• Anatoly Buchin

About neuronal models

In 1976 the statistician George Box mentioned that all models are wrong, but some are useful. He was right. When we try limit our understanding about the world and express it in the mathematical terms, almost always we would be able to find exceptions. Nevertheless, model development is important to reduce our understanding about reality into comprehensible scale, where we could figure out the causal relationships of the studied phenomenon.

In biology and neurobiology in particular, scientists are always working with the particular model. The whole animal, cell culture or even certain sub-cellular mechanism working in a Petri dish could be a model of the particular biological process. Besides the physical models, there are also mathematical ones. They usually consist of the system of equations or rules describing the particular phenomenon. Every model is usually the result of work of the research group, which has been working on it for a long time. The main aim of the whole process of modeling is to actually find the best model for the studied phenomenon, so that we could better understand it and control.

Nevertheless, often scientists have to create models consisting of a lot of objects that are similar to each other. One of these examples are the models of single neurons and the processes taking place on the neuronal membrane. Generation of action potentials in neurons of the brain is the result of interaction of multiple ion channels located in every neural cell. Ions of sodium, potassium and chloride are passing through the neuronal membrane creating the current which propagates through the whole neuron body which allows it to connect to the other cells.

To better understand how different types of neurons are generating the action potentials we have developed hundreds of models for 230 different cell types based on the data from mouse visual cortex. To achieve this goal we had to develop the whole program package to generate them at scale on high performance computer cluster. The core problem in developing of single neurons models is finding the right parameters for them. If one has just a few models, it is possible to find the parameters manually. Neuron models often contain a lot of parameters that affect its dynamics and it takes time to find them all by hand. For a long time scientists have been picking up parameters manually for every particular neuron and publishing their results for every particular neuron. This approach worked well for small number of cells, but in the brain there are about 86 trillion of cells. There is no way we could find the parameters for every recorded neuron manually in an unbiased way.

For massive generation of single neuron models we used genetic algorithms, which are well suited for non-linear optimization problems. It allowed us not only fit the parameters for every experimentally recorded neuron, but also to estimate the parameter range for every neuron class. It turned out that single neuron parameters are located in a very small subset of the all possible parameter space. These results confirmed our predictions from the previous studies, showing that the parameters for single neurons are not random. From the evolutionary point of view it is very meaningful. Neuron without proper ion channels properly adjusted could not process the information and therefore would have been eliminated by natural selection. For the normal functioning of a neuron it is necessary to keep the balance of different ionic currents, allowing the neuron to generate spikes and spread them across the other neurons in the network. Moreover, we found that similar neurons have more similar parameter values and therefore have similar input-output properties.

In the future these studies would allow us to better understand how different types of neurons are working in the brain and what function do they serve. In fact, in the process of evolution the human neocortex has expanded approximately 26 times compared to the common ancestor of all mammals. Specifically cortex is believed to be responsible for a lot of cognitive functions, such as memory, attention and learning. As evolutionary more novel structure, cortex contains substantial amount of diverse cell types compared to the other brain regions. It is still not clear what could be the function of this cell type diversity. Potential explanation could be that different cell types are performing distributed computation in the brain or that the cell types are related to the neuronal migration in the embryo during the development. On a practical side, we are starting to learn that different cortical cell types have selective vulnerability to neurological disorders, such as Alzheimer disease. In the future this knowledge of cortical cell types and their characteristics would allow us better understand the neurological disorders and hopefully find better treatments.

Bioarxiv article:


© 2020 by Anatoly Buchin