POLYGONAL ASPECTS OF CELL FACES. II. QUADRILATERALS AS THE PREVAILING TYPE

Wheeler , George E. (Brooklyn Coll., Brooklyn, New York.) Polygonal aspects of cell faces. II. Quadrilaterals as the prevailing type. Amer. Jour. Bot. 49(4): 355–362. Illus. 1962.—Quadrilateral faces are abundant and even predominant among the faces of certain types of cells. Data taken from the literature and several original samples were studied to define the conditions which foster large numbers of quadrilaterals. The presence of free faces (cells on air spaces) profoundly affects cell-face distributions. There is a great excess of quadrilaterals on cells with 2 free faces on opposite sides (cells of single layers). Among cells with 1 free face (cells of epidermises), pentagonal faces usually surpass quadrilateral faces, although they are just about equal in a few samples. Intermediate ratios of the 2 face types occur in samples which include cells having faces touching 1 free face, mixed with cells having faces between 2 free faces. The “competition” for numerical superiority shifts to pentagons vs. hexagons, among cells comprising internal tissues (cells in contact on all sides with other cells). With respect to epidermises, the relative size of epidermal and of subepidermal cells strongly influences the relative numbers of quadrilaterals and pentagons. A marked trend toward quadrilaterals may also be found in connection with a quite different set of cell relationships: if 2 layers of elongated cells occur together, and if their long axes are mutually perpendicular, then a “checkerboard” pattern may result. This arrangement favors large numbers of quadrilateral faces; in some samples, they may even dominate. It is suggested that certain modifications of this pattern may generate large numbers of triangular and of lenticular (lens-shaped) faces. Varying patterns of cell division are considered to be primarily responsible for changes in cell-face distributions and for changes in predominating face types.     

POLYGONAL ASPECTS OF CELL FACES. I. PENTAGONS AND HEXAGONS AS PREVAILING TYPES

Wheeler , George E. (Brooklyn Coll., Brooklyn, N. Y.) Polygonal aspects of cell faces. I. Pentagons and hexagons as prevailing types. Amer. Jour. Bot. 49(3): 246–252. Illus. 1962.—Different types of cell faces, classified as to polygon type (i.e., number of sides per face), may predominate in different samples of internal cells and of internal tissues; no single face type is exclusively predominant in all tissues. Pentagons usually are the most numerous type in the cell samples reported in the literature, but hexagons exceed them in some samples. Generally, these 2 “compete” for numerical supremacy. Perpetuation of an already-established, face-type dominance was studied, using data from the literature and from original diagrams. Cell-division orientation, i.e., the location and the relative positioning of new cell-division walls, was found to be the prime factor in maintaining the preponderant type. The polygon nature of the new wall is an additional, but less important, factor. Typical division events tend to favor pentagonal faces; but with an increase in cell division “regularity,” hexagons begin to rise in numbers. During the early stages in tissue differentiation, while mitosis is still occurring, one face type may replace another as the predominating type. Such a shift may be associated with the developmental characteristics of that tissue.     

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.     

The size distribution of conspecific populations: the peoples of New Guinea

The size distribution of the language populations in New Guinea, which represent over 15% of the world's languages, is analysed using models analogous to the resource division models of species abundance distribution in ecological communities. A model distribution of resource segments reflecting population size is created by repeated selection of an existing resource segment and its division into two. We found that any dependency of the selection probability on the size of the segment generated negatively skewed abundance distributions after log transformation. Asymmetric segment division further exacerbated the negative skewness. Size-independent selection produced lognormal abundance distributions, irrespective of the segment division method. Size-dependent selection and asymmetric division were deemed reasonable assumptions since large language populations are more likely to generate isolates, which develop into new populations, than small ones, and these isolates are likely to be small relative to the progenitor population. A negatively skewed distribution of the log-transformed population sizes was therefore expected. However, the observed distributions were lognormal, scale invariant for areas containing between 100 and over 1000 language populations. The dynamics of language differentiation, as reflected by the models, may therefore be unimportant relative to the effect of variable growth rates among populations. All lognormal distributions from resource division models had a higher variance than the observed one, where half of the 1053 populations had between 350 and 3000 individuals. The possible mechanisms maintaining such a low variance around a modal population size of 1000 are discussed.     

Modelling cell population growth with applications to cancer therapy in human tumour cell lines

In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.     

Abundance, diversity and body size: patterns from a grassland arthropod community

1. The empirical relationships among body size, species richness and number of individuals may give insight into the factors controlling species diversity and the relative abundances of species. To determine these relationships, we sampled the arthropods of grasslands and savannahs at Cedar Creek, MN using sweep nets (90 525 individuals of 1225 species) and pitfall traps (12 721 individuals of 92 species). Specimens were identified, enumerated and measured to determine body size.
2. Both overall and within abundant taxonomic orders, species richness and numbers of individuals peaked at body sizes intermediate for each group. Evolution could create unimodal diversity patterns by random diversification around an ancestral body size or from size-dependent fitness differences. Local processes such as competition or predation could also create unimodal diversity distributions.
3. The average body size of a species depended significantly on its taxonomic order, but on contemporary trophic role only within the context of taxonomic order.
4. Species richness ( S _i) within size classes was related to the number of individuals ( I _i) as S _i =  I i^0·5. This relationship held across a 100 000-fold range of body sizes. Within size classes, abundance distributions of size classes were all similar power functions. A general rule of resource division, together with similar minimum population sizes, is sufficient to generate the relationship between species richness and number of individuals.
5. Smaller bodied species had slightly shallower abundance distributions and may, in general, persist at lower densities than larger species.
6. Our results suggest there may be fewer undescribed small arthropod species than previously thought and that most undescribed species will be smaller than arthropods.     

RELATIONSHIPS BETWEEN GROWTH RATE,CELL SIZE,AND INDUCTION OF SPERMATOGENESIS IN THE CENTRIC DIATOM THALASSIOSIRA WEISSFLOGII (BACILLARIOPHYTA)1

Patterns of changes in cell size, growth rate, and the inducibility of spermatogenesis were followed in eight sub‐clones of two isolates of the centric diatom Thalassiosira weissflogii (Grunow) Fryxell & Hasle grown at saturating light. One isolate originated from Long Island Sound, New York, USA and the other originated from Jakarta Harbor, Indonesia. As expected from previous studies, oscillations between intervals of cell size reduction and cell size enlargement were observed for each sub‐clone. For both isolates, sperm were easily detected, but cells resembling eggs and auxospores were rarely observed and fertilization was not confirmed, suggesting that the observed cell size increases may have resulted from a combination of asexual cell enlargement and rare auxosporulation. The two isolates differed in their minimum and maximum sizes, and the threshold size for the induction of sperm formation. However, the two sets of isolated sub‐clones displayed comparable relationships between growth rate, sperm inducibility, and cell size relative to the minimum, maximum, and threshold sizes. Growth rate increased as cell size decreased during vegetative divisions until the threshold for sperm inducibility was crossed. Below the size threshold for sperm inducibility, growth rate declined as cell size continued to decrease. Smaller cells were susceptible to failure of normal cytokinesis and valve deposition, resulting in the formation of abnormally long and often multinucleate cells. Culture conditions may select against restoration of cell size via auxosporulation due to the relationship between growth rate and cell size.     

Model-based analysis of Arabidopsis leaf epidermal cells reveals distinct division and expansion patterns for pavement and guard cells

To efficiently capture sunlight for photosynthesis, leaves typically develop into a flat and thin structure. This development is driven by cell division and expansion, but the individual contribution of these processes is currently unknown, mainly because of the experimental difficulties to disentangle them in a developing organ, due to their tight interconnection. To circumvent this problem, we built a mathematic model that describes the possible division patterns and expansion rates for individual epidermal cells. This model was used to fit experimental data on cell numbers and sizes obtained over time intervals of 1 d throughout the development of the first leaf pair of Arabidopsis (Arabidopsis thaliana). The parameters were obtained by a derivative-free optimization method that minimizes the differences between the predicted and experimentally observed cell size distributions. The model allowed us to calculate probabilities for a cell to divide into guard or pavement cells, the maximum size at which it can divide, and its average cell division and expansion rates at each point during the leaf developmental process. Surprisingly, average cell cycle duration remained constant throughout leaf development, whereas no evidence for a maximum cell size threshold for cell division of pavement cells was found. Furthermore, the model predicted that neighboring cells of different sizes within the epidermis expand at distinctly different relative rates, which could be verified by direct observations. We conclude that cell division seems to occur independently from the status of cell expansion, whereas the cell cycle might act as a timer rather than as a size-regulated machinery.     

Transformation of Lipid Bodies Related to Hydrocarbon Accumulation in a Green Alga,Botryococcus braunii (Race B)

The colonial microalga Botryococcus braunii accumulates large quantities of hydrocarbons mainly in the extracellular space; most other oleaginous microalgae store lipids in the cytoplasm. Botryococcus braunii is classified into three principal races (A, B, and L) based on the types of hydrocarbons. Race B has attracted the most attention as an alternative to petroleum by its higher hydrocarbon contents than the other races and its hydrocarbon components, botryococcenes and methylsqualenes, both can be readily converted into biofuels. We studied race B using fluorescence and electron microscopy, and clarify the stage when extracellular hydrocarbon accumulation occurs during the cell cycle, in a correlation with the behavior and structural changes of the lipid bodies and discussed development of the algal colony. New accumulation of lipids on the cell surface occurred after cell division in the basolateral region of daughter cells. While lipid bodies were observed throughout the cell cycle, their size and inclusions were dynamically changing. When cells began dividing, the lipid bodies increased in size and inclusions until the extracellular accumulation of lipids started. Most of the lipids disappeared from the cytoplasm concomitant with the extracellular accumulation, and then reformed. We therefore hypothesize that lipid bodies produced during the growth of B. braunii are related to lipid secretion. New lipids secreted at the cell surface formed layers of oil droplets, to a maximum depth of six layers, and fused to form flattened, continuous sheets. The sheets that combined a pair of daughter cells remained during successive cellular divisions and the colony increased in size with increasing number of cells.     

Interpretations on chloroplast reproduction derived from correlations between cells and chloroplasts

Summary The size ranges of chloroplasts in living mesophyll cells of Spinacia oleracea, Allium cepa, Beta vulgaris (Swiss chard and red beet) and Nicotiana glutinosa are extremely wide, e.g., ranging from about 6 µ² to 103 µ² in face area for spinach. Moreover, the size distributions are positively skewed. We interpret the size range and skewed size distributions primarily to reflect an enormous growth of the bulk of the chloroplasts from small, equal-sized chloroplasts produced by fission of a small sub-population of constricted mature chloroplasts. While actual fission has never been observed, a slow division rate of the constricted chloroplasts in N. glutinosa can account for the increase in chloroplast numbers per cell during leaf development and for the presence of small, non-constricted chloroplasts after the small chloroplasts which developed during the initial meristem activity have enlarged. Chloroplast numbers and total amount of chloroplast material per cell face were positively correlated with mesophyll-cell face size. However, the fraction of the cell face occupied with chloroplasts was essentially constant and independent of cell size and cell age while being markedly different for different species of plants. There appear to be some family characteristics in that closely related species have similar size-distributions and ranges of chloroplast sizes. The observations are discussed with respect to the ontogeny of chloroplasts in higher plants.     

Spatial distributions of expansion rate, cell division rate and cell size in maize leaves: a synthesis of the effects of soil water status, evaporative demand and temperature

The spatial distributions of leaf expansion rate, cell division rate and cell size was examined under contrasting soil water conditions, evaporative demands and temperatures in a series of experiments carried out in either constant or naturally fluctuating conditions. They were examined in the epidermis and all leaf tissues. (1) Meristem temperature affected relative elongation rate by a constant ratio at all positions in the leaf. If expressed per unit thermal time, the distribution of relative expansion rate was independent of temperature and was similar in all experiments with low evaporative demand and no water deficit. This provides a reference distribution, characteristic of the studied genotype, to which any distribution in stressed plants can be compared. (2) Evaporative demand and soil water deficit affected independently the distribution of relative elongation rate and had near-additive effects. For a given stress, a nearly constant difference was observed, at all positions of the leaf, between the relative elongation rates of stressed plants and those of control plants. This caused a reduction in the length of the zone with tissue elongation. (3) Methods for calculating cell division rate in the epidermis and in all leaf tissues are proposed and discussed. In control plants, the zone with cell division was 30 mm and 60 mm long in the epidermis and in whole tissues, respectively. Both this length and relative division rate were reduced by soil water deficit. The size of epidermal and of mesophyll cells was nearly unaffected in the leaf zone with both cell division and tissue expansion, suggesting that water deficit affects tissue expansion rate and cell division rate to the same extent. Conversely, cell size of epidermis and mesophyll were reduced by water deficit in mature parts of the leaf.     

Generality of the growth kinetics of the average individual cell in different bacterial populations.

The kinetics of growth of all the cells in a population is reflected in the shape of the size distribution of the population. To ascertain whether the kinetics of growth of the average individual cell is similar for different strains or growth conditions, we compared the shape of normalized size distributions obtained from steady-state populations. Significant differences in the size distributions were found, but these could be ascribed either to the precision achieved at division or to a constriction period which is long relative to the total cell cycle time. The remaining difference is quite small. Thus, without establishing the pattern itself, it is concluded that the basic course of growth is very similar for the various Escherichia coli strains examined and probably also for other rod-shaped bacteria. The effects of differences in culture technique (batch or chemostat culture), growth rate, and differences among strains were not found to influence the shape of the size distributions and hence the growth kinetics in a direct manner; small differences were found, but only when the precision at division or the fraction of constricted cells (long constriction period) were different as well.     

Overinitiation of replication of the Escherichia coli chromosome from an integrated runaway-replication derivative of plasmid R1.

A 16-base-pair fragment, deletion of which completely inactivated oriC, was replaced by a temperature-dependent runaway-replication derivative (the copy number of which increases with temperature) of the IncFII plasmid R1. The constructed strains were temperature sensitive, and flow cytometry revealed a severalfold increase in the DNA/mass ratio following shifts to nonpermissive temperatures. The cell size distribution was broader in the constructed strains relative to that in the wild type because of asynchrony between the chromosome replication and cell division cycles. This difference was more pronounced for counterclockwise initiation of chromosomal replication, in which small DNA-less cells and long filaments were abundant. Following a temperature shift the cell size distributions became even more broad, showing that changes in the frequency of chromosomal replication affect cell division and emphasizing the interplay between these two processes.     

Body size and latitudinal gradients in regional diversity of New World birds

Are latitudinal gradients in regional diversity random or biased with respect to body size? Using data for the New World avifauna, I show that the slope of the increase in regional species richness from the Arctic to the equator is not independent of body size. The increase is steepest among small and medium‐sized species, and shallowest among the largest species. This is reflected in latitudinal variation in the shape of frequency distributions of body sizes in regional subsets of the New World avifauna. Because species are added disproportionately in small and medium size classes towards low latitudes, distributions become less widely spread along the body size axis than expected from the number of species. These patterns suggest an interaction between the effects of latitude and body size on species richness, implying that mechanisms which vary with both latitude and body size may be important determinants of high tropical diversity in New World birds.     

THE EFFECT OF AUXIN AND GUANINE ON CELL EXPANSION AND CELL DIVISION IN THE GAMETOPHYTE OF THE FERN,ONOCLEA SENSIBILIS

Miller , J. H. (Yale U., New Haven, Conn.) The effect of auxin and guanine on cell expansion and cell division in the gametophyte of the fern, Onoclea sensibilis. Amer. Jour. Bot. 48(9): 816–819. Illus. 1961.—Auxin and guanine promote cell expansion in 0. sensibilis gametophytes. The optimum concentration of auxin for total expansion is 10^−-5 M, but the optimum for elongation is 10^−-6 M. Above this concentration the cells expanded isodiametrically. Guanine is active at higher concentrations than auxin. Increasing concentrations of auxin progressively inhibit red light-induced cell division, while guanine has no effect on cell division. Neither kinetin nor adenine promotes cell expansion or cell division.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

Quantitation of particles in the freeze-fractured nuclear membrane after renal ischemia.

Changes in the number and sizes of membrane-associated particles have been quantitated in the protoplasmic (P) and exoplasmic (E) fracture faces of the outer membrane of nuclei isolated from the inner cortex following renal ischemia and reflow in the rat. No changes were observed in the inner nuclear membrane. After 20-min ischemia, the number of particles in both fracture faces decreased. With reflow, the total number of particles decreased after both 20- and 60-min ischemia. The partition coefficient (Kp = CPF/CEF) increased from 10 to 11 and 17 at 20- and 60-min ischemia then fell below control values to a Kp of 7 after 120 min. After reflow, Kp steadily decreased except after 20-min ischemia followed by 240-min reflow when Kp began to rise. The sizes of particles were predominantly 60 A in the P face of control outer membranes but became larger after ischemia. After 20- and 60-min ischemia with reflow, the size distribution became more normal. The shifts in particle numbers and sizes seem to indicate modifications within the membrane resulting from ischemia.     

Effects of nitrogen deprivation on cell division and expansion in leaves of Ricinus communis L.

The effects of nitrogen deprivation on leaf extension, cell numbers and epidermal cell size were followed in leaves of Ricinus communis L. The extent to which reductions in final cell number or final epidermal cell size contributed to the reduction in final leaf size depended on the developmental stage of the leaf at the time of N deprivation. In leaves which already had their full complement of cells (leaf 2), the reduction in final leaf size following nitrogen deprivation was associated with a reduction in final cell size. In leaves that were at earlier stages of development at the onset of N deprivation (leaves 3 and 4), the reduction in final leaf size was greater than in leaf 2. In these younger leaves, the final cell size was even smaller than in leaf 2, but the greatest contribution to reduced final leaf size was a reduction in the number of cells produced. This accounted for approximately 80% of the reduction in final leaf size in leaf 4. During leaf development, the contribution from different tissue layers to the total cell number changed. In the smallest leaf sizes, the contribution from upper and lower epidermis and spongy parenchyma was greater than that from palisade parenchyma. As the leaf size increased, cells in the palisade parenchyma continued to divide for longer than in the other layers. At final leaf size, the contribution from the different tissue layers to total cell number was the same for leaves 2, 3 and 4, irrespective of N treatment. In these final leaf structures, palisade parenchyma contributed 60% of the total cell number. Thus, although nitrogen deprivation affected leaf size variously through cell division and cell expansion, depending on leaf developmental stage at the time of nitrogen deprivation, the ratio of cell numbers and sizes in different tissue layers, at final leaf size, was unaffected.     

GROWTH REGULATION BY ETHYLENE IN FERN GAMETOPHYTES. II. INHIBITION OF CELL DIVISION

Ethylene, a natural product of sensitive fern (Onoclea sensibilis L.) gametophytes, has been demonstrated to inhibit cell division in light-grown prothallia. When plants were grown on Knop's solution plus 1 % sucrose under 300 ft-c or more of white light, all ethylene concentrations from 1–1000 μl/liter reduced the rate of increase of cell number by about one-half. The over-all rate of increase of cell number was regulated by various environmental and chemical factors, but regardless of the rate established in control cultures, ethylene treatment of 1–1000 μl/liter produced a relative 50 % depression of cell number. Ethylene was specific for inhibition of cell division and was not a general inhibitor of growth. The ethylene inhibition did not result from a reduction of photosynthesis or energy supply. Further demonstration of ethylene as the active gaseous component resulted when cultures were grown in small enclosed containers with an ethylene absorbent, mercuric perchlorate, and consequently the cell number of gametophytes was restored to the level of unenclosed controls.     

槐种子发育过程中子叶细胞显微结构的变化和过氧化物酶同工酶变化的动态

槐（SophorajaponicaL．）种子发育过程中,子叶细胞大量合成和积累储藏物质,光镜和电镜下用组织化学方法观察到开花后30d,叶肉细胞高度液泡化,其中分布着大量的质体、粗面内质网、一些线粒体和小脂体。淀粉粒开始积累。开花后60d,淀粉粒和脂体不断长大,数量明显增多,液泡中蛋白体开始形成。从花后90d开始,液泡中有大量蛋白体形成且不断长大,有些蛋白体变得不规则形。至种子成熟期,叶肉细胞几乎完全被蛋白体及脂体所填充。淀粉粒及大多数细胞器消失。基于上述观察,还对种子发育过程中子叶细胞过氧化物酶活力及同工酶港的变化进行了观察和分析。