Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Les sHsps en surera: capacitat protectora enfront l'estrés i variabilitat genètica

Els organismes responen a la temperatura i a molts altres estressos sintetitzant un grup de proteïnes anomenat proteïnes de xoc de calor (HSPs). En plantes les sHsps, d'entre 15 i 30 kDa formen el grup més abundant i divers, classificat en funció de la seva localització subcel.lular i homologia en: mitocondrials, cloroplàstiques, de reticle endoplasmàtic i citoplàsmiques de classe I i II. Les sHsps-CI s'ha descrit que s'indueixen per estrès tèrmic, hídric i oxidatiu (peròxid d'hidrògen, llum UV, ozó) i en resposta a algunes hormones. També s'expressen durant el desenvolupament, per exemple durant l'embriogènesi, on es creu que podrien tenir un paper protector de l'embrió enfront la dessecació. Tot i que hi ha abundants treballs que correlacionen la resistència a l'estrès i l'acumulació de sHsps-CI, els mecanismes moleculars d'aquesta activitat són poc conguts. Tot i això, per diverses sHsps-CI ha estat descrita una activitat xaperona in vitro i, més recentment, que la seva sobreexpressió augmenta la viabilitat de cèl.lules d'E.coli en condicions d'estrès tèrmic. L'estudi de l'acumulació de sHsps-CI en surera (Quercus suber) mitjançant immunodetecció en electroforesi bidimensional mostra uns patrons d'acumulació complexos i formats per dos grups d'espècies proteiques principals, a l'entorn dels 10 i 17 kDa respectivament, que mostren una inducció diferencial en funció del teixit i l'estrès. Mentre que les espècies proteiques de 17 kDa s'indueixen per temperatura però no per estrès oxidatiu, les de ca. 10 kDa ho fan per estrès oxidatiu i no per temperatura. Ambdós grups d'espècies proteiques s'acumulen conjuntament en fel.lema. Assajos de PCR i RT-PCR han permès clonar parcialment tres noves sHsps-CI en surera: Qshsp10-CI, QshspC-CI i QshspD-CI. Aquest fet confirma la multigeneïcitat de les sHsps-CI en surera que apuntava el patró bidimensional. Dels nous clons obtinguts destaca especialment Qshsp10-CI, un gen que presenta un codó stop enmig del domini -cristal.lí que fa que a la proteïna que se'n dedueix li manqui un 55% del domini -cristal.lí i tota l'extensió C-terminal. Es tractaria de la sHsp més petita i més truncada descrita fins al moment. L'anàlisi de l'expressió de Qshsp10-CI mitjançant RT-PCR mostra expressió en plantes tractades amb H2O2 però no en les que han estat sotmeses a un xoc de calor. Aprofitant l'oportunitat que oferia aquesta sHsp-CI de ser utilitzada com a model per l'estudi de la importància del domini -cristal.lí i l'extensió C-terminal en l'activitat protectora enfront l'estrès, es va voler determinar la capacitat que tenia d'augmentar la viabilitat de cèl.lules d'E. coli en condicions d'estrès tèrmic i oxidatiu. Els resultats mostren que la proteïna recombinant QsHsp10-CI, tot i la important truncació que té, és capaç de protegir cèl.lules d'E. coli en condicions d'estrès tèrmic i, remarcablement, en condicions d'estrès oxidatiu. Tots aquests resultats indiquen que les espècies proteiques de ca. 10 kDa podrien correspondre a Qshsp10-CI i tenir un paper en les cèl.lules del fel.lema en la protecció enfront l'estrès oxidatiu. L'estrès oxidatiu provoca lesions al DNA que poden produir errors en la replicació, transcripció o traducció i generar proteïnes aberrants. Donades les condicions d'estrès oxidatiu a les quals es troben sotmeses les cèl.lules del fel.lema, s'ha volgut estudiar la variabilitat dels seus àcids nucleics. La determinació de la taxa de mutació de la regió codificant del gen Qshsp17.4-CI en mRNA i DNA de fel.lema i àpex radicular, un teixit jove i en creixement actiu va mostrar unes taxes sorprenentment elevades en l'mRNA (1/1784 pb) i el DNA genòmic (1/1520 pb) del fel.lema. Aquestes taxes són les més altes descrites en un genoma nuclear eucariota i són similars a les dels virus d'RNA d'evolució ràpida com el virus de l'Hepatitis C. Amb aquestes taxes de mutació, un terç dels mRNAs del fel.lema de la surera contindrien missatges aberrants i la supervivència de les cel.lules es veuria compromesa. Això implica que el fel.lema hauria de ser considerat com un mosaic de cèl.lules genèticament heterogènies i, per tant, una sola seqüència no defineix en tota la seva amplitud un gen en aquest teixit. No es va detectar cap mutació en àpex de rel. Amb l'objectiu d'aprofundir en el coneixement de les mutacions que es donen en aquests dos teixits i per tal de poder fer una anàlisi qualitativa més completa que permetés especular sobre el seu origen, es va aplicar un mètode de selecció de seqüències mutants en base a la utilització d'enzims de restricció. Les mutacions detectades en fel.lema es corresponen amb les relacionades, en altres sistemes no nuclears (plasmidis, fags i DNA bacterià), amb l'estrès oxidatiu. En conseqüència, l'estrès oxidatiu al qual estan sotmeses les cèl.lules del fel.lema podria ser el causant de l'elevada taxa de mutació detectada. D'acord amb això, el tipus majoritari de productes d'oxidació de les bases del DNA que s'acumulen en brots de plàntules de surera en resposta al peròxid d'hidrògen produeixen el mateix tipus de mutacions detectades en l'mRNA del fel.lema de la surera. La major sensibilitat d'aquest nou mètode ha permès, a més, detectar mutacions en molècules d'mRNA de rel, un teixit en el qual no s'havia trobat cap mutació utilitzant el mètode de clonatge i seqüenciació directa. Tot i això, el tipus de mutacions predominants no estan relacionades amb l'estrès oxidatiu sinó amb erros en la reparació dels àcids nucleics.

Desenvolvimento relativo dos tecidos e características da carcaça de cabritos Saanen, com diferentes pesos e níveis nutricionais

Pós-graduação em Zootecnia - FCAV

Intussusceptive angiogenesis: a biologically relevant form of angiogenesis

Angiogenesis, i.e. the development and growth of blood vessels, is a major topic of research as it plays an important role in normal development and in various pathologies. Recent evidence revealed the existence of different mechanisms of blood vessel growth, including sprouting and intussusceptive angiogenesis, vascular mimicry, and blood vessel cooption. The latter two have only been observed in tumor growth, but sprouting and intussusceptive angiogenesis also occur in healthy, physiologically growing tissues. Despite this variety of angiogenic mechanisms, most of the current research is focused on the mechanism of sprouting angiogenesis because this mechanism was first described and because most existing experimental models are related to sprouting angiogenesis. Consequently, the mechanism of intussusceptive angiogenesis is often overlooked in angiogenesis research. Here, the mechanism of intussusceptive angiogenesis is reviewed and the current techniques and models for investigating intussusceptive angiogenesis are summarized. In addition, other mechanisms of vascular growth are briefly reviewed.

Active JNK-dependent secretion of Drosophila Tyrosyl-tRNA synthetase by loser cells recruits haemocytes during cell competition

Cell competition is a process by which the slow dividing cells (losers) are recognized and eliminated from growing tissues. Loser cells are extruded from the epithelium and engulfed by the haemocytes, the Drosophila macrophages. However, how macrophages identify the dying loser cells is unclear. Here we show that apoptotic loser cells secrete Tyrosyl-tRNA synthetase (TyrRS), which is best known as a core component of the translational machinery. Secreted TyrRS is cleaved by matrix metalloproteinases generating MiniTyr and EMAP fragments. EMAP acts as a guiding cue for macrophage migration in the Drosophila larvae, as it attracts the haemocytes to the apoptotic loser cells. JNK signalling and Kish, a component of the secretory pathway, are autonomously required for the active secretion of TyrRS by the loser cells. Altogether, this mechanism guarantees effective removal of unfit cells from the growing tissue.

Ubiquitous, heritable damage in cell populations that survive treatment with methotrexate

A permanent line of mouse embryo fibroblasts was treated with concentrations of the anticancer drug methotrexate (MTX) that left 20–50% surviving colonies. The surviving population initially multiplied at a much slower rate than controls after subculture in the absence of the drug, and required 9–12 days of serial subculture, with selective growth of the faster growing cells, to approximate the control rate. To determine the distribution of growth rates of cells in the original posttreatment populations, many single cells were isolated in multiwell plates immediately after the treatment period, and the resulting clones were serially subcultured. Most of the control clones underwent about 2 population doublings per day (PD/D). Almost all the survivors of MTX treatment multiplied at heterogeneously reduced rates, ranging from 0.6 PD/D to as high as control rates for a very few clones. They maintained the reduced rates through many subcultivations. The heritability of the reduced growth rates indicates that most cells that retain proliferative capacity after treatment with MTX carry random genetic damage that is perpetuated through many divisions of their progeny. Similar results have been described for cells that survive x-irradiation, and suggest random genetic damage is a common occurrence among cells in rapidly growing tissues that survive cytotoxic treatment. It also occurs in serial subcultures of cells that had been held under the constraint of confluence for extended periods, which suggests that the accumulation of random genetic damage to somatic cells during aging of mammals underlies the reduction of growth rate and function of the cells that characterizes the aging process.

Uridine 5′-Diphosphate-Glucose Dehydrogenase from Soybean Nodules

A highly purified preparation of uridine 5′-diphosphate (UDP)-glucose (Glc) dehydrogenase (DH; EC 1.1.1.22) has been characterized from soybean (Glycine max L.) nodules. The enzyme had native and subunit molecular masses of approximately 272 and 50 kD, respectively. UDP-Glc DH displayed typical hyperbolic substrate kinetics and had Km values for UDP-Glc and NAD+ of 0.05 and 0.12 mm, respectively. Thymidine 5′-diphosphate-Glc and UDP-galactose could replace UDP-Glc as the sugar nucleotide substrate to some extent, but the enzyme had no activity with NADP+. Soybean nodule UDP-Glc DH was labile in the absence of NAD+ and was inhibited by a heat-stable, low-molecular-mass solute in crude extracts of soybean nodules. UDP-Glc DH was also isolated from developing soybean seeds and shoots of 5-d-old wheat and canola seedlings and was shown to have similar affinities for UDP-Glc and NAD+ as those of the soybean nodule enzyme. UDP-Glc DH from all of these sources was most active in young, rapidly growing tissues.

Cells Tissues Organs : preface

This volume stems from the 1st International Conference on Epithelial-Mesenchymal Transitions (EMT), which was convened by the editors on October 5–8, 2003 in the beautiful setting of Port Douglas, Queensland, Australia. EMT, the name given to the transformation of cells arranged in a coherent layer – epithelial cells – to more individualistic and potential motile cells – mesenchymal cells – was recognized decades ago by Prof. Elisabeth (Betty) Hay (Harvard Medical School, Boston, Mass., USA) as a primary mechanism in embryogenesis for remodelling tissues. More recently EMT has been seen as crucial to the spread and invasion of carcinoma, and more recently still, EMT-like changes have been detected in various pathologies marked by fi brosis. Despite the basic and clinical importance of EMT, this extremely rapidly growing fi eld had never previously had a conference devoted to it, and indeed the disciplines of developmental biology, cancer and pathology rarely interact although they have much to share. The chapters assembled for this volume encompass these three major themes of the meeting, development, pathology and cancer, and further highlight the commonality in terms of mechanisms and outcomes among them...

A biomechanical analysis of growing rods used in the management of early onset scoliosis

INTRODUCTION Managing spinal deformities in young children is challenging, particularly early onset scoliosis (EOS). Surgical intervention is often required if EOS has been unresponsive to conservative treatment particularly with rapidly progressive curves. An emerging treatment option for EOS is fusionless scoliosis surgery. Similar to bracing, this surgical option potentially harnesses growth, motion and function of the spine along with correcting spinal deformity. Dual growing rods are one such fusionless treatment, which aims to modulate growth of the vertebrae. The aim of this study was to ascertain the extent to which semiconstrained growing rods (Medtronic, Sofamor, Danek, Memphis, TN) with a telescopic sleeve component, reduce rotational constraint on the spine compared with standard "constrained / rigid" rods and hence potentially provide a more physiological mechanical environment for the growing spine. METHODS Six 40-60kg English Large White porcine spines served as a model for the paediatric human spine. Each spine was dissected into a 7 level thoracolumbar multi-segment unit (MSU), removing all non-ligamentous soft tissues and leaving 3cm of ribs either side. Pure nondestructive axial rotation moments of ±4Nm at a constant rotation rate of 8deg.s-1 were applied to the mounted MSU spines using a biaxial Instron testing machine. Displacement of each vertebral level was captured using a 3D motion tracking system (Optotrak 3020, Northern Digital Inc, Waterloo, ON). Each spine was tested in an un-instrumented state first and then with appropriately sized semi-constrained growing rods and rigid rods in alternating sequence. The rods were secured by multi-axial pedicle screws (Medtronic CD Horizon) at levels 2 and 6 of the construct. The range of motion (ROM), neutral zone (NZ) size and stiffness (Nm.deg-1) were calculated from the Instron load-displacement data and intervertebral ROM was calculated through a MATLAB algorithm from Optotrak data. RESULTS Irrespective of the order of testing, rigid rods significantly reduced the total ROM compared with semi-constrained rods (p<0.05) with in a significantly stiffer spine for both left and right axial rotation (p<0.05). Analysing the intervertebral motion within the instrumented levels 2-6, rigid rods showed reduced ROM compared with semi-constrained growing rods and compared with un-instrumented motion segments. CONCLUSION Semi-constrained growing rods maintain similar stiffness in axial rotation to un-instrumented spines, while dual rigid rods significantly reduce axial rotation. Clinically the effect of semi-constrained growing rods as observed in this study is that they would be expected to allow growth via the telescopic rod components while maintaining the axial flexibility of the spine, which may reduce occurrence of the crankshaft phenomenon.

A biomechanical analysis of growing rods used in the management of early onset scoliosis

INTRODUCTION Managing spinal deformities in young children is challenging, particularly early-onset scoliosis (EOS). Any progressive spinal deformity particularly in early life presents significant health risks for the child and a challenge for the treating surgeon. Surgical intervention is often required if EOS has been unresponsive to conservative treatment particularly with rapidly progressive curves. An emerging treatment option particularly for EOS is fusionless scoliosis surgery. Similar to bracing this surgical option potentially harnesses growth, motion and function of the spine along with correcting spinal deformity. Dual growing rods is one such fusionless treatment, which aims to modulate growth of the vertebrae. The aim of this study was to ascertain the extent to which semi-constrained growing rods (Medtronic, Memphis, TN) with a telescopic sleeve component, reduce rotational constraint on the spine compared with standard rigid rods and hence potentially provide a more physiological mechanical environment for the growing spine. METHODS Six 40-60kg English Large White porcine spines served as a model for the paediatric human spine. Each spine was dissected into 7 level thoracolumbar multi-segment unit (MSU) spines, removing all non-ligamentous soft tissues. Appropriately sized semi-constrained growing rods and rigid rods were secured by multi-axial screws (Medtronic) prior to testing in alternating sequences for each spine. Pure nondestructive moments of +/4Nm at a constant rotation rate of 8deg/s was applied to the mounted MSU spines. Displacement of each level was captured using an Optotrak (Northern Digital Inc, Waterloo, ON). The range of motion (ROM), neutral zone (NZ) size and stiffness (Nm/deg) were calculated from the Instron load-displacement data and intervertebral ROM was calculated through a MATLAB algorithm from Optotrak data. RESULTS Irrespective of sequence order rigid rods significantly reduced the total ROM (deg) than compared to semi-constrained rods (p<0.05) and resulted in a significantly stiffer (Nm/deg) spine for both left and right axial rotation testing (p<0.05). Analysing the intervertebral motion within the instrumented levels, rigid rods showed reduced ROM (Deg) than compared to semi-constrained growing rods and the un-instrumented (UN-IN) test sequences. CONCLUSION The semi-constrained growing rods maintained rotation similar to UN-IN spines while the rigid rods showed significantly reduced axial rotation across all instrumented levels. Clinically the effect of semi-constrained growing rods evaluated in this study is that they will allow growth via the telescopic rod components while maintaining the axial rotation ability of the spine, which may also reduce the occurrence of the crankshaft phenomenon.

Lipid characterisation of different tissues and fillet portions of intensively farmed Murray Cod Maccullochella peelii peelii

Although many studies have focused on the lipid and fatty acids composition of farmed fish, no many have investigated their deposition pattern in different portions of the fillet. Previous studies, mainly on salmonids, have shown that lipids distribution varies greatly depending on the species, portion and type of muscle, but nevertheless, there is not accurate description of its deposition pattern in many fish, in particular in warm water, freshwater carnivorous species. Murray cod is the largest Australian native freshwater carnivorous fish and supports a small but well established and fast growing industry. The objective of this study was therefore to determine if there was any difference in lipid and fatty acid in different tissues such as muscle, liver and perivisceral fat and in different portions of the fillet of farmed Murray cod.

Three size fish (small, medium and large), all fed the same commercial diet, were selected from a commercial intensive farm. The left fillet of each fish was sectioned into nine portions, according to muscle lines and main anatomical features. The nine portions as well as whole right fillet, liver and perivisceral fat were analysed for proximate and fatty acid composition (Table 1).

Differences in lipid content were found amongst different portions of the fillet, with the dorsal/cranial portion (P1) recording the lowest and the more ventral/caudal portion (P8) recording the highest (P<0.05) value. The latter also recorded the highest amount of monounsaturated fatty acid (MUFA) and the lowest of polyunsaturated fatty acids (PUFA), arachidonic acid, 20:4n-6 (ArA), docosahexaenoic acid, 22:6n-3, (DHA) and n3/n6 ratio. In general, lipid content in the different fillet portions was inversely correlated to PUFA and directly to MUFA. Saturated fatty acid (SFA) and eicosapentaenoic acid, 20:5n-3 (EPA) did not show any discernible trend and were similar throughout, while significant differences of DHA and ArA content were observed. This study shows that lipid deposition in Murray cod varies remarkably and that different fatty acids are deposited at different rates. The results of this study show how different adjacent portions can be and therefore attention need to be paid when conducting chemical, nutritional and sensorial analyses on Murray cod.

Immune response and performance of growing Santa Ines lambs to artificial Trichostrongylus colubriformis infections

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of diet on assimilation and turnover of C-13 in the tissues of broiler chickens

1. The C-13 turnover rates of the liver and thoracic pectoral muscle of growing broilers were determined by feeding diets with varying C-13 content.2. Male chicks ( 1- d- old) were subjected to treatments based on free choice of 5 different mixes of energy and protein sources from plants with C-3 and C-4 photosynthetic pathways that had differing C-13 content. Rice bran ( R) and soybean meal ( S) were the C-3 sources, while maize ( C) and maize gluten meal ( G) were the C-4 sources. Choices were R + S, C + G, R + G, C + S or R + C +G + S. The 6th treatment was a complete feed ( CF) that was similar to a commercial broiler feed.3. The isotopic composition of the birds' tissues was representative of the isotopic composition of the diets. The assimilation was faster for C-3, in both liver and muscle, than for C-4 diets, and give the delta per mil difference between the diet and tissues.4. The liver is the most active metabolic tissue and gave more rapid isotope turnover than in muscle.