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Predicting the efficiency of cancer drugs using mathematical models

New cancer drugs are often tested on a trial and error basis. This is because little is yet known about the molecular processes that govern the action of drugs in tumour tissue. A research consortium was established at the Stuttgart Research Center Systems Biology (SRCSB) at the University of Stuttgart in January 2013 with the goal of establishing models that help predict the action of targeted therapeutics. The scientists combine molecular biology experiments with complex mathematical models in order to achieve a holistic understanding of disease and therapy. They hope that this approach will, in future, contribute to the efficient development of cancer drugs made from genetically engineered proteins. As a result they will be able to place new, promising drugs on the market faster and also at lower costs. The first drug candidates have already been developed.

Prof. Dr. Klaus Pfizenmaier is the coordinator of the project PREDICT. He hopes that together with his team he will be able to come up with a validated drug prototype for the treatment of colon cancer by the end of 2015. © SRCSB

PREDICT is short for an ambitious project entitled “Holistic multi-scale modelling of targeted protein therapeutics action: Towards predicting effective treatment of cancer” which commenced in January 2013 and brings together eight research groups from four institutes at the Universities of Stuttgart and Tübingen, the Robert Bosch Society for Medical Research, the Stuttgart-based Robert Bosch Hospital and the companies Bayer Technology Services (BTS) and Celonic GmbH. The collaborative research project is coordinated at the Stuttgart Research Center Systems Biology (SRCSB) and is supported by the BMBF with a total of 3.5 million euros. The scientists aim to develop a holistic mathematical model that enables them to predict the action of cancer drugs and hence be able to accelerate the preclinical and clinical drug development process. In parallel, molecular biologists are working on the development protein therapeutics for the treatment of colon cancer.

These mathematical models have been established using multi-scale modelling, which is a specialty of the laboratory in Stuttgart, as Prof. Dr. Dr. h.c. Matthias Reuss, who is in charge of a subproject at the SRCSB, explains: “Multi-scale modelling is used to solve problems at multiple levels. We begin at the lowest level, which is the molecules and their interactions. We then look at the chain of reactions at the subcellular level, the level of cell-cell interactions and eventually at tissue, tumours, organs and the whole body. This approach allows the researchers to simulate the dynamics of drug distribution in the body.” The methods were developed at the SRCSB in cooperation with the company Bayer Technology Services. Prerequisites for the mathematical models are inter alia experimental pharmacokinetic studies – the distribution and absorption of drugs – and pharmacodynamic studies – the physiological and biochemical effects of the drugs on the body. These results are obtained through biochemical and histological investigations as well as using imaging techniques for small animal models. The information gained is then implemented into a model. “Each tumour is unique,” says Reuss. “However, we can also group the tumours, and these groups will then be treated differently in our model.”

Mathematical models facilitate drug development

Prof. Dr. Dr. h.c. Matthias Reuss is in charge of the mathematical models produced by the project PREDICT. © SRCSB

The development and growth of tumours is rather complex and differ from tumour to tumour. Tumours are dynamic and interlinked systems that are difficult to be described linearly and thus require complex mathematical modelling. It would be a complex and time-consuming process to study all parameters purely empirically and would be impossible for practical reasons alone – with little chance of success. The gaps between the experiments in the laboratory are therefore filled using mathematical models. “We are developing mathematical models of the biological processes that lead to the development of tumours. These models then provide us with the information we need to make predictions for laboratory experiments and provide us with the basis for accelerating drug development considerably,” says Prof. Dr. Klaus Pfizenmaier, coordinator of PREDICT and head of the Institute of Cell Biology and Immunobiology at the University of Stuttgart.

Personalised cancer therapy with protein therapeutics

The models developed in Stuttgart target a new class of cancer drugs, i.e. protein therapeutics that exert their effect directly on the tumour. Such genetically engineered drugs are fusion proteins that trigger the apoptosis of tumour cells. They consist of tumour-specific antibodies and cytokines that induce the programmed death of the cells. The tumour-specific component of the fusion protein can be tailored to the specific properties of a specific type of tumour. The corresponding mathematical models are specifically designed for the development of tumour therapeutics and enable the assessment of disease progression and the prediction of which patients will respond to the drug. As part of personalised cancer therapy, the physician can then apply these patient-specific diagnostic parameters to the models in order to determine the drug which has the greatest chance of curing the patient.

In the course of therapy, new data, for example results from imaging studies, can be added to further customise the individual model. This is similar to the process used for weather forecasts. Reuss explains: “In the field of meteorology, the predictions are continuously compared with current weather data and adapted to the model. We are currently working on adapting such processes to cancer research, but the challenges we are facing are enormous.” The reason for this is the many different scales of the models. The scales “time” and “space” alone already have a wide range: “As far as biochemical aspects are concerned, we have to deal with changes that happen in seconds; as far as the clinical outcome - whether a tumour responds to treatment or not - is concerned, it might take days or even weeks before any progress can be seen,” says Reuss. “We have to look at molecular interactions on the micrometre scale, and at the metre scale when we look at the whole body. We therefore have to work out possibilities to bring these different scales together.” In addition, there is the three-dimensional space that needs to be taken into account. “This is rather challenging in mathematical terms,” says Reuss. The broad range of scales that the researchers’ approach takes into account leads to a huge amount of data that need to be processed and analysed. “Here in Stuttgart, we are in the fortunate position of having access to the High-Performance Computing Centre whose 30,000 processors enable the SRCSB researchers to carry out the complex simulations in parallel.

Schematic representation of multi-scale modelling: images of a molecule, cell, lung tissue and whole body, all connected with each other by arrows.<br />
Multi-scale modelling is used to simulate the dynamics of the distribution of cancer drugs in the body: Simulations are carried out on the level of molecules and their interactions, the cellular level, tissue level, organ level and the whole body level. © SRCSB

First drug prototype shows effect

Concrete results have already become available after only one and a half years of research: The project’s bioscientists have genetically engineered a fusion protein prototype that shows great promise in tissue models and animal experiments. In addition, the researchers have established a single-cell model that reliably simulates the programmed death of the tumour cells. However, one needs to take into account that tumours usually consist of several billions of cells and that these might be at different stages of development. The next challenge for mathematicians will therefore be to develop models that are suitable for such large cell numbers. “We have the plan to have developed our first validated prototype for a colon cancer therapeutic by the end of 2015,” explains Pfizenmaier. “And we hope that we will also find a partner who will be willing to develop the prototype further, produce it and test it in preclinical and clinical trials. These drug development steps will involve enormous costs. However, everything depends entirely on the data that will be produced next year. But it all looks pretty good so far.” 

Further information:

Prof. Dr. Klaus Pfizenmaier
Stuttgart Research Center Systems Biology (SRCSB) and 
Institute of Cell Biology and Immunology at the University of Stuttgart
Allmandring 31
70569 Stuttgart
Tel.: +49 (0)711 685-66986
E-mail: klaus.pfizenmaier@izi.uni-stuttgart.de

Website address: https://www.gesundheitsindustrie-bw.de/en/article/news/predicting-the-efficiency-of-cancer-drugs-using-mathematical-models