Day 8: Multi-level modelling in morphogenesis

The eight day of the multi-level modelling in morphogenesis course was started by Dr Yogi Jaeger giving an introductory lecture to parameter estimation using reverse-engineering. The talk was illustrated using a case study of segmentation during fly embrogenesis.

Along the way Dr Jaeger highlighted many of the pitfalls that one needs to be aware of when modelling biological systems. Particular emphasis was put on the model being a tool, not reality! An outcome of this is that one needs to pay attention to the model and understand its limitations.

In its most simple form reverse-engineering can be split into three stages:

1. Creating a dynamical model
2. Obtaining quantitative measurements of data
3. Fitting the model to the data

When fitting the model to the data there are two main questions to consider.

1. How do you measure the similarity between the data and the model?
2. Which algorithm are you going to use to fit the data?

One of the simplest ways of measuring the similarity between the model and the data is to calculate the root mean square residual. However, other measures are available and the selection of one over another is context dependent. It is therefore something that one needs to pay attention to.

Fitting the model to the data, i.e. estimating the parameters, is a global optimisation problem and there are a number of algorithms available to tackle it. Traditionally people have been using evolutionary strategy and simulated annealing algorithms for these types of problems. Evolutionary strategy algorithms are relatively quick. However, when using them one suffers from not knowing whether or not the solution identified is the real global minimum. Simulated annealing algorithms can be more robust, but they are also slower.

Dr Jaeger then mentioned that his lab has had great success with the scatter search algorithm. In his hands it can be up to ten times quicker than simulated annealing.

Once one has found a solution one needs to ask whether or not it is appropriate. This can be achieved by parameter identifiability analysis though bootstrapping, i.e. fitting the model to noisy data. The results can be projected onto the parameter landscape as ellipsoid confidence regions. However, this can be slow. A quicker way to estimate these confidence regions is to calculate the Hessian matrix of the system using linear approximation.

After lunch Dr Veronica Grieneisen gave a talk about cell polarity and how one can understand it through breaks of symmetry.

If one considers a morphogen gradient, how can it be “read” by cells? Further, how can this lead to coordinated cell orientations? Any solution will require some process of comparison.

The talk then took a slight detour into physics.

How can you make a compass? You can take a needle and magnetize it with an external field. If you have many needles they will all align in the field. Importantly each subunit (needle) will have a “north-south” polarity in the magnetic field.

Without going too far with the analogy Dr Grieneisen noted that by giving a cell the concept of polarity it is given a mechanism for aligning within a larger polarity such as a chemical gradient or a tissue polarity.

Dr Grieneisen then presented work using the cellular Potts model illustrating how small G-proteins, which can act as molecular switches, can give rise to cell polarity. However, the modelling found that there was an additional requirement. The inactive form had to be able to diffuse on a quicker time-scale than the active form. In this particular case this was achieved by the active form being constitutively membrane bound, whereas the inactive form was able to diffuse freely in the cytosol.

Dr Grieneisen pedagogical lecture was followed by a keynote lecture by Dr Jaeger giving a more detailed exposition of his top-down approach to extracting structures of networks from gene expression data and his analysis of the model by looking at phase space and the attractors within it.

By using this reverse-engineering approach Dr Jaeger managed to establish that the AC/DC circuit is a recurring motif in the gap gene network. The AC/DC circuit is interesting in that it can act both as a positive and a negative feedback loop. By analysing the phase space and attractors in the AC/DC circuit one finds that this simple network can give rise to different functions. Specifically it can act as a:

• switch
• oscillator
• damped oscillator

Dr Jaeger then showed that the AC/DC circuit in the gap system could be used to create:

• Stable boundaries in the anterior of the fly embryo, set by attractors
• Moving boundaries in the posterior of the fly embryo, governed by a damped oscillator

The participants of the course were then invited to an open-panel session to discuss “what models are for”. This was followed by more hands-on computational exercises simulating cell polarity in animal and plant cells.