Foundations of Bioelectricity

Charge, gradients, and the electrochemical engine

Every signal you will ever read on an EEG begins as the movement of charged atoms across a lipid bilayer roughly 5 nanometers thick. The neuron is, electrically, a leaky capacitor held away from equilibrium by metabolic work. The plasma membrane separates two aqueous compartments of differing ionic composition, and the selective permeability of that membrane to specific ions converts those concentration differences into a transmembrane voltage. Understanding the EEG mechanistically therefore demands that we first understand how a single cell manufactures and controls voltage, because the scalp trace is nothing more than the spatially summed extracellular consequence of millions of these tiny electrochemical machines running in partial synchrony. An expert reads the scalp as a window onto cortical current flow; that reading is only as good as the underlying intuition for where the current comes from and what makes it grow, shrink, slow, or synchronize.

Two forces act on any permeant ion. The first is the chemical (diffusional) force, which drives ions down their concentration gradient. The second is the electrical force, which drives ions according to the sign of the membrane voltage and the ion's charge. The membrane potential at which these two forces exactly cancel for a given ion is that ion's equilibrium (reversal) potential. The cell's resting state is a dynamic standoff among several such ionic tendencies, continuously maintained by active pumping. Nothing about this is passive in the thermodynamic sense - it is a steady state, not equilibrium, sustained by ATP hydrolysis. The membrane behaves as a capacitor (the bilayer storing charge) in parallel with variable resistors (the ion channels), and the whole of electrophysiology is the study of how those resistances open and close in time.

It is worth dwelling on the capacitive nature of the membrane, because it explains a great deal about EEG timing. A capacitor resists sudden changes in voltage: charging it takes current and takes time. The product of the membrane resistance and capacitance defines the membrane time constant (tau = R times C), typically on the order of 10 to 30 milliseconds in cortical pyramidal neurons (commonly cited near 20 ms, and shortened by ongoing synaptic conductance). This single number governs how briefly a synaptic input is felt and how far it can spread before it decays - and it is one reason a 1 millisecond spike contributes almost nothing to the scalp while a 50 millisecond synaptic current contributes a great deal. The bilayer also has an enormous specific capacitance (close to 1 microfarad per square centimeter, a value remarkably conserved across cell types because it is set by the physics of a thin dielectric), so a small movement of charge produces a meaningful voltage change.

The resting membrane potential: Nernst and Goldman

For a single permeant ion at body temperature, the equilibrium potential is given by the Nernst equation, E_ion = (RT/zF) ln([ion]_out / [ion]_in), which at 37 degrees Celsius reduces conveniently to roughly 61.5 mV times log10 of the concentration ratio for a monovalent cation. Here R is the gas constant, T absolute temperature, z the ionic valence, and F the Faraday constant. Plugging in physiological concentrations yields the canonical values that every electroencephalographer should hold in working memory: potassium near -90 mV, sodium near +60 mV, chloride near -65 to -75 mV (more negative, toward -90 mV, in some mature neurons), and calcium far positive at roughly +125 to +145 mV owing to its steep inward gradient and divalent charge. These are not numbers to memorize blindly; they are the levers. When extracellular potassium rises - as it does locally during intense firing or globally in renal failure - E_K moves positive, the cell depolarizes, and excitability changes in ways the trace will show.

A real membrane is permeable to several ions at once, so no single Nernst potential governs it. The Goldman-Hodgkin-Katz (GHK) voltage equation weights each ion's contribution by its relative permeability, V_m = (RT/F) ln([P_K times K_out + P_Na times Na_out + P_Cl times Cl_in] / [P_K times K_in + P_Na times Na_in + P_Cl times Cl_out]). At rest, potassium permeability dominates by roughly an order of magnitude over sodium, which is exactly why the resting potential of a cortical pyramidal neuron sits near -65 to -70 mV - close to E_K but pulled positive by the small standing sodium leak. The Na+/K+-ATPase then does the housekeeping, exporting three sodium ions for every two potassium ions imported, which both restores the gradients that conduction dissipates and contributes a small direct electrogenic hyperpolarization. The GHK equation makes a critical assumption - a constant electric field across the membrane - that is an approximation, but it captures the essential point: the resting potential is a permeability-weighted compromise, and whichever ion's permeability rises will drag V_m toward that ion's reversal potential.

The calcium entry in the table deserves emphasis because of the staggering ratio it represents. Free intracellular calcium sits near 100 nanomolar against roughly 2 millimolar outside - a gradient of about ten-thousand-fold. This is why calcium is the cell's premier signaling ion: a brief channel opening admits a flood relative to the resting level, and that flood is what couples electrical events (the action potential reaching the terminal) to chemical ones (vesicle fusion and transmitter release). It is also why calcium dysregulation is central to excitotoxicity: when energy fails and gradients collapse, pathological calcium entry through NMDA receptors and voltage-gated channels triggers the enzymatic cascades that kill neurons - the cellular substrate beneath the EEG patterns of hypoxic-ischemic injury you will later learn to recognize.

Ion channels: voltage-gated versus ligand-gated dynamics

Permeability is not fixed; it is gated. Voltage-gated channels sense the transmembrane field through charged S4 helices and open or close on a millisecond timescale in response to V_m itself. The voltage-gated sodium channel exhibits the elegant three-state behavior - closed, open, and inactivated - that gives the action potential its all-or-none upstroke and its refractory period. The inactivation gate, classically modeled as a tethered intracellular particle that swings shut after opening (the so-called ball-and-chain mechanism, formalized in the Hodgkin-Huxley framework as the h-gate), is the molecular reason a neuron cannot fire arbitrarily fast and the precise target of the most widely used sodium-channel antiseizure drugs. Voltage-gated potassium channels open more slowly and repolarize the cell. Voltage-gated calcium channels, particularly low-threshold T-type channels, are the engines of rhythmic bursting and are central to the thalamocortical oscillations that generate sleep spindles and the spike-wave of absence epilepsy.

Ligand-gated channels (ionotropic receptors) open in response to neurotransmitter binding rather than voltage, and their currents are the proximate generators of the EEG. The AMPA and NMDA glutamate receptors carry excitatory cation flux; the GABA-A receptor carries inhibitory chloride flux. The two glutamate receptors are not redundant. The AMPA receptor is fast, with a conductance lasting only a few milliseconds, and carries the bulk of moment-to-moment excitation. The NMDA receptor is slower, highly permeable to calcium, and famously voltage-dependent: at resting potential its pore is blocked by extracellular magnesium, and only when the cell is already depolarized does the magnesium leave, allowing current to flow. This makes the NMDA receptor a molecular coincidence detector - it conducts well only when presynaptic glutamate release and postsynaptic depolarization occur together - which is the biophysical basis of Hebbian synaptic plasticity and, when dysregulated, of the runaway excitation in certain encephalitides and seizures.

Critically, synaptic conductances have time courses measured in tens to hundreds of milliseconds - far longer than the ~1 ms action potential. That sluggishness is not a defect; it is precisely what allows thousands of synaptic events to overlap in time and sum into the slow, large extracellular fields that a scalp electrode can detect. A third class, the metabotropic (G-protein-coupled) receptors - including metabotropic glutamate receptors, GABA-B receptors, and the cholinergic and aminergic receptors of the ascending arousal systems - act indirectly through second messengers over hundreds of milliseconds to seconds and sculpt excitability and the slow rhythms of arousal. A great deal of what distinguishes wakefulness from sleep on the EEG is not a change in fast synaptic traffic but a change in the tonic metabotropic and potassium-channel background that sets how readily cortex synchronizes.

Cable theory: why location on the dendrite matters

A synaptic current does not act at a point; it spreads. The neuron's dendrites behave as leaky cables, and the passive spread of voltage along them is governed by cable theory, whose key parameter is the length constant (lambda) - the distance over which a steady voltage decays to about 37 percent of its value. Lambda depends on the ratio of membrane resistance to internal (axial) resistance; in cortical dendrites it is on the order of hundreds of micrometers, meaning a distal synaptic depolarization is substantially attenuated and slowed by the time it reaches the soma. This attenuation is not a nuisance to be ignored - it is central to EEG generation. The spatial separation between where current enters the cell (the synapse) and where the compensating current exits (distributed across the rest of the membrane) is exactly what creates the dipole that the next module builds upon.

Cable theory also explains why the apical dendrites of pyramidal cells are such effective EEG generators while many other cell types are electrically silent at the scalp. The pyramidal cell is an elongated, geometrically oriented cable with its synaptic input segregated by depth - thalamic and feedback inputs onto distal apical tufts, local inputs onto basal and perisomatic regions. This segregation guarantees that excitation and inhibition produce currents at different points along a consistently oriented cable, generating dipoles that point in a predictable direction and therefore add across the population rather than cancel. A spherical, symmetric cell, by contrast, has its current sinks and sources arranged radially, so the dipole moments point every which way and sum to nearly nothing - the closed-field geometry treated in Module 2.

The chloride gradient and the polarity of inhibition

One of the most consequential refinements an expert must internalize is that GABA-A receptor activation is not synonymous with hyperpolarization. The GABA-A channel conducts chloride, so its effect depends entirely on where E_Cl sits relative to the membrane potential, and that in turn depends on chloride transporters. The potassium-chloride cotransporter KCC2 extrudes chloride to keep E_Cl negative (mature neurons), while the sodium-potassium-chloride cotransporter NKCC1 imports chloride. In the mature brain KCC2 dominates, E_Cl sits near or just below rest, and opening GABA-A channels either hyperpolarizes the cell or, when E_Cl is very close to rest, produces shunting inhibition - clamping the membrane near rest and short-circuiting incoming excitation through the sheer increase in conductance, even without a large voltage change. Shunting is a powerful and underappreciated form of inhibition precisely because it can suppress firing while producing little visible deflection.

This logic has dramatic clinical reach. In the immature neonatal brain, NKCC1 predominates and E_Cl is relatively depolarized, so GABA can be excitatory early in development - one reason neonatal seizures respond poorly to GABA-enhancing drugs and a major area of active translational interest. In chronically epileptic and injured adult tissue, KCC2 is downregulated, E_Cl drifts positive, and GABAergic inhibition becomes less effective or even paradoxically excitatory, contributing to pharmacoresistance. When you see a seizure that worsens or fails to respond to benzodiazepines, the collapse of the chloride gradient is one of the mechanisms on the differential. The deceptively simple statement that benzodiazepines are inhibitory rests on an assumption about E_Cl that pathology can violate.

The action potential and the synaptic relay

When summed depolarization at the axon hillock reaches threshold (near -55 mV), voltage-gated sodium channels open regeneratively, sodium rushes in, and V_m overshoots toward E_Na in under a millisecond. Sodium inactivation and delayed potassium efflux then repolarize and briefly hyperpolarize the membrane, enforcing absolute and relative refractory periods that cap firing rate and impose directionality on propagation. The action potential is digital, stereotyped, and brief. This very brevity and the radial disorganization of axons explain why action potentials contribute almost nothing to the scalp EEG: they are too short to summate temporally and too geometrically scattered to add coherently across a population. (They are not entirely absent from all electrophysiology - the very fast oscillations and high-frequency content recordable on intracranial electrodes do carry a population-spike contribution - but at the scalp, through the low-pass filter of the skull, the spike contribution is negligible.)

At the synaptic terminal, the arriving spike opens voltage-gated calcium channels; calcium influx triggers vesicular fusion and transmitter release. Glutamate opening AMPA/NMDA channels produces an excitatory postsynaptic potential (EPSP) - a local depolarization with an associated inward current (a current sink) at the dendrite. GABA opening chloride channels produces an inhibitory postsynaptic potential (IPSP) - typically a hyperpolarization, or at least a shunting stabilization, with an outward current. These graded, overlapping postsynaptic currents, repeated across the parallel apical dendrites of cortical pyramidal cells, are the genuine current generators of the EEG, a point the next module develops in full geometric detail. The crucial conceptual move is to stop thinking of the EEG as a record of firing and start thinking of it as a record of synaptic current - the input and integration of the cortex, not its output.

Beyond the fast synaptic events, slower intrinsic conductances do much of the work of rhythm generation. The hyperpolarization-activated cation current (I_h, carried by HCN channels) and various calcium-activated potassium currents create the afterhyperpolarizations and rebound depolarizations that let thalamic and cortical neurons oscillate. When a thalamocortical neuron is hyperpolarized - as it is during drowsiness and sleep, under the influence of reduced cholinergic drive - it deinactivates its T-type calcium channels and begins to fire rhythmic bursts rather than tonic single spikes. This single biophysical switch, from tonic to burst firing, is the cellular gateway between the desynchronized waking EEG and the synchronized spindles and slow waves of sleep, and understanding it is the foundation for everything you will later learn about states of consciousness.

Energy, failure modes, and the limits of the model

The gradients that make all of this possible are expensive. The brain consumes roughly 20 percent of the body's resting oxygen and glucose despite being about 2 percent of its mass, and the lion's share of that budget services the Na+/K+-ATPase as it bails out the sodium and potassium that signaling lets leak. This tight coupling between electrical activity and metabolism is why the EEG is exquisitely sensitive to ischemia and hypoxia: when ATP falls, the pump fails, gradients run down, neurons depolarize, and the orderly synaptic currents that generate normal rhythms give way first to slowing and then, as failure deepens, to suppression. The well-known sequence by which cerebral activity slows as cerebral blood flow drops - and the recognition that synaptic transmission fails before membrane integrity is lost - is the physiological reason EEG can serve as a real-time monitor of cerebral perfusion in the operating room and intensive care unit, detecting reversible dysfunction before infarction is complete.

Finally, the expert holds the model lightly. The Hodgkin-Huxley formalism, the Nernst and GHK equations, and cable theory are powerful idealizations built on assumptions - independent ion movement, a constant field, a uniform cable - that real neurons violate in detail. Channel densities vary across the dendritic tree, ion concentrations change locally during activity (the extracellular potassium and calcium near an active synapse are not the textbook values), glia actively buffer the extracellular space, and dendrites perform nonlinear computations the simple cable does not capture. None of this invalidates the framework; it disciplines its use. When you reason from biophysics to the trace, you are reasoning with a map, and the value of the map is that it tells you which way the territory tends to run, not that it reproduces every contour.