The three-dimensional (3D) organization of chromosomes of Crépis capillaris (2n = 6) has been investigated. Root tips were fixed, macerated with enzymes and gently separated without squashing. The cells were then stained with DAPI and optically sectioned under computer control. Sections were stored as video images and processed to remove noise and out-of-focus information. Computer modelling was then used to trace the paths of each chromosome and to display the paths as a 3D wire diagram. In all, 88 sets of anaphase chromosomes were modelled from 47 optically sectioned cells. The models and the coordinates of the chromosomes were then analysed to detect non-random arrangements or preferential associations of particular pairs of chromosomes. The methods used have significant advantages over electron microscope tomography for the analysis of 3D chromosome arrangement; in particular, the large number of samples allowed more thorough statistical tests to be performed on the data obtained. No evidence was found for either non-random arrangements or homologous association and, moreover, the distances between the two larger pairs of homologues were larger than for other pairs of chromosomes. These results conflict with previous results for this and other plant species where the material was squashed before measurements were taken. We found no evidence of haploid genome separation.

There are many reports in the literature concerning the hypothesis that chromosomes are non-randomly arranged in the nucleus. The reason that such interest has been shown in this idea is because of the possible implications of a non-random arrangement for the control of nuclear events. One example is that a non-random arrangement of chromosomes, in which particular regions of a chromosome were closer to those of another or to the nuclear envelope, might in some way control gene expression. Another is that association of homologous chromosomes might point towards a mechanism for the recognition of homologues prior to the formation of synaptonemal complexes in meiosis.

In Diptera, homologous pairing of polytene chromosomes is well known but evidence for pairing from observations on diploid mitotic cells in higher animals is poorer (reviewed by Comings, 1980). In plants, a wealth of evidence has been accumulated concerning non-random chromosome arrangements in mitotic cells, particularly homologous association (reviewed by Avivi & Feldman, 1980; Comings, 1980). Many of these reports have indicated homologous pairing, although there have been some negative reports as well (Tanaka, 1981; Therman & Denniston, 1984). One of the main reasons for these conflicting results is likely to be that most of the studies mentioned were done with squashed preparations where the positions of the chromosomes were distorted and all three-dimensional (3D) information was lost. Only by analysing the 3D configurations of chromosomes in their native conformation can convincing data be obtained.

One approach to the acquisition of such 3D data is by serial electron-microscopic (EM) sectioning. This technique has been used by Bennett and co-workers to study the distribution of metaphase chromosomes in cereal hybrids. They recorded the 3D coordinates of the centromeres of each individual chromosome by examination of photographs of the serial sections and used these coordinates as markers for the relative positions of the chromosomes. Their studies have indicated that, far from there being homologous association in the cereals studied, the two haploid genomes in the hybrids are actually spatially separated from one another (Finch et al. 1981; Bennett, 1982, 1983; Heslop-Harrison & Bennett, 1983a, b; Schwarzacher-Robinson et al. 1987; Heslop-Harrison & Bennett, 1988). Bennett has also proposed a model for predicting the order of chromosomes in each haploid genome around the metaphase plate. This is based on the premise that chromosomes lie together in 401 such a way that adjacent arm lengths are similar (Bennett, 1982, 1983; Heslop-Harrison, 1983; Heslop-Harrison & Bennett, 1983b, b, c). Other workers, however, have presented evidence against this model (Maguire, 1983; Coates & Smith, 1984; Therman & Denniston, 1984) and Callow (1985) and Dorninger & Timischl (1987) have criticized the theoretical and statistical basis of it.

While serial section reconstruction is a powerful technique, in that very high-resolution information is obtained, it has the severe disadvantage that it is very timeconsuming and thus obtaining statistically adequate sample sizes is practically very difficult. An alternative method, as used here, is optical sectioning combined with fluorescence microscopy. Fluorescence microscopy allows specimens to be viewed in an almost in vivo state and, combined with immunological techniques has revolutionized light microscopy in recent years. The use of fluorescent dyes, e.g. DAPI, for visualization of chromosomes is now widespread. Optical sectioning involves the non-invasive sectioning of a 3D object by taking advantage of the limited depth of focus of a large numerical aperture objective lens. At each focus level, an image is recorded and the resultant stack of images or optical sections is combined or viewed consecutively to allow reconstruction of the object. The whole procedure may be automated and data collection can thus be very rapid. Computer processing of the optical sections to remove out-of-focus information (deblurring) and background noise markedly improves the clarity of the images. Optical sectioning techniques have been described by Weinstein & Castleman (1971), Castleman (1979) and Agard (1984).

One group of workers has employed optical sectioning together with computer modelling to investigate the spatial arrangement of Drosophila polytene chromosomes from different tissues (Agard & Sedat, 1983; Gruenbaum et al. 1984; Hochstrasser et al. 1986; Hochstrasser & Sedat, 1987a,b). Optical section stacks were collected and the chromosomes in each stack were then modelled using an Interactive Modelling Program (IMP) (Mathog et al. 1985; Mathog, 1985) to produce a ‘wirE’ model, in three dimensions, of the chromosomes. Various measurements were made on these models to examine possible non-random spatial arrangements within or between the chromosomes. In the nuclei from salivary glands and other larval tissues studied so far, these workers have failed to detect non-random arrangements between chromosomes although various intra-chromosomal motifs do appear consistently from one nucleus to the next, e.g. right-handed spirals. These methods have not so far been applied to any other organisms.

The species Crépis capillaris has been the object of cytological study for very many years as it has a small number (2n = 6) of large chromosomes. It has been reported to exhibit somatic homologous pairing (Kitani, 1963; Wagenaar, 1969; Ferrer & Lacadena, 1977). In this report, optical sectioning of DAPI-stained, mitotic, root cells of C. capillaris combined with computer modelling has been undertaken to investigate whether there is nonrandom 3D arrangement in this species and whether homologous chromosomes are associated.

Preparation of root tips

Achenes of C. capillaris were collected from plants from a small area of heathland. The achenes were germinated on moist filter paper in the dark at 23 °C and roots were harvested after 2 days when they were approximately 0 ·5-1 ·0cm long. A random sample of the root tips was incubated in tap water at 0°C for 24 h and then Toluidine Blue-stained squash preparations were prepared to check the karyotypes (Marks, 1973). The rest of the roots were fixed without pre-treatment in 4% formaldehyde buffered to pH 6 ·9 (the formaldehyde was freshly prepared from paraformaldehyde and the buffer consisted of 50 mM-Pipes, 5mM-EGTAand 5mM-MgSO4; Lloyd & Wells, 1985) at 23 °C for 1 h. They were then washed thoroughly in buffer and softened in a mixture of 5% macerozyme and 2% cellulase (‘OnozukA′ R10, Yakult Honsha Co. Ltd, Tokyo, Japan) in buffer for 1 h at 23 °C.

The terminal 3 mm of each root tip was then cut away from the rest of the root and the root cap carefully removed under an aqueous solution of 1 μgml−1 4′6-diamidino-2-phenylindole dihydrochloride hydrate (DAPI; Sigma, Fancy Road, Poole, Dorset, UK) on a microscope slide. The tissue was gently teased into small pieces using fine needles and a coverslip was placed over the top. The preparation was then tapped very gently to disperse the cells without squashing them and more stain infiltrated under the coverslip. The cells were stained for 5 min and were then infiltrated with Citifluor anti-fade mountant (The City University, Citifluor Ltd, Northampton Square, London, UK) for approximately 2h before viewing.

Optical sectioning

For optical sectioning, a modified Zeiss Universal microscope, equipped for epifluorescence, was used. For DAPI fluorescence, 365 nm bandpass excitation, 425 nm barrier and 450-490 nm bandpass emission filters were used together with a Leitz ×63/1 ·4NA objective lens. The microscope image was relayed to a high-sensitivity ISIT video camera and the video image was fed to a computer-linked framestore with video-rate averaging capabilities (GEMS Mk III, GEMS of Cambridge Ltd, Carlyle Road, Cambridge, UK). Where required, hard copy of the image was obtained by photographing the monitor screen directly with a 35 mm camera. The microscope fine focus was modified to be driven by a computer-controlled, microstepping motor (Berger-Lahr UK Ltd, St Mary’s Road, Langley, Berks), which provided 10000 steps/revolution or 50 steps μm−1. Control of data collection was then provided by a menu-driven program on a VAX 11/750 minicomputer. At each focus level, 512 video frames were averaged to reduce the noise from the ISIT camera and the averaged image was written to a disc file on the VAX. The focal plane was then raised 0 ·5 μm by the computer and another image was collected. In this way, a three-dimensional data-stack of images representing each nucleus was collected. Finally, a background image was collected by defocusing until there was no discernable structure visible.

All the data processing was carried out on the VAX using programs written in FORTRAN 77. First the background image was subtracted from each of the images in the stack. This largely removed non-random image defects arising from the ISIT camera. Then a simple deblurring algorithm was used to remove the out-of-focus information (Weinstein & Castleman, 1971; Castleman, 1979; Agard, 1984). In this algorithm, adjacent sections are ‘blurreD’ by convolution with the objective lenk 3D point spread function to give approximations to the out-of-focus components of each section and simply subtracted with an appropriate scale factor.

Modelling and analysis

Each stack of images was examined to ensure that all the chromosomes in at least one of the two anaphase sets of chromosomes in each stack could be identified morphologically (by visual comparison of the relative lengths of their arms with those of the Toluidine Blue-stained chromosome karyotype). Stacks in which this criterion was not met (a small proportion of the total number) were discarded. The chromosomes in each stack of images were then modelled using IMP (Mathog et al. 1985; Mathog, 1985). In IMP a cursor is moved in a stack of sections, both within a plane and up and down through the stack. By moving this cursor, the 3D path of each chromosome can be traced. When all the chromosomes have been modelled in this way the model can be displayed as a 3D line drawing and rotated to any orientation.

Each chromosome was identified individually in the model by a different value assigned to the string during modelling. The values were standardized between nuclei. Although the homologues were indistinguishable, the six chromosomes in each anaphase set were treated as individuals rather than one of two homologues for the purposes of some of the following analyses. In the following description of the analyses, the three types of chromosome are referred to by the letters A, B and C (A being the smallest and C the largest) and the six individual chromosomes by the numbers 1-6(1 and 2 being the homologues of chromosome A, 3 and 4, B and 5 and 6, C).

In this species, the chromosomes tend to he in a radial arrangement around the mitotic spindle axis. Thus, the models were rotated and/or projected as stereo pairs so that the radial arrangement of the chromosomes around the mitotic spindle could be visualized and recorded. The three-dimensional coordinates of the modelled points on the chromosomes were then extracted for further analysis.

Radial arrangement

(1) For each of the possible pairs chosen from the six chromosomes, the number of times a particular pair of chromosomes was observed as nearest neighbours in the radial arrangement was counted for each chromosome set. These frequencies were then tested against the expected distribution of the six possible nearest neighbour arrangements of pairs of chromosomes using a chi-square test.

(2) Three pairs of chromosomes may be arranged in a circle in 11 different ways, excluding rotations and mirror images (Heneen & Nichols, 1972). These arrangements are shown in Fig. 1, divided into classes based on the number of pairs of adjacent homologues in the arrangement. If the chromosomes were randomly arranged, arrangements 1, 5, 6 and 7 would be expected to occur twice as frequently as the other arrangements (Nur, 1973). The number of times each arrangement occurred was counted and the observed frequencies compared with the expected values by a chi-square test.

Fig. 1.

Eleven radial arrangements of six chromosomes.

Fig. 1.

Eleven radial arrangements of six chromosomes.

(3) Ferrer & Lacadena (1977) have proposed two analyses of radial arrangement, which they applied to squashed preparations of C. capillaris metaphases. Briefly, their first method expresses the distance between two homologues as the number of intervening chromosomes between them. The probability of r intervening chromosomes is given by:
formula
where 2n is the total number of chromosomes. These probabilities are then used to find expected values.

Their second method treats the set of chromosomes as a whole and counts the number of homologous pairs that are associated. They derived a formula for the expected frequencies (Lacadena et al. 1977) and compiled a table of the probabilities of j associated homologous pairs (where y can have the value 0, 1, 2 or 3) from n chromosomes; again, 2w is the total number of chromosomes (Table 2; and Ferrer & Lacadena, 1977).

Table 2.

Frequencies of pairs of chromosomes lying together

Frequencies of pairs of chromosomes lying together
Frequencies of pairs of chromosomes lying together

These methods were applied to the radial arrangement data and tested using a chi-square test.

Three-dimensional coordinate data

Programs to perform the following analyses were written in FORTRAN 77.

(1) Inter-chromosome distance (ICD) analysis: this analysis was designed to give a single value in gm for the average distance between two chromosomes. The ICD was calculated as follows from the model coordinates of each pair of chromosomes: a segment (called a leg) of the longer chromosome equal in length to the shorter chromosome was defined. This leg was then slid from one end to the other of the longer chromosome. At each position of the leg, a minimum average distance between the leg and the shorter chromosome was calculated as follows: for each coordinate (point) on the leg, the minimum distance to any point on the shorter chromosome was calculated. This was repeated for each point on the leg and the minimum distances summed and divided by the number of points. This procedure was then repeated for each point on the shorter chromosome to the points in the leg. Finally, the two averages were themselves averaged and stored as the I CD for that position of the leg. The final ICD expressed was the minimum of all the ICDs for each position of the leg along the larger chromosome.

The ICD for each chromosome pair is a single distance representing the spatial separation of the chromosomes. By statistical analysis of the results, individual chromosome pairs that are closer together than the others should be detected by having significantly smaller ICDs.

(2) Centromere and telomere analysis: one limitation of the ICD analysis is that chromosome pairs that tend to be parallel will have smaller ICDs than those that are not. Thus, it is a poor measure of the distances between single points on chromosomes, e.g. centromeres. This was rectified by also measuring the distance between centromeres (inter-centromere distance) and the average of the two distances between corresponding telomeres (inter-telomere distance) for each pair of chromosomes.

Test for separation of haploid genomes

A test was devised to detect whether haploid sets of chromosomes were spatially separated. This test was based upon the following questions: do any three chromosomes tend to be close together in three dimensions? If so, do these consist of a haploid set, i.e. an A, a B and a C chromosome? For the purposes of the test, the six chromosomes were regarded as two closed chains of three chromosomes. There are 10 ways of selecting two sets of three chromosomes (triplets) from the six chromosomes of the diploid nucleus so that they form two closed chains. The analysis found the distance travelled by ‘walking’ round each of the two closed chains for each of the 10 pairs of triplets (20 triplets in all). This was done using either the ICD distances or the inter-centromere distances and repeated for all the cells. The distances for each of the 20 triplets were then analysed to see if any of the triplets tended to have different walk distances from any others. If haploid genomes were separated, it would be expected that the triplets containing haploid sets (i.e. triplets with an A, a B and a C chromosome: 135, 145, 136, 146, 235, 236, 245 and 246) would tend to have smaller walk distances than the others.

Statistical analysis of results

Tests for normality and homogeneity of variances of the data obtained from the analyses above were carried out using two of the computer programs from the BIOM suite of statistical routines (Rohlf, Applied Biostatistics Inc., Setauket, NY, USA). A Kruskal-Wallis test for difference in location was performed using the computer program MINITAB (Minitab Inc., State College, PA., USA). This was also used to produce dotplots of the distance distributions. Programs to perform chisquare analyses and non-parametric multiple comparisons by simultaneous test procedure were written in FORTRAN 77.

We confirmed the preliminary identification of the species by examination of the karyotypes from the Toluidine Blue-stained, metaphase, squash preparations of the root tip cells (Fig. 2). There were six chromosomes identical to those described by Babcock & Jenkins (1943) and Schweizer (1973) for C. capillaris. The middle-sized pair of chromosomes was telocentric and often had small satellites. No B chromosomes were observed in this variety. Table 1A contains the results of chromosome length measurements made on the karyotypes from five preparations. Since the absolute lengths of the chromosomes vary depending on the method of preparation, we have also expressed length values as a percentage of the length of the whole genome as well as the ratios of small to long arm lengths. Our results agree with those of other workers (Kuroiwa & Tanaka, 1970; Sacristan, 1971; Tease & Jones, 1976; Ferrer & Lacadena, 1977).

Table 1.

Chromosome lengths (μm)

Chromosome lengths (μm)
Chromosome lengths (μm)
Fig. 2.

Karyotype of C. capillaris. Toluidine Blue-stained preparation, brightfield illumination. Bar, 10 μm.

Fig. 2.

Karyotype of C. capillaris. Toluidine Blue-stained preparation, brightfield illumination. Bar, 10 μm.

Phase-contrast observations of the formaldehyde-fixed root tip cell preparations showed that the plasma membrane and cell vacuole was intact and the cell contents undisturbed. Indirect immunofluorescence of microtubules (not shown) indicated that the cytoskeleton of the cells was normal with an intact cortical array of microtubules or mitotic apparatus. Nuclear preservation was also good with a clearly defined 3D structure, indicating that the cells had not been squashed.

Three optical sections near the top, middle and bottom of a typical nucleus are shown in Fig. 3 together with the same sections after deblurring. The deblurred image shows greatly improved clarity over the original. In nearly every case, deblurring of the stack of images allowed unambiguous identification of the three pairs of chromosomes in one or both anaphase sets by visual inspection of their relative arm lengths whilst moving up and down the stack. The small proportion of the stacks in which this was not the case was discarded.

Fig. 3.

Three optical sections from near the bottom, the middle and the top of a stack. A-C. Before processing. D-F. The same sections after background subtraction and deblurring.

Fig. 3.

Three optical sections from near the bottom, the middle and the top of a stack. A-C. Before processing. D-F. The same sections after background subtraction and deblurring.

In all, 47 stacks were used for modelling and from the 94 sets of anaphase chromosomes, 88 sets of chromosomes were modelled. The chromosomes in the remaining six sets could not be identified unambiguously and so were not modelled. A complete stack of modelled sections from the same cell as in Fig. 3 is shown in Fig. 4. A stereo pair of a projection of the stack of deblurred sections is shown in Fig. 5 and a stereo pair of the corresponding model in Fig. 6. Chromosomes of type A are represented by pluses, type B by squares and type C by crosses. In Fig. 7 the model has been rotated so that the axis of the mitotic spindle is approximately perpendicular to the plane of the paper (the set of chromosomes furthest from the viewer is represented by smaller symbols for clarity). The radial arrangement of the two anaphase sets can now be clearly seen.

Fig. 4.

A-S. Consecutive modelled sections from bottom to top.

Fig. 4.

A-S. Consecutive modelled sections from bottom to top.

Fig. 5.

Stereo projection of the processed stack of images.

Fig. 5.

Stereo projection of the processed stack of images.

Fig. 6.

Stereo projection of the model.

Fig. 6.

Stereo projection of the model.

Fig. 7.

Stereo projection of the model tilted to show a pole view. The right-hand set of chromosomes (in Fig. 6) is nearer the viewer.

Fig. 7.

Stereo projection of the model tilted to show a pole view. The right-hand set of chromosomes (in Fig. 6) is nearer the viewer.

From the models, the 3D coordinates of the points in each string in a set were obtained and the total lengths and the lengths of each arm of each chromosome were calculated. Chromosome lengths in absolute units and expressed as a percentage of the total for the genome are given in Table IB together with the ratios of short to long arm length. These agree well with those from the Toluidine Blue-stained karyotypes and confirm the identification of the chromosomes.

Radial arrangement analysis

The radial arrangements were recorded after visual examination of the models (see Materials and methods). In a small number of the modelled sets of chromosomes (13), the radial arrangement could not be unambiguously determined, as one or more of the chromosomes did not appear to lie in a circle defined by the others but lay inside or outside the circle. These sets were thus not included in the radial arrangement analysis although they were included in the 3D coordinate analyses below. Excluding these sets resulted in 75 sets remaining from 42 cells.

In 33 of these 42 cells, both sets were analysed. The two sets nearly always mapped onto one another so that a view from one pole showed six pairs of overlapping chromosomes (Fig. 7).

Frequency of pairs of chromosomes adjacent to one another in the radial arrangement

The frequencies of the six possible pairs derived from 75 radial arrangements are shown in Table 2. Expected frequencies were calculated on the basis that homologues (i.e. AA, BB and CC specified by 12, 34 and 56, respectively) were four times less likely to lie together than heterologues (AB specified by 13, 14, 23, 24; AC specified by 15, 16, 25, 26 and BC specified by 35, 36, 45, 46) and the difference between observed and expected frequencies tested using a chisquare test. There was no significant difference between the frequencies for each pair, indicating that there was no preference for a particular pair of chromosomes to lie together.

Frequency of radial arrangements

The frequency of each of the 11 possible arrangements (Fig. 1) is shown in Table 3 together with the expected frequencies. Again, there was no significant difference between the frequencies for each arrangement as determined using a chisquare test, indicating that there was no preference for a particular arrangement.

Table 3.

Frequency of possible radial arrangements

Frequency of possible radial arrangements
Frequency of possible radial arrangements

Analysis of Ferrer & Lacadena (1977) 

The results of this analysis are shown in Table 4. Treating the pairs of chromosomes separately (A), or as a whole (B), there was also no significant deviation from a random distribution.

Table 4.
Analysis of Ferrer & Lacadena (1977)
Analysis of Ferrer & Lacadena (1977)

These methods again indicate no preference for particular chromosomes to be associated.

3D coordinate data

A summary of the ICDs, mean inter-centromere and mean inter-telomere distances obtained from n = 88 models of sets of chromosomes from 47 cells is given in Table 5 and Fig. 8. There are 15 unique combinations of distances between the six chromosomes grouped into six classes by chromosome type. In the case of the ICD results, chromosome pairs 3-4 and 5-6 appear to have a larger distance between them and pairs 1-5, 2-5 and 2-6 a smaller distance between them than the others. There appears to be no difference between the inter-centromere distances but the inter-telomere distances of the pairs 1-2, 1-4 and 2-3 appear to be smaller than the others and especially pairs 3-5, 3-6, 4-6 and 5—6. In summary, from the plots of the inter-chromosome distances, the larger two pairs of homologues appear to be further apart than the others while the distances between the largest and smallest chromosomes appear to be small. The telomeres of the larger pairs of chromosomes appear to be further apart than those of the smaller ones. There appears to be no difference between the inter-centromere distances. As would be expected from an anaphase arrangement, overall, the inter-centromere distances are smallest, the inter-telomere distances are largest and the inter-chromosome distances are intermediate between these two.

Table 5.

Distances between pairs of individual chromosomes (μm)

Distances between pairs of individual chromosomes (μm)
Distances between pairs of individual chromosomes (μm)
Fig. 8.

Mean inter-chromosome, inter-centromere and inter-telomere distances between each pair of chromosomes. Key to chromosome pair number: 1, 1 to 2; 2, 1 to 3; 3, 1 to 4; 4, 1 to 5; 5, 1 to 6; 6, 2 to 3; 7, 2 to 4; 8, 2 to 5; 9, 2 to 6; 10, 3 to 4; 11, 3 to 5; 12, 3 to 6; 13, 4 to 5; 14, 4 to 6; 15, 5 to 6.

Fig. 8.

Mean inter-chromosome, inter-centromere and inter-telomere distances between each pair of chromosomes. Key to chromosome pair number: 1, 1 to 2; 2, 1 to 3; 3, 1 to 4; 4, 1 to 5; 5, 1 to 6; 6, 2 to 3; 7, 2 to 4; 8, 2 to 5; 9, 2 to 6; 10, 3 to 4; 11, 3 to 5; 12, 3 to 6; 13, 4 to 5; 14, 4 to 6; 15, 5 to 6.

To test for the statistical significance of these results, information is needed about the way the distances for each pair are distributed. If the distances are normally distributed and if the variances of the distributions are homogeneous among pairs, a single classification analysis of variance may be performed to test for an overall difference between the pairs. If this gives a significant result, multiple unplanned comparisons between each pair of mean distances can be carried out to determine which distances are larger or smaller than the others. If, on the other hand, the distances are not normally distributed or do not have homogeneous variances, a non parametric test should be performed instead and in the case of a significant result being obtained, non-parametric multiple comparisons between the distributions. The analysis of variance is preferred if the assumptions are entirely or even approximately held, as it is more sensitive to small differences between groups than a non-parametric test.

To test for normality, the observed distributions were tested against a normal distribution with the same mean and standard deviation using a Kolmogorov-Smirnov one-sample test against an intrinsic null hypothesis, that of normality (Sokal & Rohlf, 1981, pp. 716-721). The statistics for skewness and kurtosis were also calculated. Four out of the 15 ICD distributions were normal, 5 out of 15 inter-centromere distance distributions and 3 out of 15 inter-telomere distances distributions. The rest were significantly (P< 0’001) different from normal and all had positive skewness (more small values than expected) and kurtosis (more values near the mean than expected). These results agreed with inspection of dotplots of the distributions (not shown). The homogeneity of the variances of the distributions was tested with an Fmax test and Bartlett’s test for homogeneity (Sokal & Rohlf, 1981, pp. 404-405) and all showed significant (P<0 ·05) heterogeneity.

As a result of these tests, therefore, the use of an analysis of variance was not considered to be justified. Instead, the Kruskal-Wallis test for differences in location (Sokal & Rohlf, 1981, pp. 429-432) was performed on the 15 distance distributions with the result that there were very significant (P< 0’001) differences between the distances between pairs of chromosomes using the ICD data and the inter-telomere data but no differences using the inter-centromere data. Non-parametric, multiple comparisons by simultaneous test procedure were then performed (Sokal & Rohlf, 1981, pp. 438-439) on the ICD and inter-telomere data to examine which distances were significantly larger or smaller than the others. The results of these comparisons are shown in Tables 6 and 7.

Table 6.

Comparison of inter-chromosome distances

Comparison of inter-chromosome distances
Comparison of inter-chromosome distances
Table 7.

Comparison of inter-telomere distances

Comparison of inter-telomere distances
Comparison of inter-telomere distances

The tables may be interpreted as follows: columns or rows containing several significant differences indicate that the distances between the two chromosomes corresponding to that column or row are significantly different from the others. The plots of the means can then be examined to determine whether the significantly different distances are greater or smaller then the others. In addition, individual distances may be compared against each other at the intersection of the row and column for the pairs of distances. The results of the multiple comparisons confirmed the preliminary examination of the data. The ICD values between both the larger pairs of homologues (3-4, 5-6) were larger than those between the other chromosomes, especially the pairs 1-5, 2-5 and 2-6. As for the inter-telomere distances, the most obvious result was that the distance between the smallest homologues (1-2) was much less than that between all the other chromosomes. In addition, the distances between the larger chromosomes (3-5, 3-6, 4-6, 5-6) tended to be large and between the smaller chromosomes (1-3, 1-4, 2-3, 2-4) tended to be small.

Test for spatial separation of haploid genomes

The distances travelled by ‘walking’ round each of the 20 triplets using the ICD and the inter-centromere data are given in Table 8 and Fig. 9. The distances were examined for normality and were generally distributed as before, i.e. with positive skewness and kurtosis. A Kruskal-Wallis test was used, therefore, to test for differences in location between the distances for each of the triplets. This test revealed a highly significant (P< 0-001) difference between the triplets using the ICD data but no significant difference using the inter-centromere data. Multiple, non-parametric comparisons between the orders for the ICD data are shown in Table 9. These together with the plots of the means showed that the triplets for the combination AAC (125, 126) were smaller than several of the others. No other general trends were apparent in the data and, in particular, the triplets containing haploid sets were not especially different from the others. Thus there appears to be no support for the hypothesis of haploid genome separation in C. capillaris.

Table 8.

Test for haploid genome separation

Test for haploid genome separation
Test for haploid genome separation
Table 9.

Comparison of triplet walk distances using ICD data

Comparison of triplet walk distances using ICD data
Comparison of triplet walk distances using ICD data
Fig. 9.

Mean walk distances using ICD and inter-centromere data. Key to triplet numbers: 1, 123 (AAB); 2, 124 (AAB); 3, 125 (AAC); 4, 126 (AAC); 5, 134 (BBA); 6, 234 (BBA); 7, 345 (BBC); 8, 346 (BBC); 9, 156 (CCA); 10, 256 (CCA); 11, 356 (CCB); 12, 456 (CCB); 13, 135 (ABC); 14, 136 (ABC); 15, 145 (ABC); 16, 146 (ABC); 17, 235 (ABC); 18, 236 (ABC); 19, 245 (ABC); 246, (ABC).

Fig. 9.

Mean walk distances using ICD and inter-centromere data. Key to triplet numbers: 1, 123 (AAB); 2, 124 (AAB); 3, 125 (AAC); 4, 126 (AAC); 5, 134 (BBA); 6, 234 (BBA); 7, 345 (BBC); 8, 346 (BBC); 9, 156 (CCA); 10, 256 (CCA); 11, 356 (CCB); 12, 456 (CCB); 13, 135 (ABC); 14, 136 (ABC); 15, 145 (ABC); 16, 146 (ABC); 17, 235 (ABC); 18, 236 (ABC); 19, 245 (ABC); 246, (ABC).

Previously, optical sectioning has been used to derive three-dimensional data from the giant, polytene chromosomes of Drosophila (Agard & Sedat, 1983; Gruenbaum et al. 1984; Hochstrasser et al. 1986; Hochstrasser & Sedat, 1987a,b). We have been able to collect optical sections and model chromosomes from much smaller, diploid, plant nuclei maintained very close, in structural terms, to the in vivo state. We have analysed the radial arrangements derived from the models to detect nonrandom interactions and have used the three-dimensional coordinates of the chromosomes to perform quantitative analyses on a large number (47) of cells. We have measured pairwise distances between centromeres, telomeres and, by a novel method, the average distance between chromosomes.

Radial arrangements are derived from 2D projections of the 3D data and it might be expected that their analysis would be less sensitive than those for the full threedimensional data. They were included, however, because they enabled the observed arrangements to be tested for non-randomness and in order to compare the resultsobtained with those of previous authors. The analyses gave no significant deviations from randomness.

The ICD analysis, which measures pairwise distances between whole chromosomes, found that the two larger pairs of homologues (types B and C) were further apart than other combinations of chromosomes. We did not test against a random arrangement as it is difficult to define such an arrangement in three dimensions given the overall restrictions placed upon the chromosome positions by their attachment to the spindle. The intercentromere and inter-telomere analysis results are consistent with and probably simply reflect the gross arrangement of the chromosomes that would be expected at anaphase where the centromeres are close together near the poles and the telomeres trail out towards the metaphase plate.

Overall, we have found no evidence of homologous association in root tip cells of C. capillaris. An explanation of the contradictory findings of other workers on metaphase chromosomes of this species (Kitani, 1963; Wagenaar, 1969; Ferrer & Lacadena, 1977) probably lies in the fact that the cells were squashed before measurements were taken. This may well be true for the evidence against the present findings from other plant species (see Avivi & Feldman, 1980, for a review). Our results agree, however, with those of Heslop-Harrison & Bennett (1983a, 1988), who used three-dimensional analyses of serial EM sections to study chromosome arrangement in the cereals Aegilops umbellulata, Hordeum vulgare, Hordeum marinum and Zea mays and found no evidence for homologous association.

Our test for haploid genome separation is different from that of Bennett (1983). He compared the number of times that it is possible to draw a straight line through a radial arrangement separating two haploid sets with an expected number. For C. capillaris with 2n= 6 chromosomes this reduces to a distinction between arrangements (1) (in our Fig. 1) and the rest, and we have shown (Table 3) that there is no preference for any arrangement. We prefer to consider haploid genome separation as a tendency for three chromosomes of a haploid set to be close together. Our results did not indicate such genome separation.

In summary, we have found no evidence for any departure from randomness in these cells.

One aim that is common to many studies of mitotic chromosome arrangement is to be able to predict chromosome positions when they are genetically active, i.e. during interphase. Direct correlation between mitotic and interphase nuclei relies upon factors that are difficult to control, including chromatin condensation and methodological artefacts. Also, rapidly dividing cells (as used here) form only a subset of the population of cells in a root, and so rearrangements after division has ceased and cells have become differentiated cannot be ruled out. A consequence of the phenomenon first described by Rabi (1885) and frequently reported since, whereby centromeres and telomeres remain polarized from telophase through interphase to the following prophase, is that major reorganization of chromosome position after telophase is unlikely. However, this stability of arrangement has yet to be tested in plants using a three-dimensional analysis.

If it is assumed that the anaphase arrangement accurately reflects the interphase arrangement, the present results are in agreement with those of other studies on Sperling & Ludtke (1981) found no evidence of homologous pairing at interphase in prematurely condensed chromosomes of the Indian muntjac. Cremer et al. (1982) used ultraviolet beam microirradiation to mark a small part of the interphase chromatin of Chinese hamster cells and found few cases where homologous chromosomes lay together in the marked region. Another study, however, using autoantibodies from patients suffering from the CREST form of scleroderma to label centromeres of rat kangaroo and Indian muntjac chromosomes did produce evidence for homologous association (Hadlaczky et al. 1986). Centromeres of homologous chromosomes were associated in 20-30% of the nuclei where the chromosomes could be identified. In mammalian systems, there is evidence for the association of acrocentric chromosomes, which bear the nucleolusorganizing region (NOR) (see Kirsch-Volders et al. 1980, for references). In plants, this has not been reported and the present results would argue against such association as the distance between the NOR-bearing chromosomes in the species used here (type B chromosomes) was larger than most of the others.

There is no evidence available to explain directly our finding that larger homologues tend to be further apart than other combinations of chromosomes. There are several processes and structures that are likely to be involved, however. As the mitotic spindle is a dynamic structure, energetic constraints might limit the positions at which chromosomes can be attached to the spindle microtubules so as to keep the spindle as compact as possible. During interphase, the attachment of centromeres and telomeres to the nuclear envelope and nuclear skeleton is also likely to be involved in the maintenance of chromosome position.

Conclusive answers to questions concerning chromosome arrangement will ultimately rely on three-dimensional analyses of statistically valid numbers of nuclei such as that presented here. Elucidation of the biological significance of the results obtained will also require coordination of such studies with studies on chromosome arrangements during interphase.

We thank Drs D. A. Agard, J. W. Sedat and D. Mathog for generously providing us with their computer programs for deblurring and modelling of optical sections, Mrs P. Phillips for typing the manuscript, and Mr P. Scott and Mr A. Davies for photographic services.

This work was supported by the Agricultural and Food Research Council via a grant-in-aid to the John Innes Institute. Support was also received from the Gatsby Foundation.

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