Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma

The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed by Judah Folkman in the early 1970s and subsequently established experimentally by him and his coworkers [Ausprunk, D. H. and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis, Microvasc Res., 14, 53–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: an experimental model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease that acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then move up the TGF gradient back to the tumor, proliferating and forming a new capillary network. In the model presented here, we include two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase. Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks; (3) standard transport equations for the diffusion of molecular species in porous media. One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the onset of vascularization and the rate of capillary tip growth observed in rabbit cornea experiments [Ausprunk, D. H. and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis, Microvasc Res., 14, 73–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: An experimental model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. Furthermore, our numerical experiments agree with the observation that the tip of a growing capillary accelerates as it approaches the tumor [Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64]. An erratum to this article is available at .     

Mathematical modeling of the onset of capillary formation initiating angiogenesis

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

Plasmin-induced migration of endothelial cells. A potential target for the anti-angiogenic action of angiostatin

Angiostatin, a plasminogen fragment containing 3-4 N-terminal kringle domains, is a potent inhibitor of tumor-induced angiogenesis, but its mechanism of action is unclear. Angiostatin is a ligand for integrin alphavbeta(3) but does not induce stress fiber formation upon integrin binding, suggesting that angiostatin is a potential integrin antagonist. Plasmin, the parent molecule of angiostatin and a major extracellular protease, induces platelet aggregation, migration of peripheral blood monocytes, and release of arachidonate and leukotriene from several cell types. In the current study, we found that plasmin specifically bound to alphavbeta(3) through the kringle domains and induced migration of endothelial cells. In contrast, angiostatin did not induce cell migration. Notably, angiostatin, anti-alphavbeta(3) antibodies, RGD-peptide, and a serine protease inhibitor effectively blocked plasmin-induced cell migration. These results suggest that plasmin-induced migration of endothelial cells requires alphavbeta(3) and the catalytic activity of plasmin and that this process is a potential target for the inhibitory activity of angiostatin.     

Regulation of angiostatin production by matrix metalloproteinase-2 in a model of concomitant resistance.

We have previously reported the identification of the endogenous angiogenesis inhibitor angiostatin, a specific inhibitor of endothelial cell proliferation in vitro and angiogenesis in vivo. In our original studies, we demonstrated that a Lewis lung carcinoma (LLC-LM) primary tumor could suppress the growth of its metastases by generating angiostatin. Angiostatin, a 38-kDa internal fragment of plasminogen, was purified from the serum and urine of mice bearing LLC-LM, and its discovery provides the first proven mechanism for concomitant resistance (O'Reilly, M. S., Holmgren, L., Shing, Y., Chen, C., Rosenthal, R. A., Moses, M. A., Lane, W. S., Cao, Y., Sage, E. H., and Folkman, J. (1994) Cell 79, 315-328). Subsequently, we have shown that systemic administration of angiostatin can regress a wide variety of malignant tumors in vivo. However, at the time of our initial discovery of angiostatin, the source of the protein was unclear. We hypothesized that the tumor or stromal cells might produce an enzyme that could cleave plasminogen sequestered by the primary tumor into angiostatin. Alternatively, we speculated that the tumor cells might express angiostatin. By Northern analysis, however, we have found no evidence that the tumor cells express angiostatin or other fragments of plasminogen (data not shown). We now report that gelatinase A (matrix metalloproteinase-2), produced directly by the LLC-LM cells, is responsible for the production of angiostatin, which suppresses the growth of metastases in our original model.     

Angiostatin's molecular mechanism: aspects of specificity and regulation elucidated

Tumor growth requires the development of new vessels that sprout from pre-existing normal vessels in a process known as "angiogenesis" [Folkman (1971) N Engl J Med 285:1182-1186]. These new vessels arise from local capillaries, arteries, and veins in response to the release of soluble growth factors from the tumor mass, enabling these tumors to grow beyond the diffusion-limited size of approximately 2 mm diameter. Angiostatin, a naturally occurring inhibitor of angiogenesis, was discovered based on its ability to block tumor growth in vivo by inhibiting the formation of new tumor blood vessels [O'Reilly et al. (1994a) Cold Spring Harb Symp Quant Biol 59:471-482]. Angiostatin is a proteolytically derived internal fragment of plasminogen and may contain various members of the five plasminogen "kringle" domains, depending on the exact sites of proteolysis. Different forms of angiostatin have measurably different activities, suggesting that much remains to be elucidated about angiostatin biology. A number of groups have sought to identify the native cell surface binding site(s) for angiostatin, resulting in at least five different binding sites proposed for angiostatin on the surface of endothelial cells (EC). This review will consider the data supporting all of the various reported angiostatin binding sites and will focus particular attention on the angiostatin binding protein identified by our group: F(1)F(O) ATP synthase. There have been several developments in the quest to elucidate the mechanism of action of angiostatin and the regulation of its receptor. The purpose of this review is to describe the highlights of research on the mechanism of action of angiostatin, its' interaction with ATP synthase on the EC surface, modulators of its activity, and issues that should be explored in future research related to angiostatin and other anti-angiogenic agents.     

Flavonoids inhibit VEGF/bFGF-induced angiogenesis in vitro by inhibiting the matrix-degrading proteases

Flavonoids have been proposed to act as chemopreventive agents in numerous epidemiological studies and have been shown to inhibit angiogenesis and proliferation of tumor cells and endothelial cells in vitro. Angiogenesis requires tightly controlled extracellular matrix degradation mediated by extracellular proteolytic enzymes including matrix metalloproteinases (MMPs) and serine proteases, in particular, the urokinase-type plasminogen activator (uPA)-plasmin system. In this study, we have investigated the antiangiogenic mechanism of the flavonoids, genistein, apigenin, and 3-hydroxyflavone in a human umbilical vein endothelial cell (HUVEC) model. The stimulation of serum-starved HUVECs with vascular endothelial growth factor/basic fibroblast growth factor (VEGF/bFGF) caused marked increase in MMP-1 production and induced the pro-MMP-2 activation accompanied by the increase in MT1-MMP expression. However, pretreatment with flavonoids before VEGF/bFGF stimulation completely abolished the VEGF/bFGF-stimulated increase in MMP-1 and MT1-MMP expression and pro-MMP-2 activation. Genistein blocked VEGF/bFGF-stimulated increase in TIMP-1 expression and decrease in TIMP-2 expression. Apigenin and 3-hydroxyflavone further decreased TIMP-1 expression below basal level and completely abolished TIMP-2 expression. VEGF and bFGF stimulation also significantly induced uPA expression, most strikingly the level of 33 kDa uPA, and increased the expression of PA inhibitor (PAI)-1. Genistein, apigenin, and 3-hydroxyflavone effectively blocked the generation of 33 kDa uPA, and further decreased the activity of the 55 kDa uPA and the expression of PAI-1 below the basal level. In conclusion, these data suggest that genistein, apigenin, and 3-hydroxyflavone inhibit in vitro angiogenesis, in part via preventing VEGF/bFGF-induced MMP-1 and uPA expression and the activation of pro-MMP-2, and via modulating their inhibitors, TIMP-1 and -2, and PAI-1.     

Angiostatin inhibits bone metastasis formation in nude mice through a direct anti-osteoclastic activity

Bone is a very common metastatic site for breast cancer. In bone metastasis, there is a vicious circle wherein bone-residing metastatic cells stimulate osteoclast-mediated bone resorption, and bone-derived growth factors released from resorbed bone promote tumor growth. The contribution of tumor angiogenesis in the growth of bone metastases is, however, unknown. By using an experimental model of bone metastasis caused by MDA-MB-231/B02 breast cancer cells that quite closely mimics the conditions likely to occur in naturally arising metastatic human breast cancers, we demonstrate here that when MDA-MB-231/B02 cells were engineered to produce at the bone metastatic site an angiogenesis inhibitor, angiostatin, there was a marked inhibition in the extent of skeletal lesions. Inhibition of skeletal lesions came with a pronounced reduction in tumor burden in bone. However, although angiostatin produced by MDA-MB-231/B02 cells was effective at inhibiting in vitro endothelial cell proliferation and in vivo angiogenesis in a Matrigel implant model, we have shown that it inhibited cancer-induced bone destruction through a direct inhibition of osteoclast activity and generation. Overall, these results indicate that, besides its well known anti-angiogenic activity, angiostatin must also be considered as a very effective inhibitor of bone resorption, broadening its potential clinical use in cancer therapy.     

An Inhibitor of the F1 subunit of ATP synthase (IF1) modulates the activity of angiostatin on the endothelial cell surface

Angiostatin binds to endothelial cell (EC) surface F(1)-F(0) ATP synthase, leading to inhibition of EC migration and proliferation during tumor angiogenesis. This has led to a search for angiostatin mimetics specific for this enzyme. A naturally occurring protein that binds to the F1 subunit of ATP synthase and blocks ATP hydrolysis in mitochondria is inhibitor of F1 (IF1). The present study explores the effect of IF1 on cell surface ATP synthase. IF1 protein bound to purified F(1) ATP synthase and inhibited F(1)-dependent ATP hydrolysis consistent with its reported activity in studies of mitochondria. Although exogenous IF1 did not inhibit ATP production on the surface of EC, it did conserve ATP on the cell surface, particularly at low extracellular pH. IF1 inhibited ATP hydrolysis but not ATP synthesis, in contrast to angiostatin, which inhibited both. In cell-based assays used to model angiogenesis in vitro, IF1 did not inhibit EC differentiation to form tubes and only slightly inhibited cell proliferation compared with angiostatin. From these data, we conclude that inhibition of ATP synthesis is necessary for an anti-angiogenic outcome in cell-based assays. We propose that IF1 is not an angiostatin mimetic, but it can serve a protective role for EC in the tumor microenvironment. This protection may be overridden in a concentration-dependent manner by angiostatin. In support of this hypothesis, we demonstrate that angiostatin blocks IF1 binding to ATP synthase and abolishes its ability to conserve ATP. These data suggest that there is a relationship between the binding sites of IF1 and angiostatin on ATP synthase and that IF1 could be employed to modulate angiogenesis.     

Generation of biologically active angiostatin kringle 1-3 by activated human neutrophils

The contribution of polymorphonuclear neutrophils (PMN) to host defense and natural immunity extends well beyond their traditional role as professional phagocytes. In this study, we demonstrate that upon stimulation with proinflammatory stimuli, human PMN release enzymatic activities that, in vitro, generate bioactive angiostatin fragments from purified plasminogen. We also provide evidence that these angiostatin-like fragments, comprising kringle domain 1 to kringle domain 3 (kringle 1-3) of plasminogen, are generated as a byproduct of the selective proteolytic activity of neutrophil-secreted elastase. Remarkably, affinity-purified angiostatin kringle 1-3 fragments generated by neutrophils inhibited basic fibroblast growth factor plus vascular endothelial growth factor-induced endothelial cell proliferation in vitro, and both vascular endothelial growth factor-induced angiogenesis in the matrigel plug assay and fibroblast growth factor-induced angiogenesis in the chick embryo chorioallantoic membrane assay, in vivo. These results represent the first demonstration that biologically active angiostatin-like fragments can be generated by inflammatory human neutrophils. Because angiostatin is a potent inhibitor of angiogenesis, tumor growth, and metastasis, the data suggest that activated PMN not only act as potent effectors of inflammation, but might also play a critical role in the inhibition of angiogenesis in inflammatory diseases and tumors, by generation of a potent anti-angiogenic molecule.     

Inhibition of endothelial cell proliferation by the recombinant kringle domain of tissue-type plasminogen activator

Tissue-type plasminogen activator (tPA) is a multidomain serine protease that converts the zymogen plasminogen to plasmin. tPA contains two kringle domains which display considerable sequence identity with those of angiostatin, an angiogenesis inhibitor. TK1-2, a recombinant kringle domain composed of t-PA kringles 1 and 2 (Ala(90)-Thr(263)), was produced by both bacterial and yeast expression systems. In vitro, TK1-2 inhibited endothelial cell proliferation stimulated by basic fibroblast growth factor, vascular endothelial growth factor, and epidermal growth factor. It did not inhibit proliferation of non-endothelial cells. TK1-2 also inhibited in vivo angiogenesis in the chick embryo chorioallantoic membrane model. These results suggest that the recombinant kringle domain of t-PA is a selective inhibitor of endothelial cell growth and identifies this molecule as a novel anti-angiogenic agent.     

Regulation of angiogenesis by extracellular matrix

During angiogenesis, endothelial cell growth, migration, and tube formation are regulated by pro- and anti-angiogenic factors, matrix-degrading proteases, and cell-extracellular matrix interactions. Temporal and spatial regulation of extracellular matrix remodeling events allows for local changes in net matrix deposition or degradation, which in turn contributes to control of cell growth, migration, and differentiation during different stages of angiogenesis. Remodeling of the extracellular matrix can have either pro- or anti-angiogenic effects. Extracellular matrix remodeling by proteases promotes cell migration, a critical event in the formation of new vessels. Matrix-bound growth factors released by proteases and/or by angiogenic factors promote angiogenesis by enhancing endothelial migration and growth. Extracellular matrix molecules, such as thrombospondin-1 and -2, and proteolytic fragments of matrix molecules, such as endostatin, can exert anti-angiogenic effects by inhibiting endothelial cell proliferation, migration and tube formation. In contrast, other matrix molecules promote endothelial cell growth and morphogenesis, and/or stabilize nascent blood vessels. Hence, extracellular matrix molecules and extracellular matrix remodelling events play a key role in regulating angiogenesis.     

Human kallikrein 6 activity is regulated via an autoproteolytic mechanism of activation/inactivation

Human kallikrein 6 (protease M/zyme/neurosin) is a serine protease that has been suggested to be a serum biomarker for ovarian cancer and may also be involved in pathologies of the CNS. The precursor form of human kallikrein 6 (pro-hK6) was overexpressed in Pichia pastoris and found to be autoprocessed to an active but unstable mature enzyme that subsequently yielded the inactive, self-cleavage product, hK6 (D81-K244). Site-directed mutagenesis was used to investigate the basis for the intrinsic catalytic activity and the activation mechanism of pro-hK6. A single substitution R80 --> Q stabilized the activity of the mature enzyme, while substitution of the active site serine (S197 --> A) resulted in complete loss of hK6 proteolytic activity and facilitated protein production. Our data suggest that the enzymatic activity of hK6 is regulated by an autoactivation/autoinactivation mechanism. Mature hK6 displayed a trypsin-like activity against synthetic substrates and human plasminogen was identified as a putative physiological substrate for hK6, as specific cleavage at the plasminogen internal bond S460-V461 resulted in the generation of angiostatin, an endogenous inhibitor of angiogenesis and metastatic growth.     

Secretion of phosphoglycerate kinase from tumour cells is controlled by oxygen-sensing hydroxylases

Solid tumour cells employ glycolytic enzymes including phosphoglycerate kinase (PGK) to make ATP when their supply of oxygen is limiting. PGK is also secreted by tumour cells and facilitates cleavage of disulfide bonds in plasmin, which triggers proteolytic release of the angiogenesis inhibitor, angiostatin. Although PGK production by tumour cells was enhanced by hypoxia, its secretion was inhibited. Inhibition of secretion correlated with decrease in angiostatin formation by the tumour cells. In contrast, hypoxia did not inhibit the secretion of the angiogenesis activator, vascular endothelial cell growth factor (VEGF). PGK secretion was reversed by normoxia and was under control of the oxygen-sensing protein hydroxylases, as inhibitors of this class of enzymes mimicked the effect of hypoxia on PGK secretion. Direct hydroxylation of PGK was not the mechanism by which the protein hydroxylases controlled its secretion. These findings show that production and secretion of PGK are regulated separately and indicate that oxygen and the protein hydroxylases can control not only gene expression but also protein secretion.     

Parathyroid hormone-related peptide is a naturally occurring,protein kinase A-dependent angiogenesis inhibitor

Angiogenesis is a highly regulated process that results from the sequential actions of naturally occurring stimulators and inhibitors. Here, we show that parathyroid hormone-related peptide, a peptide hormone derived from normal and tumor cells that regulates bone metabolism and vascular tone, is a naturally occurring angiogenesis inhibitor. Parathyroid hormone-related peptide or a ten-amino-acid peptide from its N terminus inhibits endothelial cell migration in vitro and angiogenesis in vivo by activating endothelial cell protein kinase A. Activation of protein kinase A inhibits cell migration and angiogenesis by inhibiting the small GTPase Rac. In contrast, inhibition of protein kinase A reverses the anti-migratory and anti-angiogenic properties of parathyroid hormone-related peptide. These studies show that parathyroid hormone-related peptide is a naturally occurring angiogenesis inhibitor that functions by activation of protein kinase A.     

血管抑素的临床应用研究进展

血管抑素是第一个被发现的肿瘤源性血管生成抑制因子,能抑制血管内细胞的增殖和迁移,从而抑制肿瘤的生长。通过一些实验方法能够检测肿瘤患者体内的血管抑素水平。血管抑素在未来的肿瘤治疗、诊断、预后判断和新生血管疾病的治疗中有着广阔的应用前景。     

Inhibitory effect of full-length human endostatin on in vitro angiogenesis.

Endostatin, a C-terminal product of collagen XVIII, is a very powerful angiogenesis inhibitor. In vivo experiments in mice indicate that endostatin dramatically reduces tumor mass without causing the onset of any resistance to the treatment. Recently, a 12-aa shorter human endostatin has been purified from plasma, but is ineffective in in vitro angiogenesis assays. Here we report that the full-length human recombinant endostatin has a potent inhibitory activity in in vitro angiogenesis assays. Two powerful angiogenic factors were used to stimulate endothelial cells: FGF-2 and VEGF-165. Endostatin prevented cell growth both in the basal condition and after stimulation with FGF-2 or VEGF-165. Migration of microvascular endothelial cells toward FGF-2 or VEGF-165 was impaired, both when cells were pretreated with the inhibitor and when endostatin was added together with the growth factors. Furthermore, experiments of inhibition of proliferation performed on nonmicroendothelial cells showed that endostatin was ineffective. This study indicates that human endostatin is a potent angiogenesis inhibitor and suggests its use in human anticancer therapy.     

Tumor-promoting phorbol esters induce angiogenesis in vitro

A crucial event during angiogenesis is the invasion of the perivascular extracellular matrix by sprouting endothelial cells. To investigate the possible role of proteases in endothelial cell invasiveness in vitro, bovine microvascular endothelial cells (BMEC) grown on collagen gels were treated with phorbol myristate acetate (PMA), a tumor promoter that markedly increases their production of collagenase and plasminogen activator. Whereas control BMEC were confined to the surface of the gels, PMA-treated BMEC invaded the underlying collagen matrix, where they formed an extensive network of capillary-like tubular structures. This phenomenon, which mimics some of the events occurring during angiogenesis in vivo, required protein synthesis and intercellular contact, was accompanied by collagen degradation, and was prevented by the metalloprotease inhibitor 1,10-phenanthroline.     

Angiostatin antagonizes the action of VEGF-A in human endothelial cells via two distinct pathways

Angiostatin consisting of the first four-kringle domains of the plasminogen potently inhibits angiogenesis in vitro and in vivo. However, the molecular mechanism of action whereby angiostatin mediates its inhibitory effect on proliferating endothelial cells remains elusive. We therefore used the proliferating cultured human umbilical vein endothelial cells (HUVECs) promoted by vascular endothelial growth factor A to identify the endogenous signaling elements that mediate the antiangiogenic effect of angiostatin. Treatment of HUVEC with angiostatin at a concentration known to inhibit cell proliferation and induce apoptosis resulted in induction of p53-, Bax-, and tBid-mediated release of cytochrome c into the cytosol. In addition, angiostatin also activated the Fas-mediated apoptotic pathway in part via up-regulation of FasL mRNA, down-regulation of c-Flip, and activation of caspase 3. These results suggest that the anti-angiogenic action of angiostatin is likely mediated by two distinct signaling pathways, one intrinsic mediated by p53 while the other extrinsic involved in FasL engagement and mitochondria dysfunction.     

Collagen XVIII/endostatin structure and functional role in angiogenesis

The angiogenesis inhibitor endostatin is a 20 kDA C-terminal fragment of collagen XVIII, a proteoglycan/collagen found in vessel walls and basement membranes. The endostatin fragment was originally identified in conditioned media from a murine endothelial tumor cell line. Endostatin inhibits endothelial cell migration in vitro and appears to be highly effective in murine in vivo studies. The molecular mechanisms behind the inhibition of angiogenesis have not yet been elucidated. Studies of the crystal structure of endostatin have shown a compact globular fold, with one face particularly rich in arginine residues acting as a heparin-binding epitope. It was initially suggested that zinc binding was essential for the antiangiogenic mechanism but later studies indicate that zinc has a structural rather than a functional role in endostatin. The generation of endostatin or endostatin-like collagen XVIII fragments is catalyzed by proteolytic enzymes, including cathepsin L and matrix metalloproteases, that cleave peptide bonds within the protease-sensitive hinge region of the C-terminal domain. The processing of collagen XVIII to endostatin may represent a local control mechanism for the regulation of angiogenesis.