Jagged mediates differences in normal and tumorangiogenesis by affecting tip-stalk fate decisionMarcelo 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, andcancer progression. During angiogenesis, some endothelial cellsadopt a tip phenotype to lead the formation of new branchingvessels; the trailing stalk cells proliferate to develop the vessel. Notchand VEGF signaling mediate the selection of these tip endothelialcells. However, how Jagged, a Notch ligand that is overexpressed incancer, affects angiogenesis remains elusive. Here, by developing atheoretical framework for Notch-Delta-Jagged-VEGF signaling, wefound that higher production levels of Jagged destabilizes the tipand stalk cell fates and can give rise to a hybrid tip/stalk phenotypethat leads to poorly perfused and chaotic angiogenesis, which is ahallmark of cancer. Consistently, the signaling interactions thatrestrict Notch-Jagged signaling, such as Fringe, cis-inhibition, and in-creased production of Delta, stabilize tip and stalk fates and limit theexistence of hybrid tip/stalk phenotype. Our results underline howoverexpression of Jagged can transform physiological angiogenesisinto pathological one.

angiogenesis | Notch signaling | Jagged | VEGF signaling |tumor angiogenesis

Angiogenesis, the formation of new blood vessels from existingones, is a vital process during embryonic development, ho-

meostasis, and tumor progression (1). This process starts when cellsrelease angiogenic growth factors such as VEGF in response tohypoxia (lack of oxygen). These growth factors induce the forma-tion of a new sprout, and the endothelial cell at the very front ofthis angiogenic sprout is called a “tip” cell. The tip cell extendsnumerous filopodia toward the source of these growth factors andmigrates toward the direction of the upward gradient of the growthfactor concentration, thereby leading a new angiogenic branch. Thecells that follow the tip cell do not adopt a tip phenotype, butrather form the stalk of the branch and proliferate to form thevessel lumen (2). A well-regulated balance between the migrationof tip cells and proliferation of stalk cells is essential for adequatelyshaped nascent sprouts (3).The selection of the tip and the stalk cell fate is critical for de-

veloping a functional vessel. This decision is mediated by Notchsignaling pathway (2), an evolutionarily conserved cell–cell com-munication pathway involved in cell fate decisions in multiplecontexts. This pathway is activated when Notch (transmembranereceptor) belonging to a particular cell interacts with Delta orJagged (transmembrane ligands) belonging to its neighboring cell(trans-activation), thereby releasing the Notch intracellular domain(NICD). NICD then enters the nucleus and modulates the ex-pression of many target genes of the Notch pathway, including boththe ligands Delta and Jagged. However, when Notch of a cell in-teracts with Delta or Jagged belonging to the same cell, no NICD isproduced; rather, both the receptor (Notch) and ligand (Delta orJagged) are degraded (cis-inhibition) and therefore the signaling isnot activated (4).Despite generating the same signal (NICD), Notch signaling

activated via Delta and that via Jagged, or in other words, Notch-Delta (N-D) signaling and Notch-Jagged (N-J) signaling, have dif-ferent dynamics, because NICD asymmetrically modulates the ex-pression of the two ligands: it represses Delta but activates Jagged

(5, 6) (Fig. 1A). Therefore, Notch-Delta signaling between twointeracting cells forms an intercellular double negative feedbackloop, and the two cells tend to adopt different fates: one cell be-haves as a sender [high ligand (Delta), low receptor (Notch)] andthe other one behaves as a receiver [low ligand (Delta), high re-ceptor (Notch)]. This process of lateral inhibition has a crucial rolein generating a checkerboard-like or “salt-and-pepper” pattern, asobserved during bristle patterning in flies and inner ear patterningin vertebrates (7). Conversely, Notch-Jagged signaling generatesan intercellular double positive feedback loop, enabling the twointeracting cells to adopt similar fates: a hybrid sender/receiver [highligand (Jagged), high receptor (Notch)] fate. This process of lateralinduction is crucial during sensing development and the formationof a smooth muscle wall around a nascent artery (6, 8).Besides asymmetric modulation by NICD, N-D and N-J sig-

naling can also be differentially regulated by glycosyltransferaseFringe. Fringe modifies Notch such that the modified (or gly-cosylated) Notch has a higher chance to bind to Delta, but alower chance to bind to Jagged (9). Importantly, Fringe, can alsobe activated by NICD in some biological contexts (10).These different dynamics of Notch-Delta and Notch-Jagged sig-

naling allow them to play complementary roles during angiogenesis.Notch-Delta signaling plays a crucial role in selecting the tip cell inresponse to VEGF (11). The binding of VEGF-A (the key ligand ofVEGF family that responds to hypoxia) to VEGF receptor 2(VEGFR2) (the main mediator of VEGF-A signaling during an-giogenesis) up-regulates the production of Delta (DLL4) (12).DLL4 binds to Notch receptor on the neighboring cell and activatesNotch signaling (NICD) in it. NICD inhibits VEGFR2, therefore

Significance

Developing effective antiangiogenesis strategies remains clini-cally challenging. Unlike physiological angiogenesis, pathologicalangiogenesis comprises of many microvessels that do not fullymature or develop functionally, because the cell fate decisionabout which endothelial cells become the tip and lead the fol-lowing stalk cells is dysregulated. We devised a specific theoret-ical framework to decipher the cross-talk between two crucialplayers of the decision-making process of tip and stalk cell fate:VEGF and Notch-Delta-Jagged signaling. We find that high ex-pression of Jagged, but not Delta, can destabilize the terminaldifferentiation into tip or stalk cells and give rise to a hybrid tip/stalk phenotype, a phenotype that can transform physiologicalinto pathological angiogenesis. Our results offer insights intowhy tumor-stroma communication often implicates Jagged.

Author contributions: M.B., M.K.J., E.B.-J., and J.N.O. designed research; M.B. and M.K.J.performed research; M.B., M.K.J., E.B.-J., and J.N.O. analyzed data; and M.B., M.K.J.,E.B.-J., and J.N.O. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1Deceased June 5, 2015.2To whom correspondence should be addressed. Email: jonuchic@rice.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1511814112/-/DCSupplemental.

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making the adjacent cell less sensitive to the VEGF-A signal (12).The cell with high Delta (and low NICD) becomes the tip, and theadjacent ones with low levels of Delta (and high NICD) become thestalk (12). This interplay between Notch and VEGF pathways isquite tight and dose dependent, i.e., many neighboring cells dy-namically compete to adopt the tip position but only one of themwins (13). However, unlike other contexts where Notch-Delta(N-D) signaling leads to salt-and-pepper patterns, i.e., pattern ofalternate fates with a wavelength of one cell, in angiogenesis, thetwo tip cells are usually separated by a few stalk cells, all of whichhave low Delta but high Jagged (Jag1) levels (14). Thus, Notch-Jagged (N-J) signaling that regulates lateral induction (6, 8, 15), i.e.,propagation of the same cell fate in adjacent cells, might decide thedistance between two tip cells (Fig. 1B).Based on these roles of N-D and N-J signaling, it is expected that

increased production of Jagged would increase the distance be-tween two tip cells by reinforcing the lateral induction mechanismbetween the stalk cells. However, the available experimental resultsare the exact opposite: i.e., higher production rates of Jagged leadsto more tip cells (14). Further, one would also expect that in-creased production of Delta would lead to more tip cells, but asexperimentally noted, Dll4 acts as a “brake” on sprouting angio-genesis (16). These conflicting observations call for an investigationof the underlying mechanisms of tip and stalk cell-fate selectionmediated by Notch-Delta-Jagged (N-D-J) signaling.Here, we propose a specific theoretical framework to study the

interplay between N-D-J and VEGF signaling in the tip-stalk cellfate decision during sprouting angiogenesis. We show that cells canattain the stalk position by both lateral inhibition (through highlevels of Delta in the neighboring tip cells) and lateral induction(through high levels of Jagged in the neighboring stalk cells).However, Delta and Jagged have opposite roles in stabilizing thetip position: whereas a higher production rate of Jagged makes iteasier for a tip cell to lose its position to a neighboring stalk cell, ahigher production rate of Delta decreases the dynamic competitionbetween the two cells to adopt the tip position and consequentlystabilizes the tip and stalk cell fates. Our results also suggest theexistence of a hybrid or intermediate tip/stalk phenotype whenJagged is overexpressed compared with Delta. Cells in this hybridtip/stalk fate have compromised migration traits compared with tipcells; therefore, the vessels led by these cells are expected to besmaller and poorly perfused compared with those led by the tipcells. These traits of the hybrid tip/stalk fate enhance dynamic

lateral inhibition and can be critical for the emergence of a chaoticblood vessel network as seen during tumor angiogenesis. Finally,we evaluate the role of both Fringe and cis-inhibition in the tip-stalk cell fate decision.

ResultsThe Theoretical Framework. To explore the effects of Jagged in cellfate determination during angiogenesis, we generalized our earliertheoretical framework of Notch-Delta-Jagged signaling (15) toincorporate VEGF signaling. The equations that describe the dy-namics of Notch (N), Delta (D), Jagged (J), NICD (I), VEGFR2(VR), and active VEGF signaling in a cell (V) are

dNdt

=N0HS+�I, λI,N�−N

�ðkCD+ kTDextÞHS�I, λF,D�

+ ðkCJ + kTJextÞHS�I, λF,J��

− γN,[1]

dDdt

=D0HS−�I, λI,D�HS+�V , λV ,D

�−D

�kCHS�I, λF,D

�N

+ kTNext�− γD,

[2]

dJdt

= J0HS+�I, λI,J�− J

�kCHS�I, λF,J

�N + kTNext

�− γJ, [3]

dIdt

= kTN�DextHS�I, λF,D

�+ JextHS�I, λF,J

��− γSI, [4]

dVR

dt=VR0HS−�I, λI,VR

�− kTVRVext − γVR, [5]

dVdt

= kTVRVext − γSV , [6]

where γ represents the degradation rate of N, D, J, VR, and γS is thedegradation rate of I and V. N0, D0, J0, and VR0 represent innateproduction rates of the Notch, Delta, Jagged, and VEGF receptors,respectively. Next, Dext, and Jext represent the amounts of externalproteins, i.e., receptor Notch and ligands Delta and Jagged availablefrom neighboring cells. Similarly, Vext represent the amount of ex-ternal VEGF. kC represents the cis-inhibition rate, and kT representthe trans-activation rates of Notch with its ligands (Delta and

A B

Fig. 1. Overview of the intracellular and intercellular interplay between Notch and VEGF signaling pathways. (A) Notch signaling is activated when thetransmembrane 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 Fringemodifies 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 toVEGFR2, thus activating VEGF signaling in the cell that activates Delta (DLL4). (B) Cells with high levels of Delta, VEGFR2, and active VEGF signaling developfilopodia and migrate toward the VEGF-A gradient, leading the formation of the new branch and are called tip cells. DLL4 from tip cells inhibits theneighboring 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 thelateral induction characteristics of Notch-Jagged signaling, can induce neighboring cells to adopt a stalk cell, therefore elongating the lumen.

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Jagged) and the activation rate of VEGF signaling.HS+ðI, λI,NÞ andHS+ðI, λI,JÞ represent the transcriptional activation of Notch (N)and Jagged (J) by the signal NICD (I), and HS−ðI, λI,DÞ denotesthe repression of Delta (D) by I. HS+ðI, λI,NÞ, HS+ðI, λI,JÞ,HS−ðI, λI,DÞ, and HS−ðI, λI,VRÞ are shifted Hill functions. ShiftedHill functions are defined as HSðX , λX ,Y Þ=H−ðXÞ+ λX ,YH+ðXÞ,where H−ðXÞ is inhibitory Hill function and H+ðXÞ is excitatoryHill function, and λX ,Y denotes the fold change in production ofY due to X (17, 18). For activation, shifted Hill functions aredepicted by HS+ and λ> 1; for inhibition, they are depicted byHS− and λ< 1. λ= 1 denotes no effect. The effect of Fringe isconsidered to increase with the increase of the Notch signal (I)and is represented by the shifted Hill functions HSðI, λF,DÞ andHSðI, λF,JÞ (15, 19). We considered λF,D > 1 and λF,J < 1 to repre-sent Fringe-mediated increase of Notch-Delta (N-D) bindingaffinity both for trans- and cis-interactions, and the decrease ofthe 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 arediscussed in SI Appendix, section S2. The models for two inter-acting cells and many interacting cells are presented in SI Ap-pendix, sections S3 and S4, respectively. A discussion about therobustness of the model with respect to changes in parametervalues is presented in SI Appendix, section S5 and Figs. S1 and S2.The computational analysis was performed in Python usingIPython (22) and PyDSTool (23).We analyze two cases of the model: (i) single cell driven by

fixed values of external signals: Delta (Dext), Notch (Next), andJagged (Jext) representing the amount of proteins in the neigh-boring cells, and Vext representing the external signal VEGF-A;and (ii) a multicell system, where cells are coupled with eachother and communicate via the N-D-J signaling in the presenceof an external concentration of VEGF-A signal (Vext).

Notch Mediates Tip-Stalk Fate Decision. To evaluate the basic op-erating principles of cell fate decision between tip and stalk, wefirst analyze the dynamics of Notch-VEGF signaling by consid-ering one cell in contact with the external signals: Next, Dext, andJext—parameters that represent the concentration of Notch,Delta, and Jagged in the neighboring cells—and Vext—the pa-rameter that represents the amount of external VEGF releasedby cells under hypoxia. We find that the circuit is bistable withtwo 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 VEGFreceptor (VR), and high NICD (I) and Jagged (J)]. The formerstable state corresponds to a tip phenotype, and the latter onecorresponds to a stalk (Fig. 2A), i.e., the cell can adopt either ofthe two phenotypes: tip or stalk.Further, we evaluate the different states or phenotypes a cell

can adopt by varying levels of Delta in the neighboring cells(Dext). For low values of Dext, which mimics the case of neigh-boring cells being stalk cells, the cell adopts a tip phenotype(marked by the {tip} phase). Conversely, for high levels of Dext,which mimics the case of neighboring cell(s) as tip(s), the celladopts a stalk phenotype (marked by the {stalk} phase) (Fig. 2Band SI Appendix, Fig. S3). Interestingly, at intermediate levels ofDext, we observe a range of bistability, i.e., the cell can be eithertip or stalk (marked by the {tip, stalk} phase) (Fig. 2B and SIAppendix, Fig. S3), thereby reflecting phenotypic plasticity andleading to a dynamic lateral inhibition or “cell shuffling” as ex-perimentally observed in angiogenesis (13, 24). This region ofbistability—{tip, stalk} phase—exists for a large range of valuesof external VEGF signal, as long as Dext is at intermediate levels,thereby indicating the tight coupling of Notch and VEGF sig-naling in tip-stalk fate decision (Fig. 2C). Similar behavior isfound when varying Jext instead of Dext (SI Appendix, Fig. S4).

Next, we present the phase diagram driven by two control pa-rameters—Dext and Jext—denoting the varying conditions for thedifferent fates of the neighboring cells. We observe that the cellscan attain the stalk fate for both high levels ofDext and Jext, i.e., stalkcell fate can be obtained by lateral inhibition mediated largely byNotch-Delta (when neighboring cell is a tip), as well as by lateralinduction mediated largely by Notch-Jagged (when neighboringcell is a stalk) (Fig. 2D). Therefore, Notch-Jagged signaling canpropagate the stalk cell fate, or in other words, a stalk cell can useNotch-Jagged signaling to induce its neighboring cells to adopt astalk phenotype also. These stalk cells can contribute to lumenelongation and maintain the required ratio between tip and stalkcells for developing a functional blood vessel.

Overexpression of Jagged Leads to a Hybrid Tip/Stalk Phenotype.Next, we investigate the role of Jagged alongside Delta in thetip-stalk decision making for the one-cell system. We evaluate aphase diagram as a function of parameters: both the levels ofexternal Delta (Dext) and the different production levels of theligands—J0 (production rate of Jagged) andD0 (production rate ofDelta). Our results suggest that overexpression of Jagged leads tothe emergence of a previously unidentified phenotype: a hybridtip/stalk fate (marked by the {tip/stalk} phase), where the cell

A

C D

B

Fig. 2. Nullcline, bifurcation curve, and phase diagrams for the case of asingle cell driven by external proteins Notch, Delta, Jagged, and VEGF.(A) Nullclines for the case of one cell interacting with fixed levels of externalproteins (Next =Dext = Jext =Vext = 2,000 molecules). Blue nullcline is for thecondition of all ODEs being set to zero except for dI=dt and green nullcline isfor the condition of all ODEs being set to zero except for dD=dt (Eqs. 1–6).Unfilled circles represent unstable steady states, whereas red filled circlesrepresent the two stable states: tip (high Delta, low NICD) and stalk (lowDelta, high NICD). (B) Bifurcation curve of the levels of Delta (D) on themembrane as a function of the number of external Delta (Dext). At low Dext,the cell adopts the tip fate, whereas at high Dext, the cell adopts the stalkfate. At intermediate Dext, the cell can adopt either fate: tip or stalk.(C) Phase diagram (two-parameter bifurcation diagram) as a function ofexternal Delta (Dext) and VEGF (Vext). The monostable phase {tip} corre-sponds to the state [high Delta (D), VEGF receptor (VR), active VEGF signaling(V) and low NICD (I) and Jagged (J)], and monostable phase {stalk} corre-sponds to the state (low D, VR, and V; and high I and J). The bistable phase{tip, stalk} corresponds to a region of coexistence of both states: tip andstalk. (D) Phase diagram as a function of external Delta (Dext) and externalJagged (Jext). Bifurcation curves of the levels of VEGF receptor (VR), activeVEGF signaling (V ), NICD (I), and Jagged (J) are included in SI Appendix,Fig. S3.

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expresses intermediate levels of the proteins N, D, J, I, VR, and V(Fig. 3 A–C and SI Appendix, Fig. S5A). A similar hybrid state isobtained at low production rate of Delta (Fig. 3 D–F and SI Ap-pendix, Fig. S5B), therefore suggesting that the relative productionrate between Delta and Jagged in a cell determines the exis-tence of this hybrid tip/stalk phenotype (Fig. 3 C and D and SIAppendix, Fig. S5). Consistently, at a higher production rate ofDelta compared with that of Jagged, the circuit is bistable only,and therefore the cell can adopt either a tip or a stalk pheno-type (marked by the {tip, stalk} phase), but not the hybrid tip/stalk one (Fig. 3 A and F).We further investigate the dynamics of the circuit for two cells

interacting via N-D-J signaling for different values of the pro-duction rate of ligands Delta (D0) and Jagged (J0) and fixedlevels of Vext. Our results indicate that at low production rates ofboth Delta and Jagged, both cells attain the stalk fate (both cellsin monostable {stalk} phase). However, in the case of a higherproduction rate of Delta, one cell adopts the tip position, whereasthe other become a stalk (bistable {tip, stalk} phase), but when theproduction rate of Jagged is high, both cells attain the hybridtip/stalk phenotype (both cells in monostable {tip/stalk} phase),thereby being consistent with the canonical role of Notch-Delta indiversifying cell fates (tip and stalk in this context) and that ofNotch-Jagged in unifying them (the hybrid tip/stalk here) (7, 15,19) (SI Appendix, Fig. S6).The hybrid tip/stalk phenotype, obtained under high levels of

Jagged, is reminiscent of and might correspond to the tip-likethin cytoplasmic projections that extend across the vessel lumenof the tumor endothelium but not necessarily a nontumor en-dothelium (25).

Overexpression of Jagged Destabilizes the Tip and Stalk Cell Fates.To elucidate how overexpression of Jagged affects the stability ofthe three different cell fates (tip, stalk, and hybrid tip/stalk), werepresent the phase space of two interacting cells by an effectivepotential. The phase space is presented in terms of the levels ofDelta of each cell (D1, D2), such that (high D1, low D2) corre-sponds to cell 1 as a tip cell and cell 2 as a stalk cell, and vice

versa. The z axis represents the effective potential that is definedas U =−logðPÞ, where P=PðD1,D2Þ is the probability density inthe 2D phase space (D1 × D2) (26–28). This probability is cal-culated by using the Euler–Maruyama method to approximatethe ordinary differential equation to a stochastic differentialequation that can evaluate the behavior of the cells in thepresence of biological noise. In this representation, a deep basinof attraction represents that the corresponding cell fate or steadystate is very stable, or in other words, the cell is not likely toswitch its fate to a different one unless under a large amount ofbiological noise. Conversely, a shallow basin of attraction facili-tates a more dynamic fate exchange (plasticity).Using this representation, we found that a two-cell system

communicating via N-D-J signaling and responding to externalVEGF behaves differently for different values of the productionrates of Jagged (J0). At low production rates of Jagged in bothcells, the system has two stable steady states, both of which com-prises of one cell in the tip (high levels of Delta) fate or pheno-type, and the other in stalk (low levels of Delta) phenotype. In oneof these two states, cell 1 is a tip cell, and cell 2 is a stalk cell (highD1, low D2); and in the other state, its vice versa: cell 2 is a tip cell,and cell 1 is a stalk cell (low D1, high D2). Both these states have adeep potential or basin of attraction, suggesting that these cellfates are very stable and that a large perturbation is required suchthat the tip cell (irrespective of whether cell 1 or cell 2 is the tipcell) loses its position, or in other words, changes its cell fate (Fig.4A). These results are consistent with previous experimental andtheoretical observations that VEGF-VEGFR-Dll4-Notch-VEGFRintercellular feedback loop can mediate a stable tip and stalk fatedecision (11, 29), especially under conditions of nonpathologicalangiogenesis: low Jag1 and VEGF levels.However, as Jagged levels in the cells increase due to increased

J0, the potential for these two states becomes increasingly shallow,and only a small amount of noise can be sufficient to induce a cellfate transition or exchange, i.e., a tip cell can become a stalk celland vice versa (Fig. 4 B and C), hence indicating that high levels ofJagged in the cells destabilize the tip and stalk cell fates and fa-cilitate a dynamic competition for the tip position. For very high

A B C

D E F

Fig. 3. Dynamical characteristics of the one-cell system for different levels of production rates of the ligands. Bifurcation curves represent the levels of Deltain 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 isdriven by variable levels of external Delta (Dext), production rate of Delta (D0), and that of Jagged (J0). (B) Phenotype diagram for variable levels ofexternal 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.

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levels of Jagged, both cells no longer maintain their distinct tip andstalk states or phenotypes, but rather adopt the intermediate tip/stalk state with intermediate levels of Delta (Fig. 4D).Further, we calculate how the two ligands Delta and Jagged

differently regulate the switching of cell fates between tip andstalk fates. Experimental observations on dynamic lateral in-hibition shows that the cell at the tip position is replaced byanother cell in ∼2 h (13), i.e., the cell fate exchange rate isaround 0.5/h. We first determine the amount of noise in this two-cell system that can allow a fate exchange rate of 0.5/h (forD0 = 1,000 and J0 = 1,200 molecules/h; SI Appendix, Table S1)and then calculate this rate for different values of the productionof Jagged (J0) and Delta (D0), with both cases explored for thesame level of noise as determined earlier. We observed that anincrease in J0 increases this tip position exchange rate (Fig. 4E).Oppositely, an increase in the production rate of Delta (D0)significantly decreases the same (Fig. 4F).JAG1 (Jagged) and DLL4 (Delta) have been reported to play

opposite roles during angiogenesis (14). Thus, unlike high levelsof Jagged, high levels of Delta lead to a lower tip position ex-change rate and more stable tip and stalk cell fates, thereforesuggesting mutually competing roles of the two ligands in sta-bilizing the tip and stalk cell fates (Fig. 4F and SI Appendix,Fig. S7).

Production Rate of the Two Ligands Regulate Angiogenesis Differently.Next, we evaluate the dynamics of the circuit at the tissue level, i.e.,an array of cells interacting via the N-D-J signaling. We consideredthe case of a 2D layer of interacting identical cells exposed to afixed level of external VEGF (Vext). For low levels of J0 (productionrate of Jagged), there are, on average, more than one stalk cellbetween two tip cells, thereby allowing adequate development ofthe lumen (that is comprised of stalk cells) and hence a proper androbust development of the vessel branch: the case of physiologicalangiogenesis. However, as the production rate of Jagged (J0) in-creases, some cells adopt the hybrid tip/stalk phenotype. Thesecells, with somewhat compromised tip characteristics, are expectedto develop less filopodia and migrate less than the tip cells, how-ever, yet initiate a sprout; therefore, the vessels led by these cellsare expected to be relatively smaller and poorly perfused. Thus,one would expect proper development of vessels but with a highervessel density: the case of suboptimal angiogenesis. Last, whenJagged is overexpressed, most cells can adopt the hybrid tip/stalkphenotype, leading to an excessive number of small blood vesselswith quite poor perfusion: a case of nonproductive or pathologicalangiogenesis as typically observed in cancer (Fig. 5 A–C and SIAppendix, Fig. S8).The exact opposite results are observed when varying the pro-

duction rate of Delta (D0). High and intermediate levels of D0ensure physiological angiogenesis; but for low levels of D0, thenumber of the hybrid tip/stalk cells increase, thus giving rise tomany sprouts but a poorly perfused chaotic network, representingnonproductive or pathological angiogenesis (Fig. 5 A, D, and E).Our results are consistent with experimental evidence showing thatdeletion or inhibition of DLL4 promotes nonproductive angio-genesis with poorly perfused vessels (30, 31). It may be noted thathere we do not consider the effect of proliferation of stalk cells andthat of VEGF gradient: two key factors that can alter the numberof tip cells and stalk cells, as well as their spatial distribution.

Interplay Between Notch Signaling and the VEGF Gradient Guides theSelection of Tip Cell. Besides the production rates of the two ligands,VEGF gradient has been shown to influence the vascular patterning(the spatial distribution of the tip and stalk cells) (12). Therefore,we next incorporate a VEGF gradient in our two-cell system toevaluate how it alters the relative stability of the different cell fatesthe cells attain. Unlike previous cases, now, cell 2 is exposed to ahigher external VEGF signal (Vext) compared with cell 1 (Fig. 6A).Similar to the earlier case of equal Vext for both cells (Fig. 4B), weobserved two stable steady states: (high D1, low D2) or that cell 1 isa tip cell and cell 2 is a stalk cell and (low D1, high D2) or that cell 1is a stalk cell and cell 2 is a tip cell. However, in this case, both thesestable states are not equally stable; rather, the (low D1, high D2)state is more stable than the (low D2, high D1) state, or in otherwords, the cell that receives higher levels of external VEGF signal,cell 2, is more likely to be the leading tip cell (Fig. 6B). Therefore,the Notch-VEGF interplay tends to ensure that the leading cell of avascular sprout moves in the direction of the upward gradient ofVEGF. We further show that the fate exchange rate decreases withthe increase in steepness of the VEGF gradient, indicating that thecell that receives higher VEGF signal is more likely to be a tip celland maintain its fate (Fig. 6C).

Fringe Stabilizes the Tip and Stalk Cell Fates. Fringe is a glycosyl-transferase protein that is activated by NICD. It mediates theposttranslational modifications of Notch and consequentlymodulates the binding of Notch to Delta and to Jagged. Theglycosylated (or Fringe-modified) Notch has a higher bindingaffinity to Delta but lower binding affinity to Jagged (20, 21). Toevaluate the role of the glycosyltransferase Fringe in the tip-stalkfate decisions, we calculate the effective potential of a two-cellsystem interacting via N-D-J signaling and under the influence offixed external VEGF levels. Including the effect of Fringe makes

BA

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Fig. 4. 3D representation of the effective potential as a function of Delta incell 1 (D1) and in cell 2 (D2). The effective potential is defined as U=−logðPÞ,where P = PðD1,D2Þ is the probability density calculated by solving the differ-ential equations stochastically using the Euler–Maruyama method. A representsthe case of low production rate of Jagged (J0 = 1,000 molecules/h). B–D repre-sent increasingly high production rates of Jagged: J0 = 1,400 molecules/h,J0 = 1,800 molecules/h, and J0 = 2,200 molecules/h, respectively. (E) Cell fateexchange rate (a measure of plasticity of the system) for increasing values ofproduction rates of Jagged (J0). (F) Cell fate exchange rate for increasing valuesof production rates of Delta (D0). Red dot represents the standard value aspresented in SI Appendix, Table S1.

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the basin of attraction of the two states—(high D1, low D2) and(low D1, high D2)—deeper, thereby stabilizing the tip and stalkfates (Fig. 7 A and B). We further evaluate the effect of Fringe atthe tissue level and show that loss of Fringe leads to an increasein the number of cells in the hybrid tip/stalk phenotype, therebyleading to small and poorly perfused blood vessels, typical oftumor angiogenesis (Fig. 7 C and D). Importantly, this stabili-

zation effect of Fringe is observed even when Fringe is not in-cluded in the model as a downstream target of NICD, but ratheras an independent variable (SI Appendix, Fig. S9).These results offer an explanation into why aggressive tumor

types such as basal-like breast cancer often show a loss ofFringe (32–34) and have increased microvessel density (MVD)and high microvessel proliferation (MVP) compared with the

A

B C

ED

Fig. 5. Patterning at the tissue level. (A) Cartoon representation of physiological, suboptimal, and pathological angiogenesis. In physiological angiogenesis, twotip 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 adecrease 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 pathologicalangiogenesis, 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 interactingcells 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) Cartoonrepresentation 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 cellswith 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, and D are presented in SI Appendix, Fig. S8.

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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 aVEGF 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 = 1,500molecules for cell 2. (C) Fate exchange rate for different values of Vext for cell 2, whereas Vext for cell 1 remains constant (Vext = 1,000 molecules).

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relatively less aggressive ER-positive and HER2-driven sub-types (35).

cis-Inhibition Stabilizes the Tip and Stalk Cell Fates. cis-Inhibition,the intracellular binding and consequent degradation of theNotch receptor and ligands (both Delta and Jagged), has beenconsidered to be critical for lateral inhibition and pattern for-mation in multiple developmental contexts (36, 37). However, itsrole in angiogenesis remains enigmatic. cis-Inhibition betweenNotch and Jagged in the stalk cells has been suggested to com-promise the tip-to-stalk signaling (14). Thus, we decided to ex-plore the role of cis-inhibition between Notch and Delta (N-D)and Notch and Jagged (N-J) both individually and together inthe 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 onthe stability of the tip and stalk cell fates, by representing thephase space by an effective potential for the case of both lowerand higher cis-inhibition rate (kC). In both cases, two stablestates are present: one cell as tip and the other as stalk and viceversa [(high D1, low D2), and (low D1, high D2)]. However, athigher values of kC, the basin of attraction for the stable statesare deeper, therefore suggesting that cis-inhibition has an im-portant role in stabilizing the tip position (Fig. 8). These resultsare consistent with previous experimental and theoretical ob-servations that cis-inhibition facilitates pattern formation andusually confers a greater robustness to noise during adoption ofalternate fates between neighboring cells (36, 38, 39).

We also evaluate the effect of cis-inhibition between Notch-Delta and Notch-Jagged individually, by changing kC only forN-D interactions (SI Appendix, Fig. S10 A and B), and then onlyfor N-J interactions (SI Appendix, Fig. S10 C and D). Our resultssuggest that N-J cis-inhibition stabilizes the tip and stalk cellfates much strongly compared with N-D cis-inhibition, i.e., theincrease in kCJ (cis-inhibition of N-J interactions only) leads to amuch deeper potential well (or basin of attraction) for the twostates—(high D1, low D2) and (low D1, high D2)—whereas in-creasing kCD (cis-inhibition of N-D interactions only) has littleeffect (SI Appendix, Fig. S10 A and B), again highlighting the factthat high Jagged levels can destabilize the tip and stalk cell fatesand contribute to the rich cellular plasticity and chaotic behaviorof tumor-mediated angiogenesis.It has been speculated that cis-inhibition between Notch and

Jagged in the stalk cells would reduce the signaling ability ofDelta from the tip cell and hence compromise the tip-to-stalksignaling (14). Our results, however, suggest the opposite, i.e.,that cis-inhibition has a fundamental role in stabilizing the tipposition. More specifically, we suggest that Notch-Delta cis-inhibition has relatively little effect in the stability of tip cells,probably due to the low levels of Notch receptor in the tip cells.In contrast, Notch-Jagged cis-inhibition has an important role instabilizing the tip position, because it decreases the probability oftip and stalk cells communicating via Notch and Jagged, hencereducing the levels of NICD in the tip cells. Reduced NICDimplies increased VEGFR2 and consequently high Dll4 in tipcells, thereby stabilizing the tip cell fate. If N-J cis-inhibition waslow, dynamic competition for tip position would be elevated.

DiscussionNotch and VEGF signaling pathways play a crucial role duringtip-stalk cell fate decisions in both physiological and patho-logical angiogenesis (1, 12). However, the underlying principlesof tip-stalk fate selection mediated by the interplay of Notchand VEGF pathways remains largely elusive. Here, we in-troduced a specific theoretical framework to study this in-terplay. We show that tip-stalk decision is not a binary one;rather, cells can adopt a hybrid tip/stalk phenotype, whenNotch-Jagged signaling dominates over Notch-Delta signaling.This phenotype can lead to form a new sprout but has a com-promised ability to migrate and develop filopodia, therebyleading to poorly perfused blood vessels with high MVD.Therefore, the hybrid tip/stalk phenotype offers a key advan-tage in pathological conditions: it can confer rich plasticity tothe leading cell that can rapidly exchange its position with aneighbor stalk, therefore inducing a fast but irregular vessel

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Fig. 7. Effect of Fringe on tip and stalk fate decision. (A) 3D representation ofthe effective potential as a function of Delta in cell 1 (D1) and in cell 2 (D2) forthe case of no Fringe effect (f = 0.0, i.e., λF,D = λF,J = 1). B represents the effectivepotential after including Fringe effect (f = 1.0, i.e., λF,D = 3, λF,J = 0.3). The statewith high D2 and low D1, i.e., the one with high levels of Delta in cell 1 but notin cell 2, corresponds to (cell 1 as tip and cell 2 as stalk); the state with high D1

and low D2 corresponds to (cell 1 as stalk and cell 2 as tip). (C) Average of thefraction of cells in (stalk), (tip/stalk), or (tip) state as a function of the Fringeeffect. The averages were taken over 100 simulations of a 2D layer of 100 × 100interacting cells in a square lattice with periodic boundary conditions. (D) Car-toon representation of a 1D layer of interacting cells for increased values of theeffect of Fringe. The states of the cells are defined according to the amountof active VEGF signaling (V): stalk (V <100), tip/stalk (100<V < 300), and tip(V > 300 molecules). The Fringe effect is represented by the variable f. The casef = 0.0 represents the no Fringe effect, i.e., λF,D = λF,J = 1, i.e., binding affinity ofNotch to Delta and to Jagged is the same. As f increases, the values of λF,D andλF,J linearly increase and decrease, respectively, such that at f = 1.0, λF,D = 3.0and λF,J = 0.3 (SI Appendix, Table S1), i.e., Notch has higher binding affinity toDelta and lower to Jagged. Therefore, (λF,D = 1+ 2f) and (λF,J = 1− 0.7f).

Fig. 8. Effect of cis-inhibition on tip and stalk fate decision. (A) 3D repre-sentation of the effective potential as a function of Delta in cell 1 (D1) and incell 2 (D2) for the case of a decrease in 10% of the cis-inhibition strengthcompared with its standard value (kC = 4.5e− 4). B represents the case of anincrease in 10% of the cis-inhibition strength (kC = 5.5e− 4). The state withhigh D2 and low D1, i.e., the one with high levels of Delta in cell 1 but not incell 2, corresponds to (cell 1 as tip and cell 2 as stalk); that with high D1 andlow D2 corresponds to (cell 1 as stalk and cell 2 as tip).

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branch that can quickly supply oxygen in fast growing tumors.When many cells adopt this hybrid phenotype, the vasculature isexpected to be quite chaotic: excessive number of small butpoorly perfused vessels, resulting in pathological angiogenesis asobserved during tumor growth (40). Therefore, our resultsoffer a good unifying explanation for many experimental ob-servations: (i) loss of Jagged significantly decreases vascularbranching (14), (ii) loss of Delta leads to excessive non-productive or poorly perfused angiogenesis (16), and (iii) lossof Fringe is correlated with increased MVD in tumors (35).Our results also attempt to resolve an apparent paradox between

the canonical roles of Notch-Delta and Notch-Jagged signaling andthe experimental observations about the overexpression of Deltaand Jagged in angiogenesis. Neighboring cells interacting via Notch-Jagged signaling usually adopt a similar cell fate (lateral induction)(6, 8), whereas those interacting via Notch-Delta signaling adoptopposite fates (lateral inhibition) (7). Consequently, increasedproduction of Jagged would be expected to reinforce the lateralinduction mechanism between the stalk cells, hence elongating thelumen; increased production of Delta would lead to more tip cells.However, the experimental results are the exact opposite: i.e. higherJagged levels increase vascular branching (14), and Dll4 acts as abrake on sprouting angiogenesis (16). These conflicting observa-tions can be explained by the emergence of a hybrid tip/stalk phe-notype on overexpression of Jagged. Cells in this hybrid phenotypecan lead the formation of a vessel, albeit not so efficiently, therebyleading to more vascular branching. Overexpression of Delta canprevent cells from adopting this hybrid tip/stalk phenotype and canhence inhibit angiogenesis.The emergence of a hybrid tip/stalk phenotype also lends sup-

port to the emerging notion “a black and white distinction betweentip and stalk cells is an oversimplification” (1) and strengthens theincreasingly accepted notion that a hybrid state that coexpressesmarkers of two lineages is a signature of enhanced plasticity(multipotency) of a system (41–43). We find that the tendency toadopt this hybrid phenotype is reduced at high levels of Fringe, aglycosyltransferase that promotes Notch-Delta signaling at the ex-pense of Notch-Jagged signaling by modifying Notch to increase itsaffinity for Delta and decrease it for Jagged. Thus, Fringe stabilizestip and stalk fates and can help promote physiological angiogen-esis, hence acting as a critical molecular brake on deregulated/pathological angiogenesis. Loss of this brake, as seen in aggressivetumors such as basal-like breast cancer (32–34), can enable tumorsto attain sustained angiogenesis (35), which is a hallmark of cancer(44). Overall, our results about Fringe are also consistent withexperimental and theoretical observations that Fringe promoteslateral inhibition patterns (19, 45) and are reminiscent of howasymmetric modifications of transmembrane ligand-receptor pairscan govern tissue-level pattern formation (46).The importance of Notch-Jagged signaling in delineating the

difference between normal and tumor angiogenesis is furtherrevealed by the role of cis-inhibition, specifically that betweenNotch and Jagged, in affecting tip selection. cis-Inhibition be-tween Notch and Delta has been reported to offer greater ro-bustness to noise during patterning (36), but ours is the firststudy, to the best of our knowledge, exploring the role of cis-inhibition between Notch and Jagged. Our results indicate thatcis-inhibition between Notch-Jagged stabilizes tip-and-stalk fatesmore strongly than that between Notch-Delta, hence underliningthe role of maintaining low levels of Jagged1 to ensure smoothand functional, i.e., physiological angiogenesis.

The critical role of overexpression of Jagged1 in mediating suchabnormal angiogenesis might explain why tumor-stroma interplayoften involves Notch-Jagged signaling (47). The increased Notch-Jagged signaling in tumor environment can be attributed to mul-tiple specific traits of tumor endothelial cells (TECs): (i) they cansecrete Jagged in the stroma (48) that can potentially activateNotch-Jagged signaling in neighboring endothelium; (ii) they havea proinflammatory gene expression and the inflammation re-sponse regulators such as NF-κB and TNF-α can increase Jaggedin them (14, 49); and (iii) they often adhere to inflammatory cellssuch as macrophages (25) that can increase Jagged in them viaparacrine or juxtacrine signaling. Such an amplified Notch-Jaggedsignaling can give rise to hybrid tip/stalk cells that closely resemblethe observed tip-like projections of the tumor vessels that mightoverlap with each other and even form loose connections (25).As discussed here, whereas some predictions of our model are

consistent with reported experimental results, the model offerssome previously untested hypotheses that can be tested experi-mentally. Specifically, we predict that the interactions that causeenhanced Notch-Jagged signaling, such as overexpression ofJag1, repression of Dll4, and inhibition of Fringe, should lead toa more dynamic switching between tip and stalk cell fates, be-cause all these cases can cause a larger number of cells to adoptthe hybrid tip/stalk phenotype, hence enriching cellular plasticity.It might be noted that among the three different homologs ofFringe in mammals, the role of Lfng (Lunatic fringe) and Manicfringe (Mfng) might be more pertinent than that of Rfng(Radical fringe), as they both can promote N-D signaling (50).To conclude, our theoretical bottom-up modeling framework

offers important insights into the molecular interplay betweenNotch and VEGF signaling in regulating cell fate decisionsduring both physiological and pathological angiogenesis. Albeitwe do not consider any spatial effects into account, ourframework is amenable to be integrated with agent-basedmodels on angiogenesis (29) and can be used, in an iterative waywith experiments, to decipher the organizing principles ofmultilayer process of angiogenesis (51). Specifically, as re-ported here, the crucial role of Notch-Jagged signaling in me-diating differences between physiological and pathologicalangiogenesis can be used for novel therapeutic benefits suchas developing decoys that can target JAG/NOTCH selectivelyas recently attempted (52). Such attempts are likely to bemore specific in targeting tumor angiogenesis and hence pro-vide a viable and safer alternative to disrupting Notch signalingaltogether (both via Delta and Jagged), a hallmark of mostantiangiogenesis efforts.

Materials and MethodsThe equations for the mathematical model are presented in The Theoretical

Framework. The values of the parameters used for the model are given in SIAppendix, section S1. Model construction is discussed in SI Appendix, sectionS2; and the sensitivity analysis for the model is presented in SI Appendix,section S5. The computational analysis was performed in Python.

ACKNOWLEDGMENTS. This work was supported by National ScienceFoundation Grants PHY-1427654 and NSF-MCB-1214457 and the CancerPrevention and Research Institute of Texas. M.B. was also supported byFAPESP (Sao Paulo Research Foundation) Grant 2013/14438-8. E.B.-J. wasalso supported by the Tauber Family Funds and the Maguy-Glass Chair inPhysics of Complex Systems.

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