A two-phase thin-film model for cell-induced gel contraction incorporating osmotic effects.

We present a mathematical model of an experiment in which cells are cultured within a gel, which in turn floats freely within a liquid nutrient medium. Traction forces exerted by the cells on the gel cause it to contract over time, giving a measure of the strength of these forces. Building upon our previous work (Reoch et al. in J Math Biol 84(5):31, 2022), we exploit the fact that the gels used frequently have a thin geometry to obtain a reduced model for the behaviour of a thin, two-dimensional cell-seeded gel. We find that steady-state solutions of the reduced model require the cell density and volume fraction of polymer in the gel to be spatially uniform, while the gel height may vary spatially. If we further assume that all three of these variables are initially spatially uniform, this continues for all time and the thin film model can be further reduced to solving a single, non-linear ODE for gel height as a function of time. The thin film model is further investigated for both spatially-uniform and varying initial conditions, using a combination of analytical techniques and numerical simulations. We show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e., the chemical potentials) and the strength of the cell traction forces. However, unlike in the earlier one-dimensional model, we do not observe cases where the gel oscillates between swelling and contraction. For the case of initially uniform cell and gel density, our model predicts that the relative change in the gels' height and length are equal, which justifies an assumption previously used in the work of Stevenson et al. (Biophys J 99(1):19-28, 2010). Conversely, however, even for non-uniform initial conditions, we do not observe cases where the length of the gel changes whilst its height remains constant, which have been reported in another model of osmotic swelling by Trinschek et al. (AIMS Mater Sci 3(3):1138-1159, 2016; Phys Rev Lett 119:078003, 2017).

A mathematical model for nutrient-limited uniaxial growth of a compressible tissue.

We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction-diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base.

Correction: Modelling locust foraging: How and why food affects group formation.

[This corrects the article DOI: 10.1371/journal.pcbi.1008353.].

Modelling locust foraging: How and why food affects group formation.

Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the aggregation of juvenile wingless locust nymphs. In this paper we attempt to understand how the distribution of food resources affect the group formation process. We do this by introducing a multi-population partial differential equation model that includes non-local locust interactions, local locust and food interactions, and gregarisation. Our results suggest that, food acts to increase the maximum density of locust groups, lowers the percentage of the population that needs to be gregarious for group formation, and decreases both the required density of locusts and time for group formation around an optimal food width. Finally, by looking at foraging efficiency within the numerical experiments we find that there exists a foraging advantage to being gregarious.

A mathematical model for cell-induced gel contraction incorporating osmotic effects.

Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. In this paper, we present a mathematical model that incorporates cell-gel interactions together with osmotic pressure to study the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. Adopting a one-dimensional Cartesian geometry for simplicity, we use a combination of analytical techniques and numerical simulations to investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel's composition). Our results show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e. its chemical potentials) and the strength of the cell traction forces. A novel prediction of our model is that there are cases where the gel oscillates between swelling and contraction; to our knowledge, this behaviour has not been reported in experiments. We also consider how physical parameters like drag and viscosity affect the manner in which the gel evolves.

Understanding interactions between populations: Individual based modelling and quantification using pair correlation functions.

Understanding the underlying mechanisms that produce the huge variety of swarming and aggregation patterns in animals and cells is fundamental in ecology, developmental biology, and regenerative medicine, to name but a few examples. Depending upon the nature of the interactions between individuals (cells or animals), a variety of different large-scale spatial patterns can be observed in their distribution; examples include cell aggregates, stripes of different coloured skin cells, etc. For the case where all individuals are of the same type (i.e., all interactions are alike), a considerable literature already exists on how the collective organisation depends on the inter-individual interactions. Here, we focus on the less studied case where there are two different types of individuals present. Whilst a number of continuum models of this scenario exist, it can be difficult to compare these models to experimental data, since real cells and animals are discrete. In order to overcome this problem, we develop an agent-based model to simulate some archetypal mechanisms involving attraction and repulsion. However, with this approach (as with experiments), each realisation of the model is different, due to stochastic effects. In order to make useful comparisons between simulations and experimental data, we need to identify the robust features of the spatial distributions of the two species which persist over many realisations of the model (for example, the size of aggregates, degree of segregation or intermixing of the two species). In some cases, it is possible to do this by simple visual inspection. In others, the features of the pattern are not so clear to the unaided eye. In this paper, we introduce a pair correlation function (PCF), which allows us to analyse multi-species spatial distributions quantitatively. We show how the differing strengths of inter-individual attraction and repulsion between species give rise to different spatial patterns, and how the PCF can be used to quantify these differences, even when it might be impossible to recognise them visually.

An investigation of the influence of extracellular matrix anisotropy and cell-matrix interactions on tissue architecture.

Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. In this paper we develop a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell-collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell-ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell-ECM interactions.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions.

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Three-gene predictor of clinical outcome for gastric cancer patients treated with chemotherapy.

To identify transcriptional profiles predictive of the clinical benefit of cisplatin and fluorouracil (CF) chemotherapy to gastric cancer patients, endoscopic biopsy samples from 96 CF-treated metastatic gastric cancer patients were prospectively collected before therapy and analyzed using high-throughput transcriptional profiling and array comparative genomic hybridization. Transcriptional profiling identified 917 genes that are correlated with poor patient survival after CF at P<0.05 (poor prognosis signature), in which protein synthesis and DNA replication/recombination/repair functional categories are enriched. A survival risk predictor was then constructed using genes, which are included in the poor prognosis signature and are contained within identified genomic amplicons. The combined expression of three genes-MYC, EGFR and FGFR2-was an independent predictor for overall survival of 27 CF-treated patients in the validation set (adjusted P=0.017), and also for survival of 40 chemotherapy-treated gastric cancer patients in a published data set (adjusted P=0.026). Thus, combined expression of MYC, EGFR and FGFR2 is predictive of poor survival in CF-treated metastatic gastric cancer patients.

Modelling foraging competition between solitarious and gregarious organisms in increasingly heterogeneous environments.

Density dependent phase polyphenism is the exhibiting of two or more distinct phenotypes from a single genotype depending on local population density. The most well known insect to exhibit this phenomenon is the locust, with whom the profound effect on behaviour leads to the classification of the two phases; solitarious, where locusts actively avoid other locusts, and gregarious, where locusts are strongly attracted to other locusts. It has been shown that food distributions at both small and large scales have an effect on the process of gregarisation. While gregarisation offers advantages, such as greater predator avoidance, the relationship between phase polyphenism and potential foraging benefits is still not fully understood. In this paper, we explore the effect of gregarisation on foraging within increasingly heterogeneous environments using a partial differential equation model. We first consider a single two dimensional simulation of a spatially heterogeneous environment to understand the mechanics of gregarious/solitarious foraging. We then look at the steady state foraging advantage (measured as the ratio of per-capita contact with food) in environments ranging from homogeneous to very spatially heterogeneous. Finally, we perform a parameter sensitivity analysis to find which model parameters have the greatest effect on foraging advantage. We find that during the aggregation stage, prior to the onset of marching (which we do not model here), in increasingly heterogeneous food environments it is better to be gregarious than solitarious. In addition, we find that this is intrinsic to the gregarious/solitarious behavioural dynamic as it occurs almost regardless of the model parameters. That is to say, it doesn't matter how fast the organisms disperse or how strong their long range interactions as long as there is the solitarious/gregarious behaviour the gregarious foraging advantage will exist.

Benefits of exercise training on breast cancer progression and inflammation in C3(1)SV40Tag mice.

Many observational epidemiologic studies suggest an association between exercise and breast cancer risk. However, the lack of controlled experimental studies that examine this relationship and the mechanisms involved weaken the basis for inferring a causal relationship. Inflammation plays a role in breast cancer progression and exercise has been reported to reduce inflammation; however, the anti-inflammatory effects of exercise in breast cancer have yet to be established. We examined the relationship between exercise training and systemic inflammation in relation to breast cancer progression in C3(1)SV40Tag mice. Female C3(1)SV40Tag mice were assigned to either exercise (Ex) or sedentary (Sed) treatment (n=12-14/group). Beginning at 4 wks of age mice (Ex) were run on a treadmill for 60 min/d (20 m/min and 5% grade), 6 d/wk for a period of 20 wks. Mice were examined weekly for palpable tumors, and tumor number and volume were recorded. At 24 wks of age mice were sacrificed and a more direct measure of tumor number and volume, and spleen weight was recorded. Plasma was analyzed for MCP-1 and IL-6 concentration using ELISA. Ex reduced palpable tumor number at sacrifice (24 wks) by approximately 70% (P<0.05). Tumor volume was also reduced in Ex at 21-23 wks (P<0.05). This reduction in tumor progression by Ex was associated with a reduction in plasma concentration of MCP-1 and IL-6, and spleen weight (P<0.05). These data provide strong support for a beneficial effect of exercise training on tumor progression in the C3(1)SV40Tag mouse model of breast cancer that may be partly mediated by its anti-inflammatory potential.

Pathologic progression of mammary carcinomas in a C3(1)/SV40 T/t-antigen transgenic rat model of human triple-negative and Her2-positive breast cancer.

The C3(1) component of the rat prostate steroid binding protein has been used to target expression of the SV40 T/t-antigen to the mammary epithelium of mice resulting in pre-neoplastic lesions that progress to invasive and metastatic cancer with molecular features of human basal-type breast cancer. However, there are major differences in the histologic architecture of the stromal and epithelial elements between the mouse and human mammary glands. The rat mammary gland is more enriched with epithelial and stromal components than the mouse and more closely resembles the cellular composition of the human gland. Additionally, existing rat models of mammary cancer are typically estrogen receptor positive and hormone responsive, unlike most genetically engineered mouse mammary cancer models. In an attempt to develop a mammary cancer model that might more closely resemble the pathology of human breast cancer, we generated a novel C3(1)/SV40 T/t-antigen transgenic rat model that developed progressive mammary lesions leading to highly invasive adenocarcinomas. However, aggressive tumor development prevented the establishment of transgenic lines. Characterization of the tumors revealed that they were primarily estrogen receptor and progesterone receptor negative, and either her2/neu positive or negative, resembling human triple-negative or Her2 positive breast cancer. Tumors expressed the basal marker K14, as well as the luminal marker K18, and were negative for smooth muscle actin. The triple negative phenotype has not been previously reported in a rat mammary cancer model. Further development of a C3(1)SV40 T/t-antigen based model could establish valuable transgenic rat lines that develop basal-type mammary tumors.

Non-local models for the formation of hepatocyte-stellate cell aggregates.

Liver cell aggregates may be grown in vitro by co-culturing hepatocytes with stellate cells. This method results in more rapid aggregation than hepatocyte-only culture, and appears to enhance cell viability and the expression of markers of liver-specific functions. We consider the early stages of aggregate formation, and develop a new mathematical model to investigate two alternative hypotheses (based on evidence in the experimental literature) for the role of stellate cells in promoting aggregate formation. Under Hypothesis 1, each population produces a chemical signal which affects the other, and enhanced aggregation is due to chemotaxis. Hypothesis 2 asserts that the interaction between the two cell types is by direct physical contact: the stellates extend long cellular processes which pull the hepatocytes into the aggregates. Under both hypotheses, hepatocytes are attracted to a chemical they themselves produce, and the cells can experience repulsive forces due to overcrowding. We formulate non-local (integro-partial differential) equations to describe the densities of cells, which are coupled to reaction-diffusion equations for the chemical concentrations. The behaviour of the model under each hypothesis is studied using a combination of linear stability analysis and numerical simulations. Our results show how the initial rate of aggregation depends upon the cell seeding ratio, and how the distribution of cells within aggregates depends on the relative strengths of attraction and repulsion between the cell types. Guided by our results, we suggest experiments which could be performed to distinguish between the two hypotheses.

A mathematical model of liver cell aggregation in vitro.

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work.

Loss of mammary epithelial prolactin receptor delays tumor formation by reducing cell proliferation in low-grade preinvasive lesions.

Top quartile serum prolactin levels confer a twofold increase in the relative risk of developing breast cancer. Prolactin exerts this effect at an ill defined point in the carcinogenic process, via mechanisms involving direct action via prolactin receptors within mammary epithelium and/or indirect action through regulation of other hormones such as estrogen and progesterone. We have addressed these questions by examining mammary carcinogenesis in transplants of mouse mammary epithelium expressing the SV40T oncogene, with or without the prolactin receptor, using host animals with a normal endocrine system. In prolactin receptor knockout transplants the area of neoplasia was significantly smaller (7 versus 17%; P < 0.001 at 22 weeks and 7 versus 14%; P = 0.009 at 32 weeks). Low-grade neoplastic lesions displayed reduced BrdU incorporation rate (11.3 versus 17% P = 0.003) but no change in apoptosis rate. Tumor latency increased (289 days versus 236 days, P < 0.001). Tumor frequency, growth rate, morphology, cell proliferation and apoptosis were not altered. Thus, prolactin acts directly on the mammary epithelial cells to increase cell proliferation in preinvasive lesions, resulting in more neoplasia and acceleration of the transition to invasive carcinoma. Targeting of mammary prolactin signaling thus provides a strategy to prevent the early progression of neoplasia to invasive carcinoma.

Influences of transversely isotropic rheology and translational diffusion on the stability of active suspensions.

Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of 'active matter'. Examples include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely isotropic fluid (Ericksen 1960 Colloid Polym. Sci.173, 117-122 (doi:10.1007/bf01502416)) treats suspensions of non-motile particles as a continuum with an evolving preferred direction; this model describes fibrous materials as diverse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified stress tensor with four viscosity-like parameters. By making fundamental connections with recent models for active suspensions, we propose a modification to Ericksen's model, mainly the inclusion of self-motility; this can be considered the simplest description of an oriented suspension including transversely isotropic effects. Motivated by the fact that transversely isotropic fluids exhibit modified flow stability, we conduct a linear stability analysis of two distinct cases, aligned and isotropic suspensions of elongated active particles. Novel aspects include the anisotropic rheology and translational diffusion. In general, anisotropic effects increase the instability of small perturbations, while translational diffusion stabilizes a range of wave-directions and, in some cases, a finite range of wavenumbers, thus emphasizing that both anisotropy and translational diffusion can have important effects in these systems.

Pattern formation in multiphase models of chemotactic cell aggregation.

We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium. The model leads to a system of coupled nonlinear partial differential equations for the volume fraction and velocity of the cell phase, the culture medium pressure and the chemoattractant concentration, which must be solved subject to appropriate boundary and initial conditions. To gain insight into the system, we consider two model reductions, appropriate when the cell layer depth is thin compared to the typical length scale of the culture well: a (simple) 1D and a (more involved) thin-film extensional flow reduction. By investigating the resulting systems of equations analytically and numerically, we identify conditions under which small amplitude perturbations to a homogeneous steady state (corresponding to a spatially uniform cell distribution) can lead to a spatially varying steady state (pattern formation). Our analysis reveals that the simpler 1D reduction has the same qualitative features as the thin-film extensional flow reduction in the linear and weakly nonlinear regimes, motivating the use of the simpler 1D modelling approach when a qualitative understanding of the system is required. However, the thin-film extensional flow reduction may be more appropriate when detailed quantitative agreement between modelling predictions and experimental data is desired. Furthermore, full numerical simulations of the two model reductions in regions of parameter space when the system is not close to marginal stability reveal significant differences in the evolution of the volume fraction and velocity of the cell phase, and chemoattractant concentration.

Diffusion-Limited Growth of Microbial Colonies.

The emergence of diffusion-limited growth (DLG) within a microbial colony on a solid substrate is studied using a combination of mathematical modelling and experiments. Using an agent-based model of the interaction between microbial cells and a diffusing nutrient, it is shown that growth directed towards a nutrient source may be used as an indicator that DLG is influencing the colony morphology. A continuous reaction-diffusion model for microbial growth is employed to identify the parameter regime in which DLG is expected to arise. Comparisons between the model and experimental data are used to argue that the bacterium Bacillus subtilis can undergo DLG, while the yeast Saccharomyces cerevisiae cannot, and thus the non-uniform growth exhibited by this yeast must be caused by the pseudohyphal growth mode rather than limited nutrient availability. Experiments testing directly for DLG features in yeast colonies are used to confirm this hypothesis.

Loss of TGF-beta signaling contributes to autoimmune pancreatitis.

Recent observations suggest that immune response is involved in the development of pancreatitis. However, the exact pathogenesis underlying this immune-mediated response is still under debate. TGF-beta has been known to be an important regulating factor in maintaining immune homeostasis. To determine the role of TGF-beta in the initiation or progression of pancreatitis, TGF-beta signaling was inactivated in mouse pancreata by overexpressing a dominant-negative mutant form of TGF-beta type II receptor in the pancreas, under control of the pS2 mouse trefoil peptide promoter. Transgenic mice showed marked increases in MHC class II molecules and matrix metalloproteinase expression in pancreatic acinar cells. These mice also showed increased susceptibility to cerulein-induced pancreatitis. This pancreatitis was characterized by severe pancreatic edema, inflammatory cell infiltration, T- and B-cell hyperactivation, IgG-type autoantibodies against pancreatic acinar cells, and IgM-type autoantibodies against pancreatic ductal epithelial cells. Therefore, TGF-beta signaling seems to be essential either in maintaining the normal immune homeostasis and suppressing autoimmunity or in preserving the integrity of pancreatic acinar cells.

trans activation of nerve growth factor in transgenic mice containing the human T-cell lymphotropic virus type I tax gene.

Three lines of transgenic mice containing the human T-cell lymphotropic virus type I (HTLV-I) tax gene develop neurofibromas composed of perineural fibroblasts (S. H. Hinrichs, M. Nerenberg, R. K. Reynolds, G. Khoury, and G. Jay, Science 237:1340-1343, 1987; M. Nerenberg, S. H. Hinrichs, R. K. Reynolds, G. Khoury, and G. Jay, Science 237:1324-1327, 1987). Tumors and tumor cell lines derived from these mice produce neurite outgrowth from PC-12 cells and nerve growth factor (NGF), as determined by RNA (Northern) blot analysis and enzyme-linked immunosorbent assays. In vitro cotransfection studies demonstrate that Tax is able to trans activate the NGF promoter in NIH 3T3 fibroblast cells. The major cis-acting tax-responsive element in the NGF promoter (AGGGTGTGACGA) has 92% homology with a tax-responsive element contained within the 21-bp repeats of the HTLV-I long terminal repeat. The receptor for NGF is also expressed in the transgenic tumor cells, suggesting that Tax may activate an autocrine mechanism through the upregulation of NGF.