the average meiotic stage of a certain spikelet position was presented. The method was based on the assumption that all meiotic stages from pachytene to ...
H E R E G3-8
THE RELATIVE DURATION OF THE MEIOTIC STAGES IN POLLEN MOTHER CELLS OF BARLEY By DAG LINDGREN, G o S T A ERIKSSON and l N G E R EKBERG DEPARTMENT OF FOREST GENETICS, ROYAL COLLEGE O F FORESTRY, STOCKHOLM. SWEDEN
(Received March 3rd. 1969)
INTRODUCTION
T
HE present communication is an extension of a previous one (EKand ERIKSSON,1965), in which a method for calculating the average meiotic stage of a certain spikelet position was presented. The method was based on the assumption that all meiotic stages from pachytene to tetrads were of equal duration which evidently is an oversimplification. Therefore, it was necessary to develop more precise methods for determining the duration of individual stages. This is of particular interest since it has been shown that some of the meiotic stages may be highly radiosensitive compared to other stages (for references cf. ERIKSSON and TAVRIN, 1965). BERG
Material and methods Main spikes of Bonus barley were used for the cytological examination. The spikes were fixed when the height of the plants amounted to 25-31 cm. Totally 53 spikes were examined. In each spikelet the stage of development was determined in the central and one of the lateral anthers. When several different meiotic stages were present in the same anther, 100 pollen mother cells (PMC) were classified with respect to meiotic stage. To be able to calculate the duration of a meiotic stage it is necessary to make observations concerning the frequency of PMC in a certain
206
DAC LINDCREN, COSTA ERIKSSON AND INCER EKBERG
stage on different occasions during the development from prepachytene to the microspore stage. However, the present material was fixed on the same occasion and therefore it is impossible to calculate the duration of the individual stages in absolute time units. The calculations might be based on a biological time unit such as the difference in stages of development between two consecutively ranked spikelets. If this difference is constant it might be possible to estimate the duration of stages in spikelet units. The two most advanced spikelets were given the ranking value 1. The spikelets were consecutively given higher ranking values towards the base and the apex of the spike. Consequently the highest ranking values are found at the base and the top of the spike (see also I':KBERC and ERIKSSON, 1965). The duration of a stage will be equal to the area between the curve showing the percentage of PMC at this particular stage and the time axis as is shown in Figure 1. The areas calculated in this way are equal to the areas between the curves for the cumulative percentages of the stages as illustrated in Figure 2. Relative durations obtained in this way are biased as the frequency of a stage should, along the time axis (spikelet position), start at 0 "/o and pass its maximum and finally end at 0 p. This is obviously not the case in the present material (cf. Fig. 1) and different stages are differently influenced by this drawback. In spite of this the respective areas between spikelet positions 1-6 were calculated. The results are shown in column 4 of Table 3. The durations of the individual stages are directly proportional to their frequencies if the following prerequisites are fulfilled. (1) The rate of cells reaching each stage is constant. ( 2 ) The same number of cells enter and leave each stage in each moment.
This would graphically be reflected as straight and parallel lines in Figure 2. Close to spikelet position 4 the linear parts of the curves for the cumulative frequency of diplotene and tetrads respectively, constitute good approximations to straight and parallel lines. This means that the percentages of the various stages from diplotene to tetrads at spikelet position 4 (cf. column 2 of Table 3) constitute good approximations to the relative durations of these stages. In spite of this it is quite obvious from Figure 2 that the linear parts of the curves for diplotene and tetrads diverge somewhat. To make a correction for this divergence the following formula might be used:
207
DURATION OF MEIOTIC STAGES IN BARLEY
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208
DAG LINDGREN, GOSTA ERIKSSON AND INGER EKBERG Cumulative 100
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'
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2.3
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microspores
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Fig. 2. The percentage of PMCs which have passed the borders between different stages as a function of spikelet position. The values might be calculated by consecutive adding of the percentages listed in Table 1 .
f1-fz (fl-fo) (fz-fo) where T I = the relative duration of stage 1 fl=the cumulative frequency of stage 1 f z = the cumulative frequency of stage 2, which is assunied to follow stage 1 immediately f o = the ordinate of the intersection point of the approximated straight lines. Ti =
209
DURATION OF MEIOTIC STAGES IN BARLEY
TABLE 1. The number of anthers cincclysed and the percentage of PMC in different phases of development. The percentages are calculated on all analysed P M C
1
Frequency of I'MC in different stages Spikelet position
Number of anthers analysed
"repachytene
424 424 421 417 367 257
0.2 0.9 1.4 5.3 20.6 37.0
Diplotene-
15.9 32.6 44.4 55.3
15.9 19.9 17.0 4.7
Tetrads
Microspores
13.8 25.4 31.8 23.7 11.7 2.3
70.0 55.3 35.0 18.5 0.7
The formula was applied to the frequencies at spikelet position 4. The cumulative frequencies based on all PMC were calculated for the stages diplotene-tetrads. The relative duration for each stage was calculated, based on thus estimated frequencies, by using the formula given above.
RESULTS The percentage of PMC in different meiotic stages at the different spikelet positions is shown in Table 1. As the percentages of P M C in the stages diplotene-telophase I1 was considerably lower than for other stages, they are presented as one group in this table. In Table 2 the percentages of PMC in diplotene-telophase I1 are shown separately as well as the number of anthers containing these stages. Based on these frequencies it was possible to calculate the duration as described above. The results are presented in Table 3. In column 2 the relative duration of the stages diplotene-telophase I1 estimated as percentic distribution of PMC in these stages is presented. In column 3 the values following correction for the non-parallelism of the lines according to the formula given above (fo was calculated to -1.3) are compiled. In column 4 the duration is calculated based on the areas in Figure 1. Based on the data presented in Figure 2 it seems reasonable to assume that the later a P M C enters meiosis the more extended is the passing of meiosis. If this assumption is accepted the median duration of meiosis can be calculated at the 50 % level as illustrated in Figure 2. 14
- Heredifas 63
210
DAG LINDGREN, C ~ S T AERIKSSON AND INGER EKBERG
TABLE 2 . The number of cinthers containing P N C of the stages diplotene-telophrise I1 rit the different spikelet positions cis well as the percentrige of PLMC in these stages. The percentages are calculated only on the number of cells between diplotene and telophase I1
__
-
Number Spike- of anthers i n the 1)iplolet posi- following tene meiotic tion stages
8 6 30 53 23 4
36.1 43.7 22.4 19.5 28.2 32.0
\I eta-
.ha-
phase I
)base
Inter-
I
Telophase I
2.9 0.7 1.2 2.4 3.3
0.0 3.4 5.4 4.6 9.1
9.4 26.0 18.0 13.0 8.6 0.2
I I Pro-
bleta-
.haphase I1
Telophase 11
8.6 3.2 9.4 8.0 9.9 19.8
26.4 2.1 17.1 24.8 20.3 22.6
3.4 3.9 3.0 1.5 1.3 0.0
7.5 10.0 7.3 7.2 13.6 1.8
3.2 3.0 3.3 5.4 3.9 0.0
2.4 3.9 12.3 13.6 1.8 0.0 1
TABLE 3 . Observed percentnge o f PMC in different stnges at spikelet position 4 find the relritive durcitions of the stciges estimcited by t w o different methods. The percentages refer t o the duration of diplotene - telophase I1 ~
-~.
~~
Duration
hteiotie
Diplotene
Diakinesis illetaphase I Anaphase I Telophase I Interphase Prophase I 1 illetaphasc I 1 Anaphase 11 Telophase I1
Observed as percentage in spikelet position 4
19.5 8.0 24.8 2.4 4.6 13.0 1.5 7.2 5.4 13.6 100.0
Corrected by formula 1-
I1
f,
Estimated by the areas in Fig. 1
- f,
(fl - f,)
17.9 7.5 24.1 2.5 4.7 13.4 1.6 7.6 5.8 14.9 100.0
(f,- f")
II
26.6 8.7 19.1 2.2 6.2 14.0 2.1 9.0 3.9 8.2 100.0
D U R A T I O N OF MEIOTIC S T A G E S IN BARLEY
211
Even if the assumption is not valid the duration of the different stages at the 50 % level is probably representative. The median value of the total duration from diplotene to telophase I1 was estiniated to be 0.8 spikelet units (cf. Fig. 2 ) . In the same way the median duration of meiosis from pachytene to reaching of the microspore stage was estimated to 4.5 spikelet units. DISCUSSION It has clearly been demonstrated that the rate of development of a plant varies according to the temperatures prevailing during the investigation (cf. DORMLINC et d.,1967). Therefore, an investigation of the duration of individual stages in a material grown under undefined environmental conditions will be of limited value and can only be valid for that particular material. The statistical accurracy is primarily based upon the number of anthers investigated and how representative these anthers are. PMC of a particular stage is found in about 16 anthers in spikelet position 4. This value is probably the most critical one from a statistical point of view. The standard deviation which in this case is equal to the square root of 16 will amount to 25 %. Therefore, from a statistical point of view it might be stated that the present material is large enough for estimates of the relative durations of the stages. This is further supported by the fact that the two calculation methods used gave relatively similar results (compare Table 3). Furthermore, at the positions 3 and 5, where the deviations from linearity were not too great and the number of anthers relatively large, almost the same pattern as at position 4 was obtained. An initiation or ceasing of the development by an external agent might cause severe errors in the results. However, such a pattern of development is not probable as this requires that the curves in Figure 2 increase in an irregular manner, which is obviously not the case. The ranking of the duration of the stages which might be made by the aid of the percentages in Table 3 cannot yet be regarded as definite. However, it might be concluded that pachytene is of much longer duration than all other stages and that diplotene and metaphase I constitute long lasting stages in agreement with observations from other species (cf. EKBERC et d., 1967). Only some hints concerning the duration of meiosis measured in hours are available. In a material fixed 3 days later than the present material only microspores were detected. All meiotic stages from
212
DAG LINDGREN, GOSTA ERIKSSON AND INGER EKBERG
pachytene to tetrads, corresponding to 4.5 spikelet units, must be passed during this time. Therefore one “spikelet unit” must be less than 16 hours. This means that the stages of shortest duration will last for less than one hour.
SUMMARY The relative duration of individual meiotic stages in PMC of barley have been calculated by the aid of the percentages of PMC in the various stages in different spikelet positions. The obtained relative durations for the stages diplotene-telophase I1 are roughly: diplotene 20 %, diakinesis 10 %, metaphase I 20 %, anaphase I less than 5 %, telophase I 5 %, interphase 15 %, prophase I1 less than 5 %, metaphase I1 10 %, anaphase I1 5 % and telophase 11 10 %. Literature cited DORMLING, I., GUSTAFSSON,A,, JUNC, H. R. a n d VON WETTSTEIN, D. 1966. Phytotron cultivation of Svalof’s Bonus barley and its mutant Svalof’s hlari. - Hereditas 56: 221-237. EKBERG, I. and ERIKSSON, G . 1965. Demonstration of meiosis and pollen mitosis by photomicrographs and the distribution of meiotic stages in barley spikes. Ibid. 53: 127-136. EKBERG, I., ERIKSSON, G., RARTEL,N . and SUL~KOVA,Z. 1967. T h e meiotic development in male aspen. - Studia Forest. Suecica 58: 1-18. ERIKSSON, G. and TAVRIN, E. 1965. Variations in radiosensitivity during meiosis of pollen mother cells in maize. - Hereditas 54: 156-169.
