News from the world of maths: Understanding embryo development moves forward thanks to biology and maths

Research aimed at understanding the mechanisms underlying embryo development has taken a step forward thanks to collaborative work between biology and mathematics. A study of wing formation in the fruit fly (Drosophila melanogaster), led by the researchers Marco Milán and Javier Buceta, both in Barcelona, has led to the discovery of a new genetic function involved in this process, and furthers our understanding of the internal laws which regulate it.

The development of a living being is based on general laws written into the genetic code of each cell and which enable the cell to develop a specialist function, modifying the way they divide, their form and their behaviour. These changes are coordinated through a series of instructions that must be correctly interpreted within the cell, and this means that the information must pass along a pathway of signalling molecules. These pathways have been conserved across evolution, and therefore studies using models such as the fruit fly provide information about these same processes in humans and other animals.

The Developmental Biology of Drosophila Group from the IRB Barcelona, led by Marco Milán, studies the signals that guide wing development in Drosophila. The wings are generated from a set of cells grouped into different segments or compartments that never mix with one another, and which enable the symmetrical construction of the dorsal and ventral parts starting from a given limit or border. This process of subdivision into compartments also takes place during the formation of the vertebrate central nervous system, and the genes and signalling pathways involved are conserved in both Drosophila and vertebrate species.

Although biologists already had an intuitive idea of how the limit or border between these compartments was generated, there had been no systematic study taking into account all the relevant elements. Therefore, and with the backing of a group led by Javier Buceta, they decided to use mathematical modelling to better understand the internal mechanisms which regulated this process. In this way they identified certain interactions in the signalling pathways that brought to light a number of contradictions and showed that a key step was missing in their model. As Milán explains: “Thanks to this computer simulation we have found a new genetic function that ensures the stability of the system and has enabled us to test its robustness. This study shows that modelling is a highly useful tool for describing in silico new properties of a biological system and being able to corroborate them subsequently in vivo”.

In this regard, Buceta, who leads the SiMBioSys group, dedicated to modelling biological processes, explains that “the advantage of these modelling techniques is that they can simulate genetic and cell interactions as a set of mathematical equations and, therefore, to determine the feasibility of a biological mechanism”. In order to study the stability of the system they conducted around 45,000 different in silico experiments, introducing variations in twenty parameters. The results have enabled them to identify the most important system parameters and showed that the biological mechanism maintained its functionality in 91% of the cases analyzed. According to Milán and Buceta “this study confirms the hypothesis that if this gene network has been maintained across evolution in both vertebrates and insects, it is precisely because it is highly stable and robust”.

You can read the full article in the journal PLoS One. You can read more about the mathematics of embryo development in the Career interview with a biomechanical engineer on Plus.