Fig 1.
(A) Illustration of an angiogenic sprout, with EC in a “salt-and-pepper” pattern. White cells are the “active” cells with high DLL levels and purple cells are the “inactive” cells with high notch levels, the terms tip and stalk are positional and refer to cell 1 and cells 2–7 respectively. (B) Illustration of notch/VEGF lateral inhibition feedback loop between 2 adjacent ECs between quiescent state to patterned state. V.R2 = active VEGFR2 receptor, whose levels are increased in active cell1 and decreased in inactive cell2. (C) Representation of how different two nearby cell’s “umwelts” can be. For example, Cell 6 may have strong, previously patterned neighbors expressing near constant DLL, whereas Cell 2 is more in flux, due to position switching with cell 3 and experiences a changing level of DLL as it moves closer to different neighbors. Also each cell resides within a different region of the VEGF gradient (depicted by color gradient). (D) Brief overview of the notch-DLL interactions. Positive feedback from filopodia is shown in green, negative HE feedback in blue, lateral inhibition in brown. (D) Detailed 2-cell ODE model: V = VEGF ligand; R2 = VEGFR2 receptor; V.R2 = active VEGFR2; DLL = internal DLL, DLL.notch = active notch bound to DLL; nicd = NICD fragment; HE = Hes, Hey and Her combined. γ represents production rates while ϕ represents turnover rates (refer to Materials and Methods for details).
Table 1.
List of ODEs.
Table 2.
List of reaction equations.
Table 3.
Parameter values.
Fig 2.
Effect of local umwelt on EC patterning speeds.
(A) Illustration of simulation where the 2-cell model is initialized as 2 quiescent ECs (Q1 and Q2) in an environment of VEGF gradient and we ask how long does it take the 2-cell model to pattern into A:I (Active cell1:Inactive cell2) or I:A (Inactive cell1:Actitve cell2). (B) Matrix plot of the 2-cell system patterning speeds under different combinations of V1 and V2. (C) Illustration of simulation where 2-quiescent cells (Q1 and Q2) bounded by neighbors with high DLL (Dext1) and low internal DLL (Dext2) respectively. (B) Matrix plotting the patterning speeds under different combinations of V1/2 and constant Dext. (C) Illustration of simulation where 2-quiescent cells (Q1 and Q2) bounded by neighbors that can have different DLLext1/ext2 values at start of each simulation. (B) Matrix plotting the patterning speeds under different combinations of Dext1/ext2. In all conditions Active cells with high DLL are white, inactive cells with high notch are purple. Patterning time is indicated as a color scale where red indicates slow patterning speeds and color ranges of blue to white indicate faster patterning speeds.
Fig 3.
Position switching modulates the rate of state switching.
(A) In vivo scenario of 2 pre-patterned cells (cell1 and cell2, A:I) in a sprout bounded by neighbors N1 (with low DLL) and N2 (with high DLL) changing positions and switching states to I:A direction showed by dashed black arrows. There is an intermediate sate where cell1 and cell2 lie next to each other. (B) In silico illustration and measurement of state change over time with a sudden movement of cell1 away from N1 (seeing decreasing DLL) and cell2 moving toward N2 (seeing increasing DLL). (C) In silico illustration and measurement of state change over time with a gradual movement of cell1 away from N1 (seeing decreasing DLL) and cell2 moving toward N2 (seeing increasing DLL).
Fig 4.
Multistep EC pattern switching modulated by position changes.
(A) Bifurcation diagram of cel1 that starts as an active cell with high internal DLL (DLLcell1) and with changing DLLext values converts to an inactive cell with low DLL. (B) Bifurcation diagram of cell2 that starts as an inactive cell with low internal DLL (DLLcell2) and with changing DLLext converts to an active cell. Blue solid lines indicate a stable steady state while dashed green lines indicate unstable steady states. Orange regions = Active state, blue regions = pI states, green regions = Inactive states. The saddle nodes are marked as green circles. The dashed black arrows indicate the direction of state switching with changing DLLext1/ext2 values.
Fig 5.
Effect of Sirt1 on EC patterning speeds.
(A) Overview of the 2-cell model interaction with a positive regulation by Sirt1 (pink) and a negative regulation by Lfng (blue). (B) EC patterning speeds measured with different Sirt1 concentrations. Sirt1 = 1 c.u. optimal model, * and ** represent the threshold Sirt1 levels to transit from I:I →I:A/A:I and I:A/A:I→ A:A states respectively. State change in internal DLL values measured over time at (C) decreased Sirt1 (Sirt1 = 0.5 c.u.) and (D) increased Sirt1 (Sirt1 = 2 c.u.).
Fig 6.
Sirt1/Lfng together modulate EC patterning dynamics.
Bifurcation diagrams of internal DLL steady state levels in the 2-cell model perturbing DLLext levels continuously and changing Sirt1 values of (A,B) Low Sirt1 = 0.5 c.u., (C,D) control/wild type Sirt1 = 1 c.u. and (E,F) high Sirt1 = 2 c.u. in cell1 and cell2. Blue solid lines indicate a stable steady state while dashed green lines indicate unstable steady states. Orange regions = Active state, blue regions = pI states, green regions = Inactive states.
Fig 7.
Characterization of the partial states across species of the model.
Hierarchical clustering of all the species of the 2-cell model VEGFR2- Total inactive receptor; VEGFR2*- Active receptor, notch- Total inactive notch. notch* = Active notch receptor. While the columns represent the proteins, each row represents protein levels in individual cell under different simulation conditions.