A quantitative rule to explain multi-spine plasticity

Neurons receive thousands of inputs onto their dendritic arbour, where individual synapses undergo activitydependent changes in strength. The durable forms of synaptic strength change, long-term potentiation (LTP) and long-term depression (LTD) require calcium entry through N-methyl-D-aspartate receptors (NMDARs) that triggers downstream protein signalling cascades in the dendrite. Notably, changes in postsynaptic strengths associated with LTP and LTD are correlated to changes in spine head volume, referred to as structural LTP (sLTP) and structural LTD (sLTD). Intriguingly, LTP and LTD, including sLTP and sLTD, are not necessarily restricted to the active, targeted synapses (homosynapses), and the changes in synaptic strength can spread and affect the strengths of inactive or non-stimulated synapses (heterosynapses) on the same cell. Moreover, the plasticity outcome at both homo- and heterosynapses can depend on the number of stimulated sites when eliciting multi-spine plasticity. Precisely how neurons allocate resources for implementing the changes in strength at individual synapses depending on their proximity to input activity across space and time remains an open question. In order to gain insights into the elementary processes underlying multi-spine plasticity that engages both homosynaptic and heterosynaptic changes, we have combined experimental and mathematical modelling approaches. On the one hand, we used glutamate uncaging to precisely and systematically stimulate variable numbers of homosynapses sharing the same dendritic branch whilst monitoring tens of other heterosynapses on the same dendrite. Homosynaptic potentiation of clusters of dendritic spines leads to heterosynaptic changes that are dependent on NMDAR, CaMKII and calcineurin. On the other hand, inspired by the Ca2+ levels hypothesis where different amounts of Ca2+ lead to either growth or shrinkage of spines, we have built a model based on a dual-role Ca2+-dependent protein that induces sLTP or sLTD. Comparing our experimental results with model predictions, we find that (i) both collaboration and competition among spines for protein resources are key drivers of heterosynaptic plasticity and (ii) the temporal and spatial distance between simultaneously stimulated spines impact the resulting spine dynamics. Moreover, our model can reconcile disparate experimental reports of sLTP and sLTD at homo- and heterosynaptic spines. Our results provide a quantitative description of the heterosynaptic footprint over minutes and hours post-stimulation across tens of microns of dendritic space. This broadens our knowledge about the operation of non-linear dendritic summation rules and how they impact spiking decisions.