# Mathematics helps improving biological models

Many phenomena in life sciences, economics, physics and engineering can be described with mathematical models called rational systems. PhD student Jana Nĕmcová of the Centrum Wiskunde & Informatica (CWI) in Amsterdam contributed to the theory of these systems in her dissertation ‘Rational Systems in Control and System Theory’.

Many phenomena in life sciences, economics, physics and engineering can be described with mathematical models called rational systems. PhD student Jana Nĕmcová of the Centrum Wiskunde & Informatica (CWI) in Amsterdam contributed to the theory of these systems in her dissertation ‘Rational Systems in Control and System Theory’. She received her PhD degree on December 2, 2009 at the Vrije Universiteit Amsterdam. Her results are of interest for biologists and the pharmaceutical industry. In the future, this research can contribute to reducing expensive experiments and testing on animals in drug development.

Many systems in biology are still poorly understood, such as complex chemical processes in a cell. Researchers often describe this as a 'black box' system. A particular input (like a concentration of an enzyme) gives an output (such as an interesting concentration of a chemical), whereas the process in between is not known. To make nonetheless  a mathematical description of the unknown process - a model with real input and output values - researchers use often parameters (unknown numbers) in their equations. They can adjust those numbers until the model gives a realistic outcome. A mathematical model of a biological process is therefore only an approximation of reality.

Realistic models are important in biology, since a smaller amount of experiments will only be sufficient, if the results of these models are as reliable as experimental results. Therefore it is important to demonstrate whether models are realistic. In practice, almost every biologist uses a particular model. Jana Nĕmcová mathematically showed that, if certain conditions are met, the parameters of a model can in principle be uniquely determined from measured data. Where those conditions are not met, a model is not suitable and researchers should not use this model anymore. Earth and Life Sciences is an important research field of CWI. This research is a good example.