10.1 Current, voltage, and the Nernst relation #
10.1.1 The equilibrium voltage #
For one ion at equilibrium, with membrane potential defined as inside relative to outside,
E = (R T / z F) ln([out] / [in])
R is the gas constant, T absolute temperature, z the charge number, and F Faradayโs constant. (R T / F) ln(10) is about 58 mV at room temperature and about 61 mV at 37 ยฐC. What changes E is the concentration ratio and the temperature, not the number of channels. Channels decide whether the membrane actually sits at that E.
Potassium is high inside. For a mammalian neuron, with Kโบ about 140 mM inside and about 5 mM outside, E_K is near โ90 mV. Sodium is reversed, so E_Na is positive. A membrane permeable only to potassium sits at E_K. Real resting membranes are mostly, not only, potassium-permeable, so the resting potential lies near E_K and short of it. The GoldmanโHodgkinโKatz equation weights each ion by permeability P:
E_m = (R T / F) ln( (P_K[K]_o + P_Na[Na]_o + P_Cl[Cl]_i) / (P_K[K]_i + P_Na[Na]_i + P_Cl[Cl]_o) )
Chloride is swapped relative to the cations because its charge is negative. Neurobiology owns the choreography of the action potential. A recorded voltage is interpretable only if the concentrations are known.
10.1.2 Conductance and reversal #
For a channel that behaves ohmically,
I = g (V โ E_rev)
g is conductance and E_rev is the voltage at which current changes sign. If only one ion flows, E_rev equals its Nernst potential, and changing the external concentration tests selectivity: E_rev should move as that Nernst potential moves. Many channels rectify, so the current is not a straight line through E_rev. The macroscopic current is I = N P_o i, the product of channel number, open probability, and the single-channel current. A whole-cell record does not say which of the three a drug has changed.
10.2 Patch clamp #
The study of Patch clamp provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.
Patch Clamp
10.2.1 The seal #
Neher and Sakmann recorded single-channel currents. The practical form is a polished glass pipette of defined electrolyte pressed onto a clean membrane until the leak falls to about a gigaohm or more. Current through that patch has nowhere else to go, and the noise is low enough for a picoampere step. A 10 pS channel at 100 mV of driving force passes 1 pA, about six million monovalent ions per second. These notes do not describe how to make a pipette. The principle is electrical isolation of a defined patch, and the two quantities the amplifier exchanges: voltage and current.
10.2.2 Four configurations #
| Configuration | Arrangement | Face the bath can change | Principal limit |
|---|---|---|---|
| Cell-attached | seal on an intact cell | extracellular face, inside the pipette | resting potential is in series with the pipette voltage and is usually unknown, so absolute membrane potential is uncertain |
| Inside-out | excised patch, cytoplasmic face toward the bath | cytoplasmic | diffusible cellular partners are gone |
| Whole-cell | patch ruptured; pipette solution continuous with the cytoplasm | the ionic interior, by dialysis | ATP and soluble regulators wash out; pipette series resistance drops voltage when current is large |
| Outside-out | withdrawn from whole-cell so the extracellular face faces the bath | extracellular | the same excision and dialysis, on a smaller area |
Patent-Double Fold Z Configuration Monochromator Figure 1 Schematic Usre26053-0
A perforated-patch variant uses pores, often from an antibiotic such as nystatin, that pass small ions but not metabolites, trading slower access and higher series resistance for less dialysis. The table is the reason for a choice. A cytoplasmic ligand cannot be applied in the bath of a cell-attached patch. An extracellular neurotransmitter is what an outside-out patch is for. Whole-cell is wrong when the native cytoplasm must stay intact and right when the question is the total current of a defined interior.
10.2.3 A single-channel record #
The trace is a telegraph between closed and open levels at fixed voltage. Conductance is the step divided by the driving force. A few to a few tens of picosiemens is typical; some pores lie well outside that range. A partial step is a sub-conductance of that channel, not automatically a second channel. Open probability is the fraction of time open over many events. One opening is not a P_o, and an empty patch is not proof the cell lacks the channel.
Dwell times report kinetics. One exponential open-time distribution implies one open state; a sum of exponentials implies more. Openings shorter than the filter can follow are missed, and missed closures join openings, so the surviving dwells are too long. A kinetic constant from an over-filtered record is partly a property of the filter.
10.2.4 Voltage clamp and current clamp #
Voltage clamp holds potential at a command by injecting the current required, and records that current. Current clamp injects a command current, often zero, and records voltage. The same electrode answers different questions.
An inward current depolarises a cell, which opens more voltage-gated channels, which increases the current. Voltage and current then change together and cannot be assigned to a conductance. Clamp breaks that loop. Hodgkin and Huxley separated a fast inward sodium conductance from a slower outward potassium conductance because the voltage was not allowed to run away. Current clamp is the physiological event, feedback included. Voltage clamp is the conductance underneath, at a chosen voltage.
Series resistance puts the membrane off the command: V_membrane = V_command โ I R_s, worst for large currents. Space clamp fails in a cell with processes: the pipette controls the soma and does not control a distant membrane, and fast currents from the unclamped region are distorted. A quiet electronic trace can still be a poor clamp of the cell.
10.3 Cells chosen for access #
10.3.1 The squid giant axon #
The squid giant axon is up to about a millimetre across, so a wire can be threaded inside and a stretch of membrane held at one voltage in space as well as in time. That geometry, using voltage-clamp methods developed with Cole, is why Hodgkin and Huxley could measure the currents of an action potential under a voltage they actually controlled. Mammalian axons are far too thin for an axial wire. The squid was chosen for access, not because its channels obey a private physics. Patch clamp retired the need for a giant cell. The space-clamp problem reappears in any neuron whose processes escape the pipette.
10.3.2 The oocyte as an expression system #
A full-grown oocyte of Xenopus laevis is about 1 mm across. Gurdon showed that it translates injected foreign mRNA. A channel expressed from introduced RNA produces a current in a cell large enough for two-electrode voltage clamp: one electrode measures voltage, the other passes current, because the currents are too large for a single patch pipette to clamp cleanly. A current present after the RNA and absent from a water-injected control is evidence that the expressed protein can carry it. It is not evidence that the native channel has that subunit alone. The oocyte adds its own glycosylation, lipids, and sometimes its own subunits, and it has endogenous currents, including a calcium-activated chloride current that has to be distinguished from the current under study. Physiology and Neurobiology own what the channel does in the animal. These notes do not describe injection or preparation of the cell.
10.4 Extracellular recording #
10.4.1 Spikes and fields #
An extracellular electrode measures the small voltage produced by currents in the extracellular space. It does not seal, does not clamp, and does not report a conductance or an open probability.
| Recording | Scale | What is controlled | Quantity measured |
|---|---|---|---|
| Single-channel patch | one or a few channels | voltage, usually | unitary current, conductance, P_o, dwell times |
| Whole-cell voltage clamp | one cell | voltage | N P_o i, with dialysis |
| Current clamp | one cell | current | membrane potential, including spikes |
| Extracellular spike | nearby neurons | usually nothing | spike times; amplitude depends on distance and on which cell |
| EEG or field potential | a large population | nothing | summed synaptic currents, filtered by tissue |
Extracellular spikes are typically tens to hundreds of microvolts, and sorting them by shape infers which cell fired without proving it. Electroencephalography records, from the scalp, synaptic currents summed over a wide population and blurred by the skull. Time resolution is fine next to MRI. Spatial specificity is poor. Voltage-sensitive dyes and genetically encoded voltage indicators are optical proxies for membrane voltage. They do not replace a clamp when the quantity required is a picoampere or a reversal potential. No placement procedure belongs here. Finer access buys a defined current at a defined voltage. Coarser access buys timing from many cells that could not all be sealed onto.
10.5 Key terms, summary, and self-check #
Key terms. Nernst potential; GoldmanโHodgkinโKatz equation; reversal potential; conductance; gigaohm seal; cell-attached; inside-out; outside-out; whole-cell; open probability; series resistance; space clamp; two-electrode voltage clamp; extracellular spike; EEG.
Summary. The Nernst equation sets the equilibrium voltage of one ion, and the membrane potential sits at a permeability-weighted combination of those voltages. A gigaohm seal records picoampere steps. Cell-attached leaves the cytoplasm intact and the absolute voltage uncertain; inside-out and outside-out expose one face or the other; whole-cell sums the cell and dialyses it. Conductance, open probability, and dwell times come from the telegraph, and missed events bias the times. Voltage clamp separates conductances; current clamp lets the spike occur; extracellular recording measures fields and spike times. The squid axon and the oocyte were chosen because electrodes could control voltage in a large cell.
Self-check.
1. Why is E_K negative in a typical animal cell, and which equation adds the other ions once more than one permeability is open?
2. Which configuration exposes the cytoplasmic face to the bath, which dialyses the cell, and why is absolute voltage uncertain in a cell-attached patch?
3. Steps of 2 pA at 100 mV driving force correspond to what conductance? What does heavy filtering do to brief openings and to the dwell times that remain?
4. Why did separating sodium from potassium conductance require voltage clamp, and why was the squid axon the cell in which that was first done?
5. What quantity does an EEG measure, and why can it not report an open probability?
# Closing: how the chapters fit together
Chapter 1 is the reason the optical and resonance methods exist. Absorbance and circular dichroism use the ultraviolet window water still allows. Fluorescence adds a distance that reappears as a microscopic measurement in Chapter 8. Vibrational spectra report the same secondary structure as far-ultraviolet CD under a different selection rule and a worse solvent. NMR and EPR leave optics for spin. MRI is the warning that the same resonance, used on water with field gradients, is not a molecular structure.
Separation is both a preparation and a measurement: elution volume, mobility, and sedimentation coefficient have artefacts of their own. Mass spectrometry needs that separation and adds ionisation; native MS and hydrogenโdeuterium exchange hand their structural reading to Structural Biology, as a phased diffraction pattern does. Hydrodynamics and calorimetry measure solution mass, heat, and surface binding, which is where a K_d should be confirmed if a spectrum or a sensorgram is the only evidence so far.
Light microscopy is limited by diffraction, electron microscopy by dose and averaging, crystallography by missing phases and by the crystal. Force is neither a spectrum nor an image. Electrical recording measures charge movement that optical methods measure only through a proxy such as a voltage-sensitive dye.
Decision table #
| Question | Start with | Main artefact | Confirm with | Main artefact of the check |
|---|---|---|---|---|
| A K_d for a soluble complex | ITC, if binding produces heat | dilution heat, buffer mismatch, and a K_d absent from a rectangular isotherm | SPR, or a spectroscopic titration in free solution | mass transport and rebinding; inner filter or a saturated optical signal |
| A fold (secondary structure) | far-ultraviolet CD | buffer absorbance, scattering, and a non-unique decomposition | amide I infrared; an atomic method only if a model is required | water overlaps amide I; a crystal or a cryo-EM map is one averaged state |
| A polypeptide mass | intact electrospray MS | salt adducts and unresolved modifications | SDS-PAGE | anomalous migration; oligomers were dissociated on purpose |
| An assembly mass in solution | SEC-MALS | wrong dn/dc, or co-elution as a weight average | sedimentation equilibrium | non-ideality, and detergent counted as protein if vฬ is wrong |
| A localisation in a cell | fluorescence microscopy | diffraction limit, off-target label, fixation shift | a second label, immuno-electron microscopy, or a marked cell fraction | antibody cross-reaction; fractionation mixes compartments |
| A single channel | patch clamp, in the configuration that exposes the right face | missed events; unknown resting potential in cell-attached; dialysis in whole-cell | reversal potential against the Nernst equation of the suspected ion | rectification if an ohmic fit was forced; a whole-cell current hides N and P_o |
| A motor step, or an unfolding force | optical trap for processive steps; AFM for higher-force unfolding | linkage compliance; loading-rate dependence of the unfolding force | the structural repeat the step or the contour length should match | the crystal or the map is not the geometry that was pulled |
Revision checklist #
1. Write photon energy in terms of wavelength, and place NMR, EPR, infrared, visible absorption, and X-ray diffraction on that ladder.
2. Write the BeerโLambert law, define ฮต, c, and l, and state what stray light and scattering each do to a calculated concentration.
3. Say what far-ultraviolet and near-ultraviolet CD each report, and why neither is an atomic structure.
4. Write the FRET efficiency equation, state the useful distance window, and say what ฮบยฒ threatens.
5. In one sentence each, say what COSY, NOESY, and MRI report.
6. Explain how a charge-state envelope gives a protein mass, and what a decoy database is for.
7. Contrast gel filtration, SDS-PAGE, and isopycnic centrifugation by the quantity that sets the band position, and state why Svedberg units do not add.
8. List what one ITC experiment can return, what heat must be subtracted, and how rebinding in SPR fakes a K_d.
9. Compute a lateral resolution from ฮป and NA, and say how STED and localisation microscopy each get past that limit.
10. Match the four patch configurations to the face each exposes, and contrast a voltage-clamp current with an extracellular spike.
Selected sources #
These notes are an original teaching summary, not a transcript of any textbook.
- Cantor CR, Schimmel PR. Biophysical Chemistry. W. H. Freeman, 1980.
- Wilson K, Walker J (eds). Principles and Techniques of Biochemistry and Molecular Biology. Cambridge University Press.
- Sheehan D. Physical Biochemistry: Principles and Applications. 2nd ed. Wiley, 2009.
- Serdyuk IN, Zaccai NR, Zaccai J. Methods in Molecular Biophysics: Structure, Dynamics, Function. Cambridge University Press.
- Neher E, Sakmann B. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature 260:799โ802 (1976).
- Svoboda K, Schmidt CF, Schnapp BJ, Block SM. Direct observation of kinesin stepping by optical trapping interferometry. Nature 365:721โ727 (1993).
# Part C. Visual Figures & Scientific Diagrams Gallery
Comprehensive high-resolution visual reference repository for Biophysical Techniques & Instrumentation from the B10logy Visual Atlas.
Fret Jablonski
# Part C. Visual Figures & Scientific Diagrams Gallery
Essential high-resolution reference diagrams for Biophysical Techniques and Instrumentation from the B10logy Visual Atlas.
