A protein-driven multi-spine plasticity rule

Site-specific synaptic plasticity modifying the strength of a particular, individual synapse is critical to cognitive functions such as memory and learning (Kastellakis et al., 2019; Tazerart et al., 2020). This specificity coexists with the experimental observation that the dendrite-wide spine sizes and weights follow a surprisingly stable, lognormal-like distribution (Hasan et al. 2020; Eggl et al., 2023). How synaptic plasticity can be specific, yet the global synapse distribution stable, is an open question that has motivated several recent studies (Kirschner et al., 2019; Eggl et al., 2022). We aim to close this gap and propose a computational framework incorporating known plasticity-related protein families and their dynamics. We combine it with the dendritic dynamics of peri-synaptic calcium and its two principal second-messenger families: kinases (e.g., CaMKII) and phosphatases (e.g., Calcineurin, PP1) applying experimentally reported protein timescales (Pepke et al., 2010; Yasuda et al., 2022). Taking into account the glutamate uncaging effect on the different catalytic groups, we obtain a multi-compartment model that supports emerging, experimentally observed plasticity properties, such as inter-synaptic competition and cooperation. We derive an asymptotic closed-form solution that describes the spatiotemporal evolution of synaptic plasticity while linking it directly to the underlying biochemical machinery. We unite mechanistically disparate and seemingly contradicting experimental results about plasticity and spine distributions (Scanziani et al., 1996; Royer & Pare', 2003; Chater, Eggl et al. 2022, Helm et al., 2021), and provide new experimentally testable hypotheses connecting a spine's basal weight to its tendency to potentiate or depress in response to stimulation.