SLd is thus the relative drop in Rd at location d due to the acti

SLd is thus the relative drop in Rd at location d due to the activation of single (or multiple) steady conductance changes at arbitrary dendritic locations (see Figures S8 and S9 and related text available online for generalization to the transient case). The value of SLd ranges from 0 (no shunt) to 1 (infinite shunt) and depends on the particular dendritic distribution of gis. For example, SLd = 0.2 implies

that the inhibitory synapse reduced the input resistance at location d by 20%, which is also the relative drop in the steady voltage at d due to the inhibition after the injection of steady current at location d. Thus, in order to characterize the effect of the inhibitory shunt in the most general way, it is natural to ask how much increase in excitatory current is required in order to exactly counter effect the shunting inhibition. This is exactly what SL implies. Note that the SL measure is applicable also for assessing the change in input resistance due to excitatory synapses that, like inhibition, exert

a local membrane conductance change. The spatial spread of SL can be solved using cable theory for arbitrary passive dendritic trees receiving multiple inhibitory synapses (see Experimental Procedures and Supplemental Information). This solution provides several new and counterintuitive results regarding the overall impact of multiple inhibitory dendritic synapses in dendrites and explains several experimental and modeling results that were not fully understood prior to the present study. We started with a geometrically selleck compound simple case, whereby a single inhibitory synapse impinges on a dendritic cylinder that is sealed ended

at one side and is coupled to an isopotential excitable soma at the other (Figure 1A). The dendritic cylinder is comprised of a hotspot (Magee et al., 1995; Schiller et al., 1997, 2000; Larkum et al., 1999; Antic et al., 2010), which is modeled by a cluster of 20 NMDA synapses, each randomly activated at 20 Hz (red circle and red synapse in Figure 1A). We then searched for the strategic placement of the inhibitory synapse first that would effectively dampen this local dendritic hotspot. Using numerical simulations for the nonlinear cable model that includes the spiking soma and NMDA synapses depicted in Figure 1A, we found that when the inhibitory conductance change, gi, was placed distally (“off-path”) to the hotspot, the rate of the soma action potentials (black trace in Figure 1B) was reduced more effectively than when the same inhibitory synapse was placed proximally (“on-path”) at the same distance from the hotspot (orange trace in Figure 1B). Indeed, such asymmetry in the impact of proximal versus distal inhibition for dampening local dendritic hotspot was previously observed in vitro ( Miles et al., 1996; Jadi et al., 2012; Lovett-Barron et al.

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