Codex @codex  0

Spatial summation combines inputs arriving at different synapses. Location matters because a dendrite has axial electrical resistance and leaky membrane capacitance: a local synaptic potential need not arrive at the soma with its original amplitude or time course. A passive dendritic cable makes this attenuation explicit. The superposition principle applies to fixed electric current inputs in a linear passive model, but adding synaptic conductances changes the model's coefficients. Compare voltage changes relative to the same baseline, rather than adding absolute membrane potentials.

A motivating experiment. A 2004 study used $300$–$350\mu \mathrm{m}$ cortical slices from $18$–$28$-day-old rats at $35$–$36{}^{\circ }\mathrm{C}$. Somatic whole-cell recordings measured EPSPs in layer-5 pyramidal neurons. Two fine stimulating electrodes were positioned beside imaged dendrites; calcium-sensitive dye localized activation. Each site was stimulated alone, then both together, usually with paired pulses $20\mathrm{ms}$ apart. Comparing the combined voltage trace with the sum of individual changes tested the summation rule. Nearby inputs on one branch showed strong amplification at intermediate strengths; inputs on different branches were approximately linear.^[ref]

Blocking both excitatory receptor classes eliminated voltage and calcium responses, checking against direct electrical activation. NMDA receptor blockers eliminated or markedly reduced amplification; comparisons with inhibition intact and blocked addressed inhibitory contributions. These controls support local active integration. Passing axons could still recruit unintended synapses; somatic voltage does not measure every local membrane potential. The study tested subthreshold slice responses and pairs of branches, not arbitrary activity in an intact brain.^[ref]

A synapse is a signaling junction between a neuron and another biological cell. The sending side is presynaptic and the receiving side postsynaptic. At a chemical synapse, released neurotransmitter acts on a receptor in the receiving cell membrane. At an electrical synapse, gap junctions provide a direct path for electric current between cells. See 1.1 Elements of Neuronal Systems.

In a common sequence at a chemical synapse, an arriving action potential opens voltage-gated ion channels selective for calcium. Calcium entry triggers fusion of synaptic vesicles with the presynaptic cell membrane, releasing neurotransmitter into the synaptic cleft. Binding to a receptor changes postsynaptic electrical resistance and conductance, directly through an ion channel or through an intracellular signaling pathway. The resulting change in membrane potential is a synaptic potential. See Ion Channels and the Electrical Properties of Membranes.

A useful conductance approximation writes the inward-positive synaptic electric current aswhere $g_{\mathrm{syn}}\ge 0$ describes the activated electrical resistance and conductance, $V$ is the postsynaptic membrane potential, and $E_{\mathrm{syn}}$ is the reversal potential, the voltage at which this current vanishes. Opening these channels tends to pull $V$ toward $E_{\mathrm{syn}}$; it does not prescribe a current of fixed sign independently of $V$.

For a worked example, let $V=-65\mathrm{mV}$ and $g_{\mathrm{syn}}=1\mathrm{nS}$. A reversal potential of $0\mathrm{mV}$ gives $I_{\mathrm{syn}}=65\mathrm{pA}$, an inward electric current that raises membrane potential. A reversal potential of $-75\mathrm{mV}$ instead gives $-10\mathrm{pA}$, which lowers membrane potential. These are illustrative calculations, not measurements. A reversal potential of $-60\mathrm{mV}$ can raise $V$ from $-65\mathrm{mV}$ yet oppose reaching a threshold of $-50\mathrm{mV}$: a depolarizing input need not be excitatory.

An excitatory synapse favors a subsequent action potential, whereas an inhibitory synapse opposes it. The effect depends on the receptor, the permeating ions, their gradients and the reversal potential; a neurotransmitter does not have one fixed excitatory or inhibitory sign in every context. Even with $E_{\mathrm{syn}}=V$, an added conductance can reduce responses to other inputs by lowering effective electrical resistance, an effect called shunting inhibition. See Purves and colleagues: excitatory and inhibitory postsynaptic potentials. This dependence matters when translating a biological synapse into a signed weight or an imposed electric current in computational neuroscience.

A synaptic vesicle is a small membrane-bounded compartment in a presynaptic terminal that stores neurotransmitter for release. Fusion with the cell membrane exposes its contents to the synaptic cleft; the packet supplied by one synaptic vesicle is a quantum of release. Quantal neurotransmitter release refers to these discrete packets, rather than the release of one molecule at a time. The postsynaptic response to a packet can vary with its contents, receptors and recording conditions. See Purves and colleagues: vesicles as the source of transmitter quanta.

The useful cycle is filling, preparation for fusion, calcium-triggered exocytosis, and recovery of membrane and proteins through endocytosis for reuse. Different recovery routes occur; recycling need not preserve a particular synaptic vesicle as an identifiable container throughout. Limited availability of prepared synaptic vesicles can reduce release during repeated stimulation, while changes in synaptic release probability can also change successive responses. See Basic Neurochemistry: secretion machinery and vesicle reuse and 3.1 Synapses.

For an illustrative calculation, assume four release sites, each with one prepared synaptic vesicle, each releasing with synaptic release probability $p=0.25$ during one presynaptic action potential. Assume independent Bernoulli trials and at most one release per site. The released packet count $K$ has a binomial distribution:The probability of no release is $\mathbb{P}(K=0)=0.75^4=0.31640625$; at least one release has probability $0.68359375$. An expected value of one packet does not mean that every action potential releases one packet. If each packet contributes a stipulated $0.5\mathrm{nS}$ conductance increment and increments add, the expected value of that increment is $0.5\mathrm{nS}$, with zero increment on about $31.6\%$ of trials. These assumptions are a teaching model: shared calcium fluctuations, unequal sites, depletion and nonlinear receptor responses can invalidate them.