Time to Decide? Dynamical Analysis Predicts Partial Tip/Stalk Patterning States Arise during Angiogenesis

Abstract

Angiogenesis is a highly dynamic morphogenesis process; however, surprisingly little is known about the timing of the different molecular processes involved. Although the role of the VEGF-notch-DLL4 signaling pathway has been established as essential for tip/stalk cell competition during sprouting, the speed and dynamic properties of the underlying process at the individual cell level has not been fully elucidated. In this study, using mathematical modeling we investigate how specific, biologically meaningful, local conditions around and within an individual cell can influence their unique tip/stalk phenotype switching kinetics. To this end we constructed an ordinary differential equation model of VEGF-notch-DLL4 signaling in a system of two, coupled endothelial cells (EC). Our studies reveal that at any given point in an angiogenic vessel the time it takes a cell to decide to take on a tip or stalk phenotype may be drastically different, and this asynchrony of tip/stalk cell decisions along vessels itself acts to speed up later competitions. We unexpectedly uncover intermediate “partial” yet stable states lying between the tip and stalk cell fates, and identify that internal cellular factors, such as NAD-dependent deacetylase sirtuin-1 (Sirt1) and Lunatic fringe 1 (Lfng1), can specifically determine the length of time a cell spends in these newly identified partial tip/stalk states. Importantly, the model predicts that these partial EC states can arise during normal angiogenesis, in particular during cell rearrangement in sprouts, providing a novel two-stage mechanism for rapid adaptive behavior to the cells highly dynamic environment. Overall, this study demonstrates that different factors (both internal and external to EC) can be used to modulate the speed of tip/stalk decisions, opening up new opportunities and challenges for future biological experiments and therapeutic targeting to manipulate vascular network topology, and our basic understanding of developmental/pathological angiogenesis.

The temporal basis of angiogenesis

“…Interestingly simulations predict that slowing down decisions in the CPG could sometimes counter-intuitively act to increase branching, if conditions are such that cells are more active during the long ‘indecisive’ period of time rather than being regularly over inhibited by elevated Dll4 levels as they were in the SIRT1 and PlexinD1 knock-out conditions. For example, a hypothetical SIRT1 gain-of-function simulation was performed, which leaves Notch signalling so weak, due to the rapid degradation of the NICD, that not only does it take a long time to select the stalk cells, but they are all highly migratory during this time [64]. …”

Positive-feedback defines the timing and robustness of angiogenesis

“…However, we have little-to-no understanding of the underlying temporal features of these decision-making processes. Indeed, lateral inhibition is considered relatively slow, taking upwards of 6 h to complete multiple cycles of gene expression needed to amplify initially small differences in input signal [14,[16][17][18][19], which is seemingly incompatible with the rapid dynamic changes in EC state, identity and behavior observed in angiogenesis [20,21].…”

“…Such ultrasensitive responses are frequently driven by positive-feedback loops that amplify signal outputs to promote switch-like dynamics [25,26], but despite the recognized role of Notch-mediated negative-feedback in angiogenesis, the function/identity of positive-feedback modulators remains elusive. Using our previously validated ordinary differential equation (ODE) mathematical model of DLL4-Notch-mediated lateral inhibition [16], which permits rigorous, mathematical interrogation of the bifurcation dynamics in this system, we probed the ability of positive-feedback to modulate the thresholding of EC lateral inhibition. In this model, two adjacent un-patterned ECs compete for selection as either a VEGFR-active DLL4-expressing tip cell or Notch-active laterally inhibited cell using the well-established VEGFR-DLL4-Notch negative-feedback loop ( Figure 1I).…”

“…Interaction between two ECs at the growing end of the angiogenic front have been captured using coupled ordinary differential equations and the 2-cell model previously described [16]. Reactions for the ordinary differential equations of the 2-cell model were written following mass-action kinetics.…”

“…Reactions for the ordinary differential equations of the 2-cell model were written following mass-action kinetics. Details of model construction, list of ODEs, reaction equations and parameters can be found in [16]. Positive-feedback between VEGF and a VEGF-induced/activated factor (P) is captured using the equation; paraformaldehyde (PFA) overnight at 4°C and processed as described previously [48].…”