= Shunting inhibition
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<Shunting inhibition> is suppression of another input's effect through increased <synaptic conductance>: opening additional <ion channels> lowers effective <electrical resistance>, reducing the voltage response to a given added <electric current>. When the added <reversal potential> equals the resting <membrane potential>, there can be no voltage change at rest and still be inhibition of a simultaneous input. See <Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition by Wulfram Gerstner and others/1.4 Limitations of the Leaky Integrate-and-Fire Model>.
Use the passive <synaptic potential> model below with leak $g_L=10\,\mathrm{nS}$, $E_L=-65\,\mathrm{mV}$ and <capacitance> $C=200\,\mathrm{pF}$. A sustained inward test <electric current> of $I_{\mathrm{ext}}=100\,\mathrm{pA}$ alone gives a steady voltage increase of $I_{\mathrm{ext}}/g_L=10\,\mathrm{mV}$, so $V_\infty=-55\,\mathrm{mV}$. Effective <electrical resistance> is $100\,\mathrm{M\Omega}$ and the <time constant> is $20\,\mathrm{ms}$.
Now hold a shunting conductance $g_i=20\,\mathrm{nS}$ open with $E_i=E_L=-65\,\mathrm{mV}$. With no test <electric current>, rest stays at $-65\,\mathrm{mV}$. With the same $100\,\mathrm{pA}$ test <electric current>, total conductance becomes $30\,\mathrm{nS}$, so the steady voltage increase is only $100/30\simeq3.333\,\mathrm{mV}$: $V_\infty\simeq-61.667\,\mathrm{mV}$. Effective <electrical resistance> is $33.333\,\mathrm{M\Omega}$ and the <time constant> is $200/30\simeq6.667\,\mathrm{ms}$. A faster response can therefore be smaller. At the original rest the shunting <electric current> is zero; at $V=-55\,\mathrm{mV}$ it is $20(-65+55)=-200\,\mathrm{pA}$, opposing the voltage excursion.
The factor of three <reduction> applies to this constant-<electric current>, constant-conductance example. A finite pulse, conductance-driven input or spatially extended <dendrite> need not have the same <reduction>. The interesting feature is conditional action: the shunt can leave a quiet <neuron>'s voltage unchanged yet reshape its response when another input arrives. A model that represents all inhibition as a fixed outward <electric current> misses this behavior.
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