Clonal aspects of plant cell proliferation and their applications to animal cells and bacteria

Abstract

Objectives: Extensive mathematical studies have been made on cell clone development but little has been advanced in the mathematics of small clone formation and virtually no actual data of small clone size has been collected.

Materials and methods: Small clone sizes in leaf marginal cells of the aquatic plant Elodea and aleurone spot sizes in the grain of Zea were counted for later statistical analyses of mean, variance and probability distribution frequencies.

Results: Simple mathematical models were developed and their calculated results are comparable to data collected on actual plant clones. The parameters in these models were original cell size (s(0)), growth rate (T), duration of growth (t) and cell division inequality (i).

Conclusions: Given T and t, the critical parameter is s(0). Plant tissue is ideal material to collect data on clone development because growth rate is uniform across a tissue and cells remain in place, so clone size can be measured, unlike microbes and animal cells that have neither feature. In the light of the results, traditional methods for calculating cell cycle duration and mutation rate are questioned. The applications of these plant features to studies on animal cell populations are discussed.

Figure 1

Plant tissues. (a) Elodea leaf with marginal, spaced barb cells. (b) Marginal clone bracketed of Elodea leaf; barb cell at tip of clone with three unspecialized cells below. (c) Meristematic cells of clone developing from left to right (arrow). Numbers refer to number of cells in a developing clone. (d) Maize kernel with aleurone spots and added reference square for doing the fluctuation test (Table 4, column 3). (e) Aleurone spots with cells visible, clones of one cell, aa, two cells, bb, and nine cells, cc.

Figure 2

Data graphs. (a) Cell size distributions starting with doubly truncated distribution, a‐a, blue; shown as vertical bar graph, b₁–b₆, green; values converted into normal distributions, c_1–6, black, which are summed to give the final cell size distribution, d, olive; and compared to Monte Carlo data, e, red. (b) Elodea data compared to data generated by Equation (2). (c). Maize clones sizes and expected from computer model. (d) Linear correlation between log size of aleurone clone in cells against log of number of such clones or greater in size.

Figure 3

Sixteen‐celled clones. (a). Determinate clone of five levels (L) with a total of 31 cells (2^L–1). (b) An indeterminate clone with total levels of four to seven. Cell cycle duration as a function of initial cell size. (c) Logarithmic transformation of cell cycle duration to give a normal distribution indicating cell cycle duration is a lognormal distribution. Influence of sampling size. (d) Calculated frequency of cultures without mutant cells (heavy line) and mutation rate (light line). The average number of mutant cells per sample is held constant for different sample fractions.