Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis

Abstract

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, 'stabilised' tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer.

Figure 1. Overview of the spring-agent model.

(A) An endothelial cell is represented by a cylindrical, single layer square lattice mesh of agents, connected by springs, the physical properties for which follow Hookes Law. At either end (adjacent cells not shown) specialised junction springs and agents (pink) connect the cell to its neighbour cells along the vessel. (B) The underlying pathways modelled. VEGF activates VEGFR-2 receptors leading to both upregulation of Dll4 ligands and activation of actin polymerisation. Actin-based filopodia create positive feedback by increasing the cells surface area and aiding migration up the VEGF gradient, resulting in increased VEGF exposure. Dll4 binds to Notch receptors on neighbouring cells generating negative feedback by down regulating VEGFR-2 receptors. (C) To grow a filopodia a new agent and spring are created, see text for more details. When a filopodia spring exceeds the threshold length () a new node is inserted half way along the spring. It is given state ‘shaft’ and a focal adhesion. The original spring/s are deleted and new ones are created to reconnect the agents. Upon insertion of new nodes a spring connecting the top node back to the next node is also created. This is needed if the filopodia top node begins to retract. (D) As the filopodia extends shaft adhesions are created at regular intervals.

Figure 2. Flow diagram of the model.

Blue boxes indicate spring procedures. First, all membrane agents are updated in asynchronous random order, then, based on spring length adjustments, their positions are updated. Second, each cell agent updates its total protein levels across all its associated membrane agents, inserts new nodes where required and recalculates its surface agent coverage.

Figure 3. In vivo and in silico retinal sprouting, filopodia and astrocytes.

(A) A typical confocal image of the developing mouse retinal vasculature showing endothelial cells with numerous long thin, curved filopodia (pink; isolectin B4 staining) and astrocytes (blue: staining). (B) A zoomed in section of (A) used as a basis for the simulations, both . Two tip cells can be seen migrating up the prongs of an ‘A’ shaped astrocyte region. (C) The model with matching astrocyte environment. The two tip cells head towards the local point source of VEGF above. Colour indicates VEGFR-2 level (high - pink (tip cell), low - purple (stalk cell)). Junction springs are shown in white. Shaft adhesions on inserted nodes along filopodia facilitate realistic local curvature of filopodia. Shaft adhesions also inhibit veil advance (green arrows), giving more realistic cell morphology. Yellow arrow shows a filopodia where contact with a neighbour cell's filopodia has triggered veil advance. (D) Switching the shaft node mechanism off yields unrealistic shape. (E) Confocal image in the retina of a filopodia contact, which may be where signalling takes place to trigger veil advance. (F) Confocal image in the retina showing apparent inhibition of veil advance by filopodia (green arrow) and a filopodia which appears to have triggered veil advance (yellow arrow). Pink: isolectin B4 staining of endothelial cells and blue: astrocytes, staining. Tip cells labelled T, .

Figure 4. Simulation showing stalk cells flip fate upon anastomosis.

Screenshots of a simulation with seven cells on a square astrocyte lattice (blue) with two local VEGF point sources (white dots). Cell colour indicates VEGFR-2 receptor levels, pink - high (tip cells), purple - low (stalk cells). (A–D) initial tip/stalk pattern is selected by Dll4-Notch lateral inhibition. (E) fusion of two tip cells leads to disruption of the stable tip/stalk pattern, as they become inhibited. (F) a new stable tip/stalk pattern is reached. Inhibition of a fused tip cell causes the neighbouring stalk cell to ‘flip fate’ and form a second vessel loop as seen in (G,H). It can be seen from (D) that the second loop would not be possible without the flip in cell fates.

Figure 5. Graphs showing normal patterning is sensitive to fusion whereas oscillation is robust.

(A) Frequency of one hundred events where cell fate, of one stalk cell to a tip cell, flips (F) or does not flip (NF) given which tip cell has been inhibted by the first anastomosis event - correct cell (C), the tip cell next to two adjacent stalk cells, or incorrect cell (I), or instead the first fusion event was between adjacent cells (AL). (B) Cell VEGFR-2 levels over one run in normal VEGF. The light grey region indicates the first selection of tip cells into a stable pattern. This pattern is disrupted by the generation of new junction springs during the first anastomosis event (black line). A new pattern then stabilises (medium grey region). Similarly, the dark grey region indicates the third phase of tip cell selection after the second anastomosis event. In the final phase, due to the simplicity of this particular simulation, the current tip cells become inhibited but no new reversals of fate occur. However, cell division, and extra VEGF point sources further into the environment, would cause this punctuated instability of cell fates to continue. (C) In 10 times the VEGF concentration a marked difference is observed in system behaviour. In high VEGF all cells synchronously oscillate between tip and stalk cell fate, unaffected by anastomosis events. New intercellular junctions are formed at a nearly continuous rate, due to all cells moving forward at once, leading to fusion along adjacent tip cells aswell as between three and four non-adjacent tip cells.

Figure 6. In vivo and in silico elongation of cell-cell junctions by migrating tip cells.

(A) Confocal image of two tip cells (blue - isolectin B4 staining) in the mouse retina, stretching the stalk cell between them (green - Transgenic Notch Reporter signal eGFP), and significantly elongating the junction (highlighted in white). (B) This morphology, where a thin edge of the stalk cell lines the tip cell, is matched in simulation due to the low mesh spring constant. Tip cells - pink, stalk cells - purple, junction springs: white. (C) Diagram showing the vessel divided into segments to give two cells per cross section. A single offset parameter defines the position of the segments two cells. The offset runs from , where zero divides them along the top of the vessel as indicated by the dotted line. Here the offsets are, in order of segments, . Having three equal offsets in a row leads the central cells (indicated by an arrow) to have only three neighbours whereas the cells in the outer segments will have five neighbours.

Figure 7. Graphs comparing selection stabilisation rates.

Graphs showing the timestep when a salt and pepper pattern had been stable for at least 100 timesteps. Thin line - no offset, thick line - unequal neighbours, dotted line - equal offset, dashed line - unequal offset. (A) with migration, (B) no migration. Simulations were repeated but outlier runs which did not stabilise were removed. With migration (C) and without migration (D).

Figure 8. Frequency of runs which could not stabilise (outliers) for each junction arrangement setting.

(A–H)Thick line - stabilised runs, thin line - outlier runs with at least two tip cells adjacent, dotted line - outlier runs with no adjacent tip cells. (I,J) Outliers tend to have actually stabilised (not oscillating) but with just one or two sets of two adjacent tip cells (pink line), thin line - no offset, thick line - unequal neighbours, dotted line - equal offset, dashed line - unequal offset. (I) with migration, (J) no migration. (K,L) Adjacent tip cells are shown to share the smallest junction possible in that cell arrangement. Actual smallest junction size possible (MIN) and the sizes of junctions between adjacent tip cells in outlier runs, observed for unequal offset and unequal neighbour arrangements respectively (averaged over 50 runs).

Figure 9. Graphs comparing junction size range and improved behaviour of optimised junction arrangements compared with previous arrangements.

(A) minimum (grey) and maximum (black) junction sizes (measured by counting the number of memAgents along a junction, for adjacent cells if both are exposed to VEGF), averaged over 50 runs, no migration, (B) with migration. (C) Timestep at which stable runs reached the salt and pepper pattern with the optimised equal offset (dotted line) and optimized unequal offset (thin line) arrangements, with migration. (D) no migration. (E–H) frequency plots showing that the optimised arrangements have little or no outlier runs. Thick line - stable runs, thin line - outlier with adjacent tip cells, dotted line - outliers with no adjacent tip cells. (I) Graph showing that Reducing the C parameter, which scales the probability of being awarded an actin token upon receptor activation, by the same amount that VEGF has been increased by (scalar x) allows the two optimal junction arrangements to stabilise the salt and pepper pattern faster, even into very high VEGF (upto 7 times the normal setting of 0.25 molecules per grid site). Thin line - unequal optimal offset; dotted line - equal optimal offset. Scaling the C parameter, however, does not increase stabilisation rate of the no-offset arrangement as VEGF increases, as the difference is too small between minimum and maximum junction size in this arrangement. (J) the minimum and maximum junction sizes at t = 2500 when VEGF = 4 times normal setting and C is comparably scaled to one fourth its original value. With C-scaling the maximum is reduced and the minimum increased.

Figure 10. Graphs comparing in vivo and in silico filopodia contact data.

(A) Frequency plot of simulation contact time distribution, averaged over 50 runs. (B) in vivo frequency, averaged over eight anastomosis events in live imaging of the developing zebrafish. (C) Scatter plot of the time from the first contact made until fusion and time from the last contact made until fusion, in silico and (D) in vivo.

Figure 11. Spring constant sensitivity analysis results.

The average setting for each spring parameter when the four stages of development are achieved by the final time step, see Table 1. (A) runs that failed to achieve a salt and pepper pattern noticeably have very low values. (B) runs that selected tip cells but did not fuse had very low values, (C) runs where tip cells fused and one flipped fate show robustness to most parameter settings as long as the previously mentioned constants were set high. (D) Comparing the frequency of each possible outcome against runs with the parameter settings used in all other simulations, detailed in Table 1, which almost always show a flip in fate and never fail to select the salt and pepper pattern.