Chapter 3 Notes: The Neuronal Membrane at Rest
Chapter 3 Notes: The Neuronal Membrane at Rest
The Cast of Chemicals
The neuronal environment consists of three major players that establish the resting membrane potential: the cytosol (intracellular fluid), the extracellular fluid, and the membrane itself with proteins that span the phospholipid bilayer.
Water as the solvent allows ions to exist as dissolved charged particles (ions) and to move under diffusion and electrical forces.
Ions are atoms or molecules with net electrical charge. Important neuronal ions include the monovalent cations Na^+ and K^+, the divalent Ca^{2+}, and the monovalent anion Cl^-.
The resting and signaling properties of neurons depend on the unequal distribution of these ions across the membrane, and on the selective permeability conferred by membrane proteins.
Water and Ions
Water (H_2O) is a polar molecule due to uneven electron distribution: the oxygen atom acquires a partial negative charge, while the hydrogens carry partial positive charges.
Waterās polarity makes it an excellent solvent for ions and other polar molecules.
Ions are dissolved in water with a surrounding shell of water molecules called a hydration shell; this stabilizes ions and reduces direct ionic interactions.
Ions of interest in cellular neurophysiology: Na^+, K^+, Ca^{2+}, Cl^-.
Ions can be monovalent (e.g., Na^+, K^+, Cl^-), divalent (e.g., Ca^{2+}), etc.
Hydrophilic vs. hydrophobic properties determine whether molecules cross membranes easily: ions are water-loving (hydrophilic) and cannot simply diffuse through the lipid bilayer; they require channels or pumps.
The Phospholipid Membrane
Membranes are primarily composed of phospholipids that form a bilayer: hydrophilic polar heads face the aqueous environments on both sides; hydrophobic nonpolar tails face inward.
The bilayer is a two-molecule-thick barrier that isolates the cytosol from the extracellular fluid and resists water-soluble ions.
The membrane provides a hydrophobic barrier to ions and sets the stage for selective transport via proteins.
Protein
Proteins embedded in the membrane perform many pivotal roles: enzymes, cytoskeletal components, receptors, channels, and pumps.
Ion channels form pores across the membrane and are built from protein subunits; typically 4ā6 subunits assemble to form a functional channel.
Ion selectivity: channels generally favor specific ions (e.g., K^+ channels are highly selective for K^+; Na^+ channels for Na^+; Ca^{2+} channels for Ca^{2+}).
Gating: many channels open or close in response to local conditions (voltage, ligands, mechanical forces, etc.).
Protein Structure (brief review)
Proteins are polymers of amino acids connected by peptide bonds.
Four levels of structure:
Primary: amino acid sequence.
Secondary: local folds such as alpha helices and beta sheets.
Tertiary: three-dimensional folding of a single polypeptide.
Quaternary: assembly of multiple polypeptide chains into a functional protein (a subunit is a component of a larger protein).
Important for channels and pumps: subunit composition and arrangement determine properties like pore size and gating.
Ion Channels and Ion Pumps
Ion channels: protein channels spanning the membrane that create a pathway for ions to cross; the presence of channels does not guarantee current without a driving force and permeant ions.
Ion pumps: membrane-spanning enzymes (e.g., ATPases) that use energy from ATP to move ions against their gradients (often against a concentration gradient).
The sodiumāpotassium pump and the calcium pump are two critical pumps in neurons.
The Movement of Ions
Two main forces drive ion movement across membranes: diffusion and electrical force (voltage).
Diffusion: ions move down their concentration gradient from high to low concentration, driven by thermal motion.
Electrical force: ions move in response to electrical potential differences across the membrane.
A membrane must have permeant channels for diffusion to occur; electrical forces require a membrane with channels and a potential difference to drive current.
Membrane current (I) is governed by conductance (g) and the driving force (voltage):
In the simplified form used here: I = gV where V is the driving potential across the membrane (the difference across the membrane).
In more complete neurophysiology, the current for a given ion is often written as I{ ext{ion}} = g{ ext{ion}}(Vm - E{ ext{ion}}) where E_{ ext{ion}} is the equilibrium potential for that ion.
Driving force is the difference between the actual membrane potential (Vm) and the equilibrium potential of the ion (Eion). When Vm equals Eion, there is no net ionic current for that ion.
The Ionic Basis of the Resting Membrane Potential
Membrane potential (V_m) is the voltage across the neuronal membrane at any moment.
V_m can be measured with a microelectrode inserted into the cytosol and a reference electrode in the extracellular fluid (the ground).
Typical resting membrane potential for a neuron: approximately V_m ext{ is about } -65 ext{ mV} (inside relative to outside).
The resting potential is essential for the function of neurons and underlies the neuronās ability to respond to stimuli with action potentials.
Equilibrium Potentials
If a cell had only a single ion with a permeable membrane, the membrane potential would settle at the equilibrium potential for that ion (E_ion) where diffusion and electrical force balance.
Example intuition: with selective K^+ permeability, the equilibrium potential would be near EK ext{ (about } -80 ext{ mV)}; with selective Na^+ permeability, near E{ ext{Na}} ext{ (about } +62 ext{ mV)}.
Real neurons are permeable to more than one ion, so the actual resting potential lies somewhere between the individual equilibrium potentials, influenced by relative permeabilities.
Equilibrium potentials depend on ion concentrations across the membrane (inside vs. outside).
The Nernst Equation (Box 3.2)
The equilibrium potential for an ion is given by the Nernst equation:
E{ ext{ion}} = rac{RT}{zF} \, ext{log}{10} rac{[ ext{ion}]{ ext{o}}}{[ ext{ion}]{ ext{i}}}At body temperature (ā 37Ā°C): mechanics simplify to specific forms for common ions:
For potassium:
EK emporary = 61.54 ext{ mV} \, ext{log}{10} rac{[K^+]{ ext{o}}}{[K^+]{ ext{i}}}For sodium:
E{Na} = 61.54 ext{ mV} \, ext{log}{10} rac{[Na^+]{ ext{o}}}{[Na^+]{ ext{i}}}For chloride:
E{Cl} = 61.54 ext{ mV} \, ext{log}{10} rac{[Cl^-]{ ext{o}}}{[Cl^-]{ ext{i}}}For calcium:
E{Ca} = 30.77 ext{ mV} \, ext{log}{10} rac{[Ca^{2+}]{ ext{o}}}{[Ca^{2+}]{ ext{i}}}Note: The Nernst equation does not include membrane permeability; it gives the equilibrium potential for a single ion if the membrane were permeable only to that ion.
Example: if K^+ is twenty times more concentrated inside than outside, i.e., [K^+]{ ext{i}}/[K^+]{ ext{o}} = 20, then
EK = 61.54 ext{ mV} \, ext{log}{10} rac{1}{20} = -80 ext{ mV}
The Distribution of Ions Across the Membrane
Ion pumps establish concentration gradients across the membrane:
Sodiumāpotassium pump (Na^+/K^+ pump): uses ATP to move Na^+ out and K^+ in against their respective gradients.
Calcium pump (Ca^{2+} pump): actively extrudes Ca^{2+} from the cytosol to keep intracellular Ca^{2+} very low.
Typical approximate ionic distributions (inside vs outside):
K^+: inside ā 150 mM; outside ā 5 mM
Na^+: inside ā 15 mM; outside ā 150 mM
Ca^{2+}: inside ā 0.0002 mM; outside ā 2 mM
Cl^-: inside ā 13 mM; outside ā 120 mM (values vary by source)
From these gradients, the equilibrium potentials can be calculated with the Nernst equation for each ion.
The resting membrane potential is not equal to any single E_ion because the membrane is permeable to several ions with different permeabilities; the Goldman equation is used to combine permeabilities and concentrations (see Box 3.3).
The SodiumāPotassium Pump (Na^+/K^+ Pump)
An ATPase enzyme that uses metabolic energy to move ions across the membrane against their gradients.
Typical operation in neurons: exchanges internal Na^+ for external K^+; commonly described as 3 Na^+ out and 2 K^+ in (ATP hydrolysis supplies energy).
The pump maintains high intracellular K^+ and high extracellular Na^+, essential for the resting membrane potential and neuronal excitability.
The pump is energetically costly, consuming a sizable fraction of cellular ATP (estimates as high as ~70% of brain ATP usage).
The Calcium Pump (Ca^{2+} Pump)
Actively exports Ca^{2+} from the cytosol; keeps intracellular Ca^{2+} concentration very low (ā¼0.0002 mM).
Intracellular Ca^{2+} is buffered by calcium-binding proteins and sequestered by organelles (mitochondria, endoplasmic reticulum).
Relative Ion Permeabilities of the Membrane at Rest
The resting potential results from a large K^+ permeability relative to Na^+ (PK >> PNa).
If the membrane were permeable only to K^+, Vm would be EK (~ -80 mV).
If permeable only to Na^+ (PNa > 0, PK ā 0), Vm would be ENa (~ +62 mV).
In real neurons, the resting potential is closer to EK but somewhat depolarized by the small Na^+ leak; quantitatively, Vm ā -65 mV due to the relative permeabilities and gradients.
The Goldman equation (Box 3.3) is used to estimate Vm considering multiple permeant ions and their relative permeabilities (PK, P_Na, etc.).
The Wide World of Potassium Channels
Potassium selectivity arises from the pore region lined with specific amino acids that form a selectivity filter.
The discovery of the Shaker potassium channel in Drosophila (and later MacKinnonās work) revealed key structural features of K^+ channels, including a pore loop that creates the selectivity filter.
Typical potassium channels are tetrameric (four subunits giving a central pore).
Channel dysfunction (mutations in the pore region) can lead to altered ion selectivity and neurological disease (e.g., Weaver mouse with cerebellar neuron dysfunction due to mutations in a K^+ channel pore loop).
Blocking toxins (e.g., scorpion toxins) helped identify the pore region and understand how toxins block ion channels by occluding the pore.
The Importance of Regulating the External Potassium Concentration
The resting membrane potential is sensitive to extracellular [K^+]. A tenfold change in [K^+]_o (e.g., from 5 mM to 50 mM) can depolarize the membrane to about -17 ext{ mV} from -65 ext{ mV}.
This sensitivity has led to biological regulatory mechanisms to maintain extracellular potassium within a narrow range in the brain (e.g., the bloodābrain barrier and glial buffering by astrocytes).
Astrocytes take up excess extracellular K^+ when neural activity raises local [K^+]_o, store it briefly, and help dissipate it via a network of processes (potassium spatial buffering) (see Box 3.4 and Figure 3.20).
Not all excitable cells have such buffering protections; e.g., muscle cells are more vulnerable to extracellular K^+ fluctuations.
Box 3.1: Concentrations and Molarity
Concentrations are expressed as number of molecules per liter (moles per liter, M).
1 M = 1 mole per liter; 1 mM = 0.001 M.
Concentration notation uses brackets: [NaCl] = 1 mM means the concentration is 1 millimolar.
Box 3.2: The Nernst Equation (summary)
General form: E{ ext{ion}} = rac{RT}{zF} \, ext{log}{10} rac{[ ext{ion}]{ ext{o}}}{[ ext{ion}]{ ext{i}}}
At body temperature (ā 37Ā°C), simplified forms for common ions:
EK \,=\, 61.54 ext{ mV} \; \log{10} \frac{[K^+]{ ext{o}}}{[K^+]{ ext{i}}}
E{Na} \,=\, 61.54 ext{ mV} \; \log{10} \frac{[Na^+]{ ext{o}}}{[Na^+]{ ext{i}}}
E{Cl} \,=\, 61.54 ext{ mV} \; \log{10} \frac{[Cl^-]{ ext{o}}}{[Cl^-]{ ext{i}}}
E{Ca} \,=\, 30.77 ext{ mV} \; \log{10} \frac{[Ca^{2+}]{ ext{o}}}{[Ca^{2+}]{ ext{i}}}
The equation shows that E_ion depends on the concentration ratio across the membrane, not on membrane permeability.
Example: If [K^+]i/[K^+]o = 20, then EK \approx 61.54 \text{ mV} \times \log{10} 20^{-1} = -80\text{ mV}.
Box 3.3: The Goldman Equation (summary)
Real neuronal membranes are permeable to more than one ion; the Goldman equation integrates permeabilities and concentrations to give the resting potential:
Vm = 61.54\text{ mV} \; \log\left( \frac{PK [K^+]o + P{Na} [Na^+]o}{PK [K^+]i + P{Na} [Na^+]_i} \right)If one considers only K^+ and Na^+ with relative permeabilities, the resting potential approaches a weighted average of EK and ENa depending on the ratio of permeabilities (e.g., if PK is 40Ć PNa, Vm ā -65 mV rather than -80 mV or +62 mV).
The resting Vm is close to the K^+ equilibrium potential because the membrane at rest is highly permeable to K^+ but not exclusively.
Box 3.4: Path of Discovery ā Feeling Around Inside Ion Channels in the Dark (Chris Miller)
The membrane potentialās sensitivity to extracellular K^+ motivated regulatory mechanisms (bloodābrain barrier and astrocytic buffering).
Astrocytes regulate extracellular K^+ via potassium spatial buffering: K^+ enters astrocytes through channels when [K^+]_o rises, increasing intracellular [K^+] which is then dissipated across a network of astrocyte processes, helping maintain local ionic balance.
The story highlights advances in ion channel research and the shift toward reductionist artificial membranes to study channel function in controlled conditions.
Box 3.5: Of Special Interest ā Death by Lethal Injection
The ionic basis of the resting membrane potential explains why heart function stops when extracellular potassium concentration is raised via lethal injection (potassium chloride, KCl).
The resting potential underlies cardiac muscle excitability; large shifts in extracellular K^+ disrupt normal membrane potential and can halt heart activity.
This box emphasizes the practical and ethical implications of membrane physiology in medicine and life-and-death contexts.
Concluding Remarks (Summary)
The sodiumāpotassium pump generates and maintains a large intracellular K^+ gradient and extracellular Na^+ gradient.
The resting membrane potential arises primarily from the high permeability to K^+ at rest, with a small Na^+ leak contributing to the exact value ( Vm ā -65 mV in many neurons).
The negative resting potential is essential for neuronal excitability and function; without the gradients and pumps, the brain would fail to generate action potentials.
The membraneās capacitance stores charge on the inner membrane surface, enabling rapid changes during signaling without large ion concentration changes.
Understanding the resting potential lays the foundation for subsequent topics on action potentials and synaptic transmission.
Review Questions (from the text)
1) What two functions do proteins in the neuronal membrane perform to establish and maintain the resting membrane potential?
2) On which side of the neuronal membrane are Na^+ ions more abundant?
3) When the membrane is at the potassium equilibrium potential, in which direction (in or out) is there a net movement of potassium ions?
4) There is a much greater K^+ concentration inside the cell than outside. Why, then, is the resting membrane potential negative?
5) When the brain is deprived of oxygen, the mitochondria within neurons cease producing ATP. What effect would this have on the membrane potential? Why?
Connections and Implications
The resting membrane potential is a baseline from which all neuronal signaling begins; perturbations in ionic gradients or channel/pump function alter excitability and can underlie neurological disorders.
The balance between diffusion and electrostatic forces governs the flow of ions through channels, while pumps maintain the necessary gradients for sustained signaling.
Real-world relevance includes understanding conditions like hypo/hyperkalemia and their effects on neural and cardiac excitability, as well as the design of pharmacological agents that target specific channels or pumps.
Key Equations (summary)
Nernst equation for a generic ion: E = (RT/zF) * ln([Ion]outside/[Ion]inside), where E is the equilibrium potential, R is the universal gas constant, T is the temperature in Kelvin, z is the valence of the ion, and F is Faraday's constant.
At body temperature (ā 37Ā°C): E = (61.5/z) * log([Ion]outside/[Ion]inside), which simplifies the calculation of equilibrium potential for biological systems.
Goldman equation (approximate form for K^+ and Na^+ permeabilities): E = 61.5 * log((PK * [K^+]outside + PNa * [Na^+]outside) / (PK * [K^+]inside + PNa * [Na^+]inside)), where PK and PNa are the permeability coefficients for potassium and sodium ions, respectively.
Current-voltage relation (simplified):
I = gV, where I is the current, g is the conductance of the membrane, and V is the membrane potential. This relationship illustrates how changes in voltage across the neuronal membrane influence the flow of ionic current, directly impacting neuronal excitability and signal transmission.Relationship between driving force and current: The driving force on an ion is determined by the difference between its equilibrium potential and the membrane potential, expressed mathematically as: (Driving\ Force = E{ion} - V{m}). This value indicates the direction and magnitude of the ionic current, highlighting how a greater driving force can lead to an increased current flow, thereby affecting the neuron's response to stimuli.