Keratinocyte growth factor signalling: a mathematical model of dermal-epidermal interaction in epidermal wound healing

A wealth of growth factors are known to regulate the various cell functions involved in the repair process. An understanding of their therapeutic value is essential to achieve improved wound healing. Keratinocyte growth factor (KGF) seems to have a unique role as a mediator of mesenchymal-epithelial interactions: it originates from mesenchymal cells, yet acts exclusively on epithelial cells. In this paper, we study KGF's role in epidermal wound healing, since its production is substantially up-regulated after injury. We begin by modelling the dermal-epidermal signalling mechanism of KGF to investigate how this extra production affects the signal range. We then incorporate the effect of KGF on cell proliferation, and using travelling wave analysis we obtain an approximation for the rate of healing. Our modelling shows that the large up-regulation of KGF post-wounding extends the KGF signal range but is above optimal for the rate of wound closure. We predict that other functions of KGF may be more important than its role as a mitogen for the healing process.     

alpha-Tocopheryl succinate inhibits angiogenesis by disrupting paracrine FGF2 signalling

Malignant mesothelioma (MM) cells enhanced proliferation of endothelial cells (ECs) as well as their angiogenesis in vitro by secretion of fibroblast growth factor-2 (FGF2). This effect was suppressed by pre-treating MM cells with alpha-tocopheryl succinate (alpha-TOS), which inhibited FGF2 secretion by inducing mitochondria-dependent generation of reactive oxygen species. The role of FGF2 was confirmed by its down-regulation by treating MM cells with siRNA, abolishing EC proliferation and wound healing enhancement afforded by MM cells. We conclude that alpha-TOS disrupts angiogenesis mediated by MM cells by inhibiting FGF2 paracrine signalling.     

Early onset of phenotype and cell patterning in the embryonic zebrafish retina

The regular arrangement of retinal cone cells in a mosaic pattern is a common feature of teleosts. In the zebrafish, Brachydanio rerio, the retinal cone mosaic comprises parallel rows consisting of a repeating motif of four cone types. In order to elucidate the temporal and spatial aspects of the genesis of the cone mosaic in the developing retina, we generated a monoclonal antibody that specifically binds to the double cone photoreceptor of the adult. We first saw staining in the developing retina with this antibody, FRet 43, at 48 hours postfertilization, the time at which the first photoreceptor cells undergo their final mitotic division. We then injected embryonic fish with the thymidine analog, 5-bromo-2'-deoxyuridine (BrdU), confirming with a double-labeling experiment that the onset of FRet 43 antigenicity occurs within three hours of the cellular division that generates the double cone photoreceptors. Then we stained tangential sections of the 54-hour embryonic retina with FRet 43, further showing that cells devoid of staining alternate with stained pairs of cells in a pattern that is consistent with the arrangement of photoreceptors in the adult cone mosaic. These results indicate that a marker of the double cone phenotype is expressed at approximately the same time as cellular birthday and that the mosaic patterning is present within 6 hours of this expression.     

Endothelial expression of beta1 integrin is required for embryonic vascular patterning and postnatal vascular remodeling

The largest subgroup of integrins is that containing the β1 subunit. β1 integrins have been implicated in a wide array of biological processes ranging from adhesion to cell growth, organogenesis, and mechanotransduction. Global deletion of β1 integrin expression results in embryonic death at ca. embryonic day 5 (E5), a developmental time point too early to determine the effects of this integrin on vascular development. To elucidate the specific role of β1 integrin in the vasculature, we conditionally deleted the β1 gene in the endothelium. Homozygous deletion of β1 integrins in the endothelium resulted in failure of normal vascular patterning, severe fetal growth retardation, and embryonic death at E9.5 to 10, although there were no overt effects on vasculogenesis. Heterozygous endothelial β1 gene deletion did not diminish fetal or postnatal survival, but it reduced β1 subunit expression in endothelial cells from adult mice by approximately 40%. These mice demonstrated abnormal vascular remodeling in response to experimentally altered in vivo blood flow and diminished vascularization in healing wounds. These data demonstrate that endothelial expression of β1 integrin is required for developmental vascular patterning and that endothelial β1 gene dosing has significant functional effects on vascular remodeling in the adult. Understanding how β1 integrin expression is modulated may have significant clinical importance.     

Early embryonic mouse mandibular morphogenesis and cytodifferentiation in serumless, chemically defined medium: a model for studies of autocrine and/or paracrine regulatory factors

During craniofacial and mandibular development at least three interdependent processes become integrated: 1) regulation of time-dependent differential gene expression; 2) positional information resulting in pattern formations; and 3) morphogenesis. The present studies were designed to test the hypothesis that intrinsic and/or paracrine factors regulate the developmental program for embryonic mouse mandibular morphogenesis, histogenesis, and cytodifferentiation. Either E11 or E12 C57B110 (B10.A) strain mouse mandibular processes were cultured in serumless, chemically defined medium for periods up to 9 days in vitro. At selected stages of development 3H-thymidine incorporation into DNA was used to evaluate the mitotic labeling for selected tissue compartments. Macroscopic observations demonstrated that morphogenesis (shape/form) in vitro was comparable to that for in vivo controls. Histological results demonstrated that chondrogenesis, osteogenesis, tooth formation, tongue formation, lip formation, and epithelial differentiation with keratinization were expressed according to sequence, time, and positions comparable to those observed in controls. This experimental approach provided datasets to support the hypothesis that exogenous long-range factors are not required for embryonic mouse mandibular morphogenesis and further suggested that autocrine and/or paracrine factors mediate the timing and position of mandibular development.     

Airway patterning: A paradigm for restricted signalling.

Intercellular signalling is limited by the range of cell responsiveness, often mediated by repressors. A recently identified repressor, Sprouty, inhibits MAP kinase signalling in flies, mice and humans and has a conserved function in patterning the airways of these divergent species.     

Role of the extracellular matrix in cell-cell signalling: paracrine paradigms

The plant extracellular matrix (ECM) is complex and diverse, and is involved in cell-cell communication in a wide range of developmental, reproductive and pathogenic processes. Characterisation of integral ECM components is leading to improved understanding of their roles in signalling. Interactions between the extracellular domains of plant plasma membrane receptor kinases and their ligands are potentially regulated by the properties of the ECM. Several of these interactions, for example those involving the S-locus receptor kinase, are being characterised in some detail. Non-protein constituents are also implicated in regulating the movement of signalling molecules in the ECM, which is associated with developmental patterning. In contrast to the situation in animal cells, cytoskeleton-integrin-ECM signalling complexes appear not to be dominant features of signal transduction in plant cells. Nevertheless, structural adhesions between the plasma membrane and cell wall are important for a variety of functions.     

Early arterial differentiation and patterning in the avian embryo model

Of the many models to study vascular biology the avian embryo remains an informative and powerful model system that has provided important insights into endothelial cell recruitment, assembly and remodeling during development of the circulatory system. This review highlights several discoveries in the avian system that show how arterial patterning is regulated using the model of dorsal aortae development along the embryo midline during gastrulation and neurulation. These discoveries were made possible through spatially and temporally controlled gain-of-function experiments that provided direct evidence that BMP signaling plays a pivotal role in vascular recruitment, patterning and remodeling and that Notch-signaling recruits vascular precursor cells to the dorsal aortae. Importantly, BMP ligands are broadly expressed throughout embryos but BMP signaling activation region is spatially defined by precisely regulated expression of BMP antagonists. These discoveries provide insight into how signaling, both positive and negative, regulate vascular patterning. This review also illustrates similarities of early arterial patterning along the embryonic midline in amniotes both avian and mammalians including human, evolutionarily specialized from non-amniotes such as fish and frog.     

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Journal of Mathematical Biology - Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and...     

A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

A mathematical model of the role of aggregation in sonic hedgehog signalling

Effective regulation of the sonic hedgehog (Shh) signalling pathway is essential for normal development in a wide variety of species. Correct Shh signalling requires the formation of Shh aggregates on the surface of producing cells. Shh aggregates subsequently diffuse away and are recognised in receiving cells located elsewhere in the developing embryo. Various mechanisms have been postulated regarding how these aggregates form and what their precise role is in the overall signalling process. To understand the role of these mechanisms in the overall signalling process, we formulate and analyse a mathematical model of Shh aggregation using nonlinear ordinary differential equations. We consider Shh aggregate formation to comprise of multimerisation, association with heparan sulfate proteoglycans (HSPG) and binding with lipoproteins. We show that the size distribution of the Shh aggregates formed on the producing cell surface resembles an exponential distribution, a result in agreement with experimental data. A detailed sensitivity analysis of our model reveals that this exponential distribution is robust to parameter changes, and subsequently, also to variations in the processes by which Shh is recruited by HSPGs and lipoproteins. The work demonstrates the time taken for different sized Shh aggregates to form and the important role this likely plays in Shh diffusion.     

Regulation of thrombocytopoiesis studied by a mathematical model

A mathematical model of thrombocytopoiesis is proposed which accounts for the recent data on its regulation. It is shown that the compensatory response of the system to a decrease in the level of thrombocytes in the blood is controlled by the total amount of thrombocytes and megakaryocytes. The proliferation intensity of megakaryocytes and the total number of thrombocytes reveal, respectively, a lineary and a logarithmical dependence on the total number of thrombocytes and megakaryocytes. The limits of the post-transfusion level of thrombocytes are defined, within which the thrombocytopoiesis is controlled only by the number of thrombocytes. The values of parameters characterizing the behaviour of the thrombocytopoiesis system are calculated.     

Evaluation of early embryonic mortality in donor insemination by a mathematical model,globally and depending on semen quality

Stating the probability of pregnancy per cycle as P_oP_FP_v, the product of the probabilities of ovulation, fertilization, and egg viability, the model allows an estimate of P_F and P_oP_v for a series of cycles with known insemination timing. Such results obtained from a series of donor insemination (AID) compared with those generally admitted in natural reproduction suggest that the lower pregnancy rate in AID (all the lower when the postthaw motility is low) is owing to a lower egg viability. Since the abortion rate does not seem higher, there might be a sizable rate of very early embryonic deaths in AID perhaps even as early as nondeveloping eggs.     

Defective paracrine signalling by TGFbeta in yolk sac vasculature of endoglin mutant mice: a paradigm for hereditary haemorrhagic telangiectasia

Hereditary haemorrhagic telangiectasia (HHT) is an autosomal dominant disorder in humans that is characterised by multisystemic vascular dyplasia and recurrent haemorrhage. Germline mutations in one of two different genes, endoglin or ALK1 can cause HHT. Both are members of the transforming growth factor (TGF) beta receptor family of proteins, and are expressed primarily on the surface of endothelial cells (ECs). Mice that lack endoglin or activin receptor like kinase (ALK) 1 die at mid-gestation as a result of defects in the yolk sac vasculature. Here, we have analyzed TGFbeta signalling in yolk sacs from endoglin knockout mice and from mice with endothelial-specific deletion of the TGFbeta type II receptor (TbetaRII) or ALK5. We show that TGFbeta/ALK5 signalling from endothelial cells to adjacent mesothelial cells is defective in these mice, as evidenced by reduced phosphorylation of Smad2. This results in the failure of vascular smooth muscle cells to differentiate and associate with endothelial cells so that blood vessels remain fragile and become dilated. Phosphorylation of Smad2 and differentiation of smooth muscle can be rescued by culture of the yolk sac with exogenous TGFbeta1. Our data show that disruption of TGFbeta signalling in vascular endothelial cells results in reduced availability of TGFbeta1 protein to promote recruitment and differentiation of smooth muscle cells, and provide a possible explanation for weak vessel walls associated with HHT.     

A model for anteroposterior patterning of the vertebrate limb based on sequential long- and short-range Shh signalling and Bmp signalling

It has been proposed that digit identity in chick limb bud is specified in a dose-dependent fashion by a long-range morphogen, produced by the polarising region. One candidate is Sonic hedgehog (Shh) protein, but it is not clear whether Shh acts long or short range or via Bmps. Here we dissect the relationship between Shh and Bmp signalling. We show that Shh is necessary not only for initiating bmp2 expression but also for sustaining its expression during the period when additional digits are being specified. We also show that we can reproduce much of the effect of Shh during this period by applying only Bmp2. We further demonstrate that it is Bmps that are responsible for digit specification by transiently adding Noggin or Bmp antibodies to limbs treated with Shh. In such limbs, multiple additional digits still form but they all have the same identity. We also explored time dependency and range of Shh signalling by examining ptc expression. We show that high-level ptc expression is induced rapidly when either Shh beads or polarising regions are grafted to a host limb. Furthermore, we find that high-level ptc expression is first widespread but later more restricted. All these data lead us to propose a new model for digit patterning. We suggest that Shh initially acts long range to prime the region of the limb competent to form digits and thus control digit number. Then later, Shh acts short range to induce expression of Bmps, whose morphogenetic action specifies digit identity.