Analysis of clustered firing patterns in synaptically coupled networks of oscillators

Oscillators in networks may display a variety of activity patterns. This paper presents a geometric singular perturbation analysis of clustering, or alternate firing of synchronized subgroups, among synaptically coupled oscillators. We consider oscillators in two types of networks: mutually coupled, with all-to-all inhibitory connections, and globally inhibitory, with one excitatory and one inhibitory population of oscillators, each of arbitrary size. Our analysis yields existence and stability conditions for clustered states, along with formulas for the periods of such firing patterns. By using two different approaches, we derive complementary conditions, the first set stated in terms of time lengths determined by intrinsic and synaptic properties of the oscillators and their coupling and the second set stated in terms of model parameters and phase space structures directly linked to parameters. These results suggest how biological components may interact to produce the spindle sleep rhythm in thalamocortical networks. Received: 9 September 1999 / Revised version: 7 July 2000 / Published online: 24 November 2000     

High-throughput capillary electrophoresis method for plasma cysteinylglycine measurement: evidences for a clinical application

Summary. Increased levels in plasma homocysteine and cysteine, and more recently, decreased levels in cysteinylglycine have been indicated as a risk factor for vascular diseases. Most assays focused their attention only on homocysteine determination and when also other thiols were measured, analytical times drastically increased. By modifying our previous method for thiols detection, we set up a rapid capillary electrophoresis method for the selective quantification of plasma cysteinylglycine, cutting the analysis time of about 50%. Samples were treated with tri-n-butylphosphine as reducing agent, proteins were precipitated with trichloroacetic acid and released thiols were successively derivatized by the selective thiol laser-induced fluorescence-labeling agent 5-iodoacetamidofluorescein and separated by capillary electrophoresis. A baseline separation between peaks was obtained in about 2 min using 3 mmol/L sodium phosphate/2.5 mmol/L boric acid as electrolyte solution with 75 mmol/L N-methyl-D-glucamine at pH 11.25 in a 47 cm long capillary with a cartridge temperature of 45 °C. The method application was checked by measuring plasma Cys-Gly levels in a group of patients affected by retinal vein occlusion (RVO), an important cause of visual loss in the elderly. The low levels of Cys-Gly found in the RVO patients suggest that these small thiols may have importance in the disease development. Authors’ addresses: Dr. Angelo Zinellu, Dr. Ciriaco Carru, Department Biomedical Sciences, Chair of Clinical Biochemistry, University of Sassari, Viale San Pietro 43/B, 07100 Sassari, Italy     

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     

A cytoskeletal basis for wood formation in angiosperm trees: the involvement of microfilaments

The cortical microfilament (MF) component of the cytoskeleton within axial elements of the secondary vascular system of the angiosperm tree, Aesculus hippocastanum L. (horse-chestnut) was studied using transmission electron microscopy of ultrathin sections and indirect immunofluorescence microscopy of actin in thick sections. As seen by electron microscopy, MF bundles have a net axial orientation within fusiform cambial cells and their secondary vascular derivatives (i.e. in the axial xylem and phloem parenchyma, xylem fibres, vessel and sieve elements, and companion cells). Immunofluorescence studies, however, reveal that this axial orientation can be more accurately described as a helix of extremely high pitch; it is a persistent feature of all axial secondary vascular elements during their development. Helical MF arrays are the only arrangement seen in secondary phloem cells. However, in addition to helices, other MF arrays are seen in secondary xylem cells. For example, fibres possess ellipses of MFs associated with simple-pit formation, and vessel elements possess circular arrays of MFs that associate with the developing inter-vessel bordered pits, ray–vessel contact pits, and with the perforation plate. Linear MF arrays are seen co-oriented with the developing tertiary wall-thickenings in vessel elements. The possible roles of MFs during the cytodifferentiation of secondary vascular cells is discussed, and compared with that of microtubules. Received: 7 June 1999 / Accepted: 23 December 1999     

A new explicit stability criterion for human periodic breathing<--RID="*"--><--ID="*" This research was supported by grants from DRED (96-920).-->

The aim of this paper is to carry out a stability analysis for periodic breathing in humans that incorporates the dynamic characteristics of ventilation control. A simple CO₂ model that takes into account the main elements of the respiratory system, i.e. the lungs and the ventilatory controller with its dynamic properties, is presented. This model results in a three-dimensional non-linear delay differential system for which there exists a unique equilibrium point. Our stability analysis of this equilibrium point leads to the definition of a new explicit stability criterion and to the demonstration of the existence of a Hopf bifurcation. Numerical simulations illustrate the influence of physiological parameters on the stability of ventilation, and particularly the major role of the dynamic characteristics of the respiratory controller. Received: 2 February 1999 / Revised version: 18 June 1999 / Published online: 23 October 2000     

The hypersensitive response is associated with host and nonhost resistance to Phytophthora infestans

The interaction between Phytophthora infestans (Mont.) de Bary and Solanum was examined cytologically using a diverse set of wild Solanum species and potato (S. tuberosum L.) cultivars with various levels of resistance to late blight. In wild Solanum species, in potato cultivars carrying known resistance (R) genes and in nonhosts the major defense reaction appeared to be the hypersensitive response (HR). In fully resistant Solanum species and nonhosts, the HR was fast and occurred within 22 h. This resulted in the death of one to three cells. In partially resistant clones, the HR was induced between 16 and 46 h, and resulted in HR lesions consisting of five or more dead cells, from which hyphae were occasionally able to escape to establish a biotrophic interaction. These results demonstrate the quantitative nature of the resistance to P. infestans. The effectiveness of the HR in restricting growth of the pathogen differed considerably between clones and correlated with resistance levels. Other responses associated with the defense reaction were deposition of callose and extracellular globules containing phenolic compounds. These globules were deposited near cells showing the HR, and may function in cell wall strengthening. Received: 22 April 1999 / Accepted: 4 November 1999     

Actin cytoskeletal isoforms in human endothelial cellsin vitro: Alteration with cell passage

Summary The microfilamentous actin component of the cytoskeleton is crucial to endothelial angiogenesis and vascular permeability. Differences in actin cytoskeletal profiles in cultured human endothelial cells were explored: when first isolated, both primary human umbilical vein endothelial cells (HUVEC) and primary human placental microvascular endothelial cells (HPMEC) expressed F-actin, but notβ-actin orα-smooth muscle actin. A similar endothelial actin profile was observed in cryo-sections of freshly delivered term umbilical cord and placenta. In subsequent cell culture, although the actin cytoskeleton of HUVEC remained unchanged, the actin profiles of HPMEC altered after the second passage with the induction ofα-smooth muscle actin expression, which was intercellularly heterogeneous and increased to 20% at P4. This behavior occurred in HPMEC monolayers cultured on a variety of extracellular matrices. Comparisons with a spontaneously immortalized human microvascular cell-line, HGTEN 21, revealed that inprolonged passage, bothα-smooth muscle actin andβ-actin were expressed, whereas HPMEC at P4 showed a lower level ofβ-actin expression. Therefore, in comparison with large vessels, microvascular cells are more likely to dedifferentiate. This may reflect the ability of microvascular cells to remodel according to changing requirement for new vessel formation. In conclusion, passage of human microvascular endothelial cells, but not of larger vessel endothelial cells, alters the expression of actin isoforms. This may be important in relation to comparisons ofin vitro andin vivo vascular permeability; higher passage microvascular endothelial cells should thus be used with caution in such studies.     

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     

A DEFICIENS homologue is down-regulated during apomictic initiation in ovules of Hieracium

 Hieracium is a member of the Asteraceae family, and contains sexual species in addition to apomictic species that reproduce by apospory and produce seed without fertilization. A homologue of the floral organ-identity gene DEFICIENS (DEF) was isolated from an apomictic line of Hieracium piloselloides (Vill.) following differential display between mature ovules and those initiating autonomous embryogenesis. The gene termed HPDEF has 93% amino acid identity with GDEF2, a DEF homologue isolated from Gerbera hybrida (D. Yu et al., 1999, Plant J. 17: 51–62), another member of the Asteraceae. In-situ analysis showed that early in floral development HPDEF is expressed in stamen and petal primordia, indicating expected B-function activity, according to the ABC model of floral organ identity (J. L. Bowman et al., 1991, Development 112: 1–20; E. S. Coen and E. M. Meyerowitz, 1991, Nature 353: 31–37). However, HPDEF expression was also observed in ovule primordia and expression continued in developing ovules until anthesis, indicating that this gene may have a role in ovule development. Expression of HPDEF was not detected in megaspore mother cells, or in sexual or aposporous embryo sacs. In sexual Hieracium, HPDEF was uniformly expressed throughout the ovule integument until anthesis. In most ovules of the apomict, however, HPDEF expression was transiently down-regulated in a specific zone in the chalazal region where cells initiating aposporous embryo sac formation differentiate. Uniform low-level HPDEF expression was subsequently observed prior to anthesis in ovules from sexual and apomictic plants. HPDEF may be down-regulated as a consequence of apomictic initiation and/or its down-regulation may facilitate progression of apomictic events. Received: 15 September 1999 / Accepted: 12 October 1999     

Analysis of amino acids in individual wheat embryonic protoplast

Summary. Amino acids analysis in single wheat embryonic protoplast was performed using capillary electrophoresis equipped with laser-induced fluorescence (CE-LIF), combination with tissue culture technique. Reagent fluorescein isothiocyanate (FITC) was introduced into living protoplasts by electroporation for intracellular derivatization. A special osmotic buffer (0.6 mol/L mannitol, 5 mmol/L CaCl₂) was used to keep the osmotic balance of embryonic protoplasts during the protoplasts derivatization. After completion of the derivatization reaction in the protoplasts, a single protoplast was drawn into the capillary tip by electroosmotic flow. Then a 0.1 M NaOH lysing solution was injected by diffusion. The derivatized amino acids were separated by capillary electrophoresis and detected by laser-induced fluorescence detection after the protoplast was lysed Nine amino acids were quantitatively and qualitatively determined and compared in lysate and single protoplast of wheat embryonic cells respectively, with mean concentrations of amino acids ranging from 2.68×10⁻⁵ mol/L to 18.18×10⁻⁵ mol/L in single protoplast.     

Chlamydomonas contains calcium stores that are mobilized when phospholipase C is activated

Mastoparan induces Ca²⁺-dependent deflagellation of the unicellular green alga Chlamydomonas moewusii Gerloff, as well as the activation of phospholipase C and the production of inositol 1,4,5-trisphosphate (InsP₃; T. Munnik et al., 1998, Planta 207: 133–145). Even in the absence of extracellular Ca²⁺, mastoparan still induces deflagellation (L.M. Quarmby and H.C. Hartzell, 1994, J Cell Biol 124: 807–815; J.A.J. van Himbergen et al., 1999, J Exp Bot, in press) suggesting that InsP₃ mediates Ca²⁺ release from intracellular stores. To test this hypothesis, cells were pre-loaded with ⁴⁵Ca²⁺ and their plasma membranes permeabilized by digitonin. Subsequent treatment of the cells with mastoparan (3.5 μM) induced release of intracellular ⁴⁵Ca²⁺. Mastoparan also activated phospholipase C in permeabilized cells, as demonstrated by the breakdown of ³²P-phosphatidylinositol 4,5-bisphosphate and the production of diacylglycerol. The mastoparan analogues mas7 and mas17 were also effective and their efficacy was correlated with their biological activity. X-ray microanalysis showed that electron-dense bodies (EDBs) are a major Ca²⁺ store in  C. moewusii. Analysis of digitonin-permeabilized cells showed that EDBs lost calcium at digitonin concentrations that released radioactivity from ⁴⁵Ca²⁺-labelled cells, suggesting that ⁴⁵Ca²⁺ monitored the content of EDBs. X-ray microanaysis of living cells treated with mastoparan also revealed that calcium was released from EDBs. Received: 30 December 1998 / Accepted: 25 June 1999     

Intracellular chloroplast photorelocation in the moss Physcomitrella patens is mediated by phytochrome as well as by a blue-light receptor

 The light-induced intracellular relocation of chloroplasts was examined in red-light-grown protonemal cells of the moss Physcomitrella patens. When irradiated with polarized red or blue light, chloroplast distribution in the cell depended upon the direction of the electrical vector (E-vector) in both light qualities. When the E-vector was parallel to the cross-wall (i.e. perpendicular to the protonemal axis), chloroplasts accumulated along the cross-wall; however, no accumulation along the cross-wall was observed when the E-vector was perpendicular to it (i.e. parallel to the protonemal axis). When a part of the cell was irradiated with a microbeam of red or blue light, chloroplasts accumulated at or avoided the illumination point depending on the fluence rate used. Red light of 0.1–18 W m⁻² and blue light of 0.01–85.5 W m⁻² induced an accumulation response (low-fluence-rate response; LFR), while an avoidance response (high-fluence-rate response; HFR) was induced by red light of 60 W m⁻² or higher and by blue light of 285 W m⁻². The red-light-induced LFR and HFR were nullified by a simultaneous background irradiation of far-red light, whereas the blue-light-induced LFR and HFR were not affected at all by this treatment. These results show, for the first time, that dichroic phytochrome, as well as the dichroic blue-light receptor, is involved in the chloroplast relocation movement in these bryophyte cells. Further, the phytochrome-mediated responses but not the blue-light responses were revealed to be lost when red-light-grown cells were cultured under white light for 2 d. Received: 7 September 1999 / Accepted: 15 October 1999     

Ferric reduction by iron-limited Chlamydomonas cells interacts with both photosynthesis and respiration

Iron limitation led to a large increase in extracellular ferricyanide (Fe[III]) reductase activity in cells of the green alga Chlamydomonas reinhardtii Dangeard. Mass-spectrometric measurement of gas exchange indicated that ferricyanide reduction in the dark resulted in a stimulation of respiratory CO₂ production without affecting the rate of respiratory O₂ consumption, consistent with the previously postulated activation of the oxidative pentose phosphate pathway in support of Fe(III) reduction by iron-limited Chlamydomonas cells (X. Xue et al., 1998, J. Phycol. 34: 939–944). At saturating irradiance, the rate of ferricyanide reduction was stimulated almost 3-fold, and this stimulation was inhibited by 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea. Ferricyanide reduction during photosynthesis resulted in approximately a 50% inhibition of photosynthetic CO₂ fixation at saturating irradiance, and almost 100% inhibition of CO₂ fixation at sub-saturating irradiance. Photosynthesis by iron-sufficient cells was not affected by ferricyanide addition. Addition of 250 μM ferricyanide to iron-limited cells in which photosynthesis was inhibited (either by the presence of glycolaldehyde, or by maintaining the cells at the CO₂ compensation point) resulted in a stimulation in the rate of gross photosynthetic O₂ evolution. Chlorophyll a fluorescence measurements indicated a large increase in non-photochemical quenching during ferricyanide reduction in the light; the increase in nonphotochemical quenching was abolished by the addition of nigericin. These results suggest that reduction of extracellular ferricyanide (mediated at the plasma membrane) interacts with both photosynthesis and respiration, and that both of these processes contribute NADPH in the light. Received: 15 September 1999 / Accepted: 14 October 1999     

Isoforms of chalcone synthase in Daucus carota L. and their differential expression in organs from the European wild carrot and in ultraviolet-A-irradiated cell cultures

 Two isoforms of chalcone synthase (CHS) were isolated from cDNA libraries derived from UV-A-irradiated anthocyanin-accumulating (DCb) and non-accumulating (DCs) cell cultures of carrot (Daucus carota L.). The clones designated as DcCHS1, which were present only in the DCb library, had a deduced primary sequence of 389 amino acids and an expected molecular mass of 42.7 kDa, and seem to be alleles of those cloned by Ozeki et al. (1993). The second isoform (DcCHS2) was present in both libraries. It had the highest degree of similarity (97.7%) to parsley CHS over all 397 amino acids. The expected molecular mass of the corresponding protein was 43.6 kDa. Results obtained from Southern blot analysis indicated the existence of at least two CHS genes in carrot. A transient enhancement of the DcCHS1 mRNA level after continuous irradiation with UV-A light could only be observed in anthocyanin-accumulating cultures, whereas an increase in DcCHS2 mRNA was seen in both cell lines. The maximum accumulation of CHS mRNA occurred 48 h after the onset of UV-A irradiation. In the European wild carrot the accumulation of DcCHS1 mRNA was restricted to the red central flowers, whereas the DcCHS2 mRNA was detectable in all red and white petals, as well as leaves, but was absent in stems and roots. The expression of DcCHS1 was restricted to anthocyanin-accumulating cells or organs. The heterologous expression of both cDNAs in Escherichia coli resulted in immunostainable bands of different sizes on the Western blot and high levels of catalytic CHS activity. Received: 2 September 1999 / Accepted: 30 November 1999     

A mathematical model of the stress induced during avascular tumour growth

In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed. Received: 15 November 1999 / Published online: 5 May 2000     

Periodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

We obtain necessary and sufficient conditions on the existence of a unique positive equilibrium point and a set of sufficient conditions on the existence of periodic solutions for a 3-dimensional system which arises from a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Our results improve the corresponding results obtained by Hsu, Luo, and Waltman [1]. Received: 20 November 1997 / Revised version: 12 February 1999 / Published online: 20 December 2000     

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     

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Symplastic communication between the central cell and the egg apparatus cells in the embryo sac of Torenia fournieri Lind. before and during fertilization

 Various membrane-impermeable, water-soluble fluorescent tracers with different molecular weights were microinjected into the central cell of the embryo sac of Torenia fournieri Lind. before and during fertilization. Before anthesis, there was high symplastic permeability between the central cell and the egg apparatus cells. In this stage, fluorescent tracers up to 10 kDa could pass from the central cell into the egg apparatus cells, whereas those with larger molecular weight remained in the central cell. As the embryo sac matured, symplastic permeability decreased such that 2 d after anthesis only tracers less than 3 kDa could spread from the central cell into the egg cell. There appeared to be no symplastic permeability between the primary endosperm and zygote after fertilization, since tracers as small as 521 Da could not pass into the zygote in about half of the microinjected embryo sacs. This is the first report of a change in cell-to-cell communication among the cells of the female germ unit before and after fertilization. Received: 16 December 1999 / Accepted: 4 February 2000     

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