A dynamical model for plant cell wall architecture formation

We discuss a dynamical mathematical model to explain cell wall architecture in plant cells. The highly regular textures observed in cell walls reflect the spatial organisation of the cellulose microfibrils (CMFs), the most important structural component of cell walls. Based on a geometrical theory proposed earlier [A. M. C. Emons, Plant, Cell and Environment 17, 3–14 (1994)], the present model describes the space-time evolution of the density of the so-called rosettes, the CMF synthesizing complexes. The motion of these rosettes in the plasma membrane is assumed to be governed by an optimal packing constraint on the CMFs plus adherent matrix material, that couples the direction of motion, and hence the orientation of the CMF being deposited, to the local density of rosettes. The rosettes are created inside the cell in the endoplasmatic reticulum and reach the cell-membrane via vesicles derived from Golgi-bodies. After being inserted into the plasma membrane they are assumed to be operative for a fixed, finite lifetime. The plasma membrane domains within which rosettes are activated are themselves also supposed to be mobile. We propose a feedback mechanism that precludes the density of rosettes to rise beyond a maximum dictated by the geometry of the cell. The above ingredients lead to a quasi-linear first order PDE for the rosette-density. Using the method of characteristics this equation can be cast into a set of first order ODEs, one of which is retarded. We discuss the analytic solutions of the model that give rise to helicoidal, crossed polylamellate, helical, axial and random textures, since all cell walls are composed of (or combinations of) these textures. Received: 10 July 1999 / Revised version: 7 June 2000 / Published online: 16 February 2001     

Biased three-dimensional cell migration and collagen matrix modification

Various tumours can be resected even for cure with complete removal. Surgical excision with a wide margin to ensure complete removal has therefore been suggested as the primary treatment for such lesions. The histological examination of the three-dimensional (3D) excision margins (3D histology) constitutes an important part of the quality control mechanisms in tumour surgery. Understanding histologically relevant properties of the constituents of the microenvironment in tumours and the circumferential portion of non-lesional tissue is therefore critical.Accompanied by the increasing availability of high performance computers in recent decades, there has been a strong movement aiming at the development of mathematical models whose implementations allow in silico simulations of biological reaction networks. Due to its relevance in numerous biological and pathological processes, there have been various attempts to model biased migration of single cells. The model introduced in this paper plays a prominent role insofar as it covers the under-represented 3D case. Moreover, it is uniformly formulated for both two and three dimensions. The velocity of each cell is characterised by a generalised Langevin equation, a stochastic differential equation, where chemotaxis as well as contact guidance are considered to simulate selected aspects of interactions between carcinoma cell groups and fibroblast-like cells.Algorithmic and numeric aspects of the developed equations are detailed in this paper and the results of the simulations are illustrated in different manners to emphasise specific features. A simple test scenario as well as a geometry based on segmentation data of a real histological slide has served for verification of the software. The resulting morphologies closely resemble that of desmoplastic stromal reaction readily identifiable in histological slides of infiltrating carcinoma, and the images can be interpreted in the context of 3D histology.     

An alternative stochastic model of generation of oligodendrocytes in cell culture

According to our previous model, oligodendrocyte – type 2 (O-2A) astrocyte progenitor cells become competent for differentiation in vitro after they complete a certain number of critical mitotic cycles. After attaining the competency to differentiate, progenitor cells divide with fixed probability p in subsequent cycles. The number of critical cycles is random; analysis of data suggests that it varies from zero to two. The present paper presents an alternative model in which there are no critical cycles, and the probability that a progenitor cell will divide again decreases gradually to a plateau value as the number of completed mitotic cycles increases. In particular all progenitor cells have the ability to differentiate from the time of plating. The Kiefer-Wolfowitz procedure is used to fit the new model to experimental data on the clonal growth of purified O-2A progenitor cells obtained from the optic nerves of 7 day old rats. The new model is shown to fit the experimental data well, indicating that it is not possible to determine whether critical cycles exist on the basis of these experimental data. In contrast to the fit of the previous model, which suggested that the addition of thyroid hormone increased the limiting probability of differentiation as the number of mitotic cycles increases, the fit of the new model suggests that the addition of thyroid hormone has almost no effect on the limiting probability of differentiation. Received: 6 March 2000 / Revised version: 18 September 2000 / Published online: 30 April 2001     

Phototolerance of lichens, mosses and higher plants in an alpine environment: analysis of photoreactions

 Adaptation to excessive light is one of the requirements of survival in an alpine environment particularly for poikilohydric organisms which in contrast to the leaves of higher plants tolerate full dehydration. Changes in modulated chlorophyll fluorescence and 820-nm absorption were investigated in the lichens Xanthoria elegans (Link) Th. Fr. and Rhizocarpon geographicum (L.) DC, in the moss Grimmia alpestris Limpr. and the higher plants Geum montanum L., Gentiana lutea L. and Pisum sativum L., all collected at altitudes higher than 2000 m above sea level. In the dehydrated state, chlorophyll fluorescence was very low in the lichens and the moss, but high in the higher plants. It increased on rehydration in the lichens and the moss, but decreased in the higher plants. Light-induced charge separation in photosystem II was indicated by pulse-induced fluorescence increases only in dried leaves, not in the dry moss and dry lichens. Strong illumination caused photodamage in the dried leaves, but not in the dry moss and dry lichens. Light-dependent increases in 820-nm absorption revealed formation of potential quenchers of chlorophyll fluorescence in all dehydrated plants, but energy transfer to quenchers decreased chlorophyll fluorescence only in the moss and the lichens, not in the higher plants. In hydrated systems, coupled cyclic electron transport is suggested to occur concurrently with linear electron transport under strong actinic illumination particularly in the lichens because far more electrons became available after actinic illumination for the reduction of photo-oxidized P700 than were available in the pool of electron carriers between photosystems II and I. In the moss Grimmia, but not in the lichens or in leaves, light-dependent quenching of chlorophyll fluorescence was extensive even under nitrogen, indicating anaerobic thylakoid acidification by persistent cyclic electron transport. In the absence of actinic illumination, acidification by ca. 8% CO₂ in air quenched the initial chlorophyll fluorescence yield F_o only in the hydrated moss and the lichens, not in leaves of the higher plants. Under the same conditions, 8% CO₂ reduced the maximal fluorescence yield F_m strongly in the poikilohydric organisms, but only weakly or not at all in leaves. The data indicate the existence of deactivation pathways which enable poikilohydric organisms to avoid photodamage not only in the hydrated but also in the dehydrated state. In the hydrated state, strong nonphotochemical quenching of chlorophyll fluorescence indicated highly sensitive responses to excess light which facilitated the harmless dissipation of absorbed excitation energy into heat. Protonation-dependent fluorescence quenching by cyclic electron transport, P700 oxidation and, possibly, excitation transfer between the photosystems were effectively combined to produce phototolerance. Received: 10 December 1999 / Accepted: 13 April 2000     

Chemical-induced apoptotic cell death in tomato cells: involvement of caspase-like proteases

 A new system to study programmed cell death in plants is described. Tomato (Lycopersicon esculentum Mill.) suspension cells were induced to undergo programmed cell death by treatment with known inducers of apoptosis in mammalian cells. This chemical-induced cell death was accompanied by the characteristic features of apoptosis in animal cells, such as typical changes in nuclear morphology, the fragmentation of the nucleus and DNA fragmentation. In search of processes involved in plant apoptotic cell death, specific enzyme inhibitors were tested for cell-death-inhibiting activity. Our results showed that proteolysis plays a crucial role in apoptosis in plants. Furthermore, caspase-specific peptide inhibitors were found to be potent inhibitors of the chemical-induced cell death in tomato cells, indicating that, as in animal systems, caspase-like proteases are involved in the apoptotic cell death pathway in plants. Received: 5 August 1999 / Accepted: 14 March 2000     

Growth, ageing and death of a photoautotrophic plant cell culture

 Batch cultures of photoautotrophic cell suspensions of Chenopodiumrubrum L., growing in an inorganic medium on CO₂ under a daily balanced light–dark regime of 16 : 8 h could be maintained for approximately 100 d without subcultivation. The long-lived cultures showed an initial cell division phase of 4 weeks, followed by a stationary phase of another 4 weeks, after which ageing and progressive cell death reduced the number of living cells and the cultures usually expired after another 3–4 weeks. These developmental phases of the cell culture were characterised with respect to photosynthetic performance, dark respiration, content of phytohormones and capacity of cell division. Cell division of the majority of the cells finished in the G1- or G0-phase of the cell cycle, caused by a pronounced decline in the endogenous levels of auxin and cytokinins. Supply of these growth factors to resting cells resulted in resumption of cytokinesis, at least by some of the cells. However, responsiveness to the phytohomones declined during the stationary phase, and subcultivation was no longer possible beyond day 60 when the phases of ageing and death commenced. Ageing was characterised by a further decline in the photosynthetic capacity of the cells, by a climacteric enhancement of dark respiration, but also by a slight increase in the level of IAA and cytokinins concomitant with a decrease in ethylene. Similarities and differences between the development of batch-cultured photoautotrophic cells of C. rubrum and that of a leaf are discussed with respect to using the cell culture as a model for a leaf. Received: 30 April 1999 / Accepted: 21 August 1999     

Programmed cell death: similarities and differences in animals and plants. A flower paradigm

Summary. After an overview of the criteria for the definition of cell death in the animal cell and of its different types of death, a comparative analysis of PCD in the plant cell is reported. The cytological characteristics of the plant cell undergoing PCD are described. The role of plant hormones and growth factors in the regulation of this event is discussed with particular emphasis on PCD activation or prevention by polyamine treatment (doses, timing and developmental stage of the organism) in a Developmental cell death plant model: the Nicotiana tabacum (tobacco) flower corolla. Some of the effects of polyamines might be mediated by transglutaminase catalysis. The activity of this enzyme was examined in different parts of the corolla during its life span showing an acropetal trend parallel to the cell death wave. The location of transglutaminase in some sub-cellular compartments suggests that it exerts different functions in the corolla DCD.     

Isolation and characterisation of cell wall polysaccharides from cocoa (Theobroma cacao L.) beans

 Cell wall material (CWM) was prepared from sun-dried cocoa (Theobroma cacao L.) bean cotyledons before and after fermentation. The monosaccharide composition of the CWM was identical for unfermented and fermented beans. Polysaccharides of the CWM were solubilised by sequential extraction with 0.05 M trans-1,2-diaminocyclohexane-N,N,N′,N′-tetraacetic acid (CDTA), 0.05 M Na₂CO₃, and 1 M, 4 M and 8 M KOH. The non-cellulosic sugar composition for each fraction was similar for unfermented and fermented samples, indicating that fermentation caused no significant modification of the structural features of individual cell wall polysaccharides. Pectic polysaccharides accounted for 60% of the cell wall polysaccharides but only small amounts could be solubilised in solutions of CDTA, Na₂CO₃, and 1 M and 4 M KOH. The bulk of the pectic polysaccharides were solubilised in 8 M KOH and were characterised by a rhamnogalacturonan backbone heavily substituted with side-chains of 5-linked arabinose and 4-linked galactose. Linkage analysis indicated the presence of additional acidic polysaccharides, including a xylogalacturonan and a glucuronoxylan. Cellulose, xyloglucan and a galactoglucomannan accounted for 28%, 8% and 3% of the cell wall polysaccharides, respectively. It is concluded that the types and structural features of cell wall polysaccharides in cocoa beans resemble those found in the parenchymatous tissue of many fruits and vegetables rather than those reported for many seed storage polysaccharides. Received: 29 May 1999 / Accepted: 19 October 1999     

Nuclear/cytoplasmic localization of Akt activity in the cell cycle

Summary. The serine/threonine protein kinase Akt (also known as PKB) is a proto-oncogene and one of the most frequently hyperactivated kinases in human cancer. Its activation downstream of growth-factor-stimulated phosphatidylinositide-3′-OH kinase activity plays a role in the control of cell cycle, cell growth, apoptosis and cell energy metabolism. Akt phosphorylates some thousand downstream substrates, including typical cytoplasmic as well as nuclear proteins. Accordingly, it is not surprising that Akt activity can be found in both, the cytoplasm and the nucleus. Here we report the cell cycle regulation of nuclear and cytoplasmic Akt activity in mammalian cells. These data provide new insights into the regulation of Akt activity and have implications for future studies on the regulation of the wide variety of different nuclear and cytoplasmic Akt substrates.     

Analytical solutions of a minimal model of species migration in a bounded domain

 A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally. Received: 15 August 1999     

Inactivation of DNA replication origins by the cell cycle regulator, trigonelline, in root meristems of Lactuca sativa

 The effects of trigonelline (TRG) on the cell cycle in root meristems of Lactuca sativa L. were examined in the knowledge that TRG is a cell cycle regulator that causes cell arrest in G2, and prevents ligation of replicons in S-phase. The hypothesis was tested that continuous exposure to TRG would perturb DNA replication which, in turn, would lengthen the cell cycle and impair root elongation. Using DNA fibre autoradiography, mean replicon size was 31 and 13 μm in the TRG (3 mM) and control treatments, respectively. Trigonelline also resulted in a lengthening of both S-phase and the cell cycle and a decrease in primary root elongation. Hence, replicon inactivation was responsible for the protracted S-phase. Trigonelline treatment also resulted in a 1.6-fold increase in fork rate (13.8 μm h⁻¹) compared with the control (8.4 m h⁻¹). The faster fork rate in the larger replicons is in accord with the highly significant positive relationship already established between fork rate and replicon size for various unrelated higher plants. Received: 11 October 1999 / Accepted: 23 December 1999     

Glutamine synthetase and glutamate dehydrogenase isoforms in maize leaves: localization, relative proportion and their role in ammonium assimilation or nitrogen transport

 Mesophyll cells (MCs) and bundle-sheath cells (BSCs) of leaves of the C₄ plant maize (Zea mays L.) were separated by cellulase digestion to determine the relative proportion of the glutamine synthetase (GS; EC 6.3.1.2) or the NADH-glutamate dehydrogenase (GDH; EC 1.4.1.2) isoforms in each cell type. The degree of cross-contamination between our MC and BSC preparations was checked by the analysis of marker proteins in each fraction. Nitrate reductase (EC 1.6.6.1) proteins (110 kDa) were found only in the MC fraction. In contrast, ferredoxin-dependent glutamate synthase (Fd-GOGAT; EC 1.4.7.1) proteins (160 kDa) were almost exclusively present in the BSC fraction. These results are consistent with the known intercellular distribution of nitrate reductase and Fd-GOGAT proteins in maize leaves and show that the cross-contamination between our MC and BSC fractions was very low. Proteins corresponding to cytosolic GS (GS-1) or plastidic GS (GS-2) were found in both the MC and BSC fractions. While equal levels of GS-1 (40 kDa) and GS-2 (44 kDa) polypeptides were present in the BSC fraction, the GS-1 protein level in the MC fraction was 1.8-fold higher than the GS-2 protein pool. Following separation of the GS isoforms by anion-exchange chromatography of MC or BSC soluble protein extracts, the relative GS-1 activity in the MC fraction was found to be higher than the relative GS-2 activity. In the BSC fraction, the relative GS-1 activity was very similar to the relative GS-2 activity. Two isoforms of GDH with apparent molecular weights of 41 kDa and 42 kDa, respectively, were detected in the BSC fraction of maize leaves. Both GDH isoenzymes appear to be absent from the MC fraction. In the BSCs, the level of the 42-kDa GDH isoform was 1.7-fold higher than the level of the 41-kDa GDH isoform. A possible role for GS-1 and GDH co-acting in the synthesis of glutamine for the transport of nitrogen is discussed. Received: 25 January 2000 / Accepted: 30 March 2000     

A new criterion for the global stability of simultaneous cell replication and maturation processes

 We analyze a population model of cells that are capable of simultaneous and independent proliferation and maturation. This model is described by a first order partial differential equation with a time delay and a retardation of the maturation variable, both due to cell replication. We provide a general criterion for global stability in such equations. Received: 26 August 1996 / Revised version: 22 March 1997     

A Turing model with correlated random walk

 If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its rate of change of direction, and oscillating patterns are possible. Received 24 February 1995; received in revised form 6 September 1995     

Protected polymorphism in the two-locus haploid model with unpredictable fitnesses

 In an unpredictable environment, the distributions of alleles from which polymorphism can be maintained forever belong to a certain set, the C-viability kernel. Such a set is calculated in the two-locus haploid model, as well as the corresponding fitnesses at any time which make this maintenance possible. The dependence of the C-viability kernel on the set U of admissible fitnesses and on the recombination rate r is studied. Notably, the C-viability kernel varies rapidly in the neighborhood of equal fitness of AB and ab; it becomes empty when ab has a fitness below a certain function, which is delineated, of the recombination rate. The properties of the two-locus model under constraints, out of equilibrium and with unpredictable selection are thus presented. Received: 20 May 1999     

A deterministic size-structured population model for the worm Naidis elinguis

In this paper we model the population dynamics of the worm Nais elinguis, which reproduces by division into two unequal parts. By using renewal theory we derive the asymptotic behaviour of a Naidis elinguis population. In particular we prove a certain relation between the fraction of the population that was born small (respectively the fraction that was born large) and the inter-division times. Received 20 January 1999 / Revised version: 1 August 1999?Published online: 10 April 2001     

O-Acetylation of plant cell wall polysaccharides: identification and partial characterization of a rhamnogalacturonan O-acetyl-transferase from potato suspension-cultured cells

 A microsomal preparation from suspension-cultured potato stem cells (Solanum tuberosum L. cv. AZY) was incubated with [¹⁴C]acetyl-CoA resulting in a precipitable radiolabeled product. Analysis of the product revealed that it consisted mostly of acetylated proteins and cell wall polysaccharides, including xyloglucan, homogalacturonan and rhamnogalacturonan I. Thus, acetyl-CoA is a donor-substrate for the O-acetylation of wall polysaccharides. A rhamnogalacturonan acetylesterase was used to develop an assay to measure and characterize rhamnogalacturonan O-acetyl transferase activity in the microsomal preparation. Using this assay, it was shown that the transferase activity was highest during the linear growth phase of the cells, had a pH-optimum at pH 7.0, a temperature optimum at 30 °C, an apparent K _m of 35 μM and an apparent V _max of 0.9 pkat per mg protein. Further analysis of the radiolabeled acetylated product revealed that it had a molecular mass >500 kDa. Received: 3 July 1999; Accepted: 27 September 1999     

A chemotactic model of trunk neural crest cell migration

Trunk neural crest cells follow a common ventral migratory pathway but are distributed into two distinct locations to form discrete sympathetic and dorsal root ganglia along the vertebrate axis. Although fluorescent cell labeling and time‐lapse studies have recorded complex trunk neural crest cell migratory behaviors, the signals that underlie this dynamic patterning remain unclear. The absence of molecular information has led to a number of mechanistic hypotheses for trunk neural crest cell migration. Here, we review recent data in support of three distinct mechanisms of trunk neural crest cell migration and develop and simulate a computational model based on chemotactic signaling. We show that by integrating the timing and spatial location of multiple chemotactic signals, trunk neural crest cells may be accurately positioned into two distinct targets that correspond to the sympathetic and dorsal root ganglia. In doing so, we honor the contributions of Wilhelm His to his identification of the neural crest and extend the observations of His and others to better understand a complex question in neural crest cell biology.     

A dynamic model for the p53 stress response networks under ion radiation

Summary. P53 controls the cell cycle arrest and cell apoptosis through interaction with the downstream genes and their signal pathways. To stimulate the investigation into the complicated responses of p53 under the circumstance of ion radiation (IR) in the cellular level, a dynamic model for the p53 stress response networks is proposed. The model can be successfully used to simulate the dynamic processes of generating the double-strand breaks (DSBs) and their repairing, ataxia telangiectasia mutated (ATM) activation, as well as the oscillations occurring in the p53-MDM2 feedback loop.     

Decrease of phosphoribulokinase activity by antisense RNA in transgenic tobacco: definition of the light environment under which phosphoribulokinase is not in large excess

 To test the hypothesis that the contribution of phosphoribulokinase (PRK) to the control of photosynthesis changes depending on the light environment of the plant, the response of transgenic tobacco (Nicotiana tabacum L.) transformed with antisense PRK constructs to irradiance was determined. In plants grown under low irradiance (330 μmol m⁻² s⁻¹) steady-state photosynthesis was limited in plants with decreased PRK activity upon exposure to higher irradiance, with a control coefficient of PRK for CO₂ assimilation of 0.25 at and above 800 μmol m⁻² s⁻¹. The flux control coefficient of PRK for steady-state CO₂ assimilation was zero, however, at all irradiances in plant material grown at 800 μmol m⁻² s⁻¹ and in plants grown in a glasshouse during mid-summer (alternating shade and sun 300–1600 μmol m⁻² s⁻¹). To explain these differences between plants grown under low and high irradiances, Calvin cycle enzyme activities and metabolite content were determined. Activities of PRK and other non-equilibrium Calvin cycle enzymes fructose-1,6-bisphosphatase, sedoheptulose-1,7-bisphosphatase and ribulose-1,5-bisphosphate carboxylase-oxygenase were twofold higher in plants grown at 800 μmol m⁻² s⁻¹ or in the glasshouse than in plants grown at 330 μmol m⁻² s⁻¹. Activities of equilibrium enzymes transketolase, aldolase, ribulose-5-phosphate epimerase and isomerase were very similar under all growth irradiances. The flux control coefficient of 0.25 in plants grown at 330 μmol m⁻² s⁻¹ can be explained because low ribulose-5-phosphate content in combination with low PRK activity limits the synthesis of ribulose-1,5-bisphosphate. This limitation is overcome in high-light-grown plants because of the large relative increase in activities of sedoheptulose-1,7-bisphosphatase and fructose-1,6-bisphosphatase under these conditions, which facilitates the synthesis of larger amounts of ribulose-5-phosphate. This potential limitation will have maintained evolutionary selection pressure for high concentrations of PRK within the chloroplast. Received: 15 November 1999 / Accepted: 27 January 2000