2
.
4
. Estimation of cell – age distribution 6ia cell lengths
In accordance with views that plant root meris- tems consist of exponential cell – age distributions
Webster and MacLeod, 1980; Ivanov and Du- brovsky, 1997, and all cells in a meristem enter
mitosis when they obtain critical length Ivanov, 1971, a frequency distribution of cell lengths of
cells shorter than critical length in 0.5 mm root segments will be comparable to a theoretical cell –
age distribution for each species tested. Once crit- ical cell length was determined for each species,
cells were grouped within each 1.5-mm length be- tween minimum and critical lengths determined
for each root segment. A calculated cell – age dis- tribution e.g., 10, 20, etc. of the cycle com-
pleted was calculated with cell length data. For all root segments, there were a small number of
cells that were very short. For all segments, these small numbers of very short cells were grouped
with longer cells in order to obtain a more realis- tic value for the first decile 0 – 10 of the cell –
age distribution. After the number of cells of the first decile was established, cell numbers in re-
maining deciles were determined by partitioning the remaining cells in roughly equal cell length
groupings. In this manner, numbers of cells in ten decile groups were established for each segment.
From numbers of cells in deciles, percentages of cells in deciles of the cycle were calculated. Calcu-
lated percentages of cells in each decile of cycle completed were compared with expected percent-
ages of cells in deciles based upon an exponential decay formula y
t
= y
0 − kt
, where y
t
and y are
relative frequencies at time t and time 0, respec- tively Webster and MacLeod, 1980. Expected
percentages of cells in each decile of ten root samples at each tissue distance were compared
with the expected percentage with a chi-square test Mendenhall and Ott, 1972.
3. Results
3
.
1
. Lengths of mitotic and interphase cells Distributions of cell lengths of cells in mitosis
from all ten, 0.5-mm segments of P. sati6um were determined. Data in Fig. 1 show distributions of
cells in mitosis for three separate, 0.5-mm root samples three roots with the largest numbers of
cells in mitosis. Each of the three figures show two peaks which may be attributed to smaller
cells which may have been in telophase and larger cells
which may
have been
in prophase,
metaphase and anaphase. Clearly, there was no distinct separation between smaller and larger mi-
totic cells within any of the three roots. Mean length values ranged from 25.0 to 32.6 mm and
standard deviations ranged from 8.2 to 10.4 mm. Data in Table 1 show a composite distribution of
all mitotic cells from all 0.5-mm segments of P. sati6um tested. Lengths ranged from 9 to 56 mm
and showed no distinct separation between smaller and larger mitotic cells with a mean of
27.4 mm and a standard deviation of 9.2 mm. Overall, there were 24 cells 11.5 above 37.5
m m in length with no values greater than 52 mm
critical length. Data in Table 1 also show that mitotic cells of
P. sati6um were longer in 1.0 – 3.0 mm segments compared with 0.5-mm segments. For example,
for 1.0-mm segments, mean length was 25.6 mm, similar to 27.4 mm for 0.5-mm segments, while
for cells from 2.5-mm segments mean length was 49.9 mm. In accordance, 5.5 of all mitotic cells
had lengths greater than 52 mm in 1.0-mm seg- ments while 33.3 of mitotic cells in 2.5-mm
segments were greater than 52 mm. In this man- ner, mitotic cells were larger in root tissues far-
ther from terminal portions.
The distribution of lengths of interphase cells in 0.5-mm segments of P. sati6um was compared
with distributions of lengths of mitotic cells shown above in order to determine numbers and
percentages of cells longer than critical length. Lengths of interphase cells of 0.5-mm root seg-
ments of P. sati6um ranged from 7.5 to 135 mm and 8.7 of all cells had lengths greater than
critical length Table 1. As noted for mitotic cells above, interphase cells of P. sati6um were larger
in tissues farthest from terminals Table 1. For example, in 1.0-mm segments, 4.7 of all inter-
Fig. 1. A – C Frequency distributions of lengths of cells in mitosis in three individual 0.5 mm root segments of P. sati6um.
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Table 1 Cell length characteristics in various segments in roots of five plant species
Percentage of cells in relation to critical lengths STATISTICAL PARAMETERS
Number of Type of Cells
Species Criti- Minimum
Distance Maximum
More than Mean Length
Between Four Standard De-
Between Two Below One
Between One and Two
viation mm Cells
Critical and Four
and Six Criti- cal Length
Length mm mm
Six Critical Length mm
From Root Critical
Critical Lengths
Length cal Lengths
cap mm Lengths
Lengths 214
9.00 52.0
27.4 9.2
100 Mitosis
Pisum sati6um 0.5
52.5 mm 25.6
12.8 94.5
5.5 7.5
219 90.0
Mitosis 1.0
26.0 9.0
100.0 Mitosis
1.5 59
13.5 51.0
44.6 25.0
77.8 18.5
3.7 100
16.5 27
2.0 Mitosis
24.0 94.5
49.9 20.5
66.7 33.3
2.5 Mitosis
18 64.5
20.4 25.0
75.0 90.0
Mitosis 27.0
12 3.0
27.2 18.7
91.3 7.5
1.2 Interphase
0.5 509
7.5 135
38.1 29.9
79.8 15.4
4.8 195
7.5 524
1.0 Interphase
68.5 57.8
53.6 24.3
18.1 3.8
0.2 Interphase
1.5 439
9.0 420
103 82.2
31.7 29.8
26.4 11.2
559 0.9
15.0 Interphase
2.0 420
117 83.1
19.3 34.1
32.1 13.8
0.7 Interphase
2.5 405
15.0 510
135 75.8
8.9 27.9
45.4 17.2
0.6 495
Interphase 3.0
16.5 326
phase cells were longer than 105 mm compared with 46.7 in 2.5-mm segments. Thus, there was a
marked increase in cell elongation in mature root tissues.
Lengths of cells in mitosis in 0.5-mm segments of Pyrus communis are shown in Table 1. In
1.0 – 3.0 mm segments of P. communis, only nine cells were in mitosis. In 0.5-mm root segments of
P. communis, 8.1 of all interphase cells were longer than critical length 33 mm. In contrast,
more than 50 of all interphase cells were longer than critical length in 1.5-mm segments. More-
over, a few cells in 1.5-mm segments were longer than eight times critical length.
Only root segments of 0.5 and 1.0 mm were present in roots of T. aesti6um. Lengths of cells in
mitosis of 0.5 mm segments provided a critical length of 37.5 mm. Few mitotic cells were found in
0.5 mm segments and no mitotic cells were found in root segments at 1.0 mm Table 1. In 0.5 and
1.0 mm root segments of T. aesti6um, 1.8 and 57.4 of all interphase cells were longer than
critical length, respectively. In 1.0 mm segments, 19 of all interphase cells were longer than four
times critical length.
Critical length of mitotic cells in 0.5 mm seg- ments of V. faba was 48 mm Table 1. Mean
lengths of mitotic cells were similar for 0.5 – 1.5 mm segments 27.7 – 36.3 mm. Few mitotic cells
were present in 2.0 – 3.0 mm segments. In 0.5 mm segments of V. faba, 15.5 of all interphase cells
were longer than critical length and 6.4 of all interphase cells were longer than four times criti-
cal length. Twenty-five, 36, 42, 60 and 69 of all interphase cells were longer than critical length at
1.0, 1.5, 2.0, 2.5, 3.0 mm, respectively.
Few cells in mitosis were present in 0.5 and 1.0 mm root segments of Z. mays Table 1. No cells
in mitosis were present in 1.5 – 3.0 mm segments. Among interphase cells of Z. mays, 8.1 and 27.0
of interphase cells were longer than critical length 30 mm at 0.5 and 1.0 mm, respectively. In 2.5
and 3.0 mm segments, 5.4 and 3.8 of all inter- phase cells were less than critical length. Lengths
of interphase cells varied markedly in 3.0 mm segments in which 22.1, 40.4, 29.8 and 3.9 were
longer than 30, 60, 120 and 240 mm, respectively.
To test the first hypothesis, namely no inter- phase cells in root meristems will be longer than
critical length, cells in root segments of 0.5 – 3.0 mm from the root cap-founder cell boundary were
subdivided by cell length. Cells were subdivided into length groups relative to critical length of
mitotic cells of 0.5-mm segments. In general, data of all five plant species demonstrate that from 7 to
10 of all interphase cells were longer than criti- cal length in 0.5 mm root segments. Moreover,
larger percentages up to 57 of cells were longer than critical length for 1.0 mm root segments of
T. aesti6um. If a root meristem region is consid- ered to be contained in 0.5 – 3.0 mm root segments
of the five species tested, the first hypothesis is not supported.
3
.
2
. Estimation of cell – age distributions A frequency distribution of cells with cell
lengths less than critical length 56 mm for P. sati6um demonstrate that in almost all compari-
sons there was a statistically significant difference between actual percentages compared with theo-
retical values. Percentages of larger cells of P. sati6um were below expected percentages.
For P. communis, cell lengths considered for this analysis ranged from 7.5 to 34.5 mm Table
2. For statistical analysis, almost all decile groups contained cell lengths of 3 mm except cells of 15
and 16.5 and 16.5 and 18 mm Table 2. These two groups were considered as separate groups be-
cause they each had large percentages of cells. Analyses shown in Table 2 indicate better corre-
spondence between actual and theoretical data for shorter cells than for longer cells. For example,
the three groupings of longest cells had 13.2 of all cells compared with a theoretical value of
23.1. The relatively high percentages of 16.9 and 16.4 for deciles of 21 – 30 and 31 – 40 were sig-
nificantly above theoretical values of 11.7 and 10.1, respectively.
Lengths of cells of T. aesti6um did not appear to be similar to a theoretical exponential cell – age
distribution Table 2. All decile groupings con- tained cells of at least a 3-mm range Table 2.
Deciles 0 – 10, 11 – 20, 51 – 60 and 61 – 70 were most similar to theoretical percentages. However, other
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Table 2 Results of a Chi-square analysis of percentage of cells based upon cell lengths in individual roots compared with percentages based upon an exponential cell-age distribution in deciles of the
cycle completed Percentages of cells in each decile Probability
Species or Theoretical Distribution Decile
21–30 31–40
41–50 51–60
61–70 71–80
81–90 91–100
0–10 11–20
10.9 10.1
9.5 8.8
8.2 7.7
12.5 7.2
11.7 Theoretical distribution
13.4 12.1
8.1 4.3
Pisum sati6um 11.7
4.2 8.1
4.0 8.6
22.8 16.1
0.01 0.05
0.01 0.05
0.01 0.10
0.01 0.01
0.005 0.005
16.9 16.4
10.9 8.3
9.6 4.8
1.9 6.5
14.6 Pyrus communis
10.1 0.01
0.01 0.10
0.10 0.10
0.05 0.005
0.10 0.10
0.05 13.5
8.3 8.8
7.9 4.6
2.3 23.3
0.5 Triticum aeti6um
15.4 15.4
0.05 0.005
0.05 0.05
0.10 10.10
0.05 0.01
0.005 0.05
17.6 10.4
16.1 6.3
4.8 1.5
8.7 3.9
Vicia faba 14.0
16.7 0.05
0.01 0.10
0.005 0.05
0.05 0.005
0.01 0.01
0.05 9.2
11.8 26.5
13.2 5.2
8.0 4.0
4.8 8.8
8.5 Zea mays
0.10 0.005
0.05 0.01
0.10 0.01
0.05 0.01
0.01 0.005
33.0 Mitosis
22.2 6.3
100 0.5
26 13.5
Pyrus communis 33.0 mm 29.0
24.0 75
12.5 12.5
97.5 10.5
Mitosis 1.0
16 40.5
385 75
25.0 Mitosis
1.5 4
15.0 97.5
37.5 100
37.5 37.5
1 2.0
Mitosis 510
Mitosis 28.2
205 33.3
37.3 33.3
2.5 3
112 225
100 225
1 3.0
225 Mitosis
Interphase 105
18.5 11.9
91.9 6.7
1.4 0.5
422 7.5
Interphase 180
25.8 24.4
76.2 16.4
6.4 1.0
1.0 403
7.5 50.3
47.7 49.4
27.0 17.1
5.7 315
0.8 9
385 1.5
Interphase 904
Interphase 124
140 8.5
34.1 31.5
13.7 12.2
2.0 387
15 103
95 2.0
18.5 41.9
23.0 907
14.6 22.5
Interphase 2.5
356 191
156 0.6
7.4 41.4
28.1 22.5
Interphase 3.0
324 35
601 21.6
7.5 100
10.5 37.5
16 0.5
Mitosis Triticum Aestivum 37.5 mm
– –
– –
– –
– Mitosis
1.0 –
– 17.6
9.4 98.2
0.9 0.9
9 Interphase
90 219
0.5 112
46.9 25.0
42.6 38.3
19.1 1.0
141 9
Mitosis 48
27.7 7.9
100 0.5
23 Vicia faba 48.0 mm
13.5 33.4
17.0 77.8
22.2 67.5
15 18
1.0 Mitosis
Mitosis 72
36.3 20.6
63.6 36.4
1.5 11
10.5 105
100 105
105 Mitosis
2.0 1
103 56.2
50 50
Mitosis 2.5
2 63
142 Mitosis
3.0
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Table 2 Percentages of cells in each decile Probability
Species or Theoretical Distribution Decile
31–40 41–50
51–60 61–70
71–80 81–90
91–100 0–10
11–20 21–30
35.4 31
84.5 8.6
6.4 0.5
7.5 210
394 0.5
Interphase Interphase
450 39.9
45.6 74.9
17.0 7.2
0.3 0.6
1.0 387
7.5 Interphase
300 52.6
53.8 64.1
20.1 11.9
3.9 1.5
388 7.5
65.9 59.0
57.8 20.1
17.1 5.0
375 341
10.5 Interphase
2.0 345
Interphase 77.6
65.0 39.7
37.3 16.8
6.2 2.5
209 15
308 Interphase
90.8 63.3
30.8 36.7
25.0 7.5
3.0 120
18 22.1
5.7 100
18 30
4 0.5
Mitosis Zea mays 30.0 mm
20.2 13.6
75 25
Mitosis 1.0
8 7.5
48 –
– –
– –
– –
– Mitosis
– 1.5
– Mitosis
– –
– –
– –
– 2.0
– –
– –
– –
– –
Mitosis 2.5
– –
– –
– –
– –
– –
Mitosis 3.0
– Interphase
90 17.0
9.8 91.9
6.7 1.4
0.5 418
6 150
Interphase 24.3
20.7 73.0
20.2 5.8
1.0 1.0
411 6
54.9 61.0
36.0 32.2
22.8 6.4
450 2.6
311 6
Interphase 1.5
450 Interphase
106 88.0
8.1 27.3
31.1 24.2
9.3 2.0
161 15
131 Interphase
101 5.4
20.3 29.0
30.4 14.9
2.5 148
12 480
103 64.6
3.8 22.1
40.4 29.8
3.9 375
Interphase 3.0
15 104
distributions differed significantly from the theo- retical distribution. Most particularly, percentages
of larger cells were below expectations. Lengths of cells of V. faba did not resemble a
theoretical cell – age distribution Table 2. Actual percentages 17.6 and 16.1 were not similar to
theoretical percentages 10.9 and 9.5, respec- tively in 31 – 40 and 51 – 60 deciles. Moreover,
actual percentages 4.8, 1.5, and 3.9 for the three deciles of longest cells were below theoreti-
cal percentages 8.2, 7.7 and 7.2, respectively. Both percentages of smallest and largest cells were
below expectations.
Lengths of cells of Z. mays were not similar to a theoretical exponential cell – age distribution
Table 2. The actual value of 26.5 for decile 41 – 50 was almost three times larger than the
theoretical percentage 10.1.
To test the second hypothesis, namely — inter- phase cells less than critical length in root meris-
tems will
have an
exponential cell – age
distribution, distributions of lengths of cells of 0.5 mm root segments that were less than critical
length were compared with cell lengths based upon a theoretical exponential cell – age distribu-
tion. As stated above, for a theoretical exponen- tial cell – age distribution there should be two cells
at the beginning of a cell cycle for every one cell at the end of a cell cycle and the number of cells
throughout the cycle should decrease exponen- tially. Results demonstrate that actual cell length
distributions of 0.5 mm root segments of five plant species were not similar to such theoretical
distributions. Overall, percentages of the smallest cells exceeded expectations while percentages of
largest cells were below expectations. An expo- nential cell – age distribution is not supported for
0.5-mm segments of five plant species.
4. Discussion
