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

Logistic-like shapes as in the intensity plot (figure 5d), on the other hand, commonly result from variables undergoing positive feedback, where the rate of change of some value is positively proportional to its current magnitude but subject to a global resource constraint (here, the limited actin resources filopodia use to extend). Hence, the shape of the time evolution of the sensory map may indicate the positive feedback facilitated by filopodia. In the previous section, simulations predict that positive feedback from filopodia generates hysteresis and bistability in EC states. Here, by analysing through the cognitive lens we have found evidence of this positive feedback in the time evolution of the intensity measure of Vegfr activations.

When we alter the guidance parameter (G), we see that the AP signature changes in line with F LOF (figure 5e). In the normal and GOF cases (G = 0.9,1.0) the same pre-emptive, slight reduction in entropy before the Notch patterning decision is made, followed by a drop of approximately 1 bit after. Intensity also responds to GOF in the way one would expect, with a late time logistic-like shape in the case of G = 1.0 (GOF) and G = 0.9. In the LOF cases where G = 0.4, 0.0, we notice the partial and complete loss of these observed structures. This suggests that the signatures we measured correspond to the effects of active perception as a whole, rather than just one of its components.

Taken together, we find entropy and intensity of Vegfr activations on the sensory map can be used as a signature to connect the effects of the three key component parts of the system under the unified, basal cognitive conceptual umbrella of ‘basal active perception’. When active perception is present, the entropy of activations on the sensory map is reduced before a patterning decision is observable in Dll4 levels, and the intensity of activations over time has a logistic-like form at later times. These findings correspond to ways in which the cells direct their receptors to facilitate rapid and robust patterning.

Here we present the first proof of concept in silico and in vivo study supporting the theory that endothelial cells utilize filopodia as a form of sensorimotor feedback (active perception) to speed up Notch decisions during angiogenesis. This highlights the functional importance of the movement of Vegfr through the environment via a deforming surface, rather than merely its basic functionality as a receptor. We find in silico that the shape-changing movements of filopodia provide positive feedback to Vegfr–Vegf signalling, which endows the tip–stalk selection machinery with bistable, rapid and robust switch-like properties and hysteresis. Lastly, we begin to unpack the notion that filopodia on ECs may constitute a basal form of active perception. We apply information theory measures used in computational neuroscience, where AP is more well-studied, which indeed indicate that this system meets a necessary but not sufficient criterion for filopodia ‘enriching’ sensory input, providing the first rigorous step towards understanding and analysing the way sensor-motor feedback contributes to EC adaptive behaviour during angiogenesis.

Our simulations identify three critical components to the system that ensure ECs are endowed with bistable properties and complete selection rapidly—filopodia, a Vegf gradient and a direct coupling mechanism between them (e.g. guidance). However, our simulations predict that a gain in one of these components can rescue bistability and selection timing given a reduction of another. This strongly suggests the importance of the interlinked nature of these components rather than properties of the individual parts in isolation. In tissues with very shallow gradients or with minimal guidance coupling—e.g. more randomly directed filopodia as in zebrafish ISVs [44]—a GOF adaptation of filopodia extension could permit ECs to nevertheless keep selection occurring on time within tissue time constraints.

Our work raises an important new role for filopodia in ensuring the Notch selection of tip cells occurs in a timely, rapid and robust manner. Contrary to the prevailing literature that considers the role for filopodia being after tip cells are selected, here we show that they play a key role before: movement must be primary and part of the decision process rather than secondary, after the decision has been made. We thus propose a shift in perspective to considering even small cell shape-changing movements as potentially critical parts of the cellular repertoire of tools, helping them to solve complex problems during tissue morphogenesis.

The conventional way to explain biological events is at the scale of molecules, proteins and genetic pathways. But in tandem to this well-trodden explanatory framework we find viewing events and processes in terms of active perception, through the perspective of basal cognition, brings great benefits for revealing hidden mechanisms in cells for two main reasons: (1) Investigating AP naturally brings embodiment (the cells body shape and organizational material structure) to the forefront. Often, we can forget the spatial shape of cells when reducing mechanisms to molecular/genetic pathways [83]. We recently found that tip cell ECs manipulate their body shape and size during sprouting in order to bypass slow Notch selection altogether and rapidly assign one daughter (the larger cell) to be the tip [27]. This work shows that cell embodiment factors (such as shape, size and movement) can have the same importance as molecular and genetic factors in a developmental mechanism. Actively emphasizing how these dynamically couple to molecular pathways opens the door to a wealth of unexpected insights and hidden knowledge that ‘well-studied processes' considered only from a non-spatial, molecular/genetic perspective may have missed. The field of biomechanics, putting force changes on an equal footing with molecular signalling by viewing cells simultaneously from a mechanical and molecular perspective, revealed a multitude of hidden abilities of cells [84]. Yet, we are only just scratching the surface of how the dynamics of cell shape and geometry feed back to signalling [85–87].(2) Pathways are a type of model for understanding biological events at a specific molecular spatial and temporal scale.

Despite the tremendous successes of pathways centric biology, it is necessary to build on them and ask broader questions involving feedback, control and information flow if the goal is to understand and control biological outcomes at the higher scales, such as organism/tissue-level patterning and complex behaviour [67,68]. For example, if one endeavours to teach a rat a circus trick, it is advantageous to train the rat using positive and negative reinforcement rather than trying to micromanage every individual neuron in the rat's body [67]. Controlling morphogenic outcomes that result from the collective patterning decisions of cells may similarly benefit from such a behaviour-level approach, which the emerging basal cognition field can provide.

An immediate benefit of framing the tip selection process in terms of AP is the number of new and exciting questions and research directions that open up. Below we briefly highlight a selection.

Here we focused on filopodia as their presence in angiogenesis in widely characterized, yet their role has remained unclear. However, ECs also exhibit lamella-type extensions and triangular veils [25,45]. These protrusions are known to play roles in cell migration but a role in enriching sensory input to alter timing of cell decision-making (basal AP) has not been considered. Both work at a marginally slower timescale to filopodia and are generated by cross connected actin rather than parallel bundles. Furthermore, the shape change is fundamentally different; these are more convex or triangular respectively than the long thin filopodia. Altogether, shape-signalling feedback could vary greatly on each kind of cell protrusion, potentially providing a variety of basal AP mechanisms for cells to combine when enriching sensory input for problem-solving.

Here we focused on the very first, small rapid protrusive movements of ECs that are otherwise positionally fixed in a pre-existing vessel detecting a Vegf signal, before the longer-timescale full-body movements of tip cell migration during sprouting or EC tip and stalk position changes within vessels (cell rearrangement) have begun [34,35]. This was to avoid interference of other roles filopodia or longer time-scale full-body movements in this first study. However, Notch signalling continues after the first tip cells are selected, and the maintenance of a differential salt and pepper Notch pattern is required to generate differential adhesion along the sprout, which drives the cell rearrangements [23]. Thus, the ability to continually and rapidly re-establish the Notch salt and pepper pattern when individual cells change positions must still be required [9,33]. It is reasonable to hypothesize that filopodia continue to play a decision-making role on migrating ECs within sprouts when the Dll4 signal from neighbours becomes less clear after a local position-switching event disrupts the cell-by-cell Notch pattern—akin to the mid-range Dext levels in the hysteresis simulations. Indeed, in an integrated in silico/in vivo study of PFKFB3-driven glycolysis in filopodia formation we found that a reduction in filopodia perturbed cell rearrangement dynamics indirectly by impacting Notch patterning timing.

The study presented here focuses on the tip cell selection step in angiogenesis, which can be seen as a key collective coordination/decision ‘task’. However, there are many different problems cells solve in order to construct the full vascular network that could be posed as ‘tasks’ cells might efficiently solve using shape-signalling feedback, AP or other basal cognition mechanisms. For example, filopodia are known to improve tip cell fusion during anastomosis [25,47], but exactly how remains unclear. ECs in formed vessels often exhibit a cilia—a sole protrusion into the lumen—which aids the sensing of flow through its movement and thus could be a form of basal AP [88].

The really tantalizing question is how widespread basal AP mechanisms like this one may be, among the myriad of cells in tissues of different organisms? Is it an evolutionarily conserved and common mechanism employed by cells to enhance their adaptive problem-solving or a rarity, emergent only if a set of tissue conditions are met? Life-critical processes such as morphogenesis, wound healing and repair are by their nature time constrained, which we can imagine would then favour evolution of basal cognitive processes that can help to solve them faster. Cell shape changes occur as a matter of course during morphogenesis and are currently largely considered from a biomechanical stance; however, they may also confer basal AP properties by enriching sensory input, justifying wider application of the basal cognitive lens in tissue morphogenesis research. A further cell type within organisms that stands out as a prime candidate for basal AP are macrophages as they have distinctively protrusive, dynamical filopodia and lamella, which appear to play multiple roles aiding the cell to rapidly traverse very different tissue environment ‘terrains’ while finding and catching foreign bodies to phagocytose [89].

Here we co-modulated the three core interrelated components of basal AP (sensing, movement and the coupling between them) and targeted filopodia as a first coarse-grained approach. The next step is to delineate the precise molecular pathways coupling sensing and movement within filopodia, such as receptor trafficking mechanisms within filopodia and assessing whether membrane shape-detecting proteins like F-BAR [90] may play a role in coupling signalling to the shape changes. Interestingly Tm4sf18, which we found conferred positive feedback to Vegfr sensing and facilitated switch-like rapid selection in vivo, has been previously shown to increase filopodia formation [91], making it a prime target as a basal AP component. In a prior study to delineate the role of Cdc42 (a small GTPase involved in the regulation of actin-based morphogenesis and cell polarity [92–95]) in angiogenesis, we found that ECs lacking Cdc42 in the mouse retina in vivo have a competitive disadvantage to assume tip positions compared to ctrl ECs in chimaeric angiogenic sprouts [96]. Cdc42-KO-EC at tip positions lacked filopodia and instead protruded only few very short and studded protrusions from their surfaces. This suggests a crucial and cell-autonomous requirement for Cdc42 in tip cell selection. If a wider array of basal AP mechanisms were found across tissue contexts, the natural next step is to check if there is a core set of evolutionarily conserved AP molecular pathways—or if cells make use of very different proteins with the same functionality to couple sensing and motion in different contexts.

There are many opportunities but also challenges and responsibilities to carefully consider, given the impact that basal cognition-focused studies such as this could have for the field of cell and tissue biology within higher organisms. One such problem is to balance and temper the psychological concepts and claims in AP studies made with higher organisms correctly, when working at the cell level. Similarly, there is a need to consider the empirical tools and viability of features of experimental design for study of AP at the different scales.

To establish conclusive evidence for active perception, Yang et al. [22] suggest that it is necessary to compare the actions of the system in question to those of a model of what an idealized active sensor would do given the same goal (for example, a model utilizing Bayesian decision theory [55,97]). Characterizing active perception in our system this way is challenging because doing so would require assuming that endothelial cells have a known goal in their actions. Even if cells are optimizing towards a goal it is often the case that they are simultaneously solving a number of problems in parallel. This makes it hard on teleological grounds to devise a simple idealized model for comparison (except for potentially viewing the negative feedback of lateral inhibition as a form of teleology [98]). Thus, we took a simpler, indirect approach when assessing the presence and effects of active perception in angiogenesis as used by Lungarella et al. [80].

We defined, akin to Lungarella et al., basal AP for cells in tissues as specifically meaning coupled, direct two-way feedback between motion and sensing (i.e. not requiring indirect processing through gene regulation) that enriches sensory input leading to improvement of a collective cell problem-solving process in morphogenesis. This minimal definition avoids unhelpful overfitting of human-level psychological connotations to cells such as perception, action, goals and intentionality while enabling empirical testing of basal AP in the future. This enables us to now use verifiable molecular approaches in vivo and in vitro to prove the coupling between motion and sensing. Together with signature changes to the sensation enriching measures, this is a way to measure the resulting effect on the cell coordination process in question. Here we focused on the first simplest sensory enriching measures—the time evolution of receptor activations and entropy. We plan to explore and extend to more complex metrics in the future, such as using transfer entropy to assess the strength of sensorimotor coupling rather than just searching for its signatures [64,99].

Overall, we hope that this study acts as a first step into a new research programme elucidating the extent and variety of basal AP mechanisms that cells from different tissues may have evolved to enable complex collective cell coordination processes. Importantly, as many seemingly unrelated pathways may constitute component parts of basal AP mechanism, we propose that basal AP is inherently accessible to therapeutic modulation by targeting any of these to control and tune individual to collective cell behaviour in tissues.

The MSM was first developed and described in full by Bentley et al. [24,25] and has since been used in a wide range of studies to explore VEGF/Notch and tip cell dynamics during angiogenesis with many predictions being validated in vivo from this model [26,27,35,70]. Being the only angiogenesis tip selection model with sophisticated filopodia dynamics, it was the natural choice for extension in studies here. Briefly, in this model cell morphology is represented as a surface comprised many small agents (membrane agents, ‘memAgents’) connected by springs following Hooke's Law (which confer tension to the changing cell shape, akin to the actin cortex beneath a cells membrane) (figure 2b). The memAgents move in continuous space but are snapped to a gridded lattice to implement discrete local rules of agent interactions (grid sites represent 0.5 × 0.5 × 0.5-μm cubes of space). At each time-step, an equal number of the cell's current, total Vegf receptors are distributed to each memAgent over the cell's current surface shape. Dll4 ligands are only distributed to any memAgent in Moore neighbourhoods of memAgents from other cells (on the interface between cells or ‘junctions’). The ambient Vegf is modelled as a fixed linear gradient or a uniformly distributed value, where in the linear case each grid site (g) starting from y = 0 has Ig level, calculated as Ig = Vslope⋅y where y is the y-axis coordinate position of g and V is the slope of the gradient.

Model initialization and parametrization: The model was initialized with 10 cells in a row, one per vessel cross section (e.g. Figure 2b), representing a collection of endothelial cells in a pre-existing vessel competing to sprout into the space above (represented very simply here as just a fixed VEGF gradient extending into the y-axis above the horizontal row of cells). All parameters were kept the same as previously published [17,20,24,25] except those being varied to match the experimental conditions here, described below. For example, a cell is 10 µm wide and spans one cross section of a pre-existing vessel with 6 µm diameter (matching in vivo capillary dimensions). Each cell comprises approximately 1200 memAgents initially.

Signalling: Simplifying the description of the competitive receptor biology between different Vegfrs in the original MSM, as it is not the direct focus of this study, we can state that the number of active Vegf receptors of a given memAgent m is calculated as Vegfrm∗=Vegfrm⋅∑Ig—where the * denotes an activated receptor–ligand complex. Notch is activated in each memAgent (resulting in the local removal of Dll4 from neighbouring cell's memAgents), up to the value of Nm. If Dll4 < N then Notchm∗ = Dll4; if Dll4 > Notch, then Notch∗= Notchmax.

Filopodia: MemAgents extend filopodia by one grid site length at a time by creating non-branched chains of new memAgents adhered to the environment (fixed in position by adhesions to the environment every 2 µm, as per [46]). These events are stochastic, with approximate probability:P(extend filopodia)≈ F ⋅Vegfr∗where F is a tunable constant varied in simulations here. Filopodia do not extend unless they have enough available actin and Vegf receptors activate. For full rules behind the actin dynamics and spring settings driving the filopodia extension and retraction, see Bentley et al. [25]. Filopodia retract if the memAgent at the top of the chain has not extended for Fmax time steps. Retraction occurs by iteratively snapping the chain of springs connecting adhered memAgents along the filopdium back to the next memAgent in the chain, while deleting memAgents as they go (based on in vitro observations that filopodia retract in short rapid bursts to the nearest adhesion along it, which then releases, triggering the next rapid retraction back and so on). This can be imagined as similar to the way a climber inserts periodic anchors to the rope as they climb so that they only fall back quickly to the last anchor point. With filopodia, every anchor eventually is pulled away by this force in short bursts, until the filopodium has fully retracted to its base. However, their total length is limited by the total amount of actin available to the cell, which gets used up on every filopodia extension of 1 μm. The original model in Bentley et al. [25] generates full cell migration by releasing filopodia adhesions and allowing the springs to pull the cell forward akin to veil/lamella advance [46].

Here, however, we keep adhesions fixed to control variables, prohibiting these other forms of protrusions, to ask specifically whether shape changes due to filopodia play a role in selection timing.

Genetic regulation: Briefly, Notch lateral inhibition is implemented each time step as follows:Vegfrcell= Vegfrmax – σ Ncell∗′andDcell = Dcell + δ Vegfrcell∗′where σ, δ are constants and Vegfr∗′ denotes Vegfr* after a time delay (28 time steps) corresponding to the time it takes for translocation of activated receptor signalling to the nucleus, transcription to alter gene expression, and subsequently protein levels at the cell surface. The new Vegfrcell and Dcell levels are then redistributed to the memAgents and the process repeats on the next time step.

Parametrization: All parameters in the model are set as in Bentley et al. [25], which were previously calibrated to experimental data. To investigate active perception, we focus here on simulations varying filopodia extension (F) and the input signal gradient (V). For normal EC, F = 2 and V = 0.04, guidance G = 0.9. We fine tuned three parameters for this study (filspacing, tokenStrength and filtipmax) by covarying them and exploring the phase space of the system, arriving at values very close to their previously published values, giving no change to normal system behaviour, but putting the model at a more precise critical point so that varying other parameters in our LOF/GOF studies accessed different behavioural phases of the model. Parameter values are detailed in table 1. Table 1. Parameter table for in silico simulations.parameter (name/symbol)descriptionsetting value or rangejustificationPattern Dll4 criterionamount of Dll4 advantage required for cell to be declared ‘winner’600heuristically estimated: appears larger than the amplitude of possible oscillatory modesPattern Stability criterionamount of time required to be spent with advantage of Pattern Dll4 criterion until pattern declared stable100heuristically estimated: appears longer than the phase of possible oscillatory modesGuidance (G)probability that an extending filopodium will choose to step into the direction of locally maximal sensed VEGF concentrationin range (0,1), control 0.9originally set to 0.9, Bentley et al. [25]Vconcst (V)vegf concentration parameter; flat value distributed everywhere in uniform case, or defines the slope of linear gradient in gradient casegradient in range (0.01,0.04), control 0.04; uniform in range (0.5,1.4), control 0.8Bentley et al. [25]FilVary (F)filopodia propensity to extend parameterin range (0,3), control 2Bentley et al.

[25]Filtipmax (Fmax)maximum number of time steps elapsed between extensions; if more time elapses, the filopodia begins retracting instead15fine tuned; previously filtipmax = 30 in [24] and 10 in [25]TokenStrengthsimulated actin cost of extending filopodia1tine tuned; previously TokenStrength = 3 in [25]FilSpacingspacing between filopodia on cell body, in units of memAgents2tine tuned; previously FilSpacing = 1 in [25] and 4 in [24]

We switch off veil advancing, lamella mechanisms in simulations, create permanent adhesions at the base of filopodia prohibiting cell body movements and switch off cell rearrangement position changing junction-based mechanisms [23] fixing cells to their initial positions in the pre-existing vessel.

Time to pattern: To assess patterning times (when a clear and complete alternating salt and pepper pattern of tip and stalk cells have been selected) the model was run 100 times for a maximum number of time steps (2000 for Vegf gradients and 5000 for uniform Vegf). For the 10-cell version of the MSM the pattern must meet criteria as per Bentley et al. [24]. Tip cells are defined as cells that have sprouted filopodia and have not been inhibited (as per in vivo tip cell characterization). The patterning criterion is that four or five non-adjacent tip cells must be active at a given time. The stability criterion dictates that the pattern of tip cells must persist for 100 time steps (chosen as it allows for a cycle through the Notch pathway to occur which might alter the pattern if unstable). Once these criteria are met, the collective of cells is deemed ‘patterned’ and the time is recorded.

To test our hypothesis that filopodia speed up patterning due to the positive feedback of sensing and acting generating bistable properties in single cells, we developed a new simulation testbed extension to the MSM that parallels the mechanical ball and magnet example of a bistable system (figure 3a–c). We focus on how an individual cell's state changes as it experiences different, controlled levels of inhibition from two immobilized and de-coupled neighbouring cells. Lateral inhibition from these two neighbours (‘external Dll4’ or Dext) affects the individual EC under investigation (its current Dll4 level, ‘Dcell’, is used as proxy for its active/inhibited state), but these neighbours are uncoupled from being inhibited themselves (figure 4a). Dcell is therefore analogous to the ‘ball position’ in the mechanical example of a bistable system described in the Results section and the fixed neighbours Dext to the magnet position; raising Dext can push the cell into a more inhibited (low Dcell) state and vice versa.

In a hysteresis analysis, the external driving signal is quasi-statically raised and lowered in such a way that the dynamical variable stays at or close to its equilibrium value as the driving signal is varied. We start with Dext set to zero and thus simulate a fully active EC with long filopodia (figure 3c). We then slowly raise the Dext in increments of 50 until full inhibition is achieved (figure 3b), then reverse the process until it is yet again relieved. If filopodial active perception indeed creates bistability, we expect the transition between active/inhibited states to take place abruptly, at a Dext threshold that is higher for the active → inhibited transition than the reverse.