= Synaptic integration
<Synaptic integration> is the conversion of inputs at a <neuron>'s <synapses> into a changing <membrane potential> and, in a spiking <neuron>, the timing or absence of <action potentials>. <Spatial summation> concerns inputs at different locations; <temporal summation> concerns inputs at different times. A useful question is whether individually ineffective inputs can act together, and whether an <inhibitory postsynaptic potential> changes that cooperation. The answer depends on location, timing and the receiving <neuron>'s state.
A <synaptic potential> is a voltage response, whereas <synaptic conductance> describes activated <ion channels>. With inward-positive <electric current>, the contribution of input $j$ is
$$
I_j(t)=g_j(t)(E_j-V).
$$
Here $g_j$ is its <synaptic conductance>, $E_j$ its <reversal potential> and $V$ the local <membrane potential>. The driving force $E_j-V$ is an <electric potential difference>. An <EPSP> generally brings the <membrane potential> toward a more positive <reversal potential>, but its driving force shrinks during <depolarization>. An <IPSP> need not produce <hyperpolarization>: a <reversal potential> above rest but below the <neuronal firing threshold> can produce <depolarization> while opposing a larger excursion. At $E_j=V$, the added <synaptic conductance> initially carries zero <electric current> yet can cause <shunting inhibition> of another input.<Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition by Wulfram Gerstner and others/3.1 Synapses>[§3.1, equation (3.1), and §3.1.1: conductance, reversal and voltage-dependent sign; our current convention is inward-positive]{ref}
Two distinct nonlinearities matter. Even a passive <cell membrane> can show sublinear <synaptic integration> when added <synaptic conductances> reduce driving force and effective <electrical resistance>. Active <voltage-gated ion channels> and <NMDA receptors> can instead amplify sufficiently concentrated inputs and produce a <dendritic spike>. Neither summing prescribed <electric currents> nor adding separate measured <EPSPs> is an exact universal rule for a branching <neuron>.<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>[§1.4.2 and §1.4.4: shunting, saturation and active dendritic interactions]{ref}
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