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Mathematical models for predicting cellular signalling pathways

The micrometre-sized cells in organisms are biological systems in which countless vital processes take place. However, little is yet known about most of these cellular metabolic chains because they interact with each other in a complicated manner. The research carried out by junior professor Nicole Radde and her doctoral student and engineer Patrick Weber from the Institute for Systems Theory and Automated Control (IST) at the University of Stuttgart is focused on modelling the “cell” system. They combine systems theory and mathematical modelling and analysis methods with experimental techniques used in cell and molecular biology to develop models for the control of protein secretion. These models also have the potential to be used for increasing the yield of biotechnological production lines.

Physicist Dr. Nicole Radde has been junior professor in “systems theory in systems biology” at the University of Stuttgart IST since 2008. © Radde

Systems biology is still a young field of research in which biologists, mathematicians and physicists work together to obtain a detailed understanding of complex biological processes in organisms. They combine experimental with systems theory and mathematical methods in order to simulate life processes. This produces huge amounts of information that cannot be processed using conventional data analysis methods.

New data mining methods help to decipher a system’s structure and dynamics that are buried in the huge datasets; they also interpret and visualise the experimental results. In silico experiments, i.e. model-based computer simulations of the most complex biological systems such as living cells, are much cheaper and faster than laboratory experiments. Simulation scenarios can be precisely formulated and made comprehensible. In addition, in silico experiments help avoid ethically questionable animal experiments.

Mathematical models of biological processes

Engineer Patrick Weber is a specialist in simulation studies and has been at the Stuttgart IST since 2010. © Weber

Physicist and junior professor Nicole Radde is working with Patrick Weber on a systems biology project jointly run by the Institute for Systems Theory and Automated Control (IST) and the Institute of Cell Biology and Immunology (IZI) at the University of Stuttgart. The aim of the project is to investigate key molecular processes involved in the secretion of proteins in mammalian cells.

The project involves simulation methods that require a great deal of computing power. These so-called sampling-based approaches have been developed over the past few years at the IST for this particular purpose. What the methods actually do is to simulate how proteins are sorted and packaged at the Golgi apparatus. This process is characterised by the complex interaction of lipids and proteins and leads to the formation of transport compartments known as vesicles. 

An integral part of the process is the lipid transfer protein CERT, a cytosolic protein that mediates the transport of a specific lipid from the endoplasmic reticulum to the Golgi apparatus. Defective CERT function has a serious impact on the entire cellular lipid metabolism and leads to defects in membrane and protein transport, which can be lethal for the cell. Even an elevated or lower than normal CERT concentration can lead to pathophysiological alterations such as those found in cancer cells, for example.

Perturbation experiments to test hypotheses

Visualisation of a representative sample created by sampling-based methods and used to investigate parameter space and analyse insecurities. © IST Stuttgart

The Stuttgart scientists use data-driven modelling approaches to analyse large datasets. An initial model is developed from already existing data, experimental conditions and literature research data. Systems theory modelling analyses and simulation-based predictions then provide the scientists with hypotheses that can subsequently be tested in laboratory experiments.

The analysis of the experimental results leads to new hypotheses which are used to improve and expand the model. Perturbation experiments – for example external cues that lead to changes in the protein concentration – play a key role in this. “We specifically interfere with the network and observe how it reacts,” says Patrick Weber explaining the methodology used. “The information we obtain from this can be used to make a prediction, which we can subsequently test in the laboratory – where we either confirm the prediction or not, and in the latter case we then have to further expand the model.”

What at first sight sounds simple is nevertheless a long and complex process: “We are unable to experimentally test a predicted model every week, far from it. We start with a model, which then leads to a hypothesis – a new perturbation experiment for example – which leads to another hypothesis, which will once again be tested in the laboratory.” 

Huge quantities of data from several hundreds of thousands simulations

Schematic showing the molecular interactions involved in the regulation of vesicle budding at the trans-Golgi network. © IST Stuttgart
The quantity of data produced is manageable as it does not result from high-throughput experiments which involve a large number of samples. “One dataset consists of about a hundred data points,” says Weber. “But the quantity of data behind it is immense,” says the simulation experiment expert. Laboratory experiments for the most part involve Western blots with antibodies that generate rather unspecific signals. The spot pattern, which initially looks rather confusing, is then analysed as follows: it is scanned and quantified with infrared radiation, then stored as image data, which are then processed numerically with specifically developed algorithms. “Intracellular measurements can differ considerably,” says Radde. “We are developing methods that enable us to forecast uncertainties. More than one hundred thousand model simulations are carried out. This produces huge quantities of data, which then need to be processed and interpreted.” Each simulation takes just a tenth of a second. However, even a state-of-the-art computer might need more than 50 hours to run through all the simulations – depending on the set of parameters that needs to be analysed. The huge amount of data produced by different perturbation experiments eventually leads to an overall picture of the regulatory and feedback mechanisms and gives the researchers a global picture of cellular interactions. The researchers have already achieved initial concrete results and are planning to publish them in the not-too-distant future.

Model for the control of protein secretion of biotechnological production lines

The scientists’ principal aim is to develop a model that provides them with information on how to improve production cell lines and increase the yield of recombinant drugs. Preliminary work has already been carried out. Studies carried out by the IZI in cooperation with Boehringer Ingelheim Pharma GmbH have shown that the involvement of CERT in lipid transfer processes and Golgi function can also be exploited for biotechnological applications. For example, the capacity of production cells to secrete complex therapeutic proteins such as antibodies can be increased by elevating cellular CERT concentration, which is achieved by the genetic modification of cells. Perhaps in the foreseeable future this application will become suitable for use in large bioreactors.

Further information:
Jun.-Prof. Dr. rer. nat. Nicole Radde
Systems Theory and Systems Biology 
Institute for Systems Theory and Automated Control (IST)
University of Stuttgart
Pfaffenwaldring 9
70550 Stuttgart
Tel.: +49 (0)711 685 677-29
E-mail: nicole.radde(at)ist.uni-stuttgart.de

Website address: https://www.gesundheitsindustrie-bw.de/en/article/news/mathematical-models-for-predicting-cellular-signalling-pathways