for the validity of the equations

Both distribution functions (equations (2) and (7))assume that the chromatin behaves as a randompolymer coil. Z, the lower limit for m for unbrokenDNA (equation (2)), depends on the ability of thegenomic material to bend back on itself. In studiesof distances between marker sequences for DNA inmammalian cells (Hahnfeldt et al., 1993), chromatinappeared to have a persistence length of a fewkilobases; there are extensive data showing that sitesonly a kilobase or so apart on a DNA molecule canmeet (Kahn & Crothers, 1993; Schleif, 1992). Thus,Z between 1 and 4 kb seems reasonable. Fordeletions induced by breaks, the physical distance rbetween a broken end and sites a distance m downthe polymer backbone will, for m smaller than thepersistence length, be larger than calculated, andthe actual collision rate smaller than implied byequation (7); however, collisions will still take place,and the effective value of Z should be comparableto that for equation (2).

Linearity between the mean-square of thephysical distance separating two points �r2� and thecontour length m along the polymer holds in humancells for m up to about 2000 kb (Hahnfeldt et al.,1993); for larger m, the mean-square distance isless than predicted by a linear relation, becausethe random polymer coil is compressed by theboundaries of the intracellular space confining thechromosome. Points separated by >2000 kb alongthe polymer backbone will collide more frequentlythan expected from equations (2) or (7).

Experimental Data

Human hprt gene

Four papers report the presence or absence ofDNA markers within or flanking the human hprtgene (Figure 4) in lymphoblastoid TK6 cells. Two(Nelson et al., 1994, 1995) describe the same set ofmutants induced by X-rays, and the combined dataset is referred to as NEL45. A third paper (Denault& Liber, 1993) reports deletions induced by X-raysin cells irradiated in oxygen with and withoutcysteamine and in nitrogen; with no significantdifference between these data sets, they werecombined as DEN3. Because these three papers usea number of the same markers, they could bepooled, for statistical reasons, to form the data setNEL45 + DEN3. The fourth paper reports deletionsinduced by X-rays and alpha particles (Bao et al.,1995), combined as BAO5. Similar data on hprt


Figure 4. Locations, in kb, of marker sequencessurrounding the human hprt gene (Lippert et al., 1995a,b).Origin of numbering is the 5' end of the gene.

between the gene and DXS86. Large deletions arethose in which at least one distant marker had beendeleted; a few large deletions have one endpoint inthe gene. Table 2 gives more detailed information onthe large deletions.

Hamster hprt gene

Information is limited to deletion endpointswithin the gene, and includes deletion sizesdetermined by Southern blots. Data for deletionsinduced by X-rays (Morgan et al., 1990) and bygamma rays and alpha particles (Thacker et al.,1990) are plotted in Figure 5 as the number ofdeletions of size less than m, N(<m), against m ona logarithmic scale. For some deletions, only theminimum size is known, and the true curve liesbetween the filled circles (all deletions of minimumpossible size) and the open circles (all indeterminatedeletions larger than 15 kb), see the Figure legend.

Comparison of Theorywith Experiment

The theory determines numbers of one class ofdeletions relative to others, not absolute values. Forcomparisons of theory and experiment, the constantK in the equations is normalized to a suitablequantity: e.g. the total number of deletions.

Unbroken chromatin: deletions in human hprt

The calculated number of all observable deletionsis N(<[L + M + R]) (equation (4)), with L and R thedistances to the nearest essential DNA sequences oneither side of a gene of length M. Then largedeletions (Table 1) are equal to N(<[L + M+ R]) − N(<[L' + M + R ']), where L' = 400 kb andR ' = 800 − 40 = 760 kb (Figure 4). Medium deletionsare given by equation (6), with A = 400 kb, theregion between L' and the gene; B = 760 kb,between the gene and R '; C is the length M of thegene. Small deletions equal the number of deletionsentirely within the adjacent markers L' and R ',N(<[L' + M + R ']), minus the number of mediumdeletions as defined.

The size M of the human hprt gene is 40 kb(Edwards et al., 1990). A minimum deletion sizeZ = 2 kb is plausible, and calculations are notsensitive to this parameter because data for smalldeletions are limited. An essential sequence 3' to thegene can be deduced: a very slow-growing mutantincludes the DX144 marker, 1600 kb from the gene,but not 529R (Figure 4); only a single mutant lacksDX144, HX203 in the NEL5 data set (Nelson et al.,1995). The most plausible interpretation is thatHX203 is more complicated than a simple deletion,and an essential gene sequence is located near 529R,so R is 1400 − 40 = 1360 kb. The nearest essentialDNA sequence 5' to hprt is well beyond DXS53 at1750 kb (Figure 4); L is taken here as 5750 kb,because this makes the calculated number oflarge deletions equal to that observed; however,

deletions in X-irradiated primary human fibroblastcells (Morris et al., 1993) are referred to as MOR3.

In Table 1, deletions are classified in threecategories. Small deletions are those in which either(1) both endpoints are within (or very close to) thegene, or (2) one endpoint is within the gene, theother either in the gap between the 5' marker DXS79(Figure 4) and the gene, or between the gene andthe 3' marker DXS86. Medium deletions are those inwhich one endpoint is between the 5' markerDXS79 (Figure 4) and the gene, and the other

Table 1. Experimental data on the distribution in size ofhprt deletionsData set Large del. Medium del. Small del. Total

NEL45 24 17 37 78DEN3 40 20 26 86NEL45 + DEN3a 63 (63) 37 (34) 70 (73) 170BAO5 24 9 17 50(corr.)b 24 (19) 9 (10) 18 (22) 51MOR3 4 4 7 15

Calculated values based on equation (2) are in parentheses; seethe text.

a The following adjustments were made in the data in thepooled NEL45 + DEN3 data set. (1) Small deletions entirely inhprt introns, particularly introns 1 (13 kb) and 3 (11 kb), were notdetected by the methods used; such deletions were observed inthe BAO5 and MOR3 data sets. Based on computer simulationsof randomly located deletions, it was estimated that 10% of thesmall deletions were missed, and the number of small deletionswas increased accordingly; this estimate could be high or low bya factor of 2. (2) Mutant HX203 in the NEL5 data set lacks all 3'markers out to 1600 kb from the gene; this mutant may be morecomplicated than a simple deletion (see the text), and wasomitted.

b Some small deletions in intron 3 were detected in theseexperiments, but other deletions of a few kilobases wereprobably missed, so the number of small deletions was increasedby 5%.


Table 2. The distribution in size of large deletions in various data sets3' end of deletion, kb

5' end, kb 0–40 40–800 800–1200 1200–1400 Total

A. NEL45 + DEN3<−1750 1 (0.9) 19 (13.6) 7 (5.6) 2 (2.5) 29 (22.6)−1750 to −400 1 (2.0) 20 (22.2) 5 (6.3) 1 (2.5) 27 (33.0)

[2.2] [22] [4.7] [1.6] [30.5]−400 to 0 — — 5 (4.1) 1 (1.4) 6 (5.5)

[4.1] [1.3] [5.5]0 to 40 — — 1 (0.5) 0 (0.2) 1 (0.7)

[0.7] [0.2] [0.9]B. BAO5<−400 0 (0.9) 16 (13.9) 3 (4.6) 2 (2.0) 21 (21.6)−400 to 0 — — 2 (1.6) 1 (0.6) 3 (2.2)0 to 40 — — 0 (0.2) 0 (0.0) 0 (0.2)

C. MOR3 800–1000 >1000<−400 0 0 0 0 0−400 to 0 — — 2 2 4

Numbers in parentheses are normalized as in Table 1, and calculated using equation (6),which assumes that the inducing lesion does not break the chromatin, with M = 40 kb;L = 5750 kb; R = 1360 kb. Numbers in square brackets are calculated using equation (10),assuming that the inducing lesion is a chromatin break, and normalized to 71 medium and largedeletions (excluding those with 5' ends more than 1750 kb from gene, see Table 3). Dashes areentered in those fields in which there is no large deletion because of the way they are defined(see the text).

calculations are not sensitive to the exact value,since contributions from the distribution function(1/m3/2) are small at large m. The validity of thedistribution function for m > 2000 kb is discussedbelow.

Expected numbers of deletions in the various sizeclasses for the NEL45 + DEN3 data set werecalculated (Table 1, in parentheses), normalized tothe total number of deletions. The same calculationwas done for the BAO5 data set. Agreementbetween experimental and calculated values is verysatisfying. No attempt was made to fine-tune theparameters to improve agreement between theoryand experiment because of various uncertainties,including exact locations of the markers (Lippertet al., 1995b).

The numbers of large deletions of various sizeswere calculated (Table 2, in parentheses) using thesame parameter values, and are again in goodagreement with experiment. The good agreementextends to values of m much greater than 2000 kb(top row of Table 2), for which collisions will occurmore frequently than predicted by the m−3/2

dependence in equation (1) (see above). Thissuggests a compensating effect: repair of theinducing lesion during the long time before collisionof points initially far apart. Whatever the expla-nation, the theoretical expressions fit the databeyond the range justified by the derivation.

Even though there are only 15 deletions in theMOR3 data set, the lack of any extending more than400 kb 5' to the gene (Table 2) strongly suggests(p > 0.98, Fisher’s exact test) that there is somesequence in the 5' region essential for growth inculture of primary fibroblast cells, but not for theestablished TK6 lymphoblast cell line used in theother experiments.

Unbroken chromatin: deletions inhamster hprt

The plotted continuous line in Figure 5 is fromequation (3a), with gene size M = 38 kb (Rossiter

Figure 5. Cumulative number of deletions of size lessthan m, N(<m), in the hamster hprt gene, plotted againstm on a logarithmic scale (Morgan et al., 1990; Thackeret al., 1990). Only the lower limit to the size of somedeletions is known. If all such deletions were at the lowerlimit, the filled circles would represent the data; if adeletion is larger than the minimum, the correspondingpoint moves to the right as indicated by the arrow. If allundetermined deletions were larger than 15 kb, thesmallest 18 deletions would be represented by the opencircles. The true curve lies between the open and filledcircles. The three lines are calculated with M = 38 kb,Z = 1.3 kb: continuous line, equation (3b) (unbrokenchromatin); broken line, equation (8) (induced by achromatin break) with q = 6; dot-dash line, equation (8)with q = 1.


Table 3. Comparison between (adjusted) experimentaldata for deletions in the NEL45 + DEN3 data sets andcalculated values using equation (7), which assumes thatthe inducing lesion is a chromatin break

Large deletionsq value omitting >1750 kb Medium del. Small del. Total

(Expt., 34 37 70 141adjusted)

1 0 <0.1 141 (141)6 16 52 73 (141)8 33 58 50 (141)

10 47 56 38 (141)12 58 53 30 (141)12 [37] [34] [19] [90]

The second column is the number of large deletions, omittingthose extending more than 1750 kb 5' to the gene (see the text).The calculated numbers in square brackets are based on equation(7) with q = 12, and normalized to a total of 71 medium and largedeletions.

The result of assuming that deletions are formedby misjoining of broken chromatin can besummarized as follows. Equations based onequation (7) with q112 (DNA ends can diffuse longdistances in the cell before reacting) agree with datafor radiation-induced deletions in human hprt largerthan 50 to 100 kb (Tables 2 and 3), but not the datafor smaller deletions in human (Table 3) or hamster(Figure 5) hprt. Conversely, theoretical expressionswith q11 (DNA ends do not move far beforereacting) fit data for the small deletions (Figure 5and Table 3) but not the large.

Deletions in hamster aprt

Only a small fraction of radiation-inducedmutations in a hemizygous hamster aprt gene aresizeable (>1 kb) deletions: three of 55 (Grosovskyet al., 1986), and five of 85 (Miles et al., 1990). Thisis a consequence of the values of two parameters inthe expression for p(m): gene size M is only 2.1 kb(Breimer et al., 1986), and the distance R to thenearest essential sequence must be small because nodeletion extends more than a very few kilobases 3'to the gene (Grosovsky et al., 1986; Miles et al.,1990). For hamster aprt, the probability functionp(m) (Figure 2) is essentially a constant with a value(M + R) that is small compared with that for othermammalian genes. A deletion that deletes any ofthe aprt gene is quite likely to affect the nearbyessential sequence also, and not be detected becauseit is lethal. This conclusion does not depend on thesize distribution function.

Discussion

This work analyzes data on the distribution insize of radiation-induced deletions of one to severalthousand kilobases in human and hamster hprtgenes. One conclusion is that the data are fit by atheory that assumes that inducing lesion does notbreak the chromatin. A second conclusion is that atheory which assumes that deletions arise frommisjoining of broken chromatin does not fit the dataas a whole; if such breaks cause radiation-induceddeletions, either the fraction is small, or there is anadditional (unknown) process that, coincidentally,brings the overall distribution of deletion size closeto that predicted by the theory that assumes thechromatin is not broken.

These conclusions were unexpected. Agents thatform a substantial number of deletions (such asionizing radiation) make DNA double-strandbreaks. Also, restriction endonucleases that makeDNA double-strand breaks cause deletions whenintroduced into mammalian cells, e.g. in hamsterhprt (Kinashi et al., 1995). There is a tendency toassociate breaks in the chromatin with such breaks.

One possibility compatible with the availabledata is that a double-strand break in the DNA doesnot necessarily result in a break in the intracellularchromatin fiber.

et al., 1991) and minimum deletion size Z = 1.3 kb.Tests for agreement between a cumulative plot ofdata as in Figure 5 and a theoretical curve make useof Kolmogorov-Smirnov statistics (Zar, 1984). Thecalculated curve in Figure 5 agrees with either thefilled or open circles with high (00.5) probability,so equations (1) and (2) are in good agreement withexperiment. The agreement suggests also that thereis no essential DNA sequence within 10 kb or so ofthe gene.

Deletions with breaks in the chromatin

Best agreement between experiment and thetheory which assumes the chromatin is broken isobtained by omitting very large deletions with 5'ends more than 1750 kb from human hprt, adefensible step because of reservations aboutequation (7) for m > 2000 kb. Table 3 showsNEL45 + DEN3 data for human hprt, as in Table 1but without the 29 very large deletions, withcalculated numbers (normalized to the reducedtotal of 141) for selected values of q. Clearly, noexpression assuming the chromatin is broken fit thedata. Calculated numbers with q = 12 and normal-ized to a total of 71 medium and large deletions, insquare brackets in Tables 2 and 3, are in goodagreement with data for medium and largedeletions, but the calculated number of smalldeletions is very much less than that measured.

For hamster hprt, the number N(<m) of dele-tions of size less than m calculated from equation(8) is a reasonable fit if q = 1 (Figure 5). For q = 6,the theory does not fit the hamster data at all(broken line in Figure 5), and agreement is worsefor larger values of q. For q = 1, the exponentialterm in equation (7) is very small for m > 100 kb(exp(−[100]1/2/1) < 10−4); this implies that deletionslarger than 100 kb are very much rarer in hamstercells than deletions of a few kilobases, which dis-agrees with evidence for megabase deletions inthese cells (Urlaub et al., 1986).


A second possibility is that deletions may beinduced by DNA lesions other than double-strandbreaks. Ionizing radiation forms sites that canbe cleaved by the Neurospora S1 endonuclease(Andrews et al., 1984) at a greater rate thandouble-strand breaks (Geigl & Eckardt-Schupp,1991); these are probably single-strand nicks thatare repaired slowly because of closely associateddamage, and such persistent nicks have previouslybeen implicated as causes of deletions (Andersonet al., 1991; Bierne et al., 1991; Huang et al., 1989;Hutchinson, 1993).

Restriction endonucleases that first cut one strandof the double helix and then the other, formsingle-strand nicks with a yield 1/4 or more that ofdouble-strand breaks (Modrich, 1979); however,these nicks should be repaired rapidly. Mutantsinduced by restriction endonucleases frequentlyhave two or more partial deletions in the same gene(Kinashi et al., 1995), a very rare occurrence withradiation; this suggests that these deletions arisefrom clustering of lesions created by a singleenzyme molecule acting at several sites a fewkilobases apart.

Radiation-induced deletions could be caused byDNA double-strand breaks in which the chromatinfiber is not broken, or by other DNA lesions. Thesituation is analogous to the induction of chromoso-mal aberrations by ionizing radiation and byrestriction endonucleases introduced into cells(Natarajan & Obe, 1978; Obe et al., 1992); theclassic assumption is that they are induced byDNA double-strand breaks, but solid evidencefor predominantly reciprocal events stronglysuggests aberrations from interactions betweenunbroken chromatids (Revell, 1959; Savage &Harvey, 1991).

The theory put forward here assumes that themajor determinant of deletion endpoints is rate ofcollision, not sequence homology. Very limited dataon sequences at endpoints of radiation-induceddeletions (Morris & Thacker, 1993; Raha &Hutchinson, 1991) suggest that requirements forhomology may not be very strict, allowing fordeletions between a large number of sites. The exactendpoints might be influenced by sequence, withgeneral location determined by collision rate.

As formulated, the theory applies either to adeletion formed between two inducing lesions, orby a single lesion interacting with undamagedDNA. If deletions/colony-forming-unit increaselinearly with radiation dose, induction by one lesionwould be indicated; a quadratic dependence wouldsuggest two lesions. Usable data of this kind arerare, because mutagenized mammalian cells areusually grown under non-selective conditions for anumber of generations before assaying for mutation,and different growth-rates for different clones canstrongly affect the plots. A reliable method is sorelyneeded for measuring mutation frequency inmammalian cells, perhaps based on a fluctuation-type assay. If the ratio of the relatively high numberof small deletions bunched around the hprt gene

(Nelson et al., 1995) to large deletions (as defined inTable 1) were dose-dependent, this would suggestthat they are formed by different processes and castdoubt on the theory presented here.

In the view presented here, radiation-induceddeletions are formed randomly throughout thegenome. The small number observed in a gene suchas hemizygous hamster aprt is ascribed to smallgene size, compounded by an essential sequence soclose it is also deleted by most deletions affectingthe gene.

Cells have two copies of most genes and essentialsequences, so deletions usually form recessivemutations and recessive lethals. The total number ofdeletions induced in the genome can be estimatedusing equation (3a) with p(m) = G, the length of thegenome, and K properly normalized. For example,the induced mutant frequency for the NEL45 dataset was 0.87 × 10−5 for a 2 Gy exposure, and of116 mutants, 54 were deletions entirely containedbetween markers at −1750 kb and +1400 kb(Nelson et al., 1994, 1995). From equation (4),0.87 × 10−5 × 54/116 = K × 144.8, for L = 1750 andR = 1400 − 40 = 1360; then K = 2.8 × 10−8, with allDNA lengths in kb. The number of deletions of sizebetween Z and an upper limit V is:

Deletions/genome = KfG dm/m3/2

=2KGZ−1/2(1 − 4Z/V51/2)

10.1/genome, for 2 Gy (11)

for G = 3 × 106 kb, Z = 1 to 2 kb, and V�Z, and adistribution in size given by equation (2). Other datafor human hprt, including the MOR3 set for primaryfibroblasts (Morris et al., 1993), give comparablevalues. This suggests that recessive deletions are notimportant for single radiation exposures, but mightbe for 60 to 80 Gy over time as in cancerradiotherapy.

The same calculation can be made for the hamsterhprt gene. Induced rates for deletions of 10 kb or lessare 0.8 × 10−5 for 5 Gy (Thacker et al., 1990), and1.3 × 10−5 for 2 to 4 Gy (Morgan et al., 1990). Usingthe mean in equation (3b) with m = 10 kb,1 × 10−5 = 46.7K, or K = 21 × 10−8; equation (11) thengives about one deletion per genome for 3 to 4 Gy.

AcknowledgementsThis research was supported by NIH grants PO1 39238

and RO1 CA58952. The author thanks Dr Howard Liberfor unpublished data.

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Edited by F. E. Cohen

(Received 5 July 1995; accepted 12 September 1995)

analysis of deletions induced in the genome of mammalian cells by ionizing radiation

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