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Hyperpolarization makes a neuronal membrane potential more negative relative to the exterior. It is a voltage description; inhibition need not produce hyperpolarization, as shunting inhibition illustrates.

An inhibitory postsynaptic potential is a synaptic potential associated with decreased likelihood of a postsynaptic action potential. It can involve hyperpolarization or depolarization; an inhibitory conductance can even produce no measurable voltage change at rest. See synaptic potential and shunting inhibition for worked examples and sources.

An ionotropic receptor is a receptor in which binding of a ligand directly gates an ion channel within the same protein complex. The binding site detects the chemical signal; the pore supplies a path across the cell membrane. At a chemical synapse, a neurotransmitter therefore changes synaptic conductance without an obligatory intervening G protein or second messenger. ^[ref]

A familiar example is the nicotinic acetylcholine receptor of skeletal muscle: acetylcholine binding opens a pore passing cations, including sodium and potassium. The muscarinic acetylcholine receptor instead uses intracellular signal transduction; the same neurotransmitter can engage different mechanisms. Direct gating does not mean that an ionotropic receptor pumps ions: electrochemical gradients drive passage through the open ion channel. Nor does “ionotropic” specify excitation. The reversal potential, initial membrane potential and other conductances determine whether the effect favors an action potential, causes hyperpolarization, or supplies shunting inhibition. ^[ref]

A concrete electrical approximation separates opening from drive. Let $N$ identical ion channels each have open-channel electrical conductance $\gamma$ and opening probability $p(t)$. At fixed membrane potential $V$, with common reversal potential $E_{\mathrm{rev}}$, the expected value of inward-positive electric current isFor stipulated values $N=100$, $\gamma =20\mathrm{pS}$, $p=0.2$, $V=-60\mathrm{mV}$ and $E_{\mathrm{rev}}=0$, the mean open count is $20$, the population electrical conductance is $0.4\mathrm{nS}$ and $I_{\mathrm{in}}=24\mathrm{pA}$. One open ion channel carries $1.2\mathrm{pA}$. These are illustrative values, not measurements. At $V=E_{\mathrm{rev}}$, the net electric current vanishes despite open ion channels; neither binding nor opening alone determines the readout. The approximation omits changes in ion concentrations and voltage-dependent open-channel electrical conductance.

A motivating experiment made the elementary electrical events visible. As Bert Sakmann recounts, chronically denervated frog muscle fibers had acetylcholine-sensitive receptors spread beyond the original nerve contact. Mild enzyme treatment exposed the cell membrane; a polished glass pipette sealed over a small patch to reduce background noise. Two intracellular electrodes held the local membrane potential through voltage clamp, while the patch pipette recorded tiny electric currents. Applying suberyldicholine, a ligand that activates the acetylcholine receptor and prolongs openings, revealed abrupt, approximately rectangular current events. Their amplitudes agreed reasonably with estimates from whole-membrane current fluctuations. This established discrete opening and closing events; it did not make every ligand response instantaneous. Background noise and finite recording bandwidth concealed sufficiently small or brief events.^[ref]

Recording an intact membrane patch alone does not exclude intracellular relays. Tank, Huganir, Greengard and Webb supplied a complementary isolation test in 1983: they purified nicotinic acetylcholine receptors from an electric ray's electric organ, incorporated them into artificial lipid membranes, and fused small vesicles into larger vesicles by freezing and thawing. Sealed glass-pipette recordings from isolated membrane patches resolved functional ion channels with properties resembling those in muscle. Removing the intact cytoplasm and its signaling machinery supports the sufficiency of the receptor complex for channel function; an artificial lipid environment still cannot reproduce every native regulatory interaction.^[ref]

Direct gating supports millisecond communication at many chemical synapses. Response duration also depends on neurotransmitter clearance, binding and channel-state transitions. Continued ligand exposure can prolong activity. Classify an ionotropic receptor by its direct connection between recognition and pore gating, rather than a universal duration cutoff. ^[ref]

The membrane time constant of a passive uniform compartment is its membrane capacitance $C$ divided by its total fixed electrical conductance $G$. After input removal, voltage deviation from the relevant equilibrium undergoes exponential decay; in one membrane time constant it falls to $e^{-1}$ of its initial value. For leak alone, $G=g_L$; while fixed synaptic conductances are open, $G=g_L+{\sum }_j{g}_j$. Thus shunting inhibition can both reduce voltage responses and shorten the integration window. This is a local passive timescale: a branching dendrite can have several decay modes, and a time-varying synaptic conductance need not admit one constant ${\tau }_m$.

A neuron is a specialized biological cell that receives, integrates and transmits signals. Its shape separates places where inputs arrive from places where outputs reach other biological cells: this functional asymmetry is neuronal polarity. Understanding a neuron therefore means connecting its anatomy to changes in membrane potential, rather than treating it as a wire that merely forwards every input.

In a common multipolar neuron, branching dendrites receive inputs at synapses; the soma contains the cell nucleus and most major organelles; the axon carries signals to distant or nearby targets; and axon terminals form output contacts. All these regions belong to one biological cell enclosed by a continuous cell membrane. An axon can branch, allowing one neuron to influence several receiving biological cells.^[ref]

At an input chemical synapse, a neurotransmitter acts on a receptor, changing an electric current directly or through signal transduction.^[ref] A resulting synaptic potential contributes to synaptic integration in the dendrites and soma. In many spiking neurons, sufficiently strong depolarization recruits voltage-gated ion channels in the axon initial segment, initiating an action potential that propagates along the axon. At an output chemical synapse, calcium entry through voltage-gated ion channels promotes synaptic vesicle exocytosis, releasing neurotransmitter. An action potential is thus regenerated electrically along a cell membrane; it is not a packet of neurotransmitter travelling from the dendrites to the axon terminals.^[ref]

The compartments are specializations, not exclusive jobs. Inputs can contact the soma or axon as well as dendrites; dendrites can support active voltage-gated ion channels. Paired recordings from a pyramidal neuron's soma and dendrite or axon established that an action potential can begin in the axon and propagate back into the dendrites. The usual output direction therefore does not make every electrical signal strictly one-way.^[ref] An electrical synapse, which directly couples cytoplasms through gap junctions, also differs from the sending-and-receiving arrangement of a chemical synapse.^[ref]

Nor does every neuron have the upper diagram's shape. A bipolar neuron has two main processes, one dendrite and one axon; a multipolar neuron has several dendrites; and a pseudounipolar neuron has a single process from the soma that divides into peripheral and central branches. In the last arrangement, sensory signals can travel past the soma rather than obligatorily through it. These shape categories do not specify every neuron's receptor, connectivity or firing behavior.^[ref] Some neurons in the retina communicate through graded changes in membrane potential without generating action potentials.^[ref]

Why timing changes the computation. Synaptic integration can combine inputs at different locations, called spatial summation, and inputs arriving at different times, called temporal summation. A minimal example uses the leaky integrate-and-fire model with the illustrative parameters already given there: resting and reset membrane potential $-65\mathrm{mV}$, firing threshold $-50\mathrm{mV}$, electrical resistance $R=100\mathrm{M\Omega }$, capacitance $C=200\mathrm{pF}$, time constant $\tau =RC=20\mathrm{ms}$ and neuronal refractory period $2\mathrm{ms}$. These are chosen model values, not measured properties of a particular neuron. Before firing, a constant inward electric current $I$ starting from rest givesThe exponential function expresses the competition between charging the cell membrane's capacitance and leakage through its electrical resistance.^[ref]

Two $100\mathrm{pA}$ inputs, each lasting $40\mathrm{ms}$, produce different outputs depending on their timing. Either input alone reaches only $-56.3534\mathrm{mV}$. Applied together, they give $I=200\mathrm{pA}$ and reach threshold after $20\ln 4\mathrm{ms}\approx 27.7259\mathrm{ms}$, producing one action potential event during the pulse. If instead the second input begins $20\mathrm{ms}$ after the first ends, the earlier depolarization has partly decayed: the second pulse peaks at approximately $-55.9229\mathrm{mV}$ and neither pulse produces an action potential. The two-input protocols deliver the same total electric charge, $8\mathrm{pC}$, yet only the coincident protocol fires. Counting total input alone misses this timing dependence.

This example makes a neuron a detector of sufficiently clustered input, not a perfect logical gate: different parameters change the result. Actual dendrites introduce location-dependent filtering and active responses, and an inhibitory postsynaptic potential or shunting inhibition can change whether another input succeeds. The single-compartment leaky integrate-and-fire model omits these mechanisms.^[ref] Across connected neurons, branching axons distribute outputs while converging synapses combine inputs; spike trains can support temporal coding and rate coding, and synaptic plasticity changes the influence of an input. Connectivity and cellular dynamics together determine the computation.^[ref][ref]

Testing the connection between structure and function. Whole-cell recording connects anatomy to a measured membrane potential. In a published mouse protocol, a two-photon microscope guides solution-filled glass pipettes to neurons; an amplifier and bath reference electrode complete the electrical recording apparatus. A high-resistance seal forms against the cell membrane, then brief suction opens the membrane patch beneath the tip. In current clamp, the amplifier supplies a chosen electric current and records the resulting membrane potential, unlike voltage clamp, which controls voltage and measures electric current. The investigators used $500\mathrm{ms}$ current steps of several amplitudes to characterize excitability and firing, and negative current pulses to estimate input electrical resistance.^[ref]

The observable is a voltage trace, including graded responses and action potentials. Comparing injected electric current with that trace tests how input becomes output; it does not identify every underlying ion channel. The protocol checks access electrical resistance, which can distort voltage and action potential measurements, and includes intervals without stimulation to record spontaneous activity. In a teaching replication, repeated zero-input trials and monitoring baseline drift would provide further controls; these are recommended comparisons, not additional results attributed to the paper. A recording at the soma also cannot establish the local voltage everywhere in a branching dendrite, and this anesthetized preparation does not establish behavior in every awake neuron.^[ref]

A complementary experiment used simultaneous whole-cell recordings from the soma and an apical dendrite or axon of the same pyramidal neuron in a brain slice. The relative onset times of action potentials, together with sodium currents in excised dendrite membrane patches, supported axonal initiation followed by active propagation into dendrites. Pairing sites within one neuron is a useful comparison because it avoids confusing differences between cells with differences between compartments. Instrument timing and comparable recording quality would be essential controls when reproducing the inference. Only the published abstract was accessible here, so no unverified timing values, drug controls or channel distributions are supplied.^[ref]

The spatial panel uses two compartments with membrane potentials $V_s,V_d$, one representing the soma and one a dendrite. Set $v_s=V_s-E_L$, $v_d=V_d-E_L$, with leak reversal potential $E_L=-65\mathrm{mV}$, each membrane capacitance $C=100\mathrm{pF}$, each leak electrical conductance $g_L=5\mathrm{nS}$ and axial electrical conductance $g_c=10\mathrm{nS}$. Electric charge conservation givesThis chosen passive model has two decay time constants, $C/g_L=20\mathrm{ms}$ for the equal-voltage mode and $C/(g_L+2g_c)=4\mathrm{ms}$ for the voltage-difference mode. Starting from rest, a $100\mathrm{pA}$ step into the soma gives, with $u$ the time since onset,while the same step into the dendrite gives$u$ is expressed in $\mathrm{ms}$. Their long-time rises are $12$ and $8\mathrm{mV}$ respectively. Applying both inputs gives $20(1-e^{-u/20})\mathrm{mV}$ exactly: spatial attenuation coexists with linear summation of prescribed electric currents. After the steps end, both modes decay with their respective time constants. This deliberately coarse model is not a reconstructed dendrite or a fit to the experiment above.

The conductance panels use the existing one-compartment synaptic potential equation, with $C=200\mathrm{pF}$, $g_L=10\mathrm{nS}$, $E_L=-65\mathrm{mV}$ and excitatory reversal potential $E_e=0\mathrm{mV}$. For a constant excitatory synaptic conductance $g_e$, the steady state voltage rise and membrane time constant areEach isolated $2\mathrm{nS}$ input has a limiting rise $130/12\approx 10.833\mathrm{mV}$. Adding those isolated rises predicts $21.667\mathrm{mV}$, but opening both together gives $260/14\approx 18.571\mathrm{mV}$. The two conductances share a changing driving force. This is sublinear input summation even though the voltage ordinary differential equation is linear for each prescribed conductance waveform.

Add $g_i=20\mathrm{nS}$ with reversal potential $E_i=E_L$ to the joint $4\mathrm{nS}$ excitation. The limiting rise becomes $260/34\approx 7.647\mathrm{mV}$ and the membrane time constant becomes $200/34\approx 5.882\mathrm{ms}$. The shunt alone leaves rest unchanged. At the joint-excitation-only steady state $V\approx -46.429\mathrm{mV}$, however, its inward electric current would be $20(-65+46.429)\approx -371.429\mathrm{pA}$: it opposes that excursion. The finite $50\mathrm{ms}$ traces in the diagram approach, but need not reach, these limiting voltages. See shunting inhibition for the constant-electric current comparison.

A reversal potential $E_{\mathrm{rev}}$ is a membrane potential at which a specified open ion channel, or specified combination of ion channels, carries zero net electric current, with the surrounding conditions fixed; the electric current changes sign across that voltage. Specifying which current matters: an individual ion contribution and a sum of several contributions can reverse at different voltages. Zero net electric current does not mean that all ions have stopped moving. See Purves et al., Neuroscience, 2nd edition (2001): reversal of a mixed-ion channel current.

Throughout these examples, membrane potential is $V=V_{\mathrm{inside}}-V_{\mathrm{outside}}$, and conventional current is inward-positive. Positive electric current corresponds to net positive electric charge entering or net negative electric charge leaving. Negative electric current corresponds to the reverse charge transfer. A convenient Ohmic approximation iswhere $g$ is the available electrical conductance. For fixed $g>0$, $V<E_{\mathrm{rev}}$ gives positive electric current, $V=E_{\mathrm{rev}}$ gives zero, and $V>E_{\mathrm{rev}}$ gives negative electric current; the line has slope $-g$. If $g=0$, the modeled pathway carries zero electric current at every voltage: closing it does not locate its reversal potential. 3.1 Synapses (§3.1: conductance-based synaptic current) uses outward-positive $g(V-E)$; the formula here reverses that sign to match this wiki's inward-positive convention.

For the stipulated single-pathway example from ion channel, $E_{\mathrm{rev}}=-80\mathrm{mV}$ and $g=10\mathrm{nS}$ giveThe open ion channel carries zero net electric current at $-80\mathrm{mV}$ even though $g$ remains positive. Near that point a change of membrane potential changes the electric current, which is why zero current at one voltage does not make an open pathway electrically irrelevant; see shunting inhibition.

For an ion channel passing only one ion species by passive transport, its reversal potential can equal that species' Nernst equilibrium potential, where the chemical and electrical contributions to electrochemical potential balance. At that thermodynamic equilibrium, passage in both directions can continue with no net transport. For an ion channel admitting several ion species, opposing contributions can cancel while each species continues to have net transport. Such a reversal potential is not generally any one species' Nernst equilibrium potential. See the Purves reference above.

To work out that cancellation explicitly, put two Ohmic ion channel populations across the same cell membrane. Stipulate constant electrical conductances and fixed reversal potentials:The potassium and sodium contributions add because both pathways experience the same membrane potential:Thus $I_{\mathrm{total}}=12\mathrm{nS}(E_{\mathrm{eff}}-V)$. This weighted mean follows simply by expanding and regrouping the two current terms; it assumes additive Ohmic contributions and a positive total electrical conductance. At $V=E_{\mathrm{eff}}$, the inward-positive individual electric currents areThe potassium contribution is outward and the sodium contribution inward. Equal and opposite electric currents give $I_{\mathrm{total}}=0$; neither pathway has stopped transporting its ions. The calculation treats two distinct pathways. Applying it to one mixed-species ion channel would additionally require a justified decomposition into independent Ohmic contributions; a general mixed-channel reversal potential cannot be obtained by assuming those hypotheses silently.

This is an instantaneous balance of the specified passive electric currents. It would be the stationary voltage of a passive capacitance model containing only these constant pathways and no applied electric current, but it is not a complete prediction of a living cell's resting membrane potential. Other electric currents, voltage-dependent gating, and pumps involved in active transport can matter. Pumps that transfer net electric charge are electrogenic and contribute their own electric current. See Purves et al.: functional properties of the sodium/potassium pump.

The toy model holds ion concentrations and therefore the stipulated reversal potentials fixed. Continuing inward sodium and outward potassium transport would change finite reservoirs unless active transport or external control maintained them. Transport can be a small fraction of the reservoir's ions over a short interval, making fixed concentrations a useful approximation; it is not a claim that the reservoirs never change. See Gerstner et al., Neuronal Dynamics (2014), §2.1: equilibrium potentials, channel currents and maintained gradients.

A reversal potential makes the effect of opening an ion channel predictable from the present membrane potential. The same open pathway can carry inward or outward electric current as $V$ crosses its reversal potential. The two-pathway example reveals a particularly useful distinction: zero net charge transfer can coexist with continuing exchange of different substances. That distinction connects membrane transport to electric current measurements without mistaking electrical balance for thermodynamic equilibrium.

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 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 $100/30\simeq 3.333\mathrm{mV}$: $V_{\infty }\simeq -61.667\mathrm{mV}$. Effective electrical resistance is $33.333\mathrm{M\Omega }$ and the time constant is $200/30\simeq 6.667\mathrm{ms}$. 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.

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.

Synaptic conductance describes how strongly activated synaptic ion channels conduct electric current for a given driving force. In the passive approximation, $I_{\mathrm{syn}}=g_{\mathrm{syn}}(E_{\mathrm{syn}}-V)$, with inward-positive electric current. It is the electrical conductance contribution of a synapse; its postsynaptic voltage response also depends on the driving force, the other membrane electrical conductances, and the capacitance. The synaptic potential model and shunting inhibition example show why a nonzero synaptic conductance can have zero electric current at rest.

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 $j$ isHere $g_j$ 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.^[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.^[ref]

A synaptic potential is a postsynaptic change in membrane potential caused by activity at a synapse. Unlike the regenerative action potential, a passive synaptic potential is graded: its size depends on input strength, the initial membrane potential and the receiving cell membrane's properties. Local voltage changes can decay before reaching the soma; their timing and overlap help determine whether an action potential follows. See Ion Channels and the Electrical Properties of Membranes.

Depolarization means that the interior becomes less negative relative to the exterior; hyperpolarization means that it becomes more negative. Excitation and inhibition instead describe whether an input promotes or opposes postsynaptic action potential generation. An inhibitory postsynaptic potential can be depolarizing, and shunting inhibition can occur with no voltage change at rest. The receptor, permeating ions, ionic gradients and reversal potential matter. See Purves and colleagues: excitation, inhibition and depolarizing inhibition.

A worked passive model treats the receiving membrane as one compartment with capacitance $C>0$, leak conductance $g_L>0$, and activated synaptic conductances $g_e,g_i\ge 0$:All electric currents are inward-positive. Each term $g(E-V)$ vanishes at its reversal potential $E$; $\mathrm{nS}\times \mathrm{mV}=\mathrm{pA}$. With constant parameters, the ordinary differential equation hasHere $G$ is total conductance, $1/G$ is effective electrical resistance, $V_{\infty }$ is the steady state and $\tau$ the time constant. Without imposed electric current, $V_{\infty }$ is a conductance-weighted average of the reversal potentials. This approximation omits spatial structure, changing ionic gradients and active voltage-gated ion channels; it calculates passive voltage responses, not actual action potential waveforms. See 3.1 Synapses for the mechanism behind the terms; the inward-positive convention here reverses that source's synaptic-current sign.

Take the same illustrative leak and capacitance as under shunting inhibition, start at $V(0)=-65\mathrm{mV}$ and set $I_{\mathrm{ext}}=0$. Opening $g_e=2\mathrm{nS}$ with $E_e=0\mathrm{mV}$ gives $V_{\infty }=-650/12\simeq -54.167\mathrm{mV}$ and $\tau \simeq 16.667\mathrm{ms}$. Its initial inward electric current is $2(0+65)=130\mathrm{pA}$. Adding $g_i=20\mathrm{nS}$ with $E_i=-65\mathrm{mV}$ changes $V_{\infty }$ to $(-650-1300)/32=-60.9375\mathrm{mV}$ and $\tau =6.25\mathrm{ms}$. This is shunting inhibition of the same excitatory drive.

For comparison, $g_i=20\mathrm{nS}$ with $E_i=-75\mathrm{mV}$ alone gives $V_{\infty }\simeq -71.667\mathrm{mV}$: hyperpolarization. With $E_i=-60\mathrm{mV}$ instead, it alone gives $V_{\infty }\simeq -61.667\mathrm{mV}$: depolarization. Yet adding this depolarizing conductance to the $g_e=2\mathrm{nS}$ excitatory drive lowers that drive's $V_{\infty }$ from $-54.167$ to $(-650-1200)/32=-57.8125\mathrm{mV}$. At an illustrative firing threshold $V=-50\mathrm{mV}$, its electric current is $20(-60+50)=-200\mathrm{pA}$, opposing threshold approach. The combined trace initially rises faster than the excitatory drive alone, before settling below it. Thus the sign of a voltage change at rest alone does not determine excitation or inhibition; a claim about firing must specify input strength, timing and the neuron's state.