1School of Mathematics, University of Minnesota, Minneapolis, USA 2Department of Psychological and Brain Sciences, University of California, Santa Barbara, USA
*Email: mpelz@umn.edu Introduction
All vertebrate brains, from fish to humans, contain dense meshworks of axons (fibers) that release serotonin, a key signaling molecule. The role of this massive system is poorly understood, with no analogs in current AI architectures, but it appears to support neuroplasticity. Its effects on neural networks are exerted through serotonin receptors whose activation depends on serotonin molecules in the local extracellular space. Recent studies have revealed a lack of fundamental understanding of the spatiotemporal characteristics of extracellular serotonin [1]. In particular, its concentration may vary greatly within microscopic volumes and over short time frames. Such sustained heterogeneity may be a key feature of the plastic brain. Methods To investigate how the geometry of the spatial arrangement of release/reuptake sites (i.e., fiber varicosities [2,3]; Fig. 1(a), (b)) and the timing of release shape serotonin concentrations in microscopic brain volumes, we extend previous work [4] and consider a 2D compartmental-reaction diffusion system that is analytically tractable. Each varicosity is modeled as a small disk where the kinetics of serotonin release and uptake (adapted from [5]) are implemented. The disks interact with the surrounding diffusive space through an infinitely permeable boundary (Fig. 1(c), (d)). This system can be rigorously reduced to an integro-ordinary-differential system that can be numerically solved efficiently. Results Our system highlights precise coupling terms across varicosities that capture the diffusive memory dependence and global coupling and can be solved using arbitrary serotonin reaction kinetics at the varicosities. Using biologically realistic parameters, we observe that the serotonin concentration exhibits large temporal and spatial variation near varicosities, while regions farther away stabilize to a concentration that depends on the surrounding varicosity density (Fig. 1(e), (f), (g)). We are currently investigating the dependence of the serotonin concentration on the spatial distribution of varicosities (with fibers forming a regular lattice, fibers as stochastic paths [6], etc.). Discussion Neural tissue shows many features of criticality [7]. While some heterogeneities on the microscopic scale are due to noise which is not amplified by the brain, other heterogeneities may be actively maintained to support phase transitions and symmetry-breaking/pattern formation. In particular, it may be important in cortical oscillations, wakefulness-sleep transitions (e.g., no firing in REM sleep), and neuroplasticity (e.g., some psychedelics act on the serotonergic system with long-lasting therapeutic effects for some mental disorders). Further, our work will extend current reaction-diffusion pattern formation theory if nontrivial symmetry-breaking and oscillatory synchronization properties are found in this one-diffusing-species system.
Figure 1. a,b: Serotonergic fibers of a mouse brain with varicosities in dark red and light green (scale bars: 1μm (a), 5μm (b)). c: Mathematical system with well-mixed cyan varicosity neighborhoods and blue diffusing serotonin molecules (concentration). d: Zoomed into a single varicosity neighborhood. e-g: Numerical solutions for different varicosity and thus fiber arrangements (bright ~ high, dark ~ low). Acknowledgements - References ● https://doi.org/10.1111/jnc.15865 ● https://doi.org/10.1101/2023.11.25.568688 ● https://doi.org/10.3389/fnins.2022.994735 ● https://doi.org/10.48550/arXiv.2409.00623 ● https://doi.org/10.1016/j.bpj.2021.03.021 ● https://doi.org/10.3389/fncom.2023.1189853 ● https://doi.org/10.1016/j.tins.2022.08.007
