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The primary visual cortex, often abbreviated V1, is an early cortical stage of visual processing. Its neurons have receptive fields: changing a stimulus in a particular part of the visible scene can change their spike trains. Orientation selectivity adds a further distinction: at the same location, a properly aligned bar can evoke a strong response while a rotated bar evokes little. Simple cells make the dependence on local position and visual contrast especially clear. See the original experiments under orientation selectivity and simple cell.

In their 1962 study, David Hubel and Torsten Wiesel recorded from forty cats under thiopental anesthesia, maintained light anesthesia while monitoring cortical electrical activity, and used succinylcholine to stabilize the eyes. White-light patterns were projected onto a screen $1.5\mathrm{m}$ away. Extracellular single-unit recording with tungsten electrodes sampled individual units; receptive fields were mapped separately for each eye. This connected controlled stimulus geometry to individual spike trains. ^[ref]

These acute, anesthetized-cat recordings do not directly measure human perception or responses during awake behavior. The useful idea is a local description of structure: a population can distinguish where a feature lies, which way it is aligned, and which side is brighter. The signed spatial filter model of a simple cell turns that idea into a computable example. One neuron's preferred stimulus does not establish recognition of an entire object. Likewise, orientation selectivity in one neuron and an orderly map of preferences across primary visual cortex are different findings: rodents can have strong orientation selectivity without the orderly arrangement typical of some other species. ^[ref] The existing correlation-based development of visual cortical maps and orientation-map self-organization sections describe hypotheses about how organization develops.

Named for Jan Evangelista Purkyně, a cerebellar neuron receiving many parallel fiber inputs and a powerful climbing fiber input. Simple-spike and complex-spike responses provide distinct physiological readouts in studies of motor learning.

If every interspike interval is at least $t_{\mathrm{abs}}>0$, a sustained spike train has mean firing rate at most $1/t_{\mathrm{abs}}$. Across a window of duration $T$, the event count satisfies $N(T)\le 1+T/t_{\mathrm{abs}}$; dividing by $T$ and taking the long-time limit gives the bound. The extra one accounts for a possible first event. The bound permits much slower firing and says nothing about whether stronger drive can maintain the limiting rate in a real neuron.

For the chosen phenomenological paired-pulse recovery, the hold alone gives $500\mathrm{Hz}$. Add the further assumption that every successful event resets precisely the same recovery curve, with no accumulation from earlier events. Then $0.35\mathrm{nA}$ onset-timed pulses can sustain at most $1000/4.942488\approx 202.327\mathrm{Hz}$ in that model. This repeatable reset is an extra assumption: a two-pulse result alone cannot establish it. A real neuron's sustained rate also depends on neural adaptation, input delivery and evolving ion-channel inactivation. The existing leaky integrate-and-fire model similarly adds integration time to its imposed hold.

A homogeneous Poisson process of rate $\lambda$ has interspike intervals with an exponential distribution, soWith the purely illustrative choices $\lambda =100\mathrm{Hz}$ and $t_{\mathrm{abs}}=0.002\mathrm{s}$, this is $1-e^{-0.2}\approx 0.181269$. Thus about $18.13\%$ of intervals predicted by that model violate this chosen hold. Matching a mean spike train count does not make a stimulus-only Poisson process respect recent firing.

A minimal alternative is a renewal process with independent and identically distributed intervals $S=t_{\mathrm{abs}}+X$, where $X$ has an exponential distribution of rate $\lambda$. Its hazard function is zero during the hold and $\lambda$ afterwards. Its mean interval is $t_{\mathrm{abs}}+1/\lambda$ and long-run firing rate isThe same $100{\mathrm{s}}^{-1}$ rate after a $2\mathrm{ms}$ hold gives $83.333\mathrm{Hz}$, not $100\mathrm{Hz}$. This separate stochastic example has no gradual relative recovery; it illustrates why an available-state rate differs from an observed mean firing rate. Smooth dependence on time since the last event can extend the hazard function, while longer histories require more than this simple renewal process. Time-rescaled spike-train diagnostics can test the resulting history-dependent predictions against recorded spike trains.

A retinal output neuron conveying information through action potentials. Its responses reflect inputs transformed by retinal circuitry rather than a direct copy of one cone voltage.

His drawings of neurons made their branching structure visible with extraordinary clarity. The historical illustration under Purkinje cell shows how different neurons can occupy the same part of the cerebellum while having strikingly different shapes.

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.

A simple cell is a visual cortical neuron whose receptive field has spatially separable ON and OFF receptive-field subregions. Elongated neighboring subregions give a preferred orientation and a sensitivity to the location and polarity of visual contrast. “Simple” describes the response organization; it does not describe a simpler cell body or a particular shape of neuron.

Hubel and Wiesel's 1962 classification emphasized four observations: distinguishable ON and OFF receptive-field subregions, summation within each region, antagonism between regions, and qualitative prediction of responses to differently shaped stimuli from those regions' arrangement. A slit fitting an elongated center was more effective than a smaller spot; a larger patch could invade opposing flanks and lose effectiveness. An edge separating bright and dark regions could be effective when its boundary matched the boundary between subregions. These were observations about spike trains, rather than an assertion of exact linearity. ^[ref]

The following deliberately coarse signed spatial filter model of a simple cell makes the geometry easy to count. A centered bright bar contributes positively at five sites. Rotating it preserves its area but mixes positive and negative weights; shifting it preserves its orientation but changes which weights it samples. The model is useful because it predicts distinct effects of these three manipulations instead of treating any bright stimulus as equivalent.

A simple cell is not an ideal linear sensor. Its spike train is nonnegative in event count, and neural adaptation can change responsiveness. The signed spatial filter model of a simple cell supplies a useful approximation to spatial drive and an explicit output rule. Comparing predictions with unseen stimuli is more informative than assuming the rule from the name “simple”. In contrast, the existing complex cell models explore tolerance to phase and local displacement.

Measurement of the activity attributed to one neuron, commonly through extracellular electrodes and spike isolation. It permits trial-resolved tests of stimulus tuning and interactions. Failure to evoke spikes with one stimulus alone does not exclude a modulatory input from that modality.

Twelve resting volunteers wore a water-perfused suit. Tubes covered the torso, upper arms and legs; the right forearm remained uncovered for laser Doppler blood-flow measurement. Six thermocouples estimated mean skin temperature; a sublingual thermocouple measured oral temperature. A dry-air capsule measured local sweat output from outgoing air moisture. ^[ref]

After two control scans near $34{}^{\circ }\mathrm{C}$ skin temperature, the suit cooled and then warmed the skin. Mean oral temperature was $36.6{}^{\circ }\mathrm{C}$ during both cooling and early warming; mean skin readings were $30.5$ and $38.2{}^{\circ }\mathrm{C}$. Cutaneous vascular conductance fell during cooling and rose during warming. The inference is that compensatory blood-flow responses can precede an appreciable internal temperature change. ^[ref]

Repeated baselines controlled comparison within participants; closed mouths reduced oral-probe cooling artifacts. A later control with reduced oral temperature was excluded. Oral temperature is a proxy, local flow is not whole-body heat transfer, and the fixed condition order leaves time effects possible. Brain imaging measured regional blood flow, not direct neuron firing or causal necessity. ^[ref]

The space clamp problem is the failure to maintain the commanded membrane potential throughout a spatially extended biological cell. A soma voltage clamp can coexist with substantial voltage changes in distant dendrites or an axon. Reducing patch-clamp series resistance improves access at the recording site, but does not eliminate electrical separation within the neuron.

A neuron selective for a viewed location in external space. In the primate recordings motivating the term, eye-position and locomotion measurements distinguished the looked-at part of the environment from the animal’s self-location and head direction.^[ref]

A layered midbrain structure involved in orienting. Its deeper layers include neurons with visual, auditory or somatosensory influences; their spatial and temporal interactions provide an experimental model for multisensory processing. Its role in orienting does not make it a complete explanation of conscious multisensory perception.

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 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.

Synaptic release probability is the probability of release at a specified site during a specified opportunity, such as one presynaptic action potential. It depends on the site's state and conditions; it is not the probability that the receiving neuron fires. In the example under synaptic vesicle, $p$ refers to one available site, whereas $1-(1-p{)}^4$ refers to any of four independent sites releasing.

Temporal summation is overlap of responses to inputs arriving at different times. It can occur at one repeatedly activated synapse or across several synapses; it is not defined by reuse of a particular contact. For prescribed electric current inputs in a passive compartment, residual depolarization from earlier pulses changes the voltage reached by later pulses. The membrane time constant sets how rapidly that residual decays, while the duration of synaptic conductance and spatial filtering by a passive dendritic cable can add other timescales.

For the diagram, write $v=V-E_L$, choose inward-positive imposed electric current $I$, and use the ordinary differential equationA rectangular pulse of amplitude $I_0=300\mathrm{pA}$ and duration $d=5\mathrm{ms}$, starting from rest, ends withAfterwards its contribution decays as $A{e}^{-(t-d)/{\tau }_m}$. The superposition principle therefore gives, at the end of the third pulse with onset spacing $\Delta \ge d$,For $\Delta =5\mathrm{ms}$ this is $15.829\mathrm{mV}$, so the peak membrane potential is $-49.171\mathrm{mV}$. For $\Delta =30\mathrm{ms}$ it is $8.447\mathrm{mV}$, giving $-56.553\mathrm{mV}$. Both protocols inject $3I_{0}d=4.5\mathrm{pC}$ of electric charge; equal charge does not imply equal peak voltage because the leak drains charge while it is delivered.

In the adjacent-pulse case, the illustrative neuronal firing threshold $-50\mathrm{mV}$ is crossed at $10+20\log 2\approx 23.863\mathrm{ms}$. A leaky integrate-and-fire model would emit its first event there and reset, so its later trajectory would differ from the passive diagram. The widely spaced train never reaches that threshold. Thus changing input timing alone can change whether an event occurs. A real neuron's neuronal firing threshold is also state-dependent, and synaptic conductance pulses are not prescribed electric current pulses.^[ref]

Measured responses to repeated presynaptic action potentials may also change through synaptic plasticity. A larger second response can therefore reflect a stronger second input as well as residual postsynaptic voltage. To isolate passive temporal summation, compare known injected electric current waveforms with their single-pulse responses under stable recording conditions; to test actual synapses, measure whether input efficacy changes. These are proposed discriminating comparisons, not additional controls claimed for the slice experiment.^[ref]

A neuron active preferentially at a particular part of a temporally extended task or interval. Temporal selectivity can coexist with selectivity for location, behavior and sequence identity; it is not a claim that the cell is an isolated clock.

A midbrain region containing dopamine neurons and other cell types. Identifying the region does not establish the transmitter identity of every recorded unit.

Whole-cell recording establishes intracellular electrical access by rupturing the membrane under a sealed patch pipette while retaining the gigaohm seal. Under adequate voltage clamp, the measured electric current combines contributions from accessible ion channels, membrane capacitance and seal leak current. Current clamp instead follows membrane potential while supplying a chosen electric current. Whole-cell recording is useful for linking a biological cell's total electrical response to its ion channels, but neither mode automatically controls distant dendrites or preserves the original cytosol.

In the 1981 methods demonstration, a bovine chromaffin biological cell was tested before and after patch rupture. Small voltage clamp steps produced a much larger capacitive transient after break-in. Integrating it gave $5\mathrm{pF}$ for a $13\mu \mathrm{m}$ cell; its decay indicated patch-clamp series resistance below $20\mathrm{M\Omega }$. Depolarizing commands then revealed ionic electric currents. Separate current clamp recordings showed spontaneous action potentials. The comparison established access to the cell interior, rather than a claim that every pipette command equals membrane potential. Slower transients sometimes indicated incomplete rupture, and these small-cell results do not establish spatial control of a branched neuron.^[ref]