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Keywords:

  • angiogenesis;
  • human vascular endothelial cells;
  • Matrigel assay;
  • adrenomedullin;
  • image analysis;
  • Cellular Potts Model

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

A recently proposed approach was used to model the self-organization into capillary-like structures of human vascular endothelial cells cultured on Matrigel. The model combines a Cellular Potts Model, considering cell adhesion, cytoskeletal rearrangement and chemotaxis, and a Partial Differential Equation model describing the release and the diffusion of a chemoattractant. The results were compared with the data from real in vitro experiments to establish the capability of the model to accurately reproduce both the spontaneous self-assembly of unstimulated cells and their self-organization in the presence of the pro-angiogenic factor adrenomedullin. The results showed that the model can accurately reproduce the self-assembly of unstimulated cells, but it failed in reproducing the adrenomedullin-induced self-organization of the cells. The extension of the model to include cell proliferation led to a good match between simulated and experimental patterns in both cases with predicted proliferation rates in agreement with the data of cell proliferation experiments. Developmental Dynamics 238:1951–1963, 2009. © 2009 Wiley-Liss, Inc.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

Angiogenesis, the development of new blood vessels from an existing vasculature, represents an important area of the actual biological research due to its involvement in various physiological and pathological conditions (Folkman,1995). The angiogenic cascade is a complex multistep process (Risau,1997), and numerous forms of in vitro assays have been developed (see Staton et al.,2004) to study specific steps, such as cell proliferation, migration, or differentiation. In this regard, assays that stimulate the formation of capillary-like structures (see Donovan et al.,2001) by endothelial cells (EC) have become increasingly popular in recent years, because they allow the study of the EC's intrinsic ability to self-organize to form vascular-like patterns. In the most extensively used assay of this type, EC are cultured on Matrigel, a gelatinous mixture of extracellular and basement membrane proteins derived from the mouse Engelbreth-Holm-Swarm sarcoma (Lawley and Kubota,1989). When EC are seeded onto this matrix, they attach to it and rapidly form a branching meshwork of tubules. This assay is presently considered as a reliable in vitro tool to identify substances with potential anti- or pro-angiogenic properties, allowing a qualitative and quantitative evaluation of the morphological changes the EC self-organization undergoes when the cells are stimulated with such factors. Examples include pharmacological trials (Guidolin et al.,2004; Martinez-Poveda et al.,2008; Basu et al.,2008), as well as studies focused on the identification of endogenous factors involved in the modulation of the angiogenic process (Baiguera et al.,2004; Ribatti et al.,2007; Albertin et al.,2009).

The morphogenesis of the two-dimensional, vascular-like, pattern generated by EC on Matrigel was the object of a computational model, recently proposed by Merks et al. (2006), aimed to characterize what cell behaviors are essential for the pattern formation and for its morphology. This approach identified a small set of experimentally confirmed endothelial cell behaviors that sufficed to quantitatively reproduce the observed in vitro capillary-like network formation. These behaviors include (a) interaction with the matrix and with the other cells through surface adhesion molecules, (b) cytoskeleton remodeling (Moore et al.,1998) to assume an elongated shape (Dye et al.,2004), and (c) secretion of a chemoattractant (Helmlinger et al.,2000) diffusing and decaying in the extracellular matrix (ECM) and motion up the chemoattractant (Gerhardt et al.,2003). On these bases, a computer simulation of the whole process was designed, providing patterns in good agreement with those spontaneously formed by human umbilical vein EC (HUVEC) when seeded on Matrigel. However, the capability of this model (involving only three basic cell behaviors: adhesion, shape remodeling, and chemotaxis) to simulate the EC self-assembly under the action of factors modulating angiogenesis was never experimentally tested.

Thus, in the present study the approach proposed by Merks and coworkers was used to perform numerical simulations of human saphenous vein EC (HSVEC) cultured on Matrigel and stimulated with a pro-angiogenic factor, namely the peptide adrenomedullin (AM). This peptide, belonging to a family of regulatory peptides including calcitonin, amylin, and calcitonin gene-related peptide (Poyner et al.,2002), plays a key role during the development of the vascular system, as demonstrated by Shindo et al. (2001) in their study on a strain of AM knockout mice showing that homozygotes (AM−/−) died in utero due to the poor angiogenesis in the placenta. When tested in vitro, AM was shown to exert a clearcut pro-angiogenic effect with enhancement of the capillary-like tube formation by human EC cultured on Matrigel (Ribatti et al.,2003; Guidolin et al.,2008). It acts through the G protein-coupled receptor calcitonin-like receptor (CLR), its specificity for AM being conferred by dimerization with the receptor activity modifying protein 2 (RAMP2) or 3 (RAMP3) (Poyner et al.,2002) leading to the AM1 and AM2 receptors, respectively. The angiogenic activity of AM has been reported to be mediated mainly by its binding to the AM1 receptor (Albertin et al.,2006; Guidolin et al.,2008) and involves the activation of mitogen-activated protein kinase and Akt cascades in EC (Kim et al.,2003; Miyashita et al.,2003). It has also been suggested (Guidolin et al.,2008) that these key signaling events, mediating the trophic action of the peptide, could be triggered by a transactivation of the vascular endothelial growth factor (VEGF)-receptor 2 (KDR) as a consequence of the binding of AM to its AM1 receptor.

The in silico results were compared with the data obtained from in vitro experiments with the aim of examining the model's ability to predict the pattern formed by human EC in both unstimulated and AM-stimulated conditions and of identifying possible extensions of the model leading to a better match with the experimental data. In this respect, a particular attention was focused on the role of cell proliferation in the morphogenesis of the capillary-like pattern.

RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

Cell Phenotype

Immunocytochemical analysis showed that cells extracted from samples of human saphenous vein were endothelial, because more than 95% expressed von Willebrand factor (Fig. 1A). Furthermore, no expression of smooth muscle alpha-actin was detected in the cell population (not shown).

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Figure 1. AE: Immunocytochemical visualization of von Willebrand factor (A), vascular endothelial growth factor (VEGF; B), KDR (C), Flt-1 (D), calcitonin-like receptor (CLR; E, upper panel), and receptor activity modifying protein 2 (RAMP2; E, lower panel) in cultured human saphenous vein endothelial cells (HSVEC). F: A visualization of the unspecific staining (obtained by omitting the primary antibody) is provided: weakly counterstaining with hematoxylin allows an easier identification of the cells.

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As illustrated in Figure 1B–E, the isolated HSVEC also exhibited a significant expression of the AM1 receptor (as indicated by the presence of both CLR and RAMP2), VEGF, and VEGF receptors (both Flt-1 and KDR). The presence of these markers was further confirmed by reverse transcriptase-polymerase chain reaction (RT-PCR; data not shown).

Matrigel Assay

Following seeding on Matrigel, no specific sign of cell death was observed and after 18 hr, the HSVEC had spread throughout its surface and self-organized to form branching anastomosing tubes with multicentric junctions that gave rise to a meshwork of capillary-like structures (Fig. 2A). When culture medium was admixed with AM (10−8 M), a higher morphogenetic effect was observed with the formation of a meshwork of increased complexity (see Fig. 2A). Furthermore, when compared to control HSVEC, AM-treated cells appeared able to develop a more elongated shape (Fig. 2B).

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Figure 2. A: Phase contrast micrographs illustrating the arrangement of human saphenous vein endothelial cells (HSVEC) into a meshwork of capillary-like tubular structures when cultured on Matrigel for 18 hr. Unstimulated, control, cells are shown in the left panel. The right panel shows the self-arrangement of the cells in the presence of 10−8 M adrenomedullin (AM). B: Toluidine-blue stained HSVEC cultured on Matrigel. AM-treated cells (right panel) exhibit a more elongated shape when compared with unstimulated EC (left panel).

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Image analysis (Table 1) confirmed these observations. Although the mean length of the branches of the formed network resulted very similar in both unstimulated and AM-stimulated cell cultures, the capillary-like meshwork generated by AM-treated cells was significantly more complex and larger, as indicated by the significant increase of both its dimensional (percent area covered by HSVECs and total length of the network per field) and topological parameters (number of meshes and branching points per field).

Table 1. Morphometry of the In Vitro Capillary-Like Patterns (N=9)a
 Control (mean ± SEM)AM (mean ± SEM)Two-sample t-test
  • a

    AM, adrenomedullin.

Area%8.63 ± 0.4511.44 ± 0.61p<0.01
Total length (mm/mm2)3.62 ± 0.194.99 ± 0.23p<0.01
Meshes (number/mm2)1.83 ± 0.253.0 ± 0.49p<0.05
Branching points (number/mm2)17.50 ± 0.8029.83 ± 3.50p<0.01
Branch length (μm)138.9 ± 3.5144.6 ± 8.1p=0.53

As reported in Table 2, no significant changes in cell size were detected between untreated and AM-treated HSVEC. After treatment, however, a moderate (approximately 16%), but significant, increase in cell elongation was observed. As far as the mRNA expression for VEGF and/or VEGF-R was concerned, no changes were detected by RT-PCR in HSVECs following AM stimulation, indicating that the trophic and morphogenetic effect of AM was not associated with an increased expression of these markers. Immunocytochemical analysis (data not shown) provided further support to this finding.

Table 2. HSVEC Features
Morphometrics (N=50):Control (mean ± SEM)AM (10−8 M) (mean ± SEM)Two-sample t-test
  1. aHSVEC, human saphenous vein endothelial cell; AM, adrenomedullin; VEGF, vascular endothelial growth factor.

Area (μm2)653.59 ± 25.86660.48 ± 20.44p=0.835
Elongation (μm)125.46 ± 4.22145.7 ± 4.69p<0.01
VEGF-related gene expression changes following AM (10−8 M) stimulation (N=9):
 (Gene regulation factor ± SEM)One-sample t-test
VEGF1.100 ± 0.127p=0.454
Flt-1 (VEGF-R1)0.960 ± 0.093p=0.668
KDR (VEGF-R2)1.160 ± 0.133p=0.263

Simulation of the Pattern Formation

The parameters involved in the model used to simulate the self-assembly of EC on Matrigel are summarized in Table 5. As outlined in the Experimental Procedures section, they were defined consistently with the experimental findings and/or available literature data.

Table 5. Table of Model Parametersa
ParameterSymbolModel valueReference
  • a

    AM, adrenomedullin; VEGF, vascular endothelial growth factor.

Cell features:   
Initial cell densityNa185 cells/mm2Cell culture measurements (see Table 2)
Target areaA655 μm2
Target elongationL 
 Unstimulated cells 125 μm
 AM-treated cells 145 μm
Resistance to changes in sizeλA25
Resistance to changes in elongationλL25
Adhesion:   
 Cell– CellJcc10Sensitivity analysis (Merks et al.,2006)
 Cell– MatrixJcm20
Chemotaxis:   
 VEGF diffusion VEGF clearance VEGF sourceDϵα10−13 m2 s−11.8 . 10−4 s−11.8 . 10−4 s−1(Distler et al., 2004; Fernandez Sauze et al., 2003)
Strength of chemotactic responseχ8000Derived from the parameter study (see Table 4)
Table 4. Multivariate Mahalanobis Distance as a Function of the Chemotactic Strength (χ)a
χ50007000800010000
  • a

    The Mahalanobis distance is used as an estimate of the match between the patterns (after 18 h) generated by the basic model simulating an unstimulated (control) human saphenous vein endothelial cell (HSVEC) culture and those observed on real samples. The minimum Mahalanobis distance indicates the best match.

Mahalanobis distance2.041.911.0915.20
Basic model.

When the morphogenesis of the pattern formation was simulated based on the available experimental data concerning control untreated cells, both the static patterns after 18 hr of simulated time and the time course of pattern formation coincided quite well with those observed on cell cultures from both a qualitative and a quantitative (Fig. 3A–C) point of view. Moreover, it has to be observed that with the choice made (see the Experimental Procedures section) for the model space and time scales and diffusion parameters the mean virtual cell velocity resulted of 11 ± 5 μm/hr (mean ± std), with some cells moving up to 30 μm/hr, agreeing quite well with in vivo observation of endothelial cell motility during vasculogenesis (Rupp et al.,2004).

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Figure 3. A: Typical patterns generated by the basic model (see text) tuned to simulate the in vitro organization of unstimulated human saphenous vein endothelial cells (HSVEC) after 18 hr of culture. B: Each simulated pattern underwent the same morphometric analysis performed on real samples. The mean length of the branches forming the simulated network resulted of 146.1 ± 2.7 μm, a value which is not statistically different (P = 0.117) from the one observed on real samples (see Table 1). The other four parameters (Area%, Length, Number of meshes, and Number of branching points) characterizing the capillary-like meshwork are shown as a bar plot. No significant differences were detected between the simulated and experimental patterns corresponding to 18 hr of cell culture. C: Number of branching points over time for in vitro and in silico capillary-like patterns illustrating that the time course of pattern formation by unstimulated HSVEC is also well captured by the basic model. D,E: On the contrary, the patterns generated by the basic model to simulate adrenomedullin (AM) -treated cells at 18 hr of culture (D) significantly differ in their morphometric features from those observed experimentally (E). F: The time course of pattern formation by AM-treated HSVEC is also inaccurately simulated by the basic model. Data are means ± SEM. P values are shown when nonsignificant; *P < 0.05; **P < 0.01 (two-samples Student's t-test).

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On the contrary, when the basic model was run to simulate AM-treated cells the morphology of the obtained patterns resulted more complex compared to the control condition, but still significantly different than the one observed experimentally (Fig. 3D–F). Thus, despite the higher target cell elongation characterizing the AM-stimulated cells, the model based only on three basic endothelial cell behaviors (adhesion, elongation, and chemotaxis) seemed unable to accurately replicate the AM-induced pattern of HSVEC self-organization.

Extended model.

To test the hypothesis that cell proliferation could play a role in the morphogenesis of the capillary like patterns formed by AM-stimulated HSVEC seeded on Matrigel, different numbers of mitotic events were allowed to occur in the system during the 18 hr of simulated time, trying to derive predictions on the proliferation level leading to the best match between the patterns obtained and those observed experimentally. The results are illustrated in Figure 4A.

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Figure 4. A: The multivariate Mahalanobis distance between the set of values of the morphometric parameters characterizing the patterns provided by the extended model (see text) and the set of values similarly measured on real samples was used as an estimate of the match between simulated and experimental patterns. In the figure, such a distance is plotted as a function of the assumed number of mitoses (expressed as percent of the total number of cells) allowed in the cell population during the 18 hr. The dotted line indicates the 95% confidence limit around the 0 value of the distance. The highest similarity with the experimental patterns (i.e., the minimum distance) was found to correspond to a percentage of 0% of mitoses for unstimulated cells (left panel) and of 13% for adrenomedullin (AM) -treated human saphenous vein endothelial cell (HSVEC; right panel). B: Typical pattern generated by the extended model to simulate AM-treated cells undergoing a 13% of mitoses during the 18 hr of simulated time. C: The patterns obtained under this condition are characterized by a mean length of the meshwork branches of 147.8 ± 5.6 μm, a value statistically equivalent (P = 0.747) to the one observed on real samples (see Table 1). The other morphometric features evaluated are shown as a bar plot. As illustrated, no significant differences were detected when compared with the values observed on real samples. D: The time course of pattern formation by AM-stimulated HSVEC is also quite well simulated by the extended model. Data are means ± SEM. P values are shown (two-samples Student's t-test).

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As far as untreated cells are considered, a good similarity between simulated and experimental patterns was obtained when the number of mitoses allowed in the system led to a percentage increase in cell number ranging from 0% to approximately 7%, with the best match (identified by the minimum value of the multivariate Mahalanobis distance) corresponding to the condition where no proliferation occurred.

When the model was run to simulate AM-stimulated cells, the percentage increase in cell number needed to obtain a good similarity between simulated and experimental patterns ranged between 13% and 16%, with the best match corresponding to a percentage of approximately 13%.

As illustrated in Figure 4B–D, applying such a condition during the simulations led to patterns exhibiting morphometric features statistically equivalent to those observed in the AM-stimulated cell cultures.

Cell Proliferation Assay

As demonstrated by BrdU (5′-bromo-2′-deoxyuridine) incorporation experiments (Fig. 5A), when seeded on Matrigel, HSVEC still maintain some proliferative activity, which appeared enhanced by the treatment with AM (10−8 M). The results of cell counting (Fig. 5B) showed that, in unstimulated cell cultures, the increase in cell number after 18 hr was quite low (approximately 4%) when compared with the baseline value, while it was significantly higher (approximately 14%) following AM stimulation. As illustrated, the predictions derived from the extended model resulted in close agreement with these experimental findings.

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Figure 5. A: Fluorescence images of unstimulated (left panel) and adrenomedullin (AM) -treated (right panel) human saphenous vein endothelial cell (HSVEC). DAPI (4′,6-diamidine-2-phenylidole-dihydrochloride) stained nuclei are shown on the left side of each panel, proliferating cells (as indicated by their BrdU [5′-bromo-2′-deoxyuridine] -positive nucleus) are shown on the right side. B: The increase in cell number during the 18 hr of the experiment predicted by the extended model for both unstimulated and AM-treated HSVEC is in good agreement with the results of cell counts performed on real samples. Data are the mean percent ratio of the number of cells after 18 hr on Matrigel and the number of cells at baseline. No significant differences were detected between model predictions and experimental tests (two-samples Student's t-test).

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DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

In vitro angiogenesis assays offer the opportunity to investigate angiogenic mechanisms with a speed and simplicity that cannot be achieved using in vivo assays. In particular, the tubule formation Matrigel assay has become a widely used method to investigate a specific and key aspect of the angiogenic pathway, i.e., the intrinsic ability of endothelial cells to self-organize to form vascular-like patterns, and to assess the overall effect on this process of administered treatments. In the study of such a complex biological process, involving a large set of interacting components, the importance of using a combination of computation and empirical observation is of particular relevance, because detailed knowledge of the parts of a system usually provides only limited insight into the dynamics of a system as a whole (see Goncharova and Tarakanov,2007). In this respect, mathematical modeling provides a tool by which we may have an integrated view of the essential cell behaviors leading to the self-assembly, of their relative importance, and of the effect on the global system of their modulation. Of course, it is only through experimentation that we can determine whether models accurately describe real biology.

As far as the self-organization of EC in vitro is concerned, several modeling approaches have generated static patterns qualitatively resembling those observed in vitro (Manoussaki et al.,1996; Gamba et al.,2003; Serini et al,2003; Murray,2003; Namy et al.,2004; Ambrosi et al.,2004). Most of them are macroscopic models, treating the system as a continuous substance with bulk properties. However, being that the self-organization of the EC when cultured on Matrigel is the result of several intimately linked single-cell behaviors (Donovan et al.,2001), a cell-centered approach to modeling (Merks and Glazier,2005) could be more appropriate, because it provides a more detailed description of a system of this type, often reproducing experimental observations missing from continuum models. The computational model of in vitro angiogenesis recently proposed by Merks et al. (2006), provided a significant advancement on this topic being able to describe the time-course of the in vitro angiogenetic process in a good agreement with the experimental observations. The authors identified three single-cell behaviors, including cell adhesion, chemotaxis, and cytoskeleton rearrangement, which sufficed to quantitatively reproduce the spontaneous in vitro capillary-like structure formation and subsequent remodeling by HUVEC when cultured on Matrigel. No information, however, is available on the ability of this model to simulate the pattern formed by EC under the influence of factors modulating the angiogenic process. This point was addressed in the present study, where the model was tested in a more general (commonly applied during a Matrigel assay) experimental setup involving not only unstimulated (control) EC, but also cells stimulated with the pro-angiogenic factor AM.

Consistent with the results obtained by Merks et al. (2006) on HUVEC, the model based on the three above-mentioned basic cell behaviors was able to accurately reproduce the self-assembly of cultured unstimulated HSVEC, confirming that cell elongation, in conjunction with autocrine secretion of a chemoattractant, results in a cell shape-dependent motility representing the key factor driving the formation of vascular-like morphologies by endothelial cells in vitro. The chemoattractant considered in the present study was characterized by properties (slow diffusion and quite rapid inactivation) consistent with those of several growth factors of the VEGF family (Distler et al.,2003), which is considered the principal chemoattraction system driving the formation of EC networks in vitro (Helmlinger et al.,2000; Gamba et al.,2003; Serini et al.,2003). It has to be pointed out, however, that some debate still exists about the key autocrine chemoattractants involved in in vitro vascular patterning (see Merks et al.,2008, for a discussion) and only future experimental work will help to fully elucidate this aspect.

As expected (see Ribatti et al.,2003; Fernandez-Sauze et al.,2004; Guidolin et al.,2008), when the cells were stimulated with AM, an enhancement of the capillary-like tube formation was observed, leading to a meshwork of increased extension and complexity. Consistently with previously reported data (Fernandez-Sauze et al,2004; Guidolin et al.,2008), the AM action was not associated with changes in the expression of VEGF and/or its receptors. The experimental results of the present study also showed that the AM treatment induced a significant increase in the capability of the cells to elongate, a feature potentially very important for the formation of a capillary-like pattern of enhanced complexity, as demonstrated by the analysis reported by Merks et al. (2006). When the input parameters of the model were defined consistently with these experimental findings, however, the model failed in accurately reproducing the AM-induced self-assembly of the HSVEC. Thus, because cell adhesion plays a minor role in determining the overall morphology of the pattern (see Merks et al.,2006), this result indicated that other cell behaviors play a role in the process and should be included in the model to better fit the experimental data.

In this regard, cell proliferation deserves consideration. In fact, it has been demonstrated that several pro-angiogenc factors, including AM, significantly stimulate EC proliferation (Ribatti et al.,2005,2007). Thus, although seeding on Matrigel mainly shifts EC toward differentiation and self-organization (Staton et al.,2004), the possibility exists that the presence (or the stimulation) of some degree of proliferative activity could influence the morphology of the resulting pattern. To test such a hypothesis, in the present study the basic model by Merks et al. was extended to include cell proliferation. Our extended model allowed the prediction of the amount of mitotic events in the system, leading to the best match between simulated and experimental patterns. The extended model indicated that a very low (∼ 0%) proliferation level sufficed to reproduce the capillary-like patterns generated by untreated cells, while at least a 13% increase in cell number was needed to accurately simulate the AM-induced self-organization of EC. Despite the oversimplification of the proliferation scheme used here compared to other and more sophisticated implementations (see Turner and Sherratt,2002; Bauer et al.,2007), these predictions of the extended model surprisingly showed consistency with the data provided by proliferation experiments, indicating that the extended model had the power to capture, at least on average, the essential features of the process.

In recent years, modeling efforts similarly based on the cellular Potts model proved useful to study contact-inhibited chemotaxis as a mechanism of vascular patterning (Merks et al.,2008) and to describe the vasculogenic potential of bone-marrow macrophages from patients with multiple myeloma (Guidolin et al.,2007) and the mechanisms of tumor-induced angiogenesis (Bauer et al.,2007). In this context, the results of the present study further support the cellular Potts model as a particularly well suited quantitative framework to get a better understanding of the biophysical mechanisms of vascular development, to test hypotheses and to derive suggestions for new experimental tests.

EXPERIMENTAL PROCEDURES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

Reagents

Human AM was purchased from Phoenix Europe (Karlsruhe, Germany). Matrigel was obtained from Becton Dickinson Labware (Bedford, MA) and Reverse Transfection siPort NeoFx from Ambion (Austin, TX). Mouse anti-Flk-1/KDR Ab (clone CH-11) was provided by Upstate (Charlottesville, VA), rabbit anti-CRLR (sc-30028), rabbit anti-VEGF (sc-507), and rabbit anti-Flt-1 (sc-9029) Ab by Santa Cruz Biotechnology (Santa Cruz, CA). Horseradish peroxidase (HRP) -conjugated anti-mouse/rabbit IgG (ImmPress universal reagent) was purchased from Vision Biosystems (Norwell, MA). Anti–von Willebrand and anti-smooth muscle actin Ab, EC basal medium (EBM), fetal calf serum (FCS), bovine serum albumin (BSA), phosphate buffered saline (PBS), and all other chemicals and reagents were provided by Sigma-Aldrich Corp. (St. Louis, MO).

Endothelial Cells

Human saphenous vein ECs (HSVEC) were harvested from samples of the vein obtained during surgery as previously detailed (see Guidolin et al.,2008; Albertin et al.,2009). The endothelial phenotype of the isolated cells was confirmed by immunocytochemistry, using anti–von Willebrand factor and anti-smooth muscle actin antibodies. In all the experiments, cultures of HSVECs from the second to the fifth passage were used.

In Vitro Angiogenesis Assay

Growth factor-depleted Matrigel was thawed on ice overnight, and spread evenly over each well (50 μl) of a 24-well plate. The plates were incubated for 30 min at 37°C to allow Matrigel to gel, and ECs were seeded (3 × 104 cells/well) and cultured in basal medium, or supplemented with AM. The peptide was administered at the concentration of 10−8 M, the lower concentration exhibiting a significant pro-angiogenic activity in vitro (see Guidolin et al.,2008). After 6, 12, and 18 hr of incubation at 37°C, cultures were observed under the microscope at a primary magnification of ×5. Phase contrast images (each corresponding to an area of approximately 0.85 mm2) were recorded (five fields for each well: the four quadrants and the center) and saved as TIFF files.

Image analysis of the cell pattern was carried out according to a previously detailed method (Guidolin et al.,2004) and the following parameters were estimated (see Fig. 6): percent area covered by ECs, total length of EC network per field, length of the single branches, and number of meshes and branching points per field. Morphometric features (area and elongation) of 50 single cells per sample exhibiting a clearcut angiogenic phenotype were also estimated at a primary magnification of ×20 by using an interactive image analysis approach (Dispersyn et al.,2001). All the measurements were performed by using the QWin image analysis software (Leica Microsystems, Cambridge, UK).

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Figure 6. Image analysis of the pattern formed by the endothelial cells on Matrigel (Guidolin et al.,2004). After cell discrimination and removal of isolated cell profiles, the percentage area covered by the cell pattern was estimated. Further processing steps were then applied to extract the binary skeleton of the pattern (white lines) to estimate the number of closed meshes, the number of branching points (white dots) and the length of the single branches (i.e., the distance between two branching points or a branch point and a free end).

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Cell Proliferation Assay

ECs were seeded on Matrigel (3 × 104 cells/well) as described before and cultured in basal medium or supplemented with AM (10−8 M). After 3 hr of incubation, to verify the presence of proliferating cells the 5′-bromo-2′-deoxyuridine (BrdU) Labeling and detection kit I (Roche Diagnostics, Mannheim, Germany) was used according to the manufacturer directions. Briefly, BrdU (10−5 M) was added to the cell cultures and ECs were incubated for a further 15 hr. After washing in PBS, cells were fixed in an ethanol-based solution (15 mM glycine in ethanol) for 30 min at 4 °C and then incubated with a fluorescein conjugated monoclonal anti-BrdU antibody at a dilution of 1:10 for 45 min at 37°C in a humid chamber. Finally, counterstaining with DAPI (4′,6-diamidine-2-phenylidole-dihydrochloride) was applied to visualize the whole population of cell nuclei. Fluorescence images were recorded at a primary magnification of ×10 (five fields for each well: the four quadrants and the center) using a digital camera (DFC 480, Leica Microsystems, Wetzlar, Germany) connected to a DM-IRE2 inverted microscope (Leica Microsystems, Wetzlar, Germany) and saved as TIFF files.

The change in cell number was evaluated by counting the DAPI stained nuclei at baseline and after 18 hr of culture on Matrigel. The QWin image analysis software (Leica Microsystems, Cambridge, UK) was used for the analysis.

RT-PCR and Immunocytochemistry

To detect the expression of mRNA for VEGF, VEGF receptors, RAMP-2 and the changes it underwent as a consequence of the AM treatment, ECs were harvested and total RNA was extracted, purified, and reverse transcribed to cDNA (Albertin et al.,2005a). Real-time PCR was then carried out in an I-Cycler iQ detection system (Bio-Rad Laboratories, Milan, Italy), as detailed previously (Albertin et al.,2005b), using the primers reported in Table 3. The PCR program included a denaturation step at 95°C for 3 min, 40 cycles of two amplification steps (95°C for 15 sec and annealing extension at 60°C for 30 sec) and melting curve (60–90°C with a heating rate of 0.5°C/10 sec). During the exponential phase, the fluorescence signal threshold was calculated and the fraction number of PCR cycles required to reach the threshold (cycle threshold, Ct) was determined. Ct values decreased linearly with increasing input target quantity and were used to calculate the relative mRNA expression, according to the mathematical quantification model proposed by Pfaffl (2001). Following this method, the AM-induced variation in mRNA expression with respect to unstimulated control samples was estimated by calculating the regulation factor (Pfaffl et al.,2002) for each analyzed gene. When up-regulation or down-regulation of the gene occurs as an effect of the applied stimulus, this parameter is significantly greater or lower than 1.0, respectively. All samples were amplified in duplicate and glyceraldehyde 3-phosphate dehydrogenase (GAPDH) expression was used as a reference to normalize the data. The specificity of the amplification was tested at the end of each run by melting curve analysis, using the I-Cycler software 3.0.

Table 3. Sense and Antisense Sequences Used as RT-PCR Primersa
GenePrimersbpAccession no.
  • a

    Each analyzed gene is reported together with the accession number identifying it in the NCBI Nucleotide data bank. RT-PCR, reverse transcriptase-polymerase chain reaction; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; VEGF, vascular endothelial growth factor; RAMP-2, receptor activity modifying protein 2.

GAPDH5′ -CTC-TCT-GCT-CCT-CCT-GTT-CGA-C- 3′69NM_002046.3
5′–TGA-GCG-ATG-TGG-CTC-GGC-T- 3′
VEGF5′–GCC-TTG-CTG-CTC-TAC-CTC-CAC- 3′73NM_001025368
5′–GAT-TCT-GCC-CTC-CTC-CTT-CTG-C- 3′
FLT-15′ -GTT-CAA-GGA-ACC-TCG-GAC-AA- 3′192NM_002019
5′ -GCT-CAC-ACT-GCT-CAT-CCA-AA- 3′
KDR5′–GTT-CTT-GGC-TGT-GCA-AAA-GT- 3′43NM_002253.1
5′–GTC-TTC-AGT-TCC-CCT-CCA-TT- 3′
RAMP-25′–CTG-CTG-GGC-GCT-GTC-CTG-AA- 3′75NM_005854.1
3′–TTC-TGA-CCC-TGG-TGT-GCC-TGT-G- 3′

Immunocytochemistry was used to verify the expression in the ECs of the CRLR, RAMP-2, VEGF, and VEGF receptor proteins, and the changes induced by AM treatment. EC from the third passage were seeded (2 × 104 cells/well) on fibronectin-coated cover slides on a 24-well plate. After 24-hr incubation with a medium containing or not containing AM (10−8 M), they were fixed in 4% paraformaldehyde in PBS, treated with 0.1% Triton X-100 in PBS, and incubated with the blocking solution (3% BSA in PBS) for 60 min. The blocking solution was then removed and ECs were incubated overnight at 4°C with one of the following primary antibodies: rabbit anti-CRLR, rabbit anti-RAMP2, rabbit anti-VEGF, rabbit anti-Flt-1, or mouse anti-KDR. Cells were then washed in PBS for three times and incubated with HRP-conjugated anti-mouse/rabbit IgG for 30 min at room temperature. After rinsing in PBS, 3,3′-diaminobenzidine tetrachloride was applied to visualize the reaction product. To verify the specificity of the immunostaining, some sample (negative control) was similarly processed omitting the primary antibody as well as using primary antibodies preadsorbed with antigen excess.

Simulation Model

The basic model.

To study the influence of relatively simple cell behaviors on the morphogenesis of the observed patterns, the approach recently proposed by Merks et al. (2006) was used. From a computational point of view, the model proposed by Merks et al. is basically a combination of the well-known Glazier and Graner's (1993) Cellular Potts Model (CPM), modeling the cell movements, and of a Partial Differential Equation (PDE) model describing the release and the diffusion of a chemoattractant.

CPM is a simulation technique representing cells on a rectangular numerical grid (see Fig. 7A) as patches of lattice sites, x, with identical nonzero indices σx, while an index value of 0 identifies the sites corresponding to the extracellular matrix (ECM). Grid points at patch interfaces represent cell surfaces and the interaction between cell surfaces is modeled by defining coupling constants Jσxσx, representing the adhesion energy involved in the specified interaction (Glazier and Graner,1993; Turner and Sherratt,2002). Each cell also has a set of attributes, including a “target” area and elongation, which pose some constraint on the possible cell shape changes. In the CPM framework, the state of the cells with all their interactions and constraints are described by the following effective energy function (Merks et al.,2004):

  • equation image(1)

where x represents the eight neighbors of x′, λA, and λL represent resistances to changes in size and in elongation, respectively, Aσ and Lσ are the “target” values for cell area and length, aσ and lσ are the actual cell area and length values, and the Kronecker delta is δx,y = {1 if x=y; 0 if x≠y}.

thumbnail image

Figure 7. Schematic representation of the Cellular Potts Model (Glazier and Graner,1993) A: Cells are represented on a numerical grid as domains of pixels with identical index σI (shown as a specific shade of gray), while the extracellular matrix is the set of the remaining pixels (white pixels) having σ = 0 by convention. Connections between neighboring lattice sites of unlike index (some of them are indicated with arrows) represent membrane bonds, with a characteristic bond energy J, which depends on the pair of objects in contact and determine the strength of their adhesion. In the present study, all the cells are of the same type and the J coefficients can assume only two values corresponding to a cell–cell (JσIσj) and to a cell–matrix (JσI0) adhesion, respectively. Furthermore, because biological cells generally have a fixed range of sizes and shapes, additional elastic energy terms are considered whenever deviations from a target volume or elongation occur. All these contributions led to the Eq. [1], representing the energy of the system at each time instant. B: To mimic cytoskeletally driven membrane fluctuations, we randomly chose a lattice site x and attempt to copy its index σx into a randomly chosen neighboring lattice site x′. We then calculate how much the energy would change if we performed the copy. As detailed in the text, if the energy decreases, we accept the attempt; otherwise, we accept it with Boltzmann-weighted probability.

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By repeatedly replacing a value at a cell interface by a neighboring grid point's value (see Fig. 7B), it is possible to mimic active, random extensions and retractions of filopodia and lamellipodia. If the resulting variation in effective energy (ΔE) is negative, then the cell change will be accepted; conversely, if ΔE is positive, then the cell change will be accepted with Boltzmann-weighted probability (Merks et al.,2004):

  • equation image(2)

where the parameter β is a constant representing a scale factor for all the energy terms in Eq. (1). The preferential extension of filopodia in the direction of chemoattractant gradients can be implemented by including an extra reduction of energy whenever the cell protrudes into an area with a higher concentration of the chemoattractant:

  • equation image(3)

where x′ is the neighbor into which site x moves (i.e., copies its value), χ is the strength of the chemotactic response, and c(x) is the local concentration of the chemoattractant.

At each time instant, the concentrations c(x) can be estimated from the following diffusion PDE (Gamba et al.,2003; Merks et al.,2004):

  • equation image(4)

where α is the rate at which the cells release chemoattractant, ϵ is the clearance rate of the chemoattractant, and D its diffusion coefficient. The Kronecker delta simply indicates that the release occurs at the cells locations, while the factor is cleared in the ECM.

The extended model: inclusion of proliferation.

An extended model, including cell proliferation, was used to test if the presence of mitotic events in the system could allow a more accurate replication of the morphology of the pattern formed by the endothelial cells.

To this end, a very simplified approach was followed, without explicitly modeling the endothelial cell cycle. When, during a simulation, a mitotic event had to occur, a cell was random selected and divided in two child cells through its center of mass along the axis of minimum length (Mombach and Glazier,1996). The two child cells (of approximately the same size) inherited the characteristics of adhesion, chemotaxis, target size, and elongation common to any other cell in the system and evolved accordingly.

Simulation details.

All the simulations were performed by using the CompuCell3D environment (Cikcovski et al.,2007; see also http://www.compucell3d.org) and Python scripts specifically developed by the authors (the code is provided in the Supp. Materials, which are available online). Briefly, for the computer simulations of the system, we used a 300 × 300 CPM lattice, where each lattice site represents an area of 9 μm2. Thus, the simulated area is of 0.81 mm2, a value comparable to the area of the fields used to sample the cell cultures. Several virtual cells consistent with the experimentally used cell density was then generated on the grid, with each cell initially defined to occupy a set number of lattice points equal to its “target” area around a randomly chosen position within the grid. The dynamics of the system according to the above-described processes was then simulated by using the Metropolis algorithm (Metropolis et al.,1953). According to this procedure, the system evolves through discrete time steps (Monte-Carlo steps or MCS), which in our simulations corresponded to 30 sec of real time. Thus, 2,160 MCS are needed to cover the 18 hr of the in vitro experiments.

During each MCS the actual distribution of the chemoattractant was estimated from the Eq. [4]. It was solved numerically according to a finite-difference scheme on a lattice that matches the CPM lattice, using 15 diffusion steps per MCS with Δx = 3 μm and Δt = 2 s. n (where n is the number of sites in the lattice) random choices of a CPM lattice site, x, were then performed, and for each chosen site, a nearest neighbor, x′, was selected also at random. The effect on Eq. [1] of copying the value of x into x′ was then investigated and the change accepted or refused according to the above-described criterion (with β = 5).

To predict the amount of cell mitoses leading to the best match with the experimental patterns, simulations were also performed, in which different amounts of mitotic events were allowed to occur in the system. During these runs of the extended model, the required mitotic events were simply uniformly distributed throughout the 2,160 MCS.

For each condition considered, 10 simulations were performed, and the resulting patterns recorded. The morphometric parameters characterizing the simulated patterns were then obtained with the same procedure applied to the images from real samples.

Parameters.

Whenever possible, the parameters involved in the model were defined consistently with the experimental findings. In particular, cell attributes, such as target size and elongation (see Eq. [1]) were based on cell culture measurements. Thus (see Table 1), a value of 655 μm2 was assumed as target area for the cells (both untreated and AM-treated), while a target elongation of 125 μm and 145 μm was assigned to control and AM-stimulated cells respectively. Cell resistances (λA and λL in Eq. [1]) were chosen large enough to maintain the size and elongation close to the observed values.

Because endothelial cells do adhere quite strongly through adherent junctions (Gory-Fauré et al.,1999), the adhesion settings to apply in Eq. [1] have to be adhesive, i.e., the following condition must hold: Jcell,matrix ≥ Jcell,cell/2 (Merks et al.,2004). Provided such a condition is satisfied, the absolute value of the J coefficients does not influence significantly the formed pattern for a wide range of values, as demonstrated by the “parameter sensitivity analysis” reported by Merks et al. (2006). Thus, in the present study the following (mild) settings were applied: Jcc = 10 between the endothelial cells and Jcm = 20 between the cells and the matrix.

As far as the diffusion of the chemoattractant is concerned (see Eq. [4]), the same diffusion parameters proposed by Merks et al. (2006) were applied (D = 10−13 m2s−1; ϵ = 1.8 × 10−4 s−1; α = ϵ = 1.8 × 10−43 s−1), because they seem consistent with the average diffusion characteristics of VEGF (Distler et al.,2003), the factor considered the principal chemoattractor expressed by endothelial cells in culture (Helmlinger et al.,2000), and with the experimental data provided by Fernandez-Sauze et al. (2004) on VEGF secretion by endothelial cells on Matrigel.

Because no AM-induced changes in the VEGF system were experimentally observed, the chemotactic strength (χ in the Eq. [3]) was always kept to a fixed value. Such a value certainly depends on the amount of receptors for the chemoattractant expressed by the cells (Shi and Duke,1998), but it is very hard to express in measurable units and to obtain it experimentally. Thus, a parameter study was performed, in which a range of values for χ was tested to find the one leading to the best simulation of the pattern generated by unstimulated (control) endothelial cells after 18 hr of cell culture. The result is reported in Table 4.

A list of all parameter values used in the present study is provided in Table 5, including references.

Statistics

Statistical comparisons of the morphometric parameters characterizing the patterns generated on Matrigel by AM-treated and control cells were performed by two-sample Student's t-test. Data were processed by using a statistical analysis software (GraphPad Prism 3.03, Graphpad Software Inc., San Diego, CA), and α ≤ 0.05 was considered statistically significant. The same approach was applied to statistically compare the experimental results on HSVEC with those provided by the simulation model.

A multivariate approach was used to identify the amount of mitoses leading to the best match between simulated and experimental HSVEC patterns. It involved the calculation of the Mahalanobis distance (Devroye et al.,1996). The Mahalanobis distance between two sets of variables is a generalization of the conventional Euclidean distance. Because it differs from the conventional Euclidean distance in that it takes into account the correlations between the data sets and is not sensitive to the scales of the variables involved, it represents a particularly useful tool to estimate the similarity between the two sets of variables. In the present context, it was calculated between the set of morphometric parameters measured on the images of real samples and the set of values the parameters exhibited in the different groups of simulated patterns (each corresponding to a different amount of mitoses in the 18 hr of simulated time). The minimum of the Mahalanobis distance as a function of the percentage of cells that underwent mitosis was then estimated to identify the proliferation level leading to patterns having the best similarity with the real ones after 18 hr of culture.

The same approach was used in the parameter study on the strength of the chemotactic response to identify the value leading to the best match between simulation of a control EC culture and experiment.

This analysis was performed by using the public domain statistical software R 2.0.0 (R Development core team,2005).

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. RESULTS
  5. DISCUSSION
  6. EXPERIMENTAL PROCEDURES
  7. REFERENCES
  8. Supporting Information

Additional Supporting Information may be found in the online version of this article.

FilenameFormatSizeDescription
DVDY_22022_sm_SupMat.doc47KSupp Materials. A file is provided (CcellCode.doc) containing the code to build the following files: • Four files (Matrigel_xml; Matrigel.py; Matrigel_plugins.py; Matrigel_steppables.py) with the code needed to run the simulations within the CompuCell3D environment (http://www.compucell3d.org). After extracting the single files, they can be simply copied in a subfolder under the main folder of the CompuCell3D software. • Data file (cellField.pif) providing an example of a random distribution of endothelial cells from which a simulation can be started. After extraction, it has to be copied in the main folder of the CompuCell3D software.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.