# A mathematical model suggests collectivity and inconstancy enhance the efficiency of neuronal migration in the adult brain

## TL;DR

A mathematical model shows that neurons in the adult brain migrate more efficiently when they move in groups and change their behavior over time.

## Contribution

The study introduces a novel mathematical model to explain how neuroblast collectivity and behavioral inconstancy enhance migration efficiency in the adult brain.

## Key findings

- Neuroblasts form chain-like collectives through occasional contact and moderate adhesion.
- Collective migration accelerates movement by shrinking astrocytic protrusions more effectively.
- Temporal variability in neuroblast behavior enhances migration speed compared to constant behavior.

## Abstract

Neuronal regeneration in the adult brain, which is restricted compared to that in the embryonic brain, is a long-standing topic in neuroscience and medical research. Based on studies in mammals, a small number of newly generated immature neurons (neuroblasts) migrate toward damaged sites and contribute to functional recovery. During migration, neuroblasts form chain-like collectives and modify the morphology of glial cells (astrocytes), which are the main components of the surrounding environment. However, it remains unclear how neuroblasts form collectives and how efficient migration is achieved through collective formation in a pool of astrocytes. The main difficulty lies in tracking individual neuroblasts within the collective, both in vitro and in vivo, over a period. To address this impasse, we built a mathematical model of the neuroblast-astrocyte system to assess its long-term performance in silico. Our simulations showed that individual neuroblasts gathered into chain-like collectives through occasional contact, astrocyte confinement, and moderate adhesion between the neuroblasts. The forward movement of neuroblasts in an astrocyte-dense environment was accelerated if we assumed a simple interaction: the higher the number of neuroblasts near an astrocyte, the stronger the shrinkage of astrocytic protrusions. Furthermore, temporal changes in neuroblast behavior, as indicated by our observation of living neuroblasts in culture, reinforce the advantages of simulated collectives. A collective of neuroblasts with constant behavior sometimes repeated non-migratory movements, whereas those with inconstant behavior were easily untangled, resulting in a rapid migration. These results highlight the potential for neuroblast collectivity and inconstancy in enhancing neuronal regeneration in the adult brain.

Increasing the regenerative ability of the adult brain is challenging for humans. Only a limited number of newly generated nerve cells (neurons) migrate toward injured regions to participate in the functional regeneration of the adult mammalian brain. During this journey, neurons gather and modify the shape of the surrounding glial cells. Because it is difficult to observe how actual neurons within a group efficiently move in the brain for a long time, we sought to determine the key to rapid migration using a mathematical approach instead of a biological one. Computer simulations showed that, first, neurons form a chain-like group by gently sticking to each other and following the rail-like guide of glial cells. Second, a group of neurons migrates faster than a single one because they can shrink the processes of nearby glial cells more effectively than a single one. Third, a group becomes faster when the behavior of neurons varies over time, even at the same average speed. Our novel concept posits that high regeneration ability in the brain is achieved through the grouped, temporally varying migration of neurons.