Mathematical model for visual cortical development based on molecular mechanisms underlying the generation and elimination of dendritic spines

In the developing brain, neural circuits are elaborated by the activity-dependent rewiring of synaptic connections. Our earlier self-organization model, which was built on the assumption that axon terminals compete with each other to form synaptic contacts to single dendritic spines, successfully reproduced spatiotemporal receptive fields and orientation-direction joint maps (Tanaka et al., 2020). It has been reported that most synaptic contacts are en passant types rather than axonal terminals (Turegano-Lopez et al., 2024). This finding contradicts our assumption that each axon terminal selects an appropriate dendritic spine. Recent microscopic observations have shown that dendritic spines are more motile than presynaptic boutons (Bonhoeffer and Yuste, 2002; Deng and Dunaevsky, 2005). In addition, the current view of synaptic rewiring in early development is that filopodia spontaneously generated along dendrites transform into spines by establishing contacts with neighboring axonal boutons to form synapses whereas spines of inappropriate synapses are eliminated in an activity-dependent manner (Deng and Dunaevsky, 2005). In this theoretical study, we mainly focus on the processes of spine generation, maturation, and elimination to rebuild a mathematical model of synaptic rewiring, incorporating recent experimental findings on actin polymerization and depolymerization (Ridley, 2006) under the activation of Rho-GTPases (Mackay and Hall, 1998) mediated by the binding of variant forms of brain-derived neurotrophic factor (BDNF) (Binder and Scharfman, 2004; Lesmann and Brigadski, 2009; Kuczewski et al., 2009) to neurotrophin receptors such as tropomyosin kinase receptor B (TrkB) (Klein et al., 1989) and the low-affinity-nerve growth factor receptor (p75NTR) (Yamashita et al., 1999). TrkB receptors are dephosphorylated by chondroitin sulphate proteoglycans (CSPGs) (de Vivo et al., 2013) mediated by protein-tyrosine phosphatase sigma (PTPsigma (Kurihara and Yamashita, 2012) in an age-dependent manner. The model describes the generation or elimination of dendritic spines of visual cortical neurons under actin polymerization and depolymerization to establish appropriate synaptic contacts on afferent fibers of cells in the lateral geniculate nucleus. The simulations based on the new model reproduced not only simple-cell-like receptive fields (DeAngelis et al., 1999) and orientation-direction maps (Shmuel and Grinvald, 1996) but also a characteristic profile of the total number of synapses, which shows an early increase and a delayed decrease during the critical period (Li et al., 2006; White and Fitzpatrick, 2007). It is also demonstrated that whereas orientation selectivity is elevated almost monotonically throughout the critical period, the formation of direction selectivity is delayed behind the formation of orientation selectivity, which is likely promoted by the pruning of inappropriate synapses (Grigonis et al., 1988; Bourgeois et al., 1993; Elston et al., 2009; Faust et al., 2021).