Travelling waves and pattern formation in a model for fungal development

 Under a variety of conditions, the hyphal density within the expanding outer edge of growing fungal mycelia can be spatially heterogeneous or nearly uniform. We conduct an analysis of a system of reaction-diffusion equations used to model the growth of fungal mycelia and the subsequent development of macroscopic patterns produced by differing hyphal and hence biomass densities. Both local and global results are obtained using analytical and numerical techniques. The emphasis is on qualitative results, including the effects of changes in parameter values on the structure of the solution set. Received 22 November 1995; received in revised form 17 May 1996     

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     

Wood formation in poplar: identification, characterization, and seasonal variation of xylem proteins

Proteins that are preferentially produced in developing xylem may play a substantial role in xylogenesis. To reveal the identity of these proteins, comparative two-dimensional polyacrylamide gel electrophoresis was performed on young differentiating xylem, mature xylem, and bark of poplar (Populus trichocarpa Hook. cv. `Trichobel') harvested at different times of the year. The most-abundant xylem proteins were identified by microsequence analysis. For 17 of these proteins a putative function could be assigned based on similarity with previously characterized proteins, and for 15 out of these corresponding expressed sequence tags (ESTs) were found in the poplar EST database. The identified xylem–preferential proteins, defined by comparing the protein patterns from xylem and bark, were all involved in the phenylpropanoid pathway: two caffeoyl-coenzyme A O-methyltransferases (CCoAOMT), one phenylcoumaran benzylic ether reductase (PCBER), one bispecific caffeic acid/5-hydroxyferulic acid O-methyltransferase (COMT), five S-adenosyl-L-methionine synthetases, and one homologue of glycine hydroxymethyltransferase (GHMT). Remarkably, the biological function of the two most-abundant xylem-preferential proteins (PCBER and a GHMT homologue) remains unclear. In addition, several housekeeping enzymes were identified: two enolases, two glutamine synthetases, one 70-kDa heat-shock cognate, one calreticulin, and one α-tubulin. In comparison to the xylem-preferential proteins, the housekeeping proteins were expressed at significant levels in the bark as well. Also, several additional protein spots were detected for CCoAOMT, PCBER, and COMT by immunoblot. Our data show that for the study of xylogenesis, two-dimensional protein gel comparisons combined with systematic protein sequencing may yield information complementary to that from EST sequencing strategies. Received: 28 June 1999 / Accepted: 3 September 1999     

Control of gravimorphogenesis by auxin: accumulation pattern of CS-IAA1 mRNA in cucumber seedlings grown in space and on the ground

Cucumber (Cucumis sativus L.) seedlings grown in microgravity developed a peg on each side of the transition zone between hypocotyl and root, whereas seedlings grown in a horizontal position on the ground developed a peg on the concave side of the gravitropically bending transition zone. The morphological features of the space-grown seedlings were similar to those of seedlings grown in a vertical position on the ground with their radicles pointing down: both became two-pegged seedlings. Morphogenesis of cucumber seedlings is thus inhibited by gravity. Analysis by in-situ hybridization of an auxin-inducible gene, CS-IAA1, showed that its mRNA accumulated to a much greater extent on the lower side of the transition zone in the horizontally placed seedlings on the ground just prior to and during the initiation period of peg formation. On the other hand, when seedlings were grown in microgravity or in a vertical position on the ground, accumulation of CS-IAA1 mRNA occurred all around the transition zone. Accumulation of CS-IAA1 mRNA in horizontally grown seedlings appreciably decreased on the upper side of the transition zone and increased on the lower side upon gravistimulation, compared with the two-pegged seedlings. Application of IAA to seedlings in a horizontal position caused the development of a peg on each side of the transition zone, or a collar-like protuberance, depending on the concentration used. These results suggest that upon gravistimulation the auxin concentration on the upper side of the horizontally placed transition zone is reduced to a level below the threshold value necessary for peg formation. Space-grown seedlings of cucumber might develop two pegs symmetrically because the auxin level in the entire transition zone is maintained above the threshold. This spaceflight experiment verified for the first time that auxin does not redistribute in microgravity. Received: 10 February 2000 / Accepted: 15 March 2000     

A weakly nonlinear analysis of a model of avascular solid tumour growth

 In this paper we study a mathematical model that describes the growth of an avascular solid tumour. Our analysis concentrates on the stability of steady, radially-symmetric model solutions with respect to perturbations taken from the class of spherical harmonics. Using weakly nonlinear analysis, previous results are extended to show how the amplitudes of the asymmetric modes interact. Attention focuses on a special case for which the model equations simplify. Analysis of the simplified model equations leads to the identification of a two-parameter family of asymmetric steady solutions, the dimensions of whose stable and unstable manifolds depend on the system parameters. The asymmetric steady solutions limit the basin of attraction of the radially-symmetric steady state when it is linearly stable. On the basis of these numerical and analytical results we postulate the existence of fully nonlinear steady solutions which are stable with respect to time-dependent perturbations. Received: 25 October 1998 / Revised version: 20 June 1998     

Mechanisms of primordium formation during adventitious root development from walnut cotyledon explants

 In walnut (Juglans regia L.), an otherwise difficult-to-root species, explants of cotyledons have been shown to generate complete roots in the absence of exogenous growth regulators. In the present study, this process of root formation was shown to follow a pattern of adventitious, rather than primary or lateral, ontogeny: (i) the arrangement of vascular bundles in the region of root formation was of the petiole type; (ii) a typical root primordium was formed at the side of the procambium within a meristematic ring of actively dividing cells located around each vascular bundle; (iii) the developing root apical meristem was connected in a lateral way with the vascular bundle of the petiole. This adventitious root formation occurred in three main stages of cell division, primordium formation and organization of apical meristem. These stages were characterized by expression of LATERAL ROOT PRIMORDIUM-1 and CHALCONE SYNTHASE genes, which were found to be sequentially expressed during the formation of the primordium. Activation of genes related to root cell differentiation started at the early stage of primordium formation prior to organization of the root apical meristem. The systematic development of adventitious root primordia at a precise site gave indications on the positional and biochemical cues that are necessary for adventitious root formation. Received: 30 July 1999 / Accepted: 16 February 2000     

Mathematical modeling of the onset of capillary formation initiating angiogenesis

It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis. Received: 27 May 1999 / Revised version: 28 December 1999 / Published online: 16 February 2001     

The pattern of acropetal and basipetal cytoplasmic streaming velocities in Chara rhizoids and protonemata, and gravity effect on the pattern as measured by laser-Doppler-velocimetry

 The spatial pattern of acropetal and basipetal cytoplasmic streaming velocities has been studied by laser-Doppler-velocimetry (LDV) in the positively gravitropic (downward growing) rhizoids of Chara globularis Thuill. and for the first time in the negatively gravitropic (upward growing) protonemata. The LDV method proved to be precise and yielded reproducible results even when tiny differences in velocities were measured. In the apical parts of the streaming regions of both cell types, acropetal streaming was faster than basipetal streaming. Starting at the apical reversal point of streaming, the velocity increased basipetally with the distance from that point and became fairly constant close to the basal reversal point; subsequently, the velocity decreased slightly acropetally as the apical reversal point was again approached. There was no change in velocity at the basal reversal point. However, at the apical reversal point there was an abrupt decrease in velocity. The pattern of the ratio of acropetal to basipetal streaming velocity (VR) was a function of the relative distance of the site of measurement from the apical reversal point rather than a function of the absolute distance. Upon inversion of the rhizoids, the VR decreased on average by 3.8% (±0.4%), indicating that the effect of gravity on the streaming velocity was merely physical and without a physiological amplification. Rhizoids that had developed on the slowly rotating horizontal axis of a clinostat, and had never experienced a constant gravity vector, were similar to normally grown rhizoids with respect to VR pattern. In protonemata, the VR pattern was not significantly different from that in rhizoids although the direction of growth was inverse. In rhizoids, oryzalin caused the polar organization of the cell to disappear and nullified the differences in streaming velocities, and cytochalasin D decreased the velocity of basipetal streaming slightly more than that of acropetal streaming. Cyclopiazonic acid, known as an inhibitor of the Ca²⁺-ATPase of the endoplasmic reticulum, also reduced the streaming velocities in rhizoids, but had slightly more effect on the acropetal stream. It is possible that the endogenous difference in streaming velocities in both rhizoids and protonemata is caused by differences in the cytoskeletal organization of the opposing streams and/or loading of inhibitors (like Ca²⁺) from the apical/subapical zone into the basipetally streaming endoplasm. Received: 4 October 1999 / Accepted: 4 November 1999     

Lipid nitration and formation of lipid-protein adducts: biological insights

Summary. Lipid-protein adducts are formed during oxidative and nitrative stress conditions associated with increasing lipid and protein oxidation and nitration. The focus of this review is the analysis of interactions between oxidative-modified lipids and proteins and how lipid nitration can modulate lipid-protein adducts formation. For this, two biologically-relevant models will be analysed: a) human low density lipoprotein, whose oxidation is involved in the early steps of atherogenesis, and b) α-synuclein/lipid membranes system, where lipid-protein adducts are being associated with the develop of Parkinson disease and other synucleinopathies.     

Kinetics of biomarkers: biological and technical validity of isoprostanes in plasma

Summary. Isoprostanes, non-enzymatic peroxidation products of arachidonic acid, are attractive biomarkers of oxidative stress in research in biology, medicine and nutrition. For the appropriate use of biomarkers it is required that these are both biologically and technically valid. Whereas the biological validity of isoprostanes is well-established, it is technically quite complicated to measure isoprostanes and its metabolites in body fluids, and its rapid disappearance from plasma may hamper practical application. This paper shortly introduces isoprostanes as a biomarker for studies with humans, describes a novel fast and sensitive method for measuring isoprostanes in plasma by high-performance liquid chromatography and tandem mass spectrometry, and provides several examples of the use of the method in studies in humans. By taking care of the biological and technical validity of this biomarker it is possible to establish the antioxidant effects of some food ingredients in studies with human volunteers.     

DNA cleavage function of seryl-histidine dipeptide and its application

Summary. Previously published evidences highlighted the effect of transglutaminase (TG, EC 2.3.2.13) activation on the reduction of the in vitro adhesive and invasive behaviour of murine B16-F10 melanoma cells, as well as in vivo. Here, we investigated the influence of spermidine (SPD) incorporation by TG into basement membrane components i.e. laminin (LN) or Matrigel (MG), on the adhesion and invasion of B16-F10 melanoma cells by these TG/SPD-modified substrates. The adhesion assays showed that cell binding to the TG/SPD-modified LN was reduced by 30%, when compared to untreated LN, whereas the reduction obtained using TG/SPD-modified MG was 35%. Similarly, tumor cell invasion by the Boyden chamber system through TG/SPD modified LN or MG was respectively reduced by 45%, and by 69%. Evaluation of matrix metalloproteinase (gelatinases MMP-2 and MMP-9) activities by gel-zymography showed that MMP-2 activity was unaffected, while MMP-9 activity was reduced by about 32% using TG/SPD-modified substrate. These results strongly suggest that the observed antiinvasive effect of TG activation in the host may be ascribed to the covalent incorporation of polyamines, which led to the post-translational modification of some components of the cell basement membrane. This modification may interfere with the metastatic property of melanoma cells, affecting the proteolytic activity necessary for their migration and invasion activities. Authors’ address: Simone Beninati, Department of Biology, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Rome, Italy     

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     

Turing instabilities in general systems

We present necessary and sufficient conditions on the stability matrix of a general n(≥2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation. The necessary (kinetic) condition, requiring that the system be composed of an unstable (or activator) and a stable (or inhibitor) subsystem, and the sufficient condition of sufficiently rapid inhibitor diffusion relative to the activator subsystem are established in three theorems which form the core of our results. Given the possibility that the unstable (activator) subsystem involves several species (dimensions), we present a classification of the analytically deduced Turing bifurcations into p (1 ≤p≤ (n− 1)) different classes. For n = 3 dimensions we illustrate numerically that two types of steady Turing pattern arise in one spatial dimension in a generic reaction-diffusion system. The results confirm the validity of an earlier conjecture [12] and they also characterise the class of so-called strongly stable matrices for which only necessary conditions have been known before [23, 24]. One of the main consequences of the present work is that biological morphogens, which have so far been expected to be single chemical species [1–9], may instead be composed of two or more interacting species forming an unstable subsystem. Received: 21 September 1999 / Revised version: 21 June 2000 / Published online: 24 November 2000     

Polyamines: metabolism to systems biology and beyond

Summary. Polyamines and the metabolic and physiopathological processes in which they are involved represent an active field of research that has been continuously growing since the seventies. In the last years, the trends in the focused areas of interest within this field since the 1970s have been confirmed. The impact of “-omics” in polyamine research remains too low in comparison with its deep impact on other biological research areas. These high-throughput approaches, along with systems biology and, in general, more systemic and holistic approaches should contribute to a renewal of this research area in the near future.     

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     

Taurine promotes connective tissue growth factor (CTGF) expression in osteoblasts through the ERK signal pathway

Summary. Taurine is found in bone tissue, but its function in skeletal tissue is not fully understood. The present study was undertaken to investigate regulation of gene expression of connective tissue growth factor (CTGF), and the roles of mitogen-activated protein kinases (MAPKs) in murine osteoblast MC3T3-E1 cells treated with taurine. Western blot analysis showed taurine stimulated CTGF protein secretion in a dose- and time-dependent manner. Taurine induced activation of extracellular signal-regulated kinase (ERK), but not p38 and c-jun N-terminal Kinase (JNK), in osteoblasts. Furthermore, pretreatment of osteoblasts with the ERK inhibitor PD98059 abolished the taurine-induced CTGF production. These data indicate that taurine induces CTGF secretion in MC3T3-E1 cells mediated by the ERK pathway, and suggest that osteoblasts are direct targets of taurine.     

Intraprotoplasmic and wall-localised formation of arabinoxylan-bound diferulates and larger ferulate coupling-products in maize cell-suspension cultures

Maize (Zea mays L.) cell cultures incorporated radioactivity from [¹⁴C]cinnamate into hydroxycinnamoyl-CoA derivatives and then into polysaccharide-bound feruloyl residues. Within 5–20 min, the CoA pool had lost its ¹⁴C by turnover and little or no further incorporation into polysaccharides then occurred. The system was thus effectively a pulse–chase experiment. Kinetics of radiolabelling of diferulates (also known as dehydrodiferulates) varied with culture age. In young (1–3 d) cultures, polysaccharide-bound [¹⁴C]feruloyl- and [¹⁴C]diferuloyl residues were both detectable within 1 min of [¹⁴C]cinnamate feeding. Thus, feruloyl residues were dimerised <1 min after their attachment to polysaccharides. For at least the first 2.3 h after [¹⁴C]cinnamate feeding, polysaccharide-bound [¹⁴C]diferuloyl residues remained almost constant at ≈7% of the total polysaccharide-bound [¹⁴C]ferulate derivatives. Since feruloyl residues are attached to polysaccharides <1 min after the biosynthesis of the latter, and >10 min before secretion, the data show that extensive feruloyl coupling occurred intra-protoplasmically. Exogenous H₂O₂ (1 mM) caused little additional feruloyl coupling; therefore, wall-localised coupling may have been peroxidase-limited. In older (e.g. 4 d) cultures, less intraprotoplasmic coupling occurred: during the first 2.5 h, polysaccharide-bound [¹⁴C]diferuloyl residues were a steady 1.4% of the total polysaccharide-bound [¹⁴C]ferulate derivatives. In contrast to the situation in younger cultures, exogenous H₂O₂ induced a rapid 4- to 6-fold increase in all coupling products, indicating that coupling in the walls was H₂O₂-limited. In both 2- and 4-d-old cultures, polysaccharide-bound ¹⁴C-trimers and larger coupling products exceeded [¹⁴C]diferulates 3- to 4-fold, but followed similar kinetics. Thus, although all known dimers of ferulate can now be individually quantified, it appears to be trimers and larger products that make the major contribution to cross-linking of wall polysaccharides in cultured maize cells. We argue that feruloyl arabinoxylans that are cross-linked before and after secretion are likely to loosen and tighten the cell wall, respectively. The consequences for the control of cell expansion and for the response of cell walls to an oxidative burst are discussed. Received: 19 January 2000 / Accepted: 13 April 2000     

The application of atomic force microscopy to topographical studies and force measurements on the secreted adhesive of the green alga Enteromorpha

Atomic force microscopy (AFM) enables the topographical structure of cells and biological materials to be resolved under natural (physiological) conditions, without fixation and dehydration artefacts associated with imaging methods in vacuo. It also provides a means of measuring interaction forces and the mechanical properties of biomaterials. In the present study, AFM has been applied for the first time to the study of the mechanical properties of a natural adhesive produced by a green plant cell. Swimming spores of the green alga Enteromorpha linza (L.) J. Ag. (7–10 μm) secrete an adhesive glycoprotein which provides firm anchorage to the substratum. Imaging of the adhesive in its hydrated state revealed a swollen gel-like pad, approximately 1 μm thick, surrounding the spore body. Force measurements revealed that freshly released adhesive has an adhesion strength of 173 ± 1.7 mN m⁻¹ (mean ± SE; n=90) with a maximum value for a single adhesion force curve of 458 mN m⁻¹. The adhesive had a compressibility (equivalent to Young's modulus) of 0.54 × 10⁶ ± 0.05 × 10⁶ N m⁻² (mean ± SE; n=30). Within minutes of release the adhesive underwent a progressive `curing' process with a 65% reduction in mean adhesive strength within an hour of settlement, which was also reflected in a reduction in the average length of the adhesive polymer strands (polymer extension) and a 10-fold increase in Young's modulus. Measurements on the spore surface itself revealed considerably lower adhesion-strength values but higher polymer-extension values than the adhesive pad, which may reflect the deposition of different polymers on this surface as a new cell wall is formed. The study demonstrates the value of AFM to the imaging of plant cells in the absence of fixation and dehydration artefacts and to the characterisation of the mechanical properties of plant glycoproteins that have potential utility as adhesives. Received: 22 February 2000 / Accepted: 20 April 2000     

Primary kidney growth and its consequences at the onset of diabetes mellitus

Summary. Diabetes mellitus is a primary contributor to progressive kidney dysfunction leading to end-stage renal disease (ESRD). In the early phase of diabetes, prior to the onset of further complications, both kidney size and glomerular filtration rate (GFR) increase. Glomerular hyperfiltration is considered a risk factor for downstream complications and progression to ESRD. Abnormalities in vascular control have been purported to account for the glomerular hyperfiltration in early diabetes. In this review we discuss a tubulo-centric concept in which tubular growth and subsequent hyper-reabsorption contribute to the onset of glomerular hyperfiltration that demarks the early stage of diabetes. Kidney growth, in this concept, is no longer relegated to a compensatory response to hyperfiltration, but rather plays a primary and active role in its genesis and progression. As such, components of kidney growth, such as the polyamines, may provide a means of early detection of diabetic kidney dysfunction and more effective therapeutic intervention.     

Kidney growth,hypertrophy and the unifying mechanism of diabetic complications

Summary. Michael Brownlee has proposed a ‘Unifying Mechanism’ of hyperglycemia-induced damage in diabetes mellitus. At the crux of this hypothesis is the generation of reactive oxygen species (ROS), and their impact on glycolytic pathways. Diabetes is the leading cause of chronic kidney failure. In the early phase of diabetes, prior to establishment of proteinuria or fibrosis, comes kidney growth and hyperfiltration. This early growth phase consists of an early period of hyperplasia followed by hypertrophy. Hypertrophy also contributes to cellular oxidative stress, and may precede the ROS perturbation of glycolytic pathways described in the Brownlee proposal. This increase in growth promotes hyperfiltration, and along with the hypertrophic phenotype appears required for hyperglycemia-induced cell damage and the progression of downstream diabetic complications. Here we will evaluate this growth phenomenon in the context of diabetes mellitus.