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Using Mathematics to Improve Drug Therapies - The PhD program PharMetrX trains young scientists in pharmacometrics

Phot: Karla Fritze.

Phot: Karla Fritze.

Pharmaceutical research is changing: In addition to classical clinical trials, mathematical models are increasingly being used to extract new knowledge from complex datasets in order to streamline planning for pharmacological experiments and clinical trials. This demands interdisciplinary expertise: researchers need to understand both mathematics and pharmacology. The PhD program “PharMetrX” teaches young scientists crucial research methods and approaches.

A patient arrives at the ER with a fever and difficulty in breathing. Doctors diagnose pneumonia. Rapid action is required, since the mortality rate rises with every hour. The physicians first decide to administer a combination of antibiotics – hoping that one of them is the right one. But what is the best combination covering a broad spectrum of pathogens? And what dosage should be given to avoid side effects and antibiotic resistance? This is where pharmacometrics comes in, a discipline that uses and develops mathematical and statistical methods to address questions in drug development and therapeutic use. Since 2008, the PhD program “PharMetrX: Pharmacometrics & Computational Disease Modelling” – a joint initiative of Freie Universität Berlin and the University of Potsdam – trains young scientists in this emerging branch of research.

Physiological processes are represented with mathematical equations

One of the young scientists is 30-year-old PhD student Christoph Hethey. He is investigating the effectiveness of various antibiotic combinations and their interaction potential. To be able to do this, Hethey – a pharmacist – is developing new methods to simulate possible infection scenarios using comprehensive datasets from pharmacological research. The simulated data reflect what happens if bacteria and drugs interact. “Mathematics is a language that allows to express complex biological knowledge and to analyze it quantitatively,” explains Wilhelm Huisinga, Professor of Mathematical Modelling and Systems Biology at the University of Potsdam. He chairs the program, together with Charlotte Kloft, Professor of Clinical Pharmacy and Biochemistry at Freie Universität Berlin. The fate of the drugs, their absorption, distribution in the body, metabolism, and, ultimately, their effect at the target site – all of this can be represented in formulas and equations. The data on which the models are based were obtained from experiments in cell cultures, on animals, and from clinical trials on humans, i.e. from all the testing required before a new drug is approved.

PhD student Jane Knöchel is also participating in the program. While pharmacist Christoph Hethey learns the necessary mathematical methods, Knöchel – a mathematician – deepens her biological and biochemical knowledge in the program. “Pharmacists have less experience in statistics, whereas mathematicians lack pharmaceutical knowledge,” Wilhelm Huisinga summarizes. The graduate research training program complements the necessary methodological skills through tailored courses. In six one-week modules, the young researchers learn a common pharmacometric language and how physiological processes can be represented in mathematical models.

Mathematical models must be kept simple

The blood coagulation cascade is part of Knöchel’s research project. It plays a major role after an injury to stop the bleeding and follows an exact sequence of protein activation steps. Various proteins are involved that are activated, and deactivated. For physicians and pharmacists, the complex mechanism is highly interesting, since it also plays a decisive role in strokes and heart attacks. Knöchel studies it through the eyes of a mathematician: “The task is to rank the processes according to their significance within the complex process,” she explains. The starting point of her research is an existing 50-equation model. Each protein’s production and degradation rates as well as mutual interactions are described mathematically. This model is so complex that it is not suitable for many pharmacometric applications – such as the statistical analysis of clinical data. “There are too many parameters involved, so we have an identifiability problem,” Knöchel says. Her doctoral thesis, therefore, focuses on methods of simplifying a model so that it maintains all relevant processes and disregards the irrelevant ones. “The task is to develop a new mathematical method for model reduction,” the researcher outlines. For her, moving from mathematics to pharmacometrics was not too difficult, even though she had to familiarize herself with completely new scientific fields. Being able to contribute to research on both biochemistry and pharmacology was particularly attractive to her. After all, the best theory has not much impact without practical applications. “The concrete application shows how useful mathematics can be,” Knöchel says.

Christoph Hethey and Jane Knöchel are two of 53 young scientists who completed – or are about to complete – their doctoral studies within PharMetrX. The program aims to advance pharmacometrics research, implement the field at universities, and train young researchers. “PharMetrX bridges pharmacology and mathematics,” Huisinga explains. Experts in the field are in high demand, he underlines. The need is such that six research-driven pharmaceutical companies support the PharMetrX program as cooperation partners.

Pharmacometrics helps to plan optimal studies – and could even replace them

While Knöchel focuses on improving pharmacometric methods, the model developed by Christoph Hethey in his doctoral thesis deals with a more concrete topic: Which combination of antibiotics is most appropriate in which scenarios? Researchers determine this experimentally, but “if you use mathematical models instead, experiments can be planned optimally, which saves time and effort,” Hethey explains. In his model of 10 differential equations, the modes of action of the various drugs are represented at the cellular level so that possible interactions and their influence on bacterial population growth can be predicted. This example shows that pharmacometrics is not just about depicting existing knowledge mathematically but also about being able to make predictions. What happens when drugs interact in the human body? What if a patient has a dysfunctioning organ or certain genetic predispositions that lead to a faster degradation of the drug? What dosage changes would be necessary? Instead of examining such issues from scratch in laborious experiments, mathematical modeling provides new insights through which certain hypotheses can be ruled out from the start. So does that mean pharmacometrics can replace traditional experimental studies on drugs? “Under certain conditions,” mathematician Huisinga answers. Under certain conditions, clinical trials on humans are no longer necessary, since the human-drug system has been sufficiently well understood such that mathematical models can be used to make reliable predictions. This applies, for instance, to the interactions of drugs, an increasingly important problem. In this field, pharmacometrics is doing pioneering work: “Some drugs on the market use dosage adjustment in the label that have been determined based on mathematical models.”

The Graduate Research Training Program

PharMetrX: Pharmacometrics & Computational Disease Modelling was launched in 2008. Young researchers with a background in mathematics, bioinformatics, pharmacy or natural sciences are trained in the field of pharmacometrics. The discipline combines mathematical, statistical, and pharmaceutical methods and approaches. https://www.pharmetrx.de/ 

The Researchers

Prof. Dr. Wilhelm Huisinga studied mathematics in Berlin. Since 2010, he has been Professor of Mathematical Modelling and Systems Biology at the University of Potsdam. Together with Prof. Dr. Charlotte Kloft of Freie Universität Berlin, he chairs the PharMetrX PhD program.

Universität Potsdam
Institut für Mathematik
Karl-Liebknecht-Str. 24-25, 14476 Potsdam

Christoph Hethey studied pharmacy at the University of Münster and has been pursuing a doctorate at the University of Potsdam since 2013. E-Mail: christoph.hethey@uni-potsdam.nomorespam.de 

Jane Knöchel studied mathematics at Humboldt-Universität zu Berlin and started her PhD at the University of Potsdam in 2014. E-Mail: jane.knoechel@uni-potsdam.nomorespam.de

Text: Heike Kampe
Translation: Monika Wilke
Online published by: Daniela Großmann
Contact us: onlineredaktion@uni-potsdam.nomorespam.de