Meristems in land plants share conserved functions but develop highly variable structures. Meristems in seed-free plants, including ferns, usually contain one or a few pyramid-/wedge-shaped apical cells (ACs) as initials, which are lacking in seed plants. It remained unclear how ACs promote cell proliferation in fern gametophytes and whether any persistent AC exists to sustain fern gametophyte development continuously. Here, we uncovered previously undefined ACs maintained even at late developmental stages in fern gametophytes. Through quantitative live-imaging, we determined division patterns and growth dynamics that maintain the persistent AC in Sphenomeris chinensis, a representative fern. The AC and its immediate progenies form a conserved cell packet, driving cell proliferation and prothallus expansion. At the apical centre of gametophytes, the AC and its adjacent progenies display small dimensions resulting from active cell division instead of reduced cell expansion. These findings provide insight into diversified meristem development in land plants.

Cell division is a tightly regulated mechanism, notably in tissues where malfunctions can lead to tumour formation or developmental defects. This is particularly true in land plants, where cells cannot relocate and therefore cytokinesis determines tissue topology. In plants, cell division is executed in radically different manners than in animals, with the appearance of new structures and the disappearance of ancestral mechanisms. Whilst F-actin and microtubules closely co-exist, recent studies mainly focused on the involvement of microtubules in this key process. Here, we used a root tracking system to image the spatio-temporal dynamics of both F-actin reporters and cell division markers in dividing cells embedded in their tissues. In addition to the F-actin accumulation at the phragmoplast, we observed and quantified a dynamic apico-basal enrichment of F-actin from the prophase/metaphase transition until the end of the cytokinesis.

The functional partial differential equation (FPDE) for cell division,

$$ \begin{align*} &\frac{\partial}{\partial t}n(x,t) +\frac{\partial}{\partial x}(g(x,t)n(x,t))\\ &\quad = -(b(x,t)+\mu(x,t))n(x,t)+b(\alpha x,t)\alpha n(\alpha x,t)+b(\beta x,t)\beta n(\beta x,t), \end{align*} $$

$$ \begin{align*} \frac{\partial}{\partial t}n(x,t) +\frac{\partial}{\partial x}(g(x,t)n(x,t)) = -(b(x,t)+\mu(x,t))n(x,t)+F(x,t), \end{align*} $$

$F(x,t)$

$n(\alpha x,t)$

$n(\beta x,t)$

$\beta \ge 2 \ge \alpha \ge 1$

$\alpha x$

$\beta x$

The nonnegative function, $n(x,t)$, denotes the density of cells at time t with respect to cell size x. The functions $g(x,t)$, $b(x,t)$ and $\mu (x,t)$ are, respectively, the growth rate, splitting rate and death rate of cells of size x. The total number of cells, $\int _{0}^{\infty }n(x,t)\,dx$, coincides with the $L^1$ norm of n. The goal of this paper is to find estimates in $L^1$ (and, with some restrictions, $L^p$ for $p>1$) for a sequence of approximate solutions to the FPDE that are generated by solving the first-order PDE. Our goal is to provide a framework for the analysis and computation of such FPDEs, and we give examples of such computations at the end of the paper.

Growth is one of the most studied plant responses. At the cellular level, plant growth is driven by cell division and cell expansion. A means to quantify these two cellular processes is through kinematic analysis, a methodology that has been developed and perfected over the past decades, with in-depth descriptions of the methodology available. Unfortunately, after performing the lab work, researchers are required to perform time-consuming, repetitive and error-prone calculations. To lower the barrier towards this final step in the analysis and to aid researchers currently applying this technique, we have created leafkin, an R-package to perform all the calculations involved in the kinematic analysis of monocot leaves using only four functions. These functions support leaf elongation rate calculations, fitting of cell length profiles, extraction of fitted cell lengths and execution of kinematic equations. With the leafkin package, kinematic analysis of monocot leaves becomes more accessible than before.

Fosamine [ethyl hydrogen (aminocarbonyl)phosphonate] acted as a chemical inhibitor of shoot growth for periods of up to 3 yr following a single summer application to honey mesquite [Prosopis juliflora (Swartz) DC. var. glandulosa (Torr.) Cockerell] trees. Anatomical study of field, greenhouse, and seedling mesquite indicated that the inhibition of primary and secondary growth caused by fosamine was due to a general cessation of nuclear activity in apical meristems and in the vascular and cork cambia of this species.

The herbicide cinmethylin {exo-1-methyl-4-(1-methylethyl)-2-[(2-methylphenyl)methoxy]-7-oxabicyclo [2.2.1] heptane} inhibited oat (Avena sativa L. ‘Porter’) root growth during the first 6 h of treatment at a concentration of 6.7 × 10-8 M. A concentration of 1 × 10-8 M cinmethylin inhibited root growth within 12 to 18 h. Inhibition of shoot growth was less sensitive, but was inhibited by 36 to 48 h after treatment with 1 × 10-7 M and by 12 to 24 h after treatment with 1 × 10-5 M cinmethylin. Cinmethylin concentrations of 1 × 10-5 M and lower did not inhibit cell elongation in isolated oat coleoptiles during a 24-h exposure. Mitotic frequency in oat root tips was reduced after 12 h of treatment with 1 × 10-7 M cinmethylin. The frequency of all stages of mitosis (prophase, metaphase, and anaphase + telophase) was reduced. Concentrations of 1 × 10-6 M cinmethylin resulted in nearly complete arrest (87% inhibition) of mitosis. These data suggest cinmethylin inhibits growth by inhibiting entry of cells into mitosis. The cause of mitotic arrest is unknown; however, the mechanism appears to be different from other herbicides known to inhibit mitosis.

The effects of sethoxydim {2-[1-(ethoxyimino) butyl]-5-[2-(ethylthio)propyl]-3-hydroxy-2-cyclohexen-1-one} on the metabolic activity of excised root tips of corn (Zea mays, L. ‘Goldencrossbantam′) were studied under laboratory conditions. Uptake and incorporation of 14C-labeled thymidine, uridine, leucine, glucose, and acetic acid into cell constituents, as well as respiration, increased continuously with time progressions during the incubation period. Sethoxydim did not affect either the uptake of any 14C-precursor into or respiration of the root tip tissue. Although RNA and protein syntheses were not affected by the herbicide, DNA and cell wall syntheses were inhibited 120 min after treatment with sethoxydim. Incorporation of 14C-acetic acid into lipid fraction was inhibited by sethoxydim in a time- and concentration-dependent fashion. This inhibition was observed at a shorter time after sethoxydim treatment than that of any other 14C-precursor. The effect was not observed in the nonproliferative regions of corn roots, whereas cerulenin (a fatty acid synthase inhibitor) inhibited the incorporation of 14C-acetic acid both in proliferative and nonproliferative regions. It is suggested that the inhibition of lipid synthesis by sethoxydim does not play a major role in the mode of action of this herbicide. The effects of sethoxydim, including those on lipid metabolism, are closely associated with proliferative conditions of susceptible graminaceous plants.

Dinitroaniline herbicides are absorbed readily by roots and emerging shoots, but shoot exposure is more phytotoxic. Translocation within the plant varies by specific herbicide but commonly is minor. Dinitroaniline herbicides injure plants by binding to tubulin, a dimer protein in the ceil that polymerizes to form microtubules (MTs). MTs form the major part of the mitotic apparatus, including spindle fibers, which enable chromosomes to separate during cell division. Dinitroaniline herbicides prevent tubulin from polymerizing into MTs, thus arresting mitosis. This leads to abnormal cells with more than the normal complement of chromosomes and, frequently, lobed nuclei. MTs also are responsible for orienting cell wall microfibrils in such a way that they prevent lateral enlargement of cells. Treatment with dinitroaniline herbicides leads to disorientation of the microfibrils, leading to one of the common symptoms—spherical cells instead of rectangular ones. Studies on the metabolism of trifluralin in plants have shown that amination, dealkylation, and cyclization all can occur. However, metabolites often amount to a small percentage of the original herbicide. In general, trifluralin seems quite stable within the plant.

The physiological responses of corn (Zea mays L. ‘Goldencrossbantam′) and pea (Pisum sativum L. ‘Alaska′) to sethoxydim {2-[1-(ethoxyimino)butyl]-5-[2-(ethylthio) propyl]-3-hydroxy-2-cyclohexen-1-one} were investigated. Sethoxydim did not affect excised pea root growth at 1 × 10−4 M but inhibited excised corn root growth at concentrations of 1 × 10−8 M and above. Treating corn impeded root growth with 1 × 10−7 M sethoxydim within 4 h after treatment; however, little histological change of the roots was observed at 48 h. At 1 × 10−6 M, growth nearly stopped within 4 h after treatment, and clear cytological changes of the roots were observed at 24 and 48 h. Sethoxydim inhibited both mitosis and DNA synthesis of excised corn root tips between 4 and 48 h after treatment. Respiration of corn roots measured by oxygen uptake and the TTC (2,3,5-triphenyltetrazolium chloride) test was not affected by the herbicide directly. Sethoxydim (1 × 10−4 M) inhibited IAA-induced cell elongation of corn coleoptile and pea epicotyl by 37 and 12%, respectively. Sethoxydim selectively inhibited the growth of excised root tips of susceptible corn by affecting cell division rather than cell enlargement, and the inhibition mechanism of cell division (inhibition of mitosis) by the herbicide was not by direct inhibition of DNA synthesis or by effects on respiration.

Structural studies were conducted to evaluate the effects of napropamide on the growth and development of corn roots. At 1.0 and 10.0 μM napropamide, root growth was inhibited severely within 3 days of seed germination. Root diameter within 1 mm of the root apex doubled and numerous lateral root primordia were observed within 10 mm of the meristem tip in treated roots. The number of cortical parenchyma cell files, xylem vessel, and phloem sieve tube strands also significantly increased. Average cortical cell size did not change, regardless of the treatment. A lateral expansion of the meristematic region of the root coincided with a slight reduction in meristem length but resulted in an overall increase in meristem volume. However, enlargement of the meristem occurred despite a reduction in the number of mitotic figures in the root meristem. Treatment of excised root tips for 24 h with 20 μM napropamide reduced the number of mitotic figures 84%.

The single-celled green alga Chlamydomonas eugametos was found to be well suited for detecting growth inhibitor activity of chemicals. Tests consisted of solubilizing technical grade compounds in 20-ml aliquots of a 1 × 105 cells/ml zoospore culture. Commercially available growth inhibitor herbicides significantly inhibited synchronous cell population increases within 48 h at concentrations ranging from 1 × 10−4 to 1 × 10−7M. Examples of compounds that inhibited Chlamydomonas more than 50% were butylate (S-ethyl diisobutylthiocarbamate) and diallate [S-(2,3-dichloroallyl)diisopropylthiocarbamate] at 1 × 10−4M, CDEC [2 chloroallyl diethyldithiocarbamate] and propham (isopropyl carbanilate) at 1 × 10−5M, alachlor [2-chloro-2′,6′-diethyl-N-(methoxymethyl)acetanilide] and trifluralin [α,α,α-trifluoro-2,6-dinitro-N,N-dipropyl-p-toluidine] at 1 × 10−6 M, and bifenox [methyl 5-(2,4-dichlorophenoxy)-2-nitrobenzoate] at 1 × 10−7M. Ethanol, dimethylsulfoxide (DMSO), or acetone can be used to solubilize herbicides in the aqueous medium. DMSO and ethanol are not detrimental to the cells if the concentration is kept at 1% v/v or less.

Suspension cultures of proso millet cells were treated with haloxyfop at different phases of growth. Treatment of 1-d cultures with 1 μM haloxyfop completely inhibited growth within 48 h. In contrast, 1 mM haloxyfop was required to elicit a similar response in 4-, 7-, or 10-d cultures. Calculated IC50 values indicated a 300-fold decrease in haloxyfop sensitivity during the period from 1 to 4 d. The observed changes in sensitivity to haloxyfop could not be attributed to changes in cell concentration during culture growth. In both 1-d and 4-d cultures, an initial rapid uptake of radiolabel was followed by a slow loss of radiolabel from cells. Almost all radioactivity extracted from 1-d and 4-d cells was present as the parent acid. Several radiolabeled compounds in addition to the parent acid were present in media. No major differences in the amounts of these materials were found between 1-d and 4-d media. Our results indicate that a special aspect of metabolism expressed during cell division is particularly sensitive to the herbicide.

The effects of varying concentrations and duration of alachlor [2-chloro-2′,6′diethyl-N-(methoxymethyl)acetanilide] and metolachlor [2-chloro-N-(2-ethyl-6-methylphenyl)-N-(2-methoxy-1-methylethyl)acetamide] treatment on root growth, cell division, and cell enlargement were studied. Peas (Pisum sativum L. ‘Alaska’) and oats (Avena sativa L. ‘Victory’) were treated from 0 to 48 h with concentrations ranging from 1 × 10-8 to 1 × 10-3 M of each herbicide. After 48 h, average growth rates were significantly inhibited at concentrations of 1 × 10-7 M alachlor and 5 × 10−8 M metolachlor, and 5 × 10−7 M alachlor and 1 × 10-6 M metolachlor for peas and oats, respectively. When growth inhibitions were examined across time at concentrations greater than these, the degree of growth inhibition was a function of both concentration and duration of treatment. Often the greatest decrease in growth occurred between 0 and 12 h. Mitotic indices of root tip squashes from pea roots and paraffin sections from oat roots were determined. There was a significant reduction in the mitotic indices of pea roots treated for 48 h with 5 × 10−6 M alachlor or 1 × 10-5 M metolachlor. After a 30-h treatment, the mitotic indices of oat roots were significantly reduced by 1 × 10−7 M metolachlor and 1 × 10−6 M alachlor. Significant inhibition of elongation of etiolated oat coleoptiles were observed at 5 × 10−6 M alachlor (27%) and 5 × 10−5 M metolachlor (30%). Inhibition of pea hypocotyl elongation did not occur at concentrations below 5 × 10−4 M. It was concluded that the growth inhibition of plants caused by alachlor and metolachlor results from both an inhibition of cell division and cell enlargement.

One to 5.6 μM DCPA (dimethyl tetrachloroterephthalate) inhibited oat (Avena sativa L. ‘Victory’) root growth within 12 to 18 h. Treated roots were severely stunted and swollen. An analysis of cell division in roots treated with DCPA revealed a disruption of normal mitosis after prophase. Metaphase, anaphase, and telophase division figures were absent 8 to 10 h after treatment with 5.6 μM DCPA. In contrast, a 24-h treatment with 5.6 μM DCPA was necessary to eliminate prophase division figures. The number of aberrant division figures increased concomitantly with the reduction in normal division figures. The predominant type of aberrant division figure was a condensed prophase. When the aberrant division cycle was completed and cells entered interphase, the dispersed chromosomes coalesced to form large, polymorphic nuclei and, occasionally, micronuclei. Approximately 60% of the outer four tiers of cells in roots treated with 5.6 μM DCPA developed abnormal cell walls. These data suggest that DCPA causes root growth inhibition by disrupting several processes involving organized microtubules.

We consider a host-parasite model for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be of any type. The random mechanism that describes how parasites within a cell multiply and are then shared into the daughter cells is allowed to depend on the hosting mother cell as well as its daughter cells. Focusing on the subpopulation of A-cells and its parasites, our model differs from the single-type model recently studied by Bansaye (2008) in that the sharing mechanism may be biased towards one of the two types. Our main results are concerned with the nonextinctive case and provide information on the behavior, as n → ∞, of the number of A-parasites in generation n and the relative proportion of A- and B-cells in this generation which host a given number of parasites. As in Bansaye (2008), proofs will make use of a so-called random cell line which, when conditioned to be of type A, behaves like a branching process in a random environment.

At the apical tip of Drosophila testis, there is a stem cell niche known as the proliferation center, where the stem cells are maintained by hub cell cluster for the regulation of differentiation and proliferation. Germline stem cells go through mitosis four times from one primary spermatogonial cell to the 16-cell stage before the maturation. The cells derived from the same germline stem cell are located within one cyst, an enclosed system by two cyst cells, and they are connected by the intercellular bridges called ring canals. In this study, the three-dimensional (3D) structure of Drosophila testis tip was reconstructed from serial sections. The size of cells at each stage was compared in volume from the 3D structure. The stages of cells in a cyst could be distinguishable exactly by counting the cells linked with intercellular bridges in 3D-reconstructed structure. The cysts containing the same stage cells appeared in the horizontal plane. Both the germline stem cell directly attached to the hub cell and the spermatogonial cells detached from the hub cell were divided at the almost perpendicular direction to the spermatogonial cell layers. The dividing phase in one cyst was delayed gradually through the cytoplasmic region of intercellular bridge.

The aim of this study was to describe and analyze the regulation and spatio-temporaldynamics of melanocyte migration in vitro and its coupling to celldivision and interaction with the matrix. The melanocyte lineage is particularlyinteresting because it is involved in both embryonic development andoncogenesis/metastasis (melanoma). Biological experiments were performed on two melanocytecell lines established from wild-type and β-catenin-transgenic mice(bcat*). The multi-functional β-catenin molecule is known to be able toregulate the transcription of various genes involved in cell proliferation and migration,particularly in the melanocyte lineage. We also investigated fibronectin, anextra-cellular matrix protein that binds integrins, thereby providing adhesion points forcells and encouraging migration. As the migration of individual cells were followed,automated methods were required for processing the large amount of data generated by thetime-lapse video-microscopy. A model-based approach for automated cell tracking wasevaluated on a sample by comparison with manual tracking. This method was found reliablein studying overall cell behaviour. Its application to all the observed sequences providedinsight into the factors affecting melanocyte migration in vitro:melanocytes of mutated form of β-catenin showed higher division rates andno contact inhibition of growth was induced by the resulting increase in cell density.However, cell density limited the amplitude of cell displacements, although their motilitywas less affected. The high fibronectin concentration bound to substratum promoted cellmigration and motility, the effect being more intense for wild-type cells than for cellswith β-catenin over-expression. During the division process, cellmigration speed increased rapidly then decreased slowly. Analyses of such data is expectedto lead both to biological answers and to a framework for a better modeling processes inthe future.

Prototheca richardsi, an unpigmented heterotrophic alga, causes growth inhibition in amphibian larvae and has proved refractory to culture in Vitro. P. richardsi replication is dependent on regular passaging through tadpole digestive systems; uptake of thymidine by free-living Prototheca cells and incorporation into DNA are very low by comparison with leucine uptake and incorporation into protein, but DNA synthesis is detectable in cells isolated from tadpole intestines. DNA replication was elicited 6–8 h after ingestion in protothecans fed to tadpoles and subsequently re-isolated from them, providing that the tadpoles were fed subsequent to the ingestion. It appears that passaging through tadpole intestines provides an essential stimulus to maintaining an active cell division cycle in P. richardsi.

The maintenance of a stable stem cellpopulation in the epidermis is important for robust regenerationof the stratified epithelium. The population size is usuallyregulated by cell secreted extracellular signalling molecules aswell as intracellular molecules. In this paper, a simple modelincorporating both levels of regulation is developed to examinethe balance between growth and differentiation for the stem cellpopulation. In particular, the dynamics of a known differentiationregulator c-Myc, its threshold dependent differentiation, andfeedback regulation on maintaining a stable stem cell populationare investigated.