Day 9: Multi-level modelling in morphogenesis

The ninth day of the multi-level modelling in morphogenesis course was started by Professor Enrico Coen who continued on the theme of polarity.

Professor Coen did not set out to study polarity. He was interested in how tissues grew. However, after some time he came to the conclusion that to understand tissue growth he would have to understand polarity.

One of the main players of polarity in plants is the hormone auxin. In fact some of the main markers for polarity in plants are the PIN proteins, which actively transports auxin across the plasma membrane. By coordinating the location of PIN proteins to one side of all cells a tissue can create a polarity field. Furthermore, auxin gradients have been shown to regulate tissue polarity.

At the time there where two main models describing auxin regulated tissue cell polarity:

• Cell-cell comparison, a.k.a. “up-the-gradient” hypothesis
• Flux or gradients at the interface, a.k.a. “with-the-flow” hypothesis

The former could explain PIN locations and the latter veins in leafs. However, both models also had issues. How could a cell, in a cell-cell comparison scenario, know the concentration of its neighbors? On the flip-side, in the “with-the-flow” hypothesis, it was unclear how the cell would be able to measure the flux.

Professor Coen then turned the attention to animals models that had been proposed to coordinate the hair orientation in Drosophila wings. Again there were two major classes of models:

• Cell-cell comparison models
• Interface models, i.e. receptors intaracting at interfaces between cells

These were very similar to the plant models. The main difference being that plant cells could not interact directly as they are separated by a cell wall.

However, all the plant and animal models had an assumption in common. Namely that cells are unpolarised in the absence of an asymmetric ligand distribution or polarised neighbours.

But we know of at least some systems where this assumption is not true. For example budding yeast and migrating neutrophils.

Dr Coen then showed that by assuming that cells have an intrinsic polarity one can create a model where the polarised cells arrange themselves through local interactions with their neighors. For example, in an animal model, one can imagine a scenario where the cells’ “front” and “back” factors directly bind with their neighbour’s “front” and “back” factors. This leads to coordination. However, the emerging pattern is a bunch of spirals. He then showed that very strict, orientated tissue polarity can be established if organizers are located somewhere on the tissue, or the polarities interact with some kind of concentration gradient.

One way to use this to model how a plant organises polarity is to assume high auxin efflux at one end of the tissue and no export of auxin at the other end. By reading out the same concentrations between the cells, both cells tend to align. Thus, using this indirect-signalling mode, one gets a similar result to the cell-cell comparison models. This is a bit counterintuitive. The patterning is working to remove the signal that is causing the pattern.

However, one can use the same model to create a different emergent tissue polarity. A model with high auxin production at one end of the tissue and low auxin degradation at the other end. In this case one ends up with results similar to those from the “with-the-flow” hypothesis.

So in essence we have a model that produces two different behaviours, previously thought to be two different processes altogether, and consolidates them in a parsimonious and locally-based manner.

Professor Coen’s talk was followed by a presentation by Dr Alexandre J. Kabla on the mechanobiology of cell migration and cell rearrangements.

Dr Kabla started off by illustrating that there is a massive amount of motion during development. In fact most shapes are created by cell migration.

This motion arises from several different processes:

• Sheet bending/folding
• Convergence extension
• Collective migration

Dr Kabla then described a methodology for understanding some of these processes, in particular the latter two.

Using microscopy one can record time laps movies of developing embryos. These images can then be segmented into individual cells, which can be tracked over time. By looking at the motions of individual cells one can calculate velocities. All of the velocities can then be used to create a velocity field. By differentiating the velocity field one obtains a deformation field, which is a useful representation for trying to understand tissue formation by motion during development. The deformation field can, in fact, be used to identify separate tissues from a blob of cells.

Dr Kabla then went on to describe how one could analyse cell interacalation (convergence extension) in more detail using the deformation field representation.

The talk was followed by lunch, which was followed by another talk by Dr Kabla describing on how modelling can be used to study collective migration. After the talk the participants of the course were invited to try out some of these analysis using data simulated using cellular Potts model programs used earlier in the course.