# Sander Hille

The effectiveness of antibiotics and the transport of the plant hormone auxin: both can be described using mathematical models. Sander Hille is a mathematician who works at the cutting edge of biology and mathematics. His interdisciplinary research is both fundamental and applied. When working on fundamental mathematics such as stochastics or measures, Hille always has long-term applications in mind.

## Interdisciplinary research on mathematical models for biological systems

Scientist have been researching the transport of the plant growth hormone auxin for a century. However, it is still unclear how it works exactly. Combining experiments with mathematical models, scientists are gaining an understanding of the process. For this interdisciplinary research, Hille works closely with biologists at the Plant BioDynamics Laboratory of Leiden University. ‘Auxin does not show itself easily. We are like Sherlock Holmes: trying to track it down using models and targeted measurements.’

Sander Hille’s research stretches from fundamental mathematics to more applied biomathematics. His fundamental work focuses on dynamical systems in spaces of measures, which combines deterministic dynamical systems and probability theory. This technical mathematics could be used to describe, for example, a population consisting of different species of insects. They compete among each other and during the winter a certain number of insects dies. How many of them will not make it through the winter is a stochastic process, which depends on the (unpredictable) duration and toughness of the winter. To analyse and predict the influence of climate change on this type of population, Hille works on a mathematical framework which combines deterministic models with random effects.

Hille describes his application-driven fundamental mathematical work as ‘strategic research’. ‘It is mathematics which I know I will need in a few years or more’, says Hille. ‘But first I have to study the fundaments in order to gain more knowledge and develop the mathematical techniques needed to use it for applications.’

Another long-term goal is understanding the effects of randomness in biological systems, for example in the effectiveness of antibiotics. How many (infectious) bacteria will be killed by antibiotics is not always clear beforehand. The treatment has a probabilistic variance. Fundamental stochastic models could make it possible to determine how this probability influences the effectiveness of the treatment.

The most applied research Hille works on now is a mathematical model for the transport of the growth hormone auxin in stems of the flowering plant *Arabidopsis* and in fresh water algae* Chara*. He applied his mathematical skill to model the transport systems. These models are compared to experimental data of radioactive-labelled auxin, for which Hille collaborates closely with biologists. By analysing the data with these models and using them to do simulations of the auxin system, they improve the description of the transport.

In October 2018, Hille and colleagues published a paper in which they disproved an earlier hypothesis on the transport of auxin within cells. Their conclusion was purely based on mathematical models and analysis. ‘Disproving ideas is also an application of these models’, says Hille. ‘They help us focus the experiments in order to test more likely explanations.’

Hille spends one day a week at the Plant BioDynamics Laboratory to work and discuss with colleagues and to get a feeling for biological experiments. ‘We should be able to speak the same language and understand what each other’s work is about to be able to work together’, says Hille. ‘But I will never become a biologist. I will always remain a mathematician.’

## Biography

*Sander Hille (Haarlem, 1972) studied and performed his PhD in fundamental mathematics at Leiden University. After obtaining his PhD, he switched to interdisciplinary research and worked at the Telematica Instituut in Enschede, a former research institute in information technology, for almost four years. In 2003, he returned to the Mathematical Institute in Leiden to work on mathematical biology. In 2015, he initiated the minor 'Quantitative Biology' together with professor Bert van Duijn. With this minor, Hille and Van Duijn want to show students of the life sciences, physics and mathematics the importance and joy of interdisciplinary research.* * *