# Who determines how filopodia are formed in neurones?

**Project title: **Symmetry Breaking in Neurons

**Principal investigators:** Christian Engwer, Milos Galic

**Project time:** 07/2016 - 06/2018

**Project code: **FF-2016-03

In this project, mathematicians and biologists work together on research into fundamental mechanisms of neuronal development. In doing so, they link up analytical imaging processes with mathematical models in an attempt to discover to what extent the geometry or the size of neurites determine whether filopodia are formed – and, if so, how. Filopodia arise when neurites, i.e. cell protrusions of neurons, grow. The regulatory mechanisms of this process have not as yet been fully explained.

What is known is that curvature-dependent proteins determine whether filopodia are formed. At the same time, however, mathematical models predict that slight differences in the size of neurites are sufficient to influence the speed at which the signalling centres are formed. Preliminary experiments also showed that the curvature can act as initial impulse for the formation of filopodia. Now, the CiM research groups headed by mathematician Prof. Christian Engwer and biologist Dr. Milos Galic want to analyse more precisely what influence the curvature and size of neurites have on the formation of filopodia. The aim is to provide quantitative proof through a combination of a theoretical mathematical model and experiments on cells. For this purpose, the two teams of researchers working on this interdisciplinary project are first developing a mathematical framework which will enable them to simulate the behaviour of cells. The basis of the simulation is the so-called Turing mechanism, which describes in a mathematical system how structures arise spontaneously. The CiM researchers incorporate in their calculations not only the frequency of the symmetry-breaking occurrences, but also the radius of the neurites. In this way, predictions are made on the molecular mechanisms of the formation of filopodia which the biologists, in turn, validate in experiments. The researchers repeat this principle several times and, by doing so, hope that ultimately they can quantitatively decode the molecular mechanisms which determine when filopodia are formed in neurons.