The Task Dynamics of Angiogenesis

In the last two posts, I have laid out the proposal that endothelial cells seem to actively perceive their environments, and set out the details of the argument in favour of explicitly taking an ecological approach to understanding why they do what they do during angiogenesis. It's now time to develop that analysis more explicitly.

To do this, I will apply the 4 questions we proposed in Wilson & Golonka (2013) to the question of the endothelial cell behaviour.  These are

1. What is the task to be solved? 
2. What are the resources the organism has access to that might solve the task?
3. How might these resources get assembled so as to solve the task?
4. Do organisms actually do what you describe in Q3?

We gave some worked examples of this analysis in the 2013 paper, and have described how it drives my work on coordinated rhythmic movement (Golonka & Wilson, 2012, 2019). This will hopefully serve as another example.

Q1: What is the task to be solved? 

The ecological approach is a task-specific approach; we aren't looking for general purpose algorithms but smart solutions (cf Runeson, 1977). These take advantage of stable local conditions, and are generally more robust and adaptive than general purpose solutions. This means we need to appropriately characterise the task space, i.e. what is happening and what needs to happen.

Endothelial cells are responsible for growing new blood vessels so that all the surrounding tissue has access to all the resources (especially oxygen) that it needs. The relevant (relatively) distant dynamics to be perceived are cells in hypoxic (insufficient oxygen) states. The endothelial cells must detect that hypoxia, and respond by migrating to the hypoxic tissue and proliferating into new blood vessels. Migration entails cells adopting one of two roles; a tip cell, that guides the migration, and stalk cells that maintain the connection between existing blood vessels and the new tissue that will be formed when they reach the hypoxic tissue. This is the task of angiogenesis; grow new blood vessels in the right place in response to a need for those new vessels. 

Q2: What are the resources available to the organism in the task space?

Cognitive science and cell biology both tend to jump straight to internal, central resources and then try to establish how they support the behaviour in question. An ecological approach is allowed to include such resources, but critically it allows (in fact, it requires) those internal dynamics to be coupled to external dynamics, via information. The key result of the ecological approach is that when this is allowed, and when those external resources are characterised correctly, a lot of the work in explaining the behaviour is found to be done by these resources, which then radically alters the proposed role for the internal dynamics in the behaviour. 

The task of angiogenesis is established by cells becoming hypoxic; this is what makes it so that angiogenesis behaviour is required from the endothelial cells. As with animals, their behaviour begins with the detection of information about the presence of the task dynamic. This information takes the form of a vascular endothelial growth factor (VEGF) array; VEGF is the primary signal from hypoxic cells. This signal can be called an array because it is not symmetric (Bentley currently models it as a simple linear gradient running from high at the hypoxic cell to low at the endothelial cell; this is likely true, although this is not a definite fact yet. More on this later.). The relevant external resources are therefore the dynamics of hypoxic tissue, and the VEGF information array those dynamics create (see this post for more detail on this distinction). 

The first set of task-relevant internal dynamics is a genetic mechanism implementing lateral inhibition of neighbouring cells. VEGF detection leads to the up-regulation of a ligand called Dll4, which binds to and activates Notch receptors on the surface of neighbouring cells. The first effect of this activation is to reduce the neighbour cell's sensitivity to VEGF. The cell sensing the most VEGF wins the race and successfully inhibits it's neighbours while becoming active itself. This leads to a 'salt-and-pepper' alternating pattern of active (tip) and inactive (stalk) endothelial cells. This ensures that the new sprouting blood vessels are optimally spaced. This genetic mechanism requires multiple iterations to complete, each taking 4-6 hours. 

The second effect of Notch creates another set of task-relevant internal dynamics, by altering the adhesion strength of the cell membrane. Active cells produce more Notch which makes them weakly adhesive, while inactive cells produce less Notch which makes them strongly adhesive. When neighbouring cells have different levels of adhesion strength, this creates a unstable arrangement, and any random cell motion that improves that stability (by bringing strongly adhesive inactive cells closer, for example) is selected for. This leads to cell migration, which brings the Notch/Dll4 lateral inhibition mechanism back into play to restore the salt-and-pepper patterning, and the combination means that during angiogenesis behaviour, cells change roles and are somewhere along the active-inactive continuum when this happens, because adhesion-related cell migration only takes 3.7 hours on average. 

The next set of task-relevant internal dynamics is the transition of an endothelial cell to a migratory state. VEGF detection initiates the formation of mobile membrane protrusions called filopodia that carry VEGF membrane sensors out into the environment to explore the array. It also initiates the migration itself, both via the adhesion dynamics described above and by a contractile process. The filopodia begin forming and exploring on the order of minutes from the detection of VEGF. More filopodia, and better use of them to explore the VEGF array leads to more detection of VEGF, which then drives the dynamics described above (and seems to be required for this behaviour to happen in the time it does). 

3. How might these resources be assembled to solve the task?

At this point in the analysis, it's usually helpful to have a dynamical model of your task which implements as many real parts as you know about, organised in the way they are in the system to be explained. Bentley has one (Bentley et al, 2008) that implements all the internal task resources. I haven't had a chance to really get my head round the model yet, so I won't spend too much time here. Essentially, the key part here is that we have a model that implements all the known internal, task-relevant parts and processes that stands as a formal implementation of the hypothesis that endothelial cells are dynamical, perceiving-acting agents. The point of this step is to nail ourselves to as explicit an expression of the hypothesis as possible, so as to strongly guide the empirical work to come.

The model does not currently explicitly model the external hypoxic cell dynamics; it simply places a set of endothelial cells in a VEGF array (a linear gradient) which does not vary over time. This is one limitation revealed by the task analysis; while behaviour begins with the detection of information, the form of that information depends on the dynamics of the process that created it. For example, in the outfielder problem, identifying the two possible prospective, informational strategies depends on understanding how the dynamics of projectile motion unfold relative to a moving observer. For this kind of reason, Bingham's coordination model explicitly includes the dynamics of the moving limbs so as to generate the relative direction information which then serves to couple the limbs; the array is not given to the model.

So I think expanding the scope of the model to explicitly include the external dynamics will be a good idea, and this may enable us to start asking questions about the capabilities of the VEGF array to implement information variables. For example, the VEGF array is a (bio)chemical array; it will have a speed that might matter! Detected VEGF gets used up, and the dynamics of replacing it to the endothelial cell sensors could constrain perception (whereas, for example, light is so fast the optic array is effectively instantly available when the light comes on and remains so even though detected photons get used up too). The array dynamics may also constrain the kinds of invariants it can implement, or how invariant they are. For example, detected VEGF is the starting point of all the internal dynamical constraints, but each of these runs on it's own timescale while most of them (perhaps not the genetic CPG; it might just get triggered?) require active coordination and control. Are there different variables? Is it the same variable, just used differently? 

(A random thought: this could be a cool model system to develop questions and intuitions for an ecological account of smell and taste, which would be fun.)

Regardless, we are off to a good start with the existing model, which also has the benefits of being fully mechanistic (because computational biologists aren't afraid of the M word :). So far, all we seem to have are state-of-the-art problems, and those are perfectly OK. 

4. Does the system, in fact, do this?

I've already reviewed some of the evidence in favour of the hypothesis, with reference to model results as well as empirical data; see the first post and Bentley & Chakravartula (2017). So far so good; angiogenesis shows clear evidence of emergent timing constrained by the coalition of internal and external dynamics as specified in the model. It also seems clear that the filopodia, as per the hypothesis and model, are actively carrying VEGF sensors into the array to explore and guide the process (although at this point we don't know enough about the structure of the VEGF array to be able to establish how that relates to filopodia behaviour). So we have a good basis to work from so far.

Summary

This has been a hefty post as I try to specify everything I can in an ecological task dynamical analysis of angiogenesis behaviour. It's revealed some interesting gaps for us to fill, and identified the fact that there are multiple coupled dynamics at play, each with their own spatial and temporal scale and distributed over the hypoxic cell/VEGF array/endothelial cell network system. Angiogenesis is an achievement of this entire system, and Bentley has a good empirical and model based analysis of the relevant endothelial cell dynamics where a lot of the behaviour constraints are implemented. The next steps will be to expand the model scope to the full system, and develop more experiments to test the model predictions (effectively looping through Qs 3 & 4, as we do in animal behavioural research). The project can be mechanistic from the get-go, and so, if we are lucky and do good science, we will end up with a complete explanation of the behaviour of angiogenesis.