Active perception during angiogenesis: filopodia speed up Notch selection of tip cells in silico and in vivo

Assessing quasi-static equilibrium: As the model is stochastic, we use a method to evaluate the quasi-stability of the system before incrementing the Dext level as in hysteresis studies the system is expected to reach steady state before incrementing. In order to approximate quasi-static equilibrium while changing Dext, we tested the stability of Dcell levels using the following method: (i) we allowed a transient time window (250 time steps) to pass, (ii) we calculated the average and standard deviation of Dcell in two adjacent, non-overlapping sliding windows of size 250, (iii) we tested whether |μc – μp|/(μc + μp)< ε and |σc – σp|/(σc + σp)< ε, where μc/μp denote the average Dcell and σc/σp its standard deviation in the last/previous window (ε = 0.5). If the EC does not pass the test or a maximum time limit of 60 000 was not yet reached, we increment the window. Otherwise we move on to the next Dext.

Characterizing Dcell fluctuations at intermediate Dext levels in calibrating quasi-static equilibrium assessment: We arrived at the generous ε threshold value, used to assess the quasi-static equilibrium, by observing the fluctuations of Dcell close to the bistable region. Due to the stochastic nature of filopodia extensions, Dcell fluctuations close to the bistable region are large (electronic supplementary material, figure S3a,b). Because of this inherent stochasticity, the exact Dext thresholds at which abrupt transitions occur are not the same from simulation to simulation. Moreover, if the time window between increments is very large (well above the biological time scales involved in patterning), the EC may undergo stochastic transitions between metastable active/inhibited states. To understand the nature of these transitions, we set up a second set of simulations. In this case, we started the EC with Dext = 0 and ran the simulation for 104 time steps, after which we abruptly increased Dext to a non-zero target value, and performed 3 × 104 more steps. Exposure to low Dext (500) keeps the EC in an active state, albeit with sizable Dcell fluctuations (electronic supplementary material, figure S3c). At the intermediate Dext level of 850, however, the long simulation showcases abrupt, stochastic transitions between active and inhibited states (electronic supplementary material, figure S3d). Lastly, high Dext (950) causes a one-way transition from active to a strongly inhibited state (electronic supplementary material, figure S3e). Even here, the transition is not immediate (approx. 0.3 × 104 steps), but it is irreversible within the time window of the run.

The model set-up: For work involving the AP signatures, we set up a minimal two-cell MSM vessel.

Time to pattern: Rather than the Vegfr and filopodia criteria as in the first MSM simulations, here we used the simpler and filopodia-independent Dcell approach as developed in the hysteresis simulations above to determine the earliest time indicator of when the dynamical system has gone past the point of no return into the attractor of tip versus stalk. We simply measured the total Dll4 levels of the two cells and declared the system ‘patterned’ once one of the cells has maintained an advantage of 600 ligands over the other for 100 time steps (the 100 time steps of waiting were subtracted from the final number once elapsed). Once a cell achieves an advantage of 600 Dll4 (a value 6% of Dmax, decided on heuristically), in the absence of fluctuations (which we test by waiting 100 time steps), the dynamics of the system seem to always ensure that cell to be selected as the tip. This is a heuristic method and makes many assumptions such as the absence of a long-timescale fluctuations and the presence of the bistable dynamics we witnessed in §2 of this paper, reasonable for the constrained parameter ranges of F, V and G investigated here. The second assumption does not render the claims made in this paper circular, because the measures/heuristics used to characterize the bistability (thus ruling out slow fluctuations) were different from those used that involved assuming its presence.

Sensory map: To calculate the sensory map, we first calculated the displacement vector from the Vegfr activation occurring on memAgents existing away from the main cell body (e.g. on filopodia) to the centre of the circular cross section of the cylindrical cell body. Then we normalized this displacement vector and multiplied it by the radius of the blood vessel to point to the closest region on the surface of the cell to the activation. We mapped all activations out in space onto the cell surface in this way. One caveat of this approach is the activations from one cell can be attributed to the neighbour cell surface area if the filopodia reaches over it. However, the sensory map here represents the vessel level activations and sensing of the environment rather than precise individual cell sensing levels.

Estimating entropy: To estimate Shannon entropy, we used the standard binning approach and Laplace smoothing to turn the data into a distribution. We did not have to quantize any data because of the discrete nature of Vegfr activations and the discrete spatial grid that the MSM exists on.

Zebrafish embryos, larvae and adults were maintained according to UK Home Office regulations. All studies were approved by the University of Manchester Ethical Review Board. Zebrafish strains were maintained at pH 7.4, a temperature of 28°C and exposed to 14 h light and 10 h dark cycles. Zebrafish lines used in this study were the Tg(kdrl: nlsEGFP)zf109 strain [100] and Tg(kdrl:ras-mCherry)s896 strain [101].

Confocal microscopy of live Tg(kdrl:nlsEGFP)zf109 and Tg(kdrl:ras-mCherry)s896 embryos was performed as previously described [20,27]. Tg(kdrl:nlsEGFP)zf109 embryos were manually dechorionated and incubated with EtOH carrier or 0.08 µg ml−1 latrunculin B from 16 hpf prior to live imaging at 19 hpf. Tg(kdrl:ras-mCherry)s896 embryos were manually dechorionated prior to imaging at approximately 24 hpf. Embryos were mounted in 1% low-melt agarose in glass bottom dishes, which were subsequently filled with media supplemented with 0.0045% 1-phenyl-2-thiourea and 0.1% tricaine, as well as EtOH carrier or 0.08 µg ml−1 latrunculin B for Tg(kdrl:nlsEGFP)zf109 embryos. Tg(kdrl:nlsEGFP)zf109 embryos were imaged using a 20x dipping objective on a Zeiss LSM 700 confocal microscope. Tg(kdrl:ras-mCherry)s896 embryos were imaged using a 20x dipping objective on a Zeiss LSM 880 confocal microscope with Airyscan. Embryos were maintained at 28°C and stacks were recorded at every 0.3 h for Tg(kdrl:nlsEGFP)zf109 embryos or every 0.3 s for Tg(kdrl:ras-mCherry)s896 embryos. Tracking of cell motility was performed in ImageJ using the manual tracking plugin. All cell tracking recordings were normalized at each time point relative to the position of the dorsal aorta to account for any dorsal or ventral drift of embryos during imaging.

Whole-mount immunostaining for pErk was performed as previously described [20,27]. Briefly, Tg(kdrl:nlsEGFP)zf109 embryos were manually dechorionated and incubated with EtOH carrier or 0.08 µg ml−1 latrunculin B from 16 to 18 hpf prior to fixation in PFA at the indicated time points. Embryos were washed in MeOH, bleached in 3% H2O2 in MeOH, washed again in MeOH, stored in MeOH at −20°C for 2 days in MeOH before equilibration with PBT (PBS, 0.1% Tween-20). Embryos were cryoprotected in 30% sucrose in PBT before further equilibration in PBT, incubation with 150 mM Tris–HCl (pH 9.0) and heating to 70°C for 15 min. Embryos were then washed in PBT, dH2O, acetone, PBT and TBST (TBS, 0.1% Tween-20, 0.1% Triton X-100), prior to incubation overnight at 4°C with block solution (TBST, 1% BSA, 10% goat serum). Embryos were subsequently incubated overnight with anti-phospho-ERK1/2 antibody (1 : 250, Cell Signaling; #4370) in blocking buffer, washed with TBST, washed with Maleic buffer (150 mM maleic acid, 100 mM NaCl, 0.001% Tween-20, pH 7.4), blocked in 2% blocking reagent (Sigma-Aldrich) in Maleic buffer for 3 h and incubated with goat anti-rabbit IgG-HRP (1 : 1000) in 2% blocking reagent in Maleic buffer overnight at 4°C. Embryos were then washed in Maleic buffer and then PBS at room temperature prior to incubation with 50 µl amplification diluent with 1 µl Tyramide-Cy3 (Perkin Elmer) for 3 h at room temperature in the dark. Embryos were finally washed over several days in TBST at room temperature. Embryos were then mounted in 1% low-melt agarose in glass bottom dishes and imaged using a 20x dipping objective on a Zeiss LSM 700 confocal microscope. Finally, to identify pErk-positive endothelial cells, kdrl:nlsEGFP signal was used to create a binary channel mask to isolate only nuclear signal in the pErk channel.