## LiSyM director Professor Dr. med. Peter Jansen believes that mathematical models are indispensable for the research of biological systems.

“Mathematical models are indispensable for today’s systems research,” stresses Professor Dr. med. Peter Jansen, a professor of medicine from the Netherlands who is the director of LiSyM, an interdisciplinary German research network that studies the liver at all levels. LiSyM’s goal is to understand the organ as a whole, in particular to learn more about the metabolic liver disease NAFLD. “Of course, we also need to conduct experiments for this,” says Jansen, “but without mathematical models, the experimental results don’t help us make progress as quickly.” On the contrary, using mathematical models increases the value of results. They decrease the time needed to develop new tests for prevention, diagnostics, and monitoring and for therapeutic approaches. This means that mathematical models can improve and even save the lives of many liver patients in the long-term.

### Only models can reflect the dynamics and complexity of biological systems

Biological systems like the liver are extremely complex. According to Jansen, “There are all kinds of interactions occurring on different levels between different cells and cell types. This is extremely complicated, especially when we want to understand the communication between these cells across all scales.” The standard methods for visualizing biological systems have long been charts and diagrams with formulas, numbers, arrows, and other symbols. However, such charts can be confusing when they represent many different interactions on several hierarchical levels. That is why they are usually extremely simplified, or they present only part of the picture. Mathematical models, on the other hand, can reproduce entire systems without sacrificing clarity. This lets researchers emphasize certain details – such as individual chains of reaction, signaling pathways, levels of hierarchy, and other aspects – as part of the overall system.

Jansen also points out that biological systems are extremely dynamic: “If you influence the activity of one enzyme, you influence other enzymes as well.” It takes only one change in a reaction rate or another parameter within the dense networks of interactions at different levels for the system to react in several places. The disadvantage of charts is that they are static, while in simulated systems based on mathematical models, all affected places react as soon as the parameters change. That is why mathematical models and their computer simulations are the only method for adequately representing the dynamics and complexity of biological systems.

### The roots go back 100 years

The British mathematician Alan Turing had the idea that computers could make a significant contribution to systems research already in the mid-20th century. “In 1952, he published a fantastic paper on morphogenesis in nature,” says Jansen. In this ground-breaking publication, “The Chemical Basis of Morphogenesis,” Turing suggests that the chemical basis of biological pattern formation is a simple reaction-diffusion process. This is still known as the “Turing mechanism,” and the resulting patterns as “Turing patterns.” Such patterns include the spots on giraffes and cheetahs, the stripes on zebras and tigers, the regular teeth of alligators, and the growth structures of neurons.

Turing began inventing analog computers already in the 1940s and was able to crack the German encryption device called “Enigma.” Despite this, he also acknowledged the analog computer’s limits. In his scholarly paper from 1952, he speculated that only faster digital computers would be able to solve the kind of mathematical equations that are necessary to represent complex biological systems. Jansen admits, “Turing is one of my personal heroes of science.” He was not the first biomechanist, however. That honor goes to Turing’s compatriot D’Arcy Wentworth Thompson, a mathematician and biologist who already bemoaned in his book “On Growth and Form” from 1917 that the importance of mathematical equations for explaining the growth patterns of living organisms was greatly underestimated.

### “All biological processes follow certain rules”

The application of mathematical models is not limited to growth processes. “All biological processes follow certain rules!” explains LiSyM director Jansen. Specialists in the LiSyM network have formulated rules for processes and changes in the liver as mathematical equations. “We can also enter other parameters, like reaction rates or substrate concentrations,” says Jansen. Hundreds of equations and parameters have already been integrated into LiSyM’s models, and they continue to increase. The systems-based liver research done at LiSyM is constantly providing new data. In a parallel process, experts are also processing already existing data, which can also be integrated. This means that all relevant experimental results are being incorporated into LiSyM’s models, which are becoming more comprehensive and precise with each new data set.

### Heterogeneous data provide a coherent image

The interdisciplinary systems research done at LiSyM provides diverse types of data. The network brings together many different scientific disciplines in which researchers may rely on other materials. For example, they conduct in vitro experiments with cell extracts, in cultures of different cell types, with animal models, with patient tissue samples, and of course clinical trials. Although the scales and sources vary greatly, the results of comparable experiments often match and complement each other. However, in some cases they may diverge so much that it may be difficult to find a connection. “Mathematical models can bring together heterogeneous bits of information in a way that makes sense and fills the gaps in our knowledge,” explains Jansen. Thus, computer simulations not only show similarities between organisms and experimental approaches; they also highlight their differences.

“Mathematical models can also be used for imaging,” says Jansen. Images from intravital microscopy – the observation of living cells under a microscope – and other modern imaging methods can be combined with other experiment data. “This way, we can make 3-D models of all levels of the liver,” explains Jansen. “We can see which reactions take place in what liver cells, because different areas of the liver have different functions.” Other processes are still beyond the reach of researchers, however, like the dynamics of the flow of bile through the microscopically small network of canaliculi in the liver. “We are unable to research these processes through experiments at the moment, meaning we can’t measure anything there currently,” explains Jansen. However, researchers can use imaging methods to represent these processes. LiSyM experts can combine these data with other data to create 3-D models that help them develop new ideas about how the liver produces and transports bile.

### Researching processes that are inaccessible for experiments

Mathematical models make it possible to investigate areas of the liver where experiments are not possible. They also save resources. The more precisely mathematical models work, the more practical experiments they can replace. This is relevant, for example, when research materials are difficult to acquire, or when there are ethical concerns. For example, LiSyM researchers work with tissue samples usually taken from patients by biopsy. Although a biopsy is a low-risk procedure, it is not completely risk-free. Furthermore, many tests on animal models could be avoided by using mathematical models. “That is also one of our goals,” stresses Jansen, adding: “Authorities like the FDA (US Food and Drug Administration) and the EMA (European Medicines Agency) should approve mathematical models for testing new drugs. The results are just as good as, or better than results from animal testing.”

### An early and forward-thinking decision in favor of models

When Jansen became director of the network in 2015, LiSyM was already working with mathematical models. “My predecessors had the great foresight to integrate them long before. And there were no precedents back then!” he says, adding that this courageous decision certainly paid off in terms of science: “These models have played a significant role in our success.” LiSyM has not only been able to shed light on the transport of bile and bile acids using these models; its researchers have also demonstrated, among other things, that everyday drugs like nicotine can produce false results in the widely used LiMAx liver function test. They were also able to show how this test can be made more specific, and how liver functions are divided, sometimes epigenetically, into spatial zones by methylation.

### It takes continuity to establish models

Many requirements must be met to be able to conduct systems research with mathematical models. First, as much data as possible must be collected from many different sources in order to increase their applicability and validity. Second, not only are experts from a variety of scientific fields needed, but also experts who can build bridges between bioscience and mathematical modeling. “These people are really in high demand right now,” says Jansen, adding: “Large precise models that bring together all the data of one field are like the Holy Grail of systems research.” However, because it takes several years to develop such models, interdisciplinary research networks need sufficient secure, long-term funding. This enables mathematical models to lead to new drugs even more quickly, helping physicians to make diagnoses and prescribe treatment, and making an important contribution to personalizing cancer treatment. With this expectation in mind, LiSyM director Peter Jansen says, “I’m convinced that we can increase the value of biological systems research significantly by integrating mathematical models.”

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