A mathematical theory of the affective psychoses

The theory introduces two variables ϕ and ψ. The first represents the intensity of emotion, the second measures the intensity of activity. A set of integrodifferential equations is assumed to govern the variation of ϕ and ψ with respect to time. Since for increasing values of ϕ the conduct of the organism varies from great impassivity through a normal level of feeling to extremes of a circular depression or catatonic excitement; whereas an increase of ψ results in a transition from stupor to manic excitement, the solutions of the equations represent quatitative specifications of different psychotic states.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

Modelling biological cell attachment and growth on adherent surfaces

A mathematical model, in the form of an integro-partial differential equation, is presented to describe the dynamics of cells being deposited, attaching and growing in the form of a monolayer across an adherent surface. The model takes into account that the cells suspended in the media used for the seeding have a distribution of sizes, and that the attachment of cells restricts further deposition by fragmenting the parts of the domain unoccupied by cells. Once attached the cells are assumed to be able to grow and proliferate over the domain by a process of infilling of the interstitial gaps; it is shown that without cell proliferation there is a slow build up of the monolayer but if the surface is conducive to cell spreading and proliferation then complete coverage of the domain by the monolayer can be achieved more rapidly. Analytical solutions of the model equations are obtained for special cases, and numerical solutions are presented for parameter values derived from experiments of rat mesenchymal stromal cells seeded onto thin layers of collagen-coated polyethylene terephthalate electrospun fibers. The model represents a new approach to describing the deposition, attachment and growth of cells over adherent surfaces, and should prove useful for studying the dynamics of the seeding of biomaterials.     

A demographic analysis of population responses to the manipulation of adult males in <Emphasis Type="Italic">Calomys venustus</Emphasis> (Rodentia,Sigmodontinae)

In many species of mammals, adults play an important role in influencing the survival and/or reproduction of juveniles. Adult males could have a negative effect on population density when their absence becomes a limiting factor in female fertilization. We tested the hypotheses that the absence of overwintering males (adult males) reduces the population growth rate through a delay in the onset of reproductive activity of Cohort 1 females in Calomys venustus populations. The study was carried out in two control and two experimental enclosures (0.25 ha). Adult males were removed after their offspring were born. Weekly trapping sessions were carried out from spring to autumn. To estimate population growth rates (λ), apparent survival (ϕ) and seniority probability (γ) were estimated using capture–mark-recapture models. Models were constructed with these two parameters and recapture probability (p) constrained to vary as a function of time, enclosure and/or treatment. We derived estimates of population growth rates through the estimates of ϕ and γ. The best models for ϕ and γ did not show a treatment effect. Variability between the four enclosures was greater than between control and experimental enclosures. Enclosures had different growth rates at the beginning of the study but were equaled at the end. Temporal variation in population growth rates was a result of temporal variation of γ. The two controls showed the highest growth rates earlier in time. The results did not support the hypothesis tested in this study. It seems that the number of overwintering males do not affect the population growth rate.     

Cytokine production by a megakaryocytic cell line

Summary The regulation of megakaryopoeisis by cytokines is not yet well understood. It is possible that autocrine loops are established during megakaryocyte growth and differentiation, aiding in the maturation of these cells. The CHRF-288-11 human megakaryoblastic cell line has been examined for cytokine production in growing cells and cells stimulated to differentiate by the addition of phorbol esters. It has been demonstrated that these cells produce RNA corresponding to the interleukins IL-1α, 1β, 3, 7, 8, and 11, granulocyte-macrophage colony stimulating factor (GM-CSF), stem cell factor (SCF), transforming growth factor-β (TGF-β), tumor necrosis factor-α (TNF-α), interferon-α (INF-α), and basic fibroblast growth factor (bFGF). Additionaly, RNA corresponding to the receptors for IL-6, GM-CSF, SCF, INF-α,β, bFGF, and monocyte colony stimulating factor (M-CSF) were also expressed by the cells. The receptor for TNF-α was detected immunologically. Analysis at the protein level demonstrated that significant amounts of INF-α, TNF-α, GM-CSF, SCF, IL-1α, and a soluble form of the IL-6 receptor were produced by the cells. Addition of phorbol esters to CHRF-288-11 cells enhances their megakaryocytic phenotype; such treatment also results in increased secretion of INF-α, TNF-α, and GM-CSF. These results suggest that potential autocrine loops are established during the differentiation of CHRF-288-11 cells, which may alter the capability of the cell to differentiate. These findings are similar to those recently obtained for marrow-derived megakaryocytes (Jiang et al.) suggesting that CHRF-288-11 cells provide a useful model system for the study of cytokine release during megakaryocyte differentiation.     

Growth stimulating activity of heat shock protein 90α to lymphoid cell lines in serum-free medium

A growth stimulating factor was purified from the culture supernatant of human-human hybridoma SH-76 cells in serum-free RPMI 1640 medium by the serial use of DEAE anion and heparin affinity chromatographies. The factor was a 85 kDa protein on SDS-polyacrylamide gel electrophoresis. N-terminal amino acid sequence (PEETQTQDQPME) of the protein was coincident with that of heat shock protein 90α (HSP90α). The protein reacted with anti-HSP90 monoclonal antibody. These results suggest that the protein was a member of HSP90α family after taking other circumstantial evidence into account. The protein stimulated the growth of some lymphoid cell lines such as human B-lymphoblastoid cell line HO-323-3 hybridomas derived from HO-323, and several other lymphoid cell lines. There were several lymphoid cell lines which did not respond to the protein. Growth stimulating activity of the protein was heat-unstable and significantly decreased at above 60°C. These are the first data that describe growth-stimulating activity of heat shock protein 90α.     

The occurrence of protein kinase C ϕ and λ isoforms in retina of different species

The localization and immunochemical identification of the novel protein kinase C ϕ (nPKC ϕ) and the atypical protein kinase C λ (aPKC λ) isoforms in retinas of different species were analyzed by immunohistochemistry and SDS-PAGE/Western blotting. nPKC ϕ immunoreactivity is associated with bipolar cells of mammalian (rabbit, rat and guinea pig) retinas but not the non-mammalian goldfish retina which has a lower concentration of nPKC ϕ. However, SDS-PAGE and Western blotting data indicate the antigen recognized by the nPKC ϕ monoclonal antibody in the retina is of a lower molecular weight than that expected for nPKC ϕ. This would suggest nPKC ϕ is more susceptible to degradation/breakdown than other PKC isoforms found in the retina or that the nPKC ϕ antibody may be recognizing an unknown retinal antigen. A comparison of nPKC ϕ and nPKC ϕ is present in the developing retina at an earlier stage than cPKC α. The typical ‘transport’ of cPKC α toward axonal terminals by phorbol-12,13-dibutyrate does not occur for nPKC ϕ yet both are translocated from the cytosolic to membrane compartments. The inner plexiform layer and the inner nuclear layer (putative horizontal cells) of all species examined (rabbit, rat, guinea pig and goldfish) exhibited positive immunoreactivity for aPKC λ as confirmed by SDS-PAGE/Western blotting. Special issue dedicated to Dr. Kinya Kuriyama.     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997     

Human T lymphocyte activation in the presence of acute myelogenous leukaemia blasts; studies of normal polyclonal T cells and T lymphocyte clones derived early after allogeneic bone marrow transplantation

 T cell clones (CD4⁺CD8^–TCRαβ⁺γδ^–) derived from bone marrow transplant recipients were stimulated with phytohaemagglutinin (PHA) +interleukin-2 (IL-2) in the presence of irradiated (50 Gy) peripheral blood mononuclear cells (PBMC) derived from acute leukaemia patients(leukaemic PBMC containing more than 95% blast cells). Leukaemic PBMC could function as accessory cells during mitogenic T cell activation resulting in both T cell proliferation and a broad T cell cytokine response [IL-3, IL-4, IL-10, granulocyte/macrophage-colony-stimulating factor (GM-CSF) tumour necrosis factor α (TNFα) and interferon γ (IFNγ) secretion]. Blockade of IL-1 effects by adding IL-1 receptor antagonist together with PHA+IL-2+leukaemia blasts increased T cell proliferation, whereas IL-6-neutralizing antibodies did not alter T cell proliferation. A qualitatively similar T cell cytokine response and a similar cytokine profile (highest levels detected for GM-CSF and IFNγ) were detected when normal polyclonal T cell lines were stimulated with PHA in the presence of non-irradiated leukaemic PBMC. When leukaemic PBMC derived from 18 acute myelogenous leukaemia patients were cultured with PHA and cells from a polyclonal T cell line, increased concentrations of the T cell cytokines IFNγ and IL-4 were detected for all patients. We conclude that T cell activation resulting in proliferation and a broad cytokine response can take place in the presence of excess acute myelogenous leukaemia blasts. Received: 30 November 1995 / Accepted: 9 January 1996     

Rescuing of deficient killing and phagocytic activities of macrophages derived from non-obese diabetic mice by treatment with geldanamycin or heat shock: potential clinical implications

Diabetes mellitus type 1 (DMT1) is an autoimmune disease characterized by the destruction of insulin-producing cells in the pancreas. Diabetic patients are more susceptible to recurrent and uncontrolled infections, with worse prognoses than in healthy individuals. Macrophages (Mϕs) derived from DMT1 individuals have compromised mounting of inflammatory and immune responses. The mechanisms responsible for these alterations remain unknown. It has been shown that the presence of extra- and intracellular heat shock proteins (hsp) positively modulates immune cell function. Using naive Mϕs derived from non-obese diabetic (NOD) mice, a well-established mouse model for DMT1, we demonstrate that heat shock (HS) as well as treatment with geldanamycin (GA), significantly improves diabetic Mϕ activation, resulting in increased phagocytosis and killing of bacteria. Induction of HS did not affect the aberrant NOD-Mϕ cytokine profile, which is characterized by elevated IL-10 levels and normal tumor necrosis factor alpha. Our observations were consistent at pre-diabetic (normal random blood glucose) and diabetic (random blood glucose greater than 250 mg/dl) stages, suggesting that HS and GA treatment may compensate for intrinsic genetic alterations present in diabetic cells regardless of the stage of the disease. The mechanisms associated to this phenomenon are unknown, but they may likely be associated with the induction of hsp expression, a common factor between HS and GA treatment. Our results may open a new field for non-classical function of hsp and indicate that hsp expression may be used as a part of therapeutic approaches for the treatment of complications associated with DMT1 as well as other autoimmune diseases.     

The Effect of Rhamnolipid Biosurfactant Produced by <Emphasis Type="Italic">Pseudomonas fluorescens</Emphasis> on Model Bacterial Strains and Isolates from Industrial Wastewater

In this study, the effect of rhamnolipid biosurfactant produced by Pseudomonas fluorescens on bacterial strains, laboratory strains, and isolates from industrial wastewater was investigated. It was shown that biosurfactant, depending on the concentration, has a neutral or detrimental effect on the growth and protein release of model Gram (+) strain Bacillus subtilis 168. The growth and protein release of model Gram (−) strain Pseudomonas aeruginosa 1390 was not influenced by the presence of biosurfactant in the medium. Rhamnolipid biosurfactant at the used concentrations supported the growth of some slow growing on hexadecane bacterial isolates, members of the microbial community. Changes in cell surface hydrophobicity and permeability of some Gram (+) and Gram (−) isolates in the presence of rhamnolipid biosurfactant were followed in experiments in vitro. It was found that bacterial cells treated with biosurfactant became more or less hydrophobic than untreated cells depending on individual characteristics and abilities of the strains. For all treated strains, an increase in the amount of released protein was observed with increasing the amount of biosurfactant, probably due to increased cell permeability as a result of changes in the organization of cell surface structures. The results obtained could contribute to clarify the relationships between members of the microbial community as well as suggest the efficiency of surface properties of rhamnolipid biosurfactant from Pseudomonas fluorescens making it potentially applicable in bioremediation of hydrocarbon-polluted environments.     

Studies in mathematical biosociology of imitative behavior: I. Effects of income distribution

In connection with previous studies (Rashevsky,Mathematical Biology of Social Behavior, chap. xii), a situation is investigated in which the two mutually exclusive possible behaviors of a society consist of the desire to keep the present socioeconomical situation and the desire to change it inany way. The psychophysiological tendency ϕ towards either of the behaviors is considered to be proportional to the difference between the actual incomei of the individual and his needsi′. Assuming that the distribution functionN ₁(i′) of the needs is a given characteristic of the population, it is shown that the distribution functionN(ϕ) of ϕ in the society can be derived fromN ₁(i′) and from the distributionN ₂(i) of the incomesi. A particular case is worked out as an example. Conditions of stability of a socioeconomic structure are studied in their dependence on the income distribution.     

Effect of the population heterogeneity on growth behavior and its estimation

Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be rather limited in the case of N(t_0)=N_0. Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N0 from heteroge-neous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth progress, termed as θ, and thus, ddNt not only depends on N, but also on θ. So θ is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in widely used growth models. However, combining together the two factors (N0 and θ ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (Vinst) to express growth progress. Previous studies in our laboratory sug-gested that the Vinst curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably distinguished. In the present study, the Gaussian dis-tribution function was transformed approximately into an analytical form (0.5x ibxYi αe=20) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also discussed.     

The role of cell-cell interactions in a two-phase model for avascular tumour growth

 A two-phase model is presented to describe avascular tumour growth. Conservation of mass equations, including oxygen-dependent cell growth and death terms, are coupled with equations of momentum conservation. The cellular phase behaves as a viscous liquid, while the viscosity of the extracellular water manifests itself as an interphase drag. It is assumed that the cells become mechanically stressed if they are too densely packed and that the tumour will try to increase its volume in order to relieve such stress. By contrast, the overlapping filopodia of sparsely populated cells create short-range attractive effects. Finally, oxygen is consumed by the cells as it diffuses through the tumour. The resulting system of equations are reduced to three, which describe the evolution of the tumour cell volume fraction, the cell speed and the oxygen tension. Numerical simulations indicate that the tumour either evolves to a travelling wave profile, in which it expands at a constant rate, or it settles to a steady state, in which the net rates of cell proliferation and death balance. The impact of varying key model parameters such as cellular viscosity, interphase drag, and cellular tension are discussed. For example, tumours consisting of well-differentiated (i.e. viscous) cells are shown to grow more slowly than those consisting of poorly-differentiated (i.e. less viscous) cells. Analytical results for the case of oxygen-independent growth are also presented, and the effects of varying the key parameters determined (the results are in line with the numerical simulations of the full problem). The key results and their biological implications are then summarised and future model refinements discussed. Received: 3 May 2001 / Revised version: 7 January 2002 / Published online: 17 July 2002     

Transforming growth factor-β1 (TGF-β1) and acetylcholine (ACh) alter nitric oxide (NO) and interleukin-1β (IL-1β) secretion in human colon adenocarcinoma cells

Colon adenocarcinoma is one of the most common fatal malignancies in Western countries. Progression of this cancer is dependent on tumor microenvironmental signaling molecules such as transforming growth factor-β (TGF-β) or acetylcholine (ACh). The present study was conducted to assess the influence of recombinant human transforming growth factor (rhTGF)-β1 or ACh on nitric oxide (NO) and interleukin-1β (IL-1β) secretion by three human colon adenocarcinoma cell lines: HT29, LS180, and SW948, derived from different grade tumors (Duke’s stage). The cells were cultured in 2D and 3D (spheroids) conditions. Colon carcinoma cells exhibited different sensitivities to rhTGF-β1 or ACh dependent on the tumor grade and the culture model. ACh exhibited significant inhibitory effects towards NO, endothelial nitric oxide synthase (eNOS), and IL-1β secretion especially by tumor cells derived form Duke’s C stage of colon carcinoma. rhTGF-β1 also decreased NO, IL-1β, and eNOS expression, but its effect was lower than that observed after the administration of ACh. The inhibition of NO and IL-1β production was more striking in 3D tumor spheroids than in 2D culture monolayers. Taken together, the TGF-β1–ACh axis may regulate colon carcinoma progression and metastasis by altering NO secretion and influence inflammatory responses by modulating IL-1β production.     

The root–soil system of Norway spruce subjected to turning moment: resistance as a function of rotation

The reactions of trees to wind, rockfall, and snow and debris flow depend largely on how strong and deformable their anchorage in the soil is. Here, the resistive turning moment M of the root–soil system as a function of the rotation ϕ at the stem base plays the major role. M(ϕ) describes the behavior of the root–soil system when subject to rotational moment, with the maximum M(ϕ) indicating the anchorage strength M _a of the tree. We assessed M(ϕ) of 66 Norway spruce (Picea abies L. Karst) by pulling them over with a winch. These 45- to 170-year-old trees grew at sites of low and high elevation, with a diameter at breast height DBH = 14–69 cm and a height H = 9–42 m. M(ϕ) displayed a strong nonlinear behavior. M _a was reached at a lower ϕ for large trees than for small trees. Thus overhanging tree weight contributed less to M _a for the large trees. Overturning also occurred at a lower ϕ for the large trees. These observations show that the rotational ductility of the root–soil system is higher for small trees. M _a could be described by four monovariate linear regression equations of tree weight, stem weight, stem volume and DBH ² ·H (0.80 < R ² < 0.95), and ϕ at M _a, ϕ _a, by a power law of DBH²·H (R ² = 0.85). We found significantly higher M _a for the low-elevation spruces than for the high-elevation spruces, which were more shallowly anchored, but no significant difference in ϕ _a. The 66 curves of M(ϕ), normalized (_n) by M _a in M-direction and by ϕ _a in ϕ-direction, yielded one characteristic average curve: . Using and the predictions of M _a and ϕ _a, it is shown that M(ϕ) and the curves associated with M(ϕ) can be predicted with a relative standard error ≤25%. The parameterization of M(ϕ) by tree size and weight is novel and provides useful information for predicting with finite-element computer models how trees will react to natural hazards.     

The cytogenetic,proliferative and viability effects of four bacteriophages on human lymphocytes

Summary Certain bacteriophages have been found in live, virus vaccines, while a few others have been associated with disease states. Some of these phages have produced abnormal growth of eukaryotic tissue cultures. For this reason bacteriophages ϕX-174, MS2, T2 and an isolate from live virus vaccines, ϕV-1, were incubated with human cell cultures for examination of chromosomal effects, cell proliferation and viability. Mitogen-stimulated lymphocytes and human embryonic kidney tissue cultures showed no increase in chromosomal abnormalities for high doses of phage-infected versus control cultures. Tritiated-thymidine uptake, correlated with mitotic indices for phage-treated lymphocyte culture, indicated a reduction in cell division, while 51-chromium release studies showed no cell death occurring in these cultures. This suggested that inhibition of DNA synthesis was occurring in some cells. The presence of phage in the supernate of cells that were exposed to phage suggested the possibility of phage attachment to the plasma membranes of lymphocytes, which may in turn affect the suppression of DNA synthesis. This work was supported by HEW/FDA Grant No. 223-73-1171.     

Macrophages from lupus-prone MRL mice have a conditional signaling abnormality that leads to dysregulated expression of numerous genes

Macrophages (mϕ) from pre-diseased mice of the major murine inbred models of spontaneous autoimmunity (AI), including multiple lupus-prone strains and the type I diabetes-prone NOD (non-obese diabetic) strain, have identical apoptotic target-dependent abnormalities. This characteristic feature of mϕ from AI-prone mice suggests that abnormal signaling events induced within mϕ following their interaction with apoptotic targets may predispose to AI. Such signaling abnormalities would affect predominantly the processing and presentation of self-antigen (i.e., derived from apoptotic targets), while sparing the processing and presentation of foreign antigen (i.e., derived from non-apoptotic sources). Here, we used DNA microarrays to test the hypothesis that mϕ from AI-prone mice (MRL/MpJ [MRL/+] or MRL/MpJ-Tnfrsf6 ^lpr [MRL/lpr]) differentially express multiple genes in comparison to non-AI mϕ (BALB/c), but do so in a largely apoptotic cell-dependent manner. Mϕ were stimulated with lipopolysaccharide, a potent innate stimulus, in the presence or absence of serum (an experimental surrogate for apoptotic targets). In accord with our hypothesis, the number of genes differentially expressed by MRL mϕ was significantly increased in the presence vs. the absence of serum, the apoptotic target surrogate (n = 401 vs. n = 201). Notably, for genes differentially expressed by MRL mϕ in the presence of serum, serum-free culture normalized their expression to a level statistically indistinguishable from that by non-AI mϕ. Comparisons of mϕ from AI-prone NOD and non-AI C57BL/6 mice corroborated these findings. Together, these data support the hypothesis that mϕ from MRL and other AI-prone mice are characterized by a conditional abnormality elicited by serum lipids or apoptotic targets.     

In situ separation of root hydraulic redistribution of soil water from liquid and vapor transport

Nocturnal increases in water potential (ψ) and water content (θ) in the upper soil profile are often attributed to root water efflux, a process termed hydraulic redistribution (HR). However, unsaturated liquid or vapor flux of water between soil layers independent of roots also contributes to the daily recovery in θ (Δθ), confounding efforts to determine the actual magnitude of HR. We estimated liquid (J _l) and vapor (J _v) soil water fluxes and their impacts on quantifying HR in a seasonally dry ponderosa pine (Pinus ponderosa) forest by applying existing datasets of ψ, θ and temperature (T) to soil water transport equations. As soil drying progressed, unsaturated hydraulic conductivity declined rapidly such that J _l was irrelevant (<2E−05 mm h⁻¹ at 0–60 cm depths) to total water flux by early August. Vapor flux was estimated to be the highest in upper soil (0–15 cm), driven by large T fluctuations, and confounded the role of HR, if any, in nocturnal θ dynamics. Within the 15–35 cm layer, J _v contributed up to 40% of hourly increases in nocturnal soil moisture. While both HR and net soil water flux between adjacent layers contribute to θ in the 15–65 cm soil layer, HR was the dominant process and accounted for at least 80% of the daily recovery in θ. The absolute magnitude of HR is not easily quantified, yet total diurnal fluctuations in upper soil water content can be quantified and modeled, and remain highly applicable for establishing the magnitude and temporal dynamics of total ecosystem water flux.     

A Continuum Mathematical Model of the Developing Murine Retinal Vasculature

Angiogenesis, the process of new vessel growth from pre-existing vasculature, is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis is also a key regulator of pathogenesis in many clinically important disease processes, for instance, solid tumour progression and ocular diseases. Over the past 10–20 years, tumour-induced angiogenesis has received a lot of attention in the mathematical modelling community and there have also been some attempts to model angiogenesis during wound healing. However, there has been little modelling work of vascular growth during normal development. In this paper, we describe an in silico representation of the developing retinal vasculature in the mouse, using continuum mathematical models consisting of systems of partial differential equations. The equations describe the migratory response of cells to growth factor gradients, the evolution of the capillary blood vessel density, and of the growth factor concentration. Our approach is closely coupled to an associated experimental programme to parameterise our model effectively and the simulations provide an excellent correlation with in vivo experimental data. Future work and development of this model will enable us to elucidate the impact of molecular cues upon vasculature development and the implications for eye diseases such as diabetic retinopathy and neonatal retinopathy of prematurity.