Computational models reveal how chloride dynamics determine the optimal distribution of inhibitory synapses to minimise dendritic excitability

Many neurons in the mammalian central nervous system have complex dendritic arborisations and active dendritic conductances that enable these cells to perform sophisticated computations. How dendritically targeted inhibition affects local dendritic excitability is not fully understood. Here we use computational models of branched dendrites to investigate where GABAergic synapses should be placed to minimise dendritic excitability over time. To do so, we formulate a metric we term the “Inhibitory Level” (IL), which quantifies the effectiveness of synaptic inhibition for reducing the depolarising effect of nearby excitatory input. GABAergic synaptic inhibition is dependent on the reversal potential for GABA(A) receptors (EGABA), which is primarily set by the transmembrane chloride ion (Cl(-)) concentration gradient. We, therefore, investigated how variable EGABA and dynamic chloride affects dendritic inhibition. We found that the inhibitory effectiveness of dendritic GABAergic synapses combines at an encircled branch junction. The extent of this inhibitory accumulation is dependent on the number of branches and location of synapses but is independent of EGABA. This inhibitory accumulation occurs even for very distally placed inhibitory synapses when they are hyperpolarising–but not when they are shunting. When accounting for Cl(-) fluxes and dynamics in Cl(-) concentration, we observed that Cl(-) loading is detrimental to inhibitory effectiveness. This enabled us to determine the most inhibitory distribution of GABAergic synapses which is close to–but not at–a shared branch junction. This distribution balances a trade-off between a stronger combined inhibitory influence when synapses closely encircle a branch junction with the deleterious effects of increased Cl(-) by loading that occurs when inhibitory synapses are co-located.