“Without models, we would be lost”
The brain is both a thinking organ and a collection of cells. Its overall function still eludes us. That is beyond our capacity at the moment. What we can begin to understand is how brain cells work and interact, and try to relate those findings to thought processes.
I design detailed models of individual neurons and neuronal circuits to find out how cells communicate via synapses or in other, unconventional ways. Then I connect these models to experiments that observe in-vitro brain slices or also humans.
To make a model of a cell, you have to experimentally specify the properties of the membrane, which actually resembles an undersea communication cable. In fact, it can be described by the same partial differential equation. You also need to define the properties of the proteins that live in the membrane and change their behaviour depending on the local electric field. Electrical signals propagate and influence chemical signals and vice versa. Then you put all that information together. My work requires enormous data processing and storage capacities and years of research. Longevity is the key. The model I use the most took me five years to develop; it contains some 35,000 lines of code and thousands of cells.
At the moment, the most important application area for my models is in epilepsy research. Surprisingly enough, we found that the electrical activity patterns occurring in the brain during a seizure can be replicated in an in-vitro system and understood in relatively great detail. This is an active research area here at the Charité in Berlin. Years ago, my colleagues and I came up with a model that describes how the sharp waves that occur during a seizure are generated. We suggested that they were closely linked to “gap junctions” between the principal neurons. Many experiments conducted in Berlin support this model. If it is correct, the results would be quite revolutionary: we would be able to demonstrate that synapses are not the only pathway through which brain activities occur. It might even be possible to suppress an epileptic seizure by regulating gap junctions.
Mathematical models are essential for brain research because the brain – with its myriad systems of cells and circuits – is incredibly complex. We need a theory, not like relativity theory, but a model that enables a host of equations and simulations. Without models, we would be lost. It would be like trying to run a meteorology station without numbers or equations, only words.
Photo: Pablo Castagnola