Push-and-pull protein dynamics leads to log-normal synaptic sizes and probabilistic multi-spine plasticity

A typical neuron receives thousands of inputs and is able to adapt the strength of its synapses to store new information and meet ongoing computational demands. The synaptic response to plasticity induction is stochastic and spatially structured but is traditionally described by deterministic models representing the "average" dynamics. Growing experimental evidence indicates that not only the stimulation protocol determines the plasticity outcome but that the initial synaptic sizes, their fluctuations, and the spatial competition for the plasticity-relevant proteins play a decisive role. This probabilistic perspective makes it hard to predict the fate of a given synapse and requires a conceptual shift from a single synapse view to a probabilistic multi-spine competitive process where the plasticity needs and the available resources are considered together. Here, we propose a data-driven modeling framework able to predict collective plasticity outcomes along a dendrite based on the initial size, the number, and the spatial distance between simultaneously stimulated synapses. Our data analysis reveals a log-normal distribution of protein numbers for many plasticity-mediating proteins and shows that this log-normal protein allocation constrains and controls the collective plasticity outcome across multiple stimulated and non-stimulated synapses while preserving a global size distribution. Our findings highlight how local stochastic processes and global protein allocation rules give rise to synaptic plasticity outcomes, offering a new framework to understand and predict dendritic computation.