Jagged Mediates Differences in Normal and Tumor Angiogenesis by Affecting Tip-Stalk Fate Decision

Jagged mediates differences in normal and tumor angiogenesis by affecting tip-stalk fate decision

Marcelo Boaretoa,b, Mohit Kumar Jollya,c, Eshel Ben-Jacoba,d,1, and José N. Onuchica,2

aCenter for Theoretical Biological Physics, Rice University, Houston, TX 77005; bInstitute of Physics, University of Sao Paulo, Sao Paulo 05508, Brazil; cDepartment of Bioengineering, Rice University, Houston, TX 77005; and dSchool of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

Contributed by José N. Onuchic, June 19, 2015 (sent for review April 30, 2015) Angiogenesis is critical during development, wound repair, and (5, 6) (Fig. 1A). Therefore, Notch-Delta signaling between two cancer progression. During angiogenesis, some endothelial cells interacting cells forms an intercellular double negative feedback adopt a tip phenotype to lead the formation of new branching loop, and the two cells tend to adopt different fates: one cell be- vessels; the trailing stalk cells proliferate to develop the vessel. Notch haves as a sender [high ligand (Delta), low receptor (Notch)] and and VEGF signaling mediate the selection of these tip endothelial the other one behaves as a receiver [low ligand (Delta), high re- cells. However, how Jagged, a Notch ligand that is overexpressed in ceptor (Notch)]. This process of lateral inhibition has a crucial role cancer, affects angiogenesis remains elusive. Here, by developing a in generating a checkerboard-like or “salt-and-pepper” pattern, as theoretical framework for Notch-Delta-Jagged-VEGF signaling, we observed during bristle patterning in flies and inner ear patterning found that higher production levels of Jagged destabilizes the tip in vertebrates (7). Conversely, Notch-Jagged signaling generates and stalk cell fates and can give rise to a hybrid tip/stalk phenotype an intercellular double positive feedback loop, enabling the two that leads to poorly perfused and chaotic angiogenesis, which is a interacting cells to adopt similar fates: a hybrid sender/receiver [high hallmark of cancer. Consistently, the signaling interactions that ligand (Jagged), high receptor (Notch)] fate. This process of lateral cis- restrict Notch-Jagged signaling, such as Fringe, inhibition, and in- induction is crucial during sensing development and the formation creased production of Delta, stabilize tip and stalk fates and limit the of a smooth muscle wall around a nascent artery (6, 8). existence of hybrid tip/stalk phenotype. Our results underline how Besides asymmetric modulation by NICD, N-D and N-J sig- overexpression of Jagged can transform physiological angiogenesis naling can also be differentially regulated by glycosyltransferase into pathological one. Fringe. Fringe modifies Notch such that the modified (or glycosylated) Notch has a higher chance to bind to Delta, but a angiogenesis | Notch signaling | Jagged | VEGF signaling | lower chance to bind to Jagged (9). Importantly, Fringe, can also tumor angiogenesis be activated by NICD in some biological contexts (10). These different dynamics of Notch-Delta and Notch-Jagged sig- ngiogenesis, the formation of new blood vessels from existing naling allow them to play complementary roles during angiogenesis. Aones, is a vital process during embryonic development, ho- Notch-Delta signaling plays a crucial role in selecting the tip cell in meostasis, and tumor progression (1). This process starts when cells response to VEGF (11). The binding of VEGF-A (the key ligand of release angiogenic growth factors such as VEGF in response to VEGF family that responds to hypoxia) to VEGF receptor 2 hypoxia (lack of oxygen). These growth factors induce the forma- (VEGFR2) (the main mediator of VEGF-A signaling during an- tion of a new sprout, and the endothelial cell at the very front of “ ” giogenesis) up-regulates the production of Delta (DLL4) (12). this angiogenic sprout is called a tip cell. The tip cell extends DLL4 binds to Notch receptor on the neighboring cell and activates numerous filopodia toward the source of these growth factors and Notch signaling (NICD) in it. NICD inhibits VEGFR2, therefore migrates toward the direction of the upward gradient of the growth factor concentration, thereby leading a new angiogenic branch. The cells that follow the tip cell do not adopt a tip phenotype, but Significance rather form the stalk of the branch and proliferate to form the vessel lumen (2). A well-regulated balance between the migration Developing effective antiangiogenesis strategies remains clini- of tip cells and proliferation of stalk cells is essential for adequately cally challenging. Unlike physiological angiogenesis, pathological shaped nascent sprouts (3). angiogenesis comprises of many microvessels that do not fully The selection of the tip and the stalk cell fate is critical for de- mature or develop functionally, because the cell fate decision veloping a functional vessel. This decision is mediated by Notch about which endothelial cells become the tip and lead the fol- signaling pathway (2), an evolutionarily conserved cell–cell com- lowing stalk cells is dysregulated. We devised a specific theoret- munication pathway involved in cell fate decisions in multiple ical framework to decipher the cross-talk between two crucial contexts. This pathway is activated when Notch (transmembrane players of the decision-making process of tip and stalk cell fate: receptor) belonging to a particular cell interacts with Delta or VEGF and Notch-Delta-Jagged signaling. We find that high ex- Jagged (transmembrane ligands) belonging to its neighboring cell pression of Jagged, but not Delta, can destabilize the terminal (trans-activation), thereby releasing the Notch intracellular domain differentiation into tip or stalk cells and give rise to a hybrid tip/ (NICD). NICD then enters the nucleus and modulates the ex- stalk phenotype, a phenotype that can transform physiological into pathological angiogenesis. Our results offer insights into pression of many target genes of the Notch pathway, including both why tumor-stroma communication often implicates Jagged. the ligands Delta and Jagged. However, when Notch of a cell in-

teracts with Delta or Jagged belonging to the same cell, no NICD is Author contributions: M.B., M.K.J., E.B.-J., and J.N.O. designed research; M.B. and M.K.J. produced; rather, both the receptor (Notch) and ligand (Delta or performed research; M.B., M.K.J., E.B.-J., and J.N.O. analyzed data; and M.B., M.K.J., Jagged) are degraded (cis-inhibition) and therefore the signaling is E.B.-J., and J.N.O. wrote the paper. not activated (4). The authors declare no conflict of interest. Despite generating the same signal (NICD), Notch signaling Freely available online through the PNAS open access option. activated via Delta and that via Jagged, or in other words, Notch- 1Deceased June 5, 2015. Delta (N-D) signaling and Notch-Jagged (N-J) signaling, have dif- 2To whom correspondence should be addressed. Email: [email protected]. ferent dynamics, because NICD asymmetrically modulates the ex- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. pression of the two ligands: it represses Delta but activates Jagged 1073/pnas.1511814112/-/DCSupplemental.

E3836–E3844 | PNAS | Published online July 7, 2015 www.pnas.org/cgi/doi/10.1073/pnas.1511814112 Downloaded by guest on October 1, 2021 AB PNAS PLUS

Fig. 1. Overview of the intracellular and intercellular interplay between Notch and VEGF signaling pathways. (A) Notch signaling is activated when the transmembrane receptor of one cell (Notch) binds to the transmembrane ligand (Delta or Jagged) of the neighboring cell (trans-activation). This trans- activation cleaves Notch to produce Notch Intracellular Domain (NICD) that is released in the cytoplasm and then enters the nucleus to modulate the tran- scription of many target genes. NICD can activate Notch and Jagged and inhibit Delta and VEGF receptor 2 (VEGFR2). Glycosylation of Notch by Fringe modifies Notch to have a higher affinity for binding to Delta and a lower affinity for binding to Jagged. Interaction between Notch receptor and ligands (Delta or Jagged) of the same cell (cis-inhibition) leads to the degradation of both the receptor and the ligand; thus, no NICD is generated. VEGF-A binds to VEGFR2, thus activating VEGF signaling in the cell that activates Delta (DLL4). (B) Cells with high levels of Delta, VEGFR2, and active VEGF signaling develop filopodia and migrate toward the VEGF-A gradient, leading the formation of the new branch and are called tip cells. DLL4 from tip cells inhibits the neighboring cells to also adopt a tip phenotype, thereby forcing them to adopt the stalk fate (low Dll4, high Jagged1, and NICD). Stalk cells, by virtue of the lateral induction characteristics of Notch-Jagged signaling, can induce neighboring cells to adopt a stalk cell, therefore elongating the lumen.

making the adjacent cell less sensitive to the VEGF-A signal (12). lateral inhibition and can be critical for the emergence of a chaotic The cell with high Delta (and low NICD) becomes the tip, and the blood vessel network as seen during tumor angiogenesis. Finally, adjacent ones with low levels of Delta (and high NICD) become the we evaluate the role of both Fringe and cis-inhibition in the tip- stalk (12). This interplay between Notch and VEGF pathways is stalk cell fate decision. quite tight and dose dependent, i.e., many neighboring cells dynamically compete to adopt the tip position but only one of them Results wins (13). However, unlike other contexts where Notch-Delta The Theoretical Framework. To explore the effects of Jagged in cell (N-D) signaling leads to salt-and-pepper patterns, i.e., pattern of fate determination during angiogenesis, we generalized our earlier alternate fates with a wavelength of one cell, in angiogenesis, the theoretical framework of Notch-Delta-Jagged signaling (15) to two tip cells are usually separated by a few stalk cells, all of which incorporate VEGF signaling. The equations that describe the dy- have low Delta but high Jagged (Jag1) levels (14). Thus, Notch- namics of Notch (N), Delta (D), Jagged (J), NICD (I), VEGFR2 Jagged (N-J) signaling that regulates lateral induction (6, 8, 15), i.e., (VR), and active VEGF signaling in a cell (V)are propagation of the same cell fate in adjacent cells, might decide the À Á Â À Á distance between two tip cells (Fig. 1B). dN S+ S = N0H I, λI,N − N ðkCD + kT DextÞH I, λF,D Based on these roles of N-D and N-J signaling, it is expected that dt À ÁÃ [1] increased production of Jagged would increase the distance be- S + ðkCJ + kT JextÞH I, λF,J − γN, tween two tip cells by reinforcing the lateral induction mechanism between the stalk cells. However, the available experimental results À Á À Á Â À Á dD S− S+ S are the exact opposite: i.e., higher production rates of Jagged leads = D0H I, λI,D H V, λV ,D − D kCH I, λF,D N to more tip cells (14). Further, one would also expect that in- dt Ã [2] creased production of Delta would lead to more tip cells, but as + kT Next − γD, experimentally noted, Dll4 acts as a “brake” on sprouting angiogenesis (16). These conflicting observations call for an investigation dJ À Á Â À Á Ã = J HS+ I λ − J k HS I λ N + k N − γJ [3] of the underlying mechanisms of tip and stalk cell-fate selection dt 0 , I,J C , F,J T ext , mediated by Notch-Delta-Jagged (N-D-J) signaling. Here, we propose a specific theoretical framework to study the Â À Á À ÁÃ dI S S interplay between N-D-J and VEGF signaling in the tip-stalk cell = kT N DextH I, λF,D + JextH I, λF,J − γSI, [4] fate decision during sprouting angiogenesis. We show that cells can dt attain the stalk position by both lateral inhibition (through high À Á levels of Delta in the neighboring tip cells) and lateral induction dVR S− = VR H I, λI V − kT VRVext − γVR, [5] (through high levels of Jagged in the neighboring stalk cells). dt 0 , R However, Delta and Jagged have opposite roles in stabilizing the tip position: whereas a higher production rate of Jagged makes it dV = kT VRVext − γSV, [6] easier for a tip cell to lose its position to a neighboring stalk cell, a dt BIOPHYSICS AND higher production rate of Delta decreases the dynamic competition COMPUTATIONAL BIOLOGY between the two cells to adopt the tip position and consequently where γ represents the degradation rate of N, D, J, VR,andγS is the stabilizes the tip and stalk cell fates. Our results also suggest the degradation rate of I and V. N0, D0, J0,andVR0 represent innate existence of a hybrid or intermediate tip/stalk phenotype when production rates of the Notch, Delta, Jagged, and VEGF receptors, Jagged is overexpressed compared with Delta. Cells in this hybrid respectively. Next, Dext,andJext represent the amounts of external tip/stalk fate have compromised migration traits compared with tip proteins, i.e., receptor Notch and ligands Delta and Jagged available cells; therefore, the vessels led by these cells are expected to be from neighboring cells. Similarly, Vext represent the amount of ex- smaller and poorly perfused compared with those led by the tip ternal VEGF. kC represents the cis-inhibition rate, and kT represent cells. These traits of the hybrid tip/stalk fate enhance dynamic the trans-activation rates of Notch with its ligands (Delta and

Boareto et al. PNAS | Published online July 7, 2015 | E3837 Downloaded by guest on October 1, 2021 S+ Jagged) and the activation rate of VEGF signaling. H ðI, λI,N Þ and S+ A B H ðI, λI,J Þ represent the transcriptional activation of Notch (N) S− and Jagged (J)bythesignalNICD(I), and H ðI, λI,DÞ denotes S+ S+ the repression of Delta (D)byI. H ðI, λI,N Þ, H ðI, λI,J Þ, HS−ðI λ Þ HS−ðI λ Þ , I,D , and , I,VR are shifted Hill functions. Shifted S − + Hill functions are defined as H ðX, λX,Y Þ = H ðXÞ + λX,Y H ðXÞ, where H−ðXÞ is inhibitory Hill function and H+ðXÞ is excitatory Hill function, and λX,Y denotes the fold change in production of Y due to X (17, 18). For activation, shifted Hill functions are depicted by HS+ and λ > 1; for inhibition, they are depicted by HS− and λ < 1. λ = 1 denotes no effect. The effect of Fringe is considered to increase with the increase of the Notch signal (I) CD S and is represented by the shifted Hill functions H ðI, λF,DÞ and S H ðI, λF,J Þ (15, 19). We considered λF,D > 1 and λF,J < 1 to represent Fringe-mediated increase of Notch-Delta (N-D) binding affinity both for trans- and cis-interactions, and the decrease of the same for Notch-Jagged (N-J) interactions (20, 21). The values of the parameters are detailed in SI Appendix, section S1 and Table S1. The details of model construction are discussed in SI Appendix, section S2. The models for two interacting cells and many interacting cells are presented in SI Ap- pendix, sections S3 and S4, respectively. A discussion about the robustness of the model with respect to changes in parameter values is presented in SI Appendix, section S5 and Figs. S1 and S2. Fig. 2. Nullcline, bifurcation curve, and phase diagrams for the case of a single cell driven by external proteins Notch, Delta, Jagged, and VEGF. The computational analysis was performed in Python using (A) Nullclines for the case of one cell interacting with fixed levels of external IPython (22) and PyDSTool (23). proteins (Next = Dext = Jext = Vext = 2,000 molecules). Blue nullcline is for the We analyze two cases of the model: (i) single cell driven by condition of all ODEs being set to zero except for dI=dt and green nullcline is fixed values of external signals: Delta (Dext), Notch (Next), and for the condition of all ODEs being set to zero except for dD=dt (Eqs. 1–6). Jagged (Jext) representing the amount of proteins in the neigh- Unfilled circles represent unstable steady states, whereas red filled circles boring cells, and Vext representing the external signal VEGF-A; represent the two stable states: tip (high Delta, low NICD) and stalk (low and (ii) a multicell system, where cells are coupled with each Delta, high NICD). (B) Bifurcation curve of the levels of Delta (D)onthe membrane as a function of the number of external Delta (D ). At low D , other and communicate via the N-D-J signaling in the presence ext ext the cell adopts the tip fate, whereas at high Dext, the cell adopts the stalk of an external concentration of VEGF-A signal (Vext). fate. At intermediate Dext, the cell can adopt either fate: tip or stalk. (C) Phase diagram (two-parameter bifurcation diagram) as a function of Notch Mediates Tip-Stalk Fate Decision. To evaluate the basic op- external Delta (Dext) and VEGF (Vext). The monostable phase {tip} corre- erating principles of cell fate decision between tip and stalk, we sponds to the state [high Delta (D), VEGF receptor (VR), active VEGF signaling first analyze the dynamics of Notch-VEGF signaling by consid- (V) and low NICD (I) and Jagged (J)], and monostable phase {stalk} corre- ering one cell in contact with the external signals: Next, Dext, and sponds to the state (low D, VR,andV; and high I and J). The bistable phase {tip, stalk} corresponds to a region of coexistence of both states: tip and Jext—parameters that represent the concentration of Notch, stalk. (D) Phase diagram as a function of external Delta (D ) and external Delta, and Jagged in the neighboring cells—and Vext—the pa- ext Jagged (Jext). Bifurcation curves of the levels of VEGF receptor (VR), active rameter that represents the amount of external VEGF released VEGF signaling (V), NICD (I),andJagged(J) are included in SI Appendix, by cells under hypoxia. We find that the circuit is bistable with Fig. S3. two stable states as (i) [high Delta (D), active VEGF signaling (V) and VEGF receptor (VR), and low NICD (I) and Jagged (J)] and (ii) [low Delta (D), active VEGF signaling (V) and VEGF Next, we present the phase diagram driven by two control pa- receptor (VR), and high NICD (I) and Jagged (J)]. The former rameters—Dext and Jext—denoting the varying conditions for the stable state corresponds to a tip phenotype, and the latter one different fates of the neighboring cells. We observe that the cells corresponds to a stalk (Fig. 2A), i.e., the cell can adopt either of can attain the stalk fate for both high levels of Dext and Jext,i.e.,stalk the two phenotypes: tip or stalk. cell fate can be obtained by lateral inhibition mediated largely by Further, we evaluate the different states or phenotypes a cell Notch-Delta (when neighboring cell is a tip), as well as by lateral can adopt by varying levels of Delta in the neighboring cells induction mediated largely by Notch-Jagged (when neighboring (Dext). For low values of Dext, which mimics the case of neigh- cell is a stalk) (Fig. 2D). Therefore, Notch-Jagged signaling can boring cells being stalk cells, the cell adopts a tip phenotype propagate the stalk cell fate, or in other words, a stalk cell can use (marked by the {tip} phase). Conversely, for high levels of Dext, Notch-Jagged signaling to induce its neighboring cells to adopt a which mimics the case of neighboring cell(s) as tip(s), the cell stalk phenotype also. These stalk cells can contribute to lumen adopts a stalk phenotype (marked by the {stalk} phase) (Fig. 2B elongation and maintain the required ratio between tip and stalk and SI Appendix, Fig. S3). Interestingly, at intermediate levels of cells for developing a functional blood vessel. Dext, we observe a range of bistability, i.e., the cell can be either tip or stalk (marked by the {tip, stalk} phase) (Fig. 2B and SI Overexpression of Jagged Leads to a Hybrid Tip/Stalk Phenotype. Appendix, Fig. S3), thereby reflecting phenotypic plasticity and Next, we investigate the role of Jagged alongside Delta in the leading to a dynamic lateral inhibition or “cell shuffling” as ex- tip-stalk decision making for the one-cell system. We evaluate a perimentally observed in angiogenesis (13, 24). This region of phase diagram as a function of parameters: both the levels of bistability—{tip, stalk} phase—exists for a large range of values external Delta (Dext) and the different production levels of the of external VEGF signal, as long as Dext is at intermediate levels, ligands—J0 (production rate of Jagged) and D0 (production rate of thereby indicating the tight coupling of Notch and VEGF sig- Delta). Our results suggest that overexpression of Jagged leads to naling in tip-stalk fate decision (Fig. 2C). Similar behavior is the emergence of a previously unidentified phenotype: a hybrid found when varying Jext instead of Dext (SI Appendix, Fig. S4). tip/stalk fate (marked by the {tip/stalk} phase), where the cell

E3838 | www.pnas.org/cgi/doi/10.1073/pnas.1511814112 Boareto et al. Downloaded by guest on October 1, 2021 expresses intermediate levels of the proteins N, D, J, I, VR,andV versa. The z axis represents the effective potential that is defined PNAS PLUS (Fig. 3 A–C and SI Appendix, Fig. S5A). A similar hybrid state is as U = −logðPÞ, where P = PðD1, D2Þ is the probability density in obtained at low production rate of Delta (Fig. 3 D–F and SI Ap- the 2D phase space (D1 × D2) (26–28). This probability is cal- pendix,Fig.S5B), therefore suggesting that the relative production culated by using the Euler–Maruyama method to approximate rate between Delta and Jagged in a cell determines the exis- the ordinary differential equation to a stochastic differential tence of this hybrid tip/stalk phenotype (Fig. 3 C and D and SI equation that can evaluate the behavior of the cells in the Appendix,Fig.S5). Consistently, at a higher production rate of presence of biological noise. In this representation, a deep basin Delta compared with that of Jagged, the circuit is bistable only, of attraction represents that the corresponding cell fate or steady and therefore the cell can adopt either a tip or a stalk pheno- state is very stable, or in other words, the cell is not likely to type (marked by the {tip, stalk} phase), but not the hybrid tip/ switch its fate to a different one unless under a large amount of stalk one (Fig. 3 A and F). biological noise. Conversely, a shallow basin of attraction facili- We further investigate the dynamics of the circuit for two cells tates a more dynamic fate exchange (plasticity). interacting via N-D-J signaling for different values of the pro- Using this representation, we found that a two-cell system duction rate of ligands Delta (D0) and Jagged (J0) and fixed communicating via N-D-J signaling and responding to external levels of Vext. Our results indicate that at low production rates of VEGF behaves differently for different values of the production both Delta and Jagged, both cells attain the stalk fate (both cells rates of Jagged (J0). At low production rates of Jagged in both in monostable {stalk} phase). However, in the case of a higher cells, the system has two stable steady states, both of which com- production rate of Delta, one cell adopts the tip position, whereas prises of one cell in the tip (high levels of Delta) fate or pheno- the other become a stalk (bistable {tip, stalk} phase), but when the type, and the other in stalk (low levels of Delta) phenotype. In one production rate of Jagged is high, both cells attain the hybrid of these two states, cell 1 is a tip cell, and cell 2 is a stalk cell (high tip/stalk phenotype (both cells in monostable {tip/stalk} phase), D1,lowD2); and in the other state, its vice versa: cell 2 is a tip cell, thereby being consistent with the canonical role of Notch-Delta in and cell 1 is a stalk cell (low D1,highD2). Both these states have a diversifying cell fates (tip and stalk in this context) and that of deep potential or basin of attraction, suggesting that these cell Notch-Jagged in unifying them (the hybrid tip/stalk here) (7, 15, fates are very stable and that a large perturbation is required such 19) (SI Appendix,Fig.S6). that the tip cell (irrespective of whether cell 1 or cell 2 is the tip The hybrid tip/stalk phenotype, obtained under high levels of cell) loses its position, or in other words, changes its cell fate (Fig. Jagged, is reminiscent of and might correspond to the tip-like 4A). These results are consistent with previous experimental and thin cytoplasmic projections that extend across the vessel lumen theoretical observations that VEGF-VEGFR-Dll4-Notch-VEGFR of the tumor endothelium but not necessarily a nontumor en- intercellular feedback loop can mediate a stable tip and stalk fate dothelium (25). decision (11, 29), especially under conditions of nonpathological angiogenesis: low Jag1 and VEGF levels. Overexpression of Jagged Destabilizes the Tip and Stalk Cell Fates. However, as Jagged levels in the cells increase due to increased To elucidate how overexpression of Jagged affects the stability of J0, the potential for these two states becomes increasingly shallow, the three different cell fates (tip, stalk, and hybrid tip/stalk), we and only a small amount of noise can be sufficient to induce a cell represent the phase space of two interacting cells by an effective fate transition or exchange, i.e., a tip cell can become a stalk cell potential. The phase space is presented in terms of the levels of and vice versa (Fig. 4 B and C), hence indicating that high levels of Delta of each cell (D1, D2), such that (high D1, low D2) corre- Jagged in the cells destabilize the tip and stalk cell fates and fa- sponds to cell 1 as a tip cell and cell 2 as a stalk cell, and vice cilitate a dynamic competition for the tip position. For very high

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Fig. 3. Dynamical characteristics of the one-cell system for different levels of production rates of the ligands. Bifurcation curves represent the levels of Delta in response to varying Dext for different production rates of the ligands Delta and Jagged. (A) D0 = 1,000, J0 = 800; (C) D0 = 1,000, J0 = 1,800; (D) D0 = 800, J0 = 1,400; and (F) D0 = 1,600, J0 = 1,400 (all units in molecules/h). The phenotype diagrams (center) show the different possible phases when the circuit is driven by variable levels of external Delta (Dext), production rate of Delta (D0),andthatofJagged(J0). (B) Phenotype diagram for variable levels of external Delta (Dext) and production rate of Jagged (J0). (E) Phenotype diagram for variable levels of external Delta (Dext) and production rate of Delta (D0). Bifurcation curve of the levels of VEGF receptor (VR), active VEGF signaling (V), NICD (I), and Jagged (J) for cases C and D are included in SI Appendix,Fig.S5.

Boareto et al. PNAS | Published online July 7, 2015 | E3839 Downloaded by guest on October 1, 2021 Production Rate of the Two Ligands Regulate Angiogenesis Differently. A B Next,weevaluatethedynamicsofthecircuitatthetissuelevel,i.e., an array of cells interacting via the N-D-J signaling. We considered the case of a 2D layer of interacting identical cells exposed to a fixed level of external VEGF (Vext). For low levels of J0 (production rate of Jagged), there are, on average, more than one stalk cell between two tip cells, thereby allowing adequate development of the lumen (that is comprised of stalk cells) and hence a proper and robust development of the vessel branch: the case of physiological angiogenesis. However, as the production rate of Jagged (J0)increases, some cells adopt the hybrid tip/stalk phenotype. These C D cells, with somewhat compromised tip characteristics, are expected to develop less filopodia and migrate less than the tip cells, however, yet initiate a sprout; therefore, the vessels led by these cells are expected to be relatively smaller and poorly perfused. Thus, one would expect proper development of vessels but with a higher vessel density: the case of suboptimal angiogenesis. Last, when Jagged is overexpressed, most cells can adopt the hybrid tip/stalk phenotype, leading to an excessive number of small blood vessels with quite poor perfusion: a case of nonproductive or pathological E 2.5 F 2.5 angiogenesis as typically observed in cancer (Fig. 5 A–C and SI ) ) Appendix,Fig.S8). -1 -1 2.0 2.0 The exact opposite results are observed when varying the pro- D D 1.5 1.5 duction rate of Delta ( 0). High and intermediate levels of 0 ensure physiological angiogenesis; but for low levels of D0,the 1.0 1.0 number of the hybrid tip/stalk cells increase, thus giving rise to

0.5 0.5 many sprouts but a poorly perfused chaotic network, representing fate exchange rate (h fate exchange fate exchange rate (h fate exchange nonproductive or pathological angiogenesis (Fig. 5 A, D,andE). 0.0 0.0 1000 120020 1400 1600 1800 2000 800 1000 1200 1400 1600 1800 Our results are consistent with experimental evidence showing that Jagged production rate (J0) (molec/h) Delta production rate (D0) (molec/h) deletion or inhibition of DLL4 promotes nonproductive angiogenesis with poorly perfused vessels (30, 31). It may be noted that Fig. 4. 3D representation of the effective potential as a function of Delta in here we do not consider the effect of proliferation of stalk cells and cell 1 (D )andincell2(D ). The effective potential is defined as U = −logðPÞ, 1 2 that of VEGF gradient: two key factors that can alter the number where P = PðD1, D2Þ is the probability density calculated by solving the differential equations stochastically using the Euler–Maruyama method. A represents of tip cells and stalk cells, as well as their spatial distribution. the case of low production rate of Jagged (J0 = 1,000 molecules/h). B–D represent increasingly high production rates of Jagged: J0 = 1,400 molecules/h, Interplay Between Notch Signaling and the VEGF Gradient Guides the J0 = 1,800 molecules/h, and J0 = 2,200 molecules/h, respectively. (E) Cell fate Selection of Tip Cell. Besides the production rates of the two ligands, exchange rate (a measure of plasticity of the system) for increasing values of VEGF gradient has been shown to influence the vascular patterning production rates of Jagged (J0). (F) Cell fate exchange rate for increasing values (the spatial distribution of the tip and stalk cells) (12). Therefore, of production rates of Delta (D0). Red dot represents the standard value as we next incorporate a VEGF gradient in our two-cell system to presented in SI Appendix,TableS1. evaluate how it alters the relative stability of the different cell fates the cells attain. Unlike previous cases, now, cell 2 is exposed to a V A levels of Jagged, both cells no longer maintain their distinct tip and higher external VEGF signal ( ext) compared with cell 1 (Fig. 6 ). Similar to the earlier case of equal Vext for both cells (Fig. 4B), we stalk states or phenotypes, but rather adopt the intermediate tip/ observed two stable steady states: (high D ,lowD )orthatcell1is stalk state with intermediate levels of Delta (Fig. 4D). 1 2 a tip cell and cell 2 is a stalk cell and (low D1,highD2)orthatcell1 Further, we calculate how the two ligands Delta and Jagged is a stalk cell and cell 2 is a tip cell. However, in this case, both these differently regulate the switching of cell fates between tip and stable states are not equally stable; rather, the (low D1,highD2) stalk fates. Experimental observations on dynamic lateral in- state is more stable than the (low D2,highD1)state,orinother hibition shows that the cell at the tip position is replaced by words, the cell that receives higher levels of external VEGF signal, another cell in ∼2 h (13), i.e., the cell fate exchange rate is cell 2, is more likely to be the leading tip cell (Fig. 6B). Therefore, around 0.5/h. We first determine the amount of noise in this two- the Notch-VEGF interplay tends to ensure that the leading cell of a cell system that can allow a fate exchange rate of 0.5/h (for vascular sprout moves in the direction of the upward gradient of D0 = 1,000 and J0 = 1,200 molecules/h; SI Appendix, Table S1) VEGF. We further show that the fate exchange rate decreases with and then calculate this rate for different values of the production the increase in steepness of the VEGF gradient, indicating that the of Jagged (J ) and Delta (D ), with both cases explored for the cell that receives higher VEGF signal is more likely to be a tip cell 0 0 C same level of noise as determined earlier. We observed that an and maintain its fate (Fig. 6 ). increase in J increases this tip position exchange rate (Fig. 4E). 0 Fringe Stabilizes the Tip and Stalk Cell Fates. Fringe is a glycosyl- Oppositely, an increase in the production rate of Delta (D0) F transferase protein that is activated by NICD. It mediates the significantly decreases the same (Fig. 4 ). posttranslational modifications of Notch and consequently JAG1 (Jagged) and DLL4 (Delta) have been reported to play modulates the binding of Notch to Delta and to Jagged. The opposite roles during angiogenesis (14). Thus, unlike high levels glycosylated (or Fringe-modified) Notch has a higher binding of Jagged, high levels of Delta lead to a lower tip position ex- affinity to Delta but lower binding affinity to Jagged (20, 21). To change rate and more stable tip and stalk cell fates, therefore evaluate the role of the glycosyltransferase Fringe in the tip-stalk suggesting mutually competing roles of the two ligands in sta- fate decisions, we calculate the effective potential of a two-cell bilizing the tip and stalk cell fates (Fig. 4F and SI Appendix, system interacting via N-D-J signaling and under the influence of Fig. S7). fixed external VEGF levels. Including the effect of Fringe makes

E3840 | www.pnas.org/cgi/doi/10.1073/pnas.1511814112 Boareto et al. Downloaded by guest on October 1, 2021 A PNAS PLUS

D E

Fig. 5. Patterning at the tissue level. (A) Cartoon representation of physiological, suboptimal, and pathological angiogenesis. In physiological angiogenesis, two tip cells are separated by a few stalk cells, allowing a proper and robust development of the blood vessel. In the suboptimal case, angiogenesis is increased by a decrease in the number of stalk cells and the emergence of some hybrid tip/stalk cells that lead to some small blood vessels and poor perfusion. For pathological angiogenesis, an excessive number of tip/stalk cells lead to a large number of small blood vessels, leading to excessive but nonproductive angiogenesis. (B) Average of the fraction of cells in (tip), (tip/stalk), or (tip) state as a function of the production of Jagged (J0). (C) Cartoon representation of 1D layer of interacting cells for increased values of J0.(D) Average of the fraction of cells in (tip), (tip/stalk), or (tip) state as a function of the production of Delta (D0). (E)Cartoon representation of 1D layer of interacting cells for increased values of D0. The averages were taken over 100 simulations of a 2D layer of 100 × 100 interacting cells with a periodic boundary condition. The states of the cells are defined according to the amount of VEGF signal (V): stalk, V < 100; tip/stalk, 100 < V < 300; and tip, V > 300 molecules. Bidimensional patterning figures representing the levels of V, I, J,andD are presented in SI Appendix,Fig.S8.

the basin of attraction of the two states—(high D1, low D2) and zation effect of Fringe is observed even when Fringe is not in- (low D1, high D2)—deeper, thereby stabilizing the tip and stalk cluded in the model as a downstream target of NICD, but rather fates (Fig. 7 A and B). We further evaluate the effect of Fringe at as an independent variable (SI Appendix, Fig. S9). the tissue level and show that loss of Fringe leads to an increase These results offer an explanation into why aggressive tumor in the number of cells in the hybrid tip/stalk phenotype, thereby types such as basal-like breast cancer often show a loss of leading to small and poorly perfused blood vessels, typical of Fringe (32–34) and have increased microvessel density (MVD) tumor angiogenesis (Fig. 7 C and D). Importantly, this stabili- and high microvessel proliferation (MVP) compared with the

AB C

0.55 Cell #1 Cell #2 0.50

0.45

0.40 BIOPHYSICS AND VEGF-A

VEGF-A COMPUTATIONAL BIOLOGY 0.35 exchange rate (1/h) rate exchange 0.30

0.25 1000 1500 2000 2500 Vext in cell #2

Fig. 6. Effect of VEGF gradient on tip and stalk fate decision. (A) Cartoon representation. We simulate two cells interacting via Notch signaling in the presence of a VEGF gradient: cell 2 receives more VEGF-A signal than cell 1. (B) Effective potential representation for the case of Vext = 1,000 molecules for cell 1 and Vext = 1,500 molecules for cell 2. (C) Fate exchange rate for different values of Vext forcell2,whereasVext for cell 1 remains constant (Vext = 1,000 molecules).

Boareto et al. PNAS | Published online July 7, 2015 | E3841 Downloaded by guest on October 1, 2021 AB We also evaluate the effect of cis-inhibition between Notch- Delta and Notch-Jagged individually, by changing kC only for N-D interactions (SI Appendix, Fig. S10 A and B), and then only for N-J interactions (SI Appendix, Fig. S10 C and D). Our results suggest that N-J cis-inhibition stabilizes the tip and stalk cell fates much strongly compared with N-D cis-inhibition, i.e., the increase in kCJ (cis-inhibition of N-J interactions only) leads to a much deeper potential well (or basin of attraction) for the two states—(high D1, low D2) and (low D1, high D2)—whereas increasing kCD (cis-inhibition of N-D interactions only) has little CD effect (SI Appendix, Fig. S10 A and B), again highlighting the fact stalk tip/stalk tip that high Jagged levels can destabilize the tip and stalk cell fates 1.0 and contribute to the rich cellular plasticity and chaotic behavior 0.8 of tumor-mediated angiogenesis.

0.6 It has been speculated that cis-inhibition between Notch and f Jagged in the stalk cells would reduce the signaling ability of 0.4 Delta from the tip cell and hence compromise the tip-to-stalk Fraction of Fraction cellsof 0.2 signaling (14). Our results, however, suggest the opposite, i.e., 0.0 cis- 0.0 0.2 0.4 0.6 0.8 1.0 that inhibition has a fundamental role in stabilizing the tip eﬀect of Fringe (f) position. More specifically, we suggest that Notch-Delta cis- inhibition has relatively little effect in the stability of tip cells, Fig. 7. Effect of Fringe on tip and stalk fate decision. (A) 3D representation of probably due to the low levels of Notch receptor in the tip cells. the effective potential as a function of Delta in cell 1 (D1) and in cell 2 (D2)for cis- the case of no Fringe effect (f = 0.0, i.e., λF,D = λF,J = 1). B represents the effective In contrast, Notch-Jagged inhibition has an important role in potential after including Fringe effect (f = 1.0, i.e., λF,D = 3, λF,J = 0.3). The state stabilizing the tip position, because it decreases the probability of with high D2 and low D1, i.e., the one with high levels of Delta in cell 1 but not tip and stalk cells communicating via Notch and Jagged, hence in cell 2, corresponds to (cell 1 as tip and cell 2 as stalk); the state with high D1 reducing the levels of NICD in the tip cells. Reduced NICD and low D2 corresponds to (cell 1 as stalk and cell 2 as tip). (C) Average of the implies increased VEGFR2 and consequently high Dll4 in tip fraction of cells in (stalk), (tip/stalk), or (tip) state as a function of the Fringe cis- × cells, thereby stabilizing the tip cell fate. If N-J inhibition was effect. The averages were taken over 100 simulations of a 2D layer of 100 100 low, dynamic competition for tip position would be elevated. interacting cells in a square lattice with periodic boundary conditions. (D)Car- toon representation of a 1D layer of interacting cells for increased values of the Discussion effect of Fringe. The states of the cells are defined according to the amount of active VEGF signaling (V): stalk (V < 100), tip/stalk (100 < V < 300), and tip Notch and VEGF signaling pathways play a crucial role during (V > 300 molecules). The Fringe effect is represented by the variable f.Thecase tip-stalk cell fate decisions in both physiological and patho- = λ = λ = f 0.0 represents the no Fringe effect, i.e., F,D F,J 1, i.e., binding affinity of logical angiogenesis (1, 12). However, the underlying principles λ Notch to Delta and to Jagged is the same. As f increases, the values of F,D and of tip-stalk fate selection mediated by the interplay of Notch λ = λ = F,J linearly increase and decrease, respectively, such that at f 1.0, F,D 3.0 and VEGF pathways remains largely elusive. Here, we in- λ = and F,J 0.3 (SI Appendix,TableS1), i.e., Notch has higher binding affinity to troduced a specific theoretical framework to study this in- Delta and lower to Jagged. Therefore, (λ = 1 + 2f)and(λ = 1 − 0.7f). F,D F,J terplay. We show that tip-stalk decision is not a binary one; rather, cells can adopt a hybrid tip/stalk phenotype, when relatively less aggressive ER-positive and HER2-driven sub- Notch-Jagged signaling dominates over Notch-Delta signaling. types (35). This phenotype can lead to form a new sprout but has a compromised ability to migrate and develop filopodia, thereby cis-Inhibition Stabilizes the Tip and Stalk Cell Fates. cis-Inhibition, leading to poorly perfused blood vessels with high MVD. the intracellular binding and consequent degradation of the Therefore, the hybrid tip/stalk phenotype offers a key advan- Notch receptor and ligands (both Delta and Jagged), has been tage in pathological conditions: it can confer rich plasticity to considered to be critical for lateral inhibition and pattern for- the leading cell that can rapidly exchange its position with a mation in multiple developmental contexts (36, 37). However, its neighbor stalk, therefore inducing a fast but irregular vessel role in angiogenesis remains enigmatic. cis-Inhibition between Notch and Jagged in the stalk cells has been suggested to compromise the tip-to-stalk signaling (14). Thus, we decided to explore the role of cis-inhibition between Notch and Delta (N-D) and Notch and Jagged (N-J) both individually and together in the context of the tip selection process during angiogenesis. To evaluate the role of cis-inhibition between Notch and both its ligands Dll4 and Jag1 in angiogenesis, we analyze its effect on the stability of the tip and stalk cell fates, by representing the phase space by an effective potential for the case of both lower and higher cis-inhibition rate (kC). In both cases, two stable states are present: one cell as tip and the other as stalk and vice versa [(high D1, low D2), and (low D1, high D2)]. However, at higher values of kC, the basin of attraction for the stable states Fig. 8. Effect of cis-inhibition on tip and stalk fate decision. (A) 3D repre- are deeper, therefore suggesting that cis-inhibition has an im- sentation of the effective potential as a function of Delta in cell 1 (D1)andin portant role in stabilizing the tip position (Fig. 8). These results cell 2 (D2) for the case of a decrease in 10% of the cis-inhibition strength compared with its standard value (kC = 4.5e − 4). B represents the case of an are consistent with previous experimental and theoretical ob- = − cis- increase in 10% of the cis-inhibition strength (kC 5.5e 4). The state with servations that inhibition facilitates pattern formation and high D2 and low D1, i.e., the one with high levels of Delta in cell 1 but not in usually confers a greater robustness to noise during adoption of cell 2, corresponds to (cell 1 as tip and cell 2 as stalk); that with high D1 and alternate fates between neighboring cells (36, 38, 39). low D2 corresponds to (cell 1 as stalk and cell 2 as tip).

E3842 | www.pnas.org/cgi/doi/10.1073/pnas.1511814112 Boareto et al. Downloaded by guest on October 1, 2021 branch that can quickly supply oxygen in fast growing tumors. The critical role of overexpression of Jagged1 in mediating such PNAS PLUS When many cells adopt this hybrid phenotype, the vasculature is abnormal angiogenesis might explain why tumor-stroma interplay expected to be quite chaotic: excessive number of small but often involves Notch-Jagged signaling (47). The increased Notch- poorly perfused vessels, resulting in pathological angiogenesis as Jagged signaling in tumor environment can be attributed to mul- observed during tumor growth (40). Therefore, our results tiple specific traits of tumor endothelial cells (TECs): (i)theycan offer a good unifying explanation for many experimental ob- secrete Jagged in the stroma (48) that can potentially activate i servations: ( ) loss of Jagged significantly decreases vascular Notch-Jagged signaling in neighboring endothelium; (ii)theyhave branching (14), (ii) loss of Delta leads to excessive non- iii a proinflammatory gene expression and the inflammation re- productive or poorly perfused angiogenesis (16), and ( )loss sponse regulators such as NF-κB and TNF-α can increase Jagged of Fringe is correlated with increased MVD in tumors (35). in them (14, 49); and (iii) they often adhere to inflammatory cells Our results also attempt to resolve an apparent paradox between such as macrophages (25) that can increase Jagged in them via the canonical roles of Notch-Delta and Notch-Jagged signaling and the experimental observations about the overexpression of Delta paracrine or juxtacrine signaling. Such an amplified Notch-Jagged and Jagged in angiogenesis. Neighboring cells interacting via Notch- signaling can give rise to hybrid tip/stalk cells that closely resemble Jagged signaling usually adopt a similar cell fate (lateral induction) the observed tip-like projections of the tumor vessels that might (6, 8), whereas those interacting via Notch-Delta signaling adopt overlap with each other and even form loose connections (25). opposite fates (lateral inhibition) (7). Consequently, increased As discussed here, whereas some predictions of our model are production of Jagged would be expected to reinforce the lateral consistent with reported experimental results, the model offers induction mechanism between the stalk cells, hence elongating the some previously untested hypotheses that can be tested experi- lumen; increased production of Delta would lead to more tip cells. mentally. Specifically, we predict that the interactions that cause However, the experimental results are the exact opposite: i.e. higher enhanced Notch-Jagged signaling, such as overexpression of Jagged levels increase vascular branching (14), and Dll4 acts as a Jag1, repression of Dll4, and inhibition of Fringe, should lead to brake on sprouting angiogenesis (16). These conflicting observa- a more dynamic switching between tip and stalk cell fates, be- tions can be explained by the emergence of a hybrid tip/stalk phe- cause all these cases can cause a larger number of cells to adopt notype on overexpression of Jagged. Cells in this hybrid phenotype the hybrid tip/stalk phenotype, hence enriching cellular plasticity. can lead the formation of a vessel, albeit not so efficiently, thereby It might be noted that among the three different homologs of leading to more vascular branching. Overexpression of Delta can Fringe in mammals, the role of Lfng (Lunatic fringe) and Manic prevent cells from adopting this hybrid tip/stalk phenotype and can fringe (Mfng) might be more pertinent than that of Rfng hence inhibit angiogenesis. (Radical fringe), as they both can promote N-D signaling (50). The emergence of a hybrid tip/stalk phenotype also lends sup- “ To conclude, our theoretical bottom-up modeling framework port to the emerging notion a black and white distinction between offers important insights into the molecular interplay between tip and stalk cells is an oversimplification” (1) and strengthens the Notch and VEGF signaling in regulating cell fate decisions increasingly accepted notion that a hybrid state that coexpresses during both physiological and pathological angiogenesis. Albeit markers of two lineages is a signature of enhanced plasticity (multipotency) of a system (41–43). We find that the tendency to we do not consider any spatial effects into account, our adopt this hybrid phenotype is reduced at high levels of Fringe, a framework is amenable to be integrated with agent-based glycosyltransferase that promotes Notch-Delta signaling at the ex- models on angiogenesis (29) and can be used, in an iterative way pense of Notch-Jagged signaling by modifying Notch to increase its with experiments, to decipher the organizing principles of affinity for Delta and decrease it for Jagged. Thus, Fringe stabilizes multilayer process of angiogenesis (51). Specifically, as re- tip and stalk fates and can help promote physiological angiogen- ported here, the crucial role of Notch-Jagged signaling in me- esis, hence acting as a critical molecular brake on deregulated/ diating differences between physiological and pathological pathological angiogenesis. Loss of this brake, as seen in aggressive angiogenesis can be used for novel therapeutic benefits such tumors such as basal-like breast cancer (32–34), can enable tumors as developing decoys that can target JAG/NOTCH selectively to attain sustained angiogenesis (35), which is a hallmark of cancer as recently attempted (52). Such attempts are likely to be (44). Overall, our results about Fringe are also consistent with more specific in targeting tumor angiogenesis and hence pro- experimental and theoretical observations that Fringe promotes vide a viable and safer alternative to disrupting Notch signaling lateral inhibition patterns (19, 45) and are reminiscent of how altogether (both via Delta and Jagged), a hallmark of most asymmetric modifications of transmembrane ligand-receptor pairs antiangiogenesis efforts. can govern tissue-level pattern formation (46). The importance of Notch-Jagged signaling in delineating the Materials and Methods difference between normal and tumor angiogenesis is further The equations for the mathematical model are presented in The Theoretical cis- revealed by the role of inhibition, specifically that between Framework. The values of the parameters used for the model are given in SI Notch and Jagged, in affecting tip selection. cis-Inhibition be- Appendix, section S1. Model construction is discussed in SI Appendix, section tween Notch and Delta has been reported to offer greater ro- S2; and the sensitivity analysis for the model is presented in SI Appendix, bustness to noise during patterning (36), but ours is the first section S5. The computational analysis was performed in Python. study, to the best of our knowledge, exploring the role of cis- inhibition between Notch and Jagged. Our results indicate that ACKNOWLEDGMENTS. This work was supported by National Science cis-inhibition between Notch-Jagged stabilizes tip-and-stalk fates Foundation Grants PHY-1427654 and NSF-MCB-1214457 and the Cancer Prevention and Research Institute of Texas. M.B. was also supported by more strongly than that between Notch-Delta, hence underlining FAPESP (Sao Paulo Research Foundation) Grant 2013/14438-8. E.B.-J. was BIOPHYSICS AND

the role of maintaining low levels of Jagged1 to ensure smooth also supported by the Tauber Family Funds and the Maguy-Glass Chair in COMPUTATIONAL BIOLOGY and functional, i.e., physiological angiogenesis. Physics of Complex Systems.

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