have attempted to simplify the linear growth of roots Erickson and Sax, 1956 and to minimize
the variability of the types of cells that compose the terminal root area Webster, 1980. Mathe-
matical models and functions have helped re- searchers understand cell cycle kinetics and how
roots grow Erickson and Sax, 1956; Webster and MacLeod, 1980; Bertaud et al., 1986; Ivanov and
Dubrovsky, 1997. By their nature, mathematical models and functions simplify otherwise complex
processes. Over-simplification of otherwise com- plex processes may lead to false conclusions. This
paper addresses the conclusion that all cells of root terminals are proliferative Webster and
MacLeod, 1980; Ivanov and Dubrovsky, 1997. Our approach used data of cell lengths from six
locations from terminal root portions from five plant species to determine percentages of cells
greater than critical length the length of the longest cell in mitosis in the terminal portion and
the distribution of cell lengths that are shorter than critical length. If all cells shorter than critical
length are proliferative, then they should approxi- mate an exponential cell-age distribution. To date,
data of cell lengths in roots have not been used to address these issues.
If the assertion that all cells are dividing at the same rate so there are no slow cycling or non-cy-
cling cells Webster and MacLeod, 1980; Ivanov and Dubrovsky, 1997 is true and if cells do not
slide relative to their neighbors Sinnot and Bloch, 1939; Brumfield, 1942 then all cells of root meris-
tems should have a maximum cell length equal to cells in prophase. Green 1976, Webster and
MacLeod 1980 argued that if cells become non- proliferative and miss n cycles, such cells should
be 2n times longer than cells which remain prolif- erative at an equivalent position along roots.
Ivanov 1971 described a critical cell length for mitosis in roots of Zea mays, in which he stated
that practically all cells in a tissue enter mitosis upon reaching ‘critical length’. Brumfield 1942
also cited research by Abele 1936 that supported the idea of a critical length. From all the above
information, lengths of cells can be used to deter- mine relative numbers of cell cycles among neigh-
boring cells. To date, few data with only limited numbers of cells have been used to determine
diversities of cell lengths within terminal root portions. Therefore, the first hypothesis addressed
herein was: because all cells of root meristems are proliferative and because all proliferative cells are
shorter than critical length in root meristems, there are no interphase cells longer than critical
length.
Webster and MacLeod 1980, Ivanov and Du- brovsky 1997 concluded that all cells in root
meristems are dividing and that the population of proliferative cells is expanding exponentially.
Since the cell population is expanding exponen- tially, it should have an exponential cell – age dis-
tribution in which there are two cells beginning interphase for every cell terminating interphase.
In addition, there should be an exponential decay formula for cells between these two stages. Al-
though an exponential condition has been as- sumed Webster and MacLeod, 1980; Ivanov and
Dubrovsky, 1997, few databases from terminal root portions have been compared with an expo-
nential cell – age distribution. The second aspect assumed that interphase cells with less than criti-
cal length in terminal root portions are all prolif- erative and that cell populations are growing
exponentially Webster and MacLeod, 1980; Ivanov and Dubrovsky, 1997. In this manner, the
second hypothesis was: cells in terminal root por- tions that are less than critical length will have an
exponential cell – age distribution based upon cell lengths.
2. Materials and methods
2
.
1
. Microscope slides All microscope slides used in this study were
purchased from Triarch Incorporated Ripon, WI in 1998. This procedure of using commer-
cially prepared microscope slides is not novel. Webster 1980 used microslides from a commer-
cial source for his study. Ten microscope slides of median longitudinal sections of terminal root por-
tions each of five plant species Pisum sati6um only eight microscope slides, Pyrus communis,
Triticum aesti6um, Vicia faba, and Z. mays were purchased. In addition, ten microscope slides of
median longitudinal root sections of P. sati6um specifically stained to highlight chromosomes
were purchased to insure that cells in mitosis for P. sati6um would be evaluated most effectively.
The procedures to produce the excellently pre- pared microslides were provided by Dr Paul L.
Conant of Triarch personal communication. All species P. sati6um, P. communis, T. sati6um, V.
faba and Z. mays were commercial materials purchased from Burpee Seed Co. Roots from P.
communis were obtained from plants grown in aquaculture while roots of all other species were
obtained from germinating seedlings. Seeds of these latter species were germinated on wet filter
paper. All plants were grown at 21°C. Selected roots were cut from plants and fixed immediately
in FAA or Navashin’s mixture Sass, 1958. Roots were dehydrated using an ethanol – normal
butanol series and transferred to paraffin. Tissues of P. sati6um, P. communis, T. aesti6um, V. faba
and Z. mays were sectioned at 10, 10, 8, 8 and 12
m m, respectively. Root sections were stained with
a quadruple stain of safranin, crystal violet, fast green and orange G.
2
.
2
. Determination of cell lengths Lengths of individual cells were evaluated un-
der 1000 times magnification. A scale in one microscope ocular, in which one ocular unit was
equal to 1.50 mm at the magnification used, was used to determine cell lengths. To determine cell
locations relative to the root terminus, all dis- tances were determined relative to the founder
cellroot cap boundary. Lengths of individual cells were determined in roots at distances of 0.5, 1.0,
1.5, 2.0, 2.5 and 3.0 mm from the founder cell root cap boundary. Not every median longitudi-
nal section had tissues at all distances. Cell lengths lengths parallel with the long axis of the
root of all cells from the epidermis on one side of a median section radially across the entire section
to the epidermis on the opposite side of a section were evaluated. Thus, only one cell from each cell
file was evaluated at each distance described above. During evaluations, cell lengths were de-
termined in ocular units and later converted to micrometer units. Cells were categorized as either
in mitosis prophase, metaphase, anaphase, or telophase or in interphase. There was no attempt
to determine the phase prophase, metaphase, anaphase, or telophase of individual mitotic cells.
2
.
3
. Lengths of mitotic and interphase cells To determine percentages of cells longer than
critical length, data from each segment e.g. 0.5 mm of all roots of a species were pooled for
analysis. From these pooled data, the length of the longest cell in mitosis from all 0.5-mm seg-
ments of a species was deemed critical length. For data of mitotic cells, minimum, maximum, mean
and standard deviation of cell lengths were determined.
In accordance with views of Green 1976, Webster and MacLeod 1980, if a cell becomes
non-proliferative and misses n cycles, it should be 2n times longer than cells which have remained
proliferative at an equivalent position along the axis. Data from each segment from all roots of a
species were pooled since there were no statisti- cally significant differences in cell lengths among
segments. First, minimum, maximum, mean, and standard deviation of lengths of all interphase
cells were determined. Second, lengths of inter- phase cells relative to critical length were deter-
mined. For this step, percentages of mitotic and interphase cells in each of five categories were
determined separately:
1. Cells less than or equal to critical length. Such cells may not have missed a cell division.
2. Cells longer than critical length but less than or equal to twice critical length. Such cells may
have missed one cell division. 3. Cells longer than twice critical length but less
than or equal to four times critical length. Such cells may have missed two cell divisions.
4. Cells equal to or longer than four times critical length but less than or equal to six times
critical length. Such cells may have missed three cell divisions.
5. Cells longer than six times critical length. Such cells may have missed more than three cell
divisions.
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
