Transmembrane Transport

• Importance of Transmembrane Transport

  • Understanding the movement of ions and molecules across cell membranes is fundamental to understanding general biology, drug mechanisms and pharmacological actions, and the physiology of nerve conduction.

• Structure and Physical Properties of the Cell Membrane

  • Selective Barrier: The primary function of the cell membrane is to serve as a selective permeability barrier, maintaining distinct ionic concentrations between the intracellular and extracellular environments, enabling nutrient uptake, and expelling metabolic waste products.

  • Capacitance: An additional critical biophysical function is capacitance, which is the storage of electrical charge across the hydrophobic lipid core.

  • Dimensions and Composition: The cell membrane is a lipid bilayer with embedded proteins and non-phospholipid lipids (such as cholesterol), measuring $5\text{--}7\text{ nm}$ in thickness.

  • Dynamic Properties: The membrane is fluid and self-sealing, properties that are necessary for fundamental cellular processes including cell division, endocytosis, and exocytosis.

  • Cell Cortex: The structural stability of the fluid membrane is provided by an underlying meshwork of structural proteins known as the cell cortex.

• Chemical Polarity and Solubilities

  • Water Polarity: Water ($H_2O$) is a polar molecule characterized by partial positive charges (\text{H}^{\text{̢+}}) on hydrogen atoms and partial negative charges (\text{O}^{\text{̢-}}) on oxygen atoms.

  • Hydrogen Bonding: The permanent charge polarity of water allows extensive intermolecular hydrogen bonding, which produces strong cohesion and results in a high boiling point.

  • Hydration Shells: Due to its polarity, water forms a structured "hydration shell" around dissolved charged ions, surrounding both cations and anions, as well as small and large charged molecules.

  • Non-polar Molecules: Alkanes such as methane ($CH_4$) and ethane ($C_2H_6$) lack charge polarity and are non-polar.

  • Hydrophobic Effect: Non-polar molecules are insoluble in water (hydrophobic). Oil and water separate into distinct phases because non-polar molecules cannot participate in hydrogen bonding with water molecules.

• Phospholipid Structure and Self-Assembly

  • Amphipathic Molecular Structure: Phospholipids consist of:

    • A Hydrophilic Head: Formed by a charged choline group attached to a phosphate group and a glycerol backbone.

    • A Hydrophobic Tail: Formed by two long-chain hydrocarbon fatty acid tails.

  • Bilayer Formation: In aqueous environments (extracellular fluid and cytoplasm), amphipathic phospholipids spontaneously orient into a bilayer, positioning hydrophobic tails inward away from water and hydrophilic heads outward toward the aqueous solution.

  • Micelles: The most thermodynamically stable globular single-layer aggregate formed by amphipathic lipids in aqueous environments is the micelle.

• Membrane Fluidity and Cholesterol

  • Cholesterol Structure: Cholesterol possesses rigid sterol ring structures and a polar hydroxyl head group.

  • Stiffening Effect: Cholesterol intercalates between phospholipid molecules in the membrane. Its rigid ring structure immobilizes regions of the hydrocarbon chains, creating a cholesterol-stiffened membrane region while leaving deeper regions relatively fluid.

Vesicular Transport and Selective Permeability

• Endocytosis and Exocytosis

  • Endocytosis: A cellular process in which the plasma membrane invaginates to engulf extracellular material or particles (e.g., an immune cell engulfing pathogenic bacteria).

  • Exocytosis: A vesicular fusion process essential for the cellular secretion of substances, such as the quantal release of neurotransmitters at chemical synapses.

  • Regulation and Compartmentalization: Vesicular trafficking (endocytosis and exocytosis) is tightly regulated by specific membrane and cytosolic proteins. Contents inside transport vesicles remain membrane-bound and topologically separated from the cytosol.

• Selective Permeability of the Lipid Bilayer

  • Small Non-polar / Hydrophobic Molecules: Rapidly diffuse directly through the lipid bilayer (e.g., $O_2$, $N_2$, benzene).

  • Small Uncharged Polar Molecules: Cross the lipid bilayer passively, but at significantly reduced rates (e.g., $H_2O$, urea, glycerol, $CO_2$).

  • Large Uncharged Polar Molecules: Impermeable to simple passive diffusion through the hydrophobic lipid core; require transport proteins (e.g., glucose, sucrose).

  • Ions (Charged Species): Highly impermeable to the pure lipid bilayer due to their charge and associated hydration shells; require specialized ion channels or transport proteins (e.g., $H^+$, $Na^+$, $HCO_3^-$, $K^+$, $Ca^{2+}$, $Cl^-$, $Mg^{2+}$).

Categories and Mechanisms of Transmembrane Transport

• Passive Transport (Down-Gradient)

  • Does not consume cellular energy ($ATP$); transport occurs spontaneously down a concentration or electrochemical gradient.

  • Simple Diffusion: Direct passage of small, uncharged or hydrophobic molecules across the lipid bilayer or through un-gated pore channels without conformational changes in protein carriers.

  • Facilitated Diffusion: Transmembrane passage mediated by specialized transport proteins, including:

    • Channel Proteins: Pore-forming proteins allowing rapid passive flux (e.g., ion channels).

    • Carrier Proteins: Transporters that bind specific substrates (e.g., glucose) and undergo conformational changes to shuttle them across the membrane down their concentration gradient.

• Active Transport (Up-Gradient)

  • Energy-consuming movement of solutes against their established concentration or electrochemical gradients.

  • Primary Active Transport: Direct utilization of cellular energy ($ATP$ hydrolysis) by pump enzymes (e.g., $Na^+/K^+$ ATPase) to drive solutes against gradients.

  • Secondary Active Transport: Utilizes the potential energy stored in an established ion gradient (typically the $Na^+$ gradient set up by primary active transport) to drive another solute against its gradient:

    • Symport: Both driving and co-transported solutes move in the same directional vector across the membrane (e.g., $Na^+$/glucose or $Na^+$/amino acid co-transporters).

    • Antiport: Driving ion and transported ion move in opposite directional vectors across the membrane (e.g., $Na^+/Ca^{2+}$ exchanger, $Na^+/H^+$ exchanger, $Na^+/K^+$ pump).

• The Sodium-Potassium Pump ($Na^+/K^+$ ATPase)

  • Stoichiometric Transport: Primary active membrane pump enzyme that hydrolyzes one molecule of $ATP$ to $ADP + P_i$ to actively transport $3\text{ Na}^+$ ions out of the cell and $2\text{ K}^+$ ions into the cell.

*   **Experimental Evidence:**
    *   Demonstrated via radiotracer flux studies using radioactive isotopes $^{24}Na$ and $^{42}K$ in red blood cell "ghosts" (osmotically swelled and re-sealed erythrocyte membranes) and via microinjection into giant squid axons.
*   **Operational Substrate Requirements:**
    *   $Na^+$ and $ATP$ must be present on the intracellular (cytosolic) side of the membrane.
    *   $K^+$ must be present on the extracellular side of the membrane.
*   **Pharmacological and Metabolic Inhibition:**
    *   Metabolic poisons that block mitochondrial oxidative phosphorylation and $ATP$ synthesis, such as cyanide, abolish pump activity.
    *   Cardiac glycosides such as ouabain specifically bind to extracellular $K^+$ binding sites and block pump function.
*   **Electrogenic Property:**
    *   Because it exports 3 positive charges ($Na^+$) for every 2 positive charges ($K^+$) imported, the pump generates a net outward ionic current. This electrogenic action directly contributes a hyperpolarizing voltage of approximately $-10\text{ mV}$ to the cell interior.
*   **Cell Volume Regulation:**
    *   Critical for preventing osmotic cell lysis. By extruding $Na^+$ ions, it counteracts intracellular osmotic pressure exerted by impermeable macromolecules and inorganic anions, preventing water influx and maintaining osmotic equilibrium.

Electrochemical Equilibria and Resting Membrane Potential

• Intracellular vs. Extracellular Ionic Concentrations

  • Typical physiological ion distribution across the plasma membrane:

    • $\text{Sodium (Na}^+\text{)}:$ Intracellular $[\text{Na}^+]_i = 10\text{ mM}$; Extracellular $[\text{Na}^+]_o = 140\text{ mM}$ (Ratio $1:14$).

    • $\text{Potassium (K}^+\text{)}:$ Intracellular $[\text{K}^+]_i = 140\text{ mM}$; Extracellular $[\text{K}^+]_o = 10\text{ mM}$ (Ratio $14:1$).

    • $\text{Chloride (Cl}^-\text{)}:$ Intracellular $[\text{Cl}^-]_i = 10\text{ mM}$; Extracellular $[\text{Cl}^-]_o = 140\text{ mM}$ (Ratio $1:14$).

    • $\text{Calcium (Ca}^{2+}\text{)}:$ Intracellular free $[\text{Ca}^{2+}]_i = 10^{-3}\text{ mM}$ (1\text{ }̢M or $10^{-6}\text{ mM}$); Extracellular $[\text{Ca}^{2+}]_o = 1.0\text{ to }2.5\text{ mM}$ (Ratio $1:>1000$).

• Electrochemical Forces

  • Concentration Gradient: Chemical driving force moving ions passively from areas of higher concentration to lower concentration.

  • Electrical Gradient: Electrostatic force attracting cations toward negatively charged compartments and anions toward positively charged compartments.

• The Nernst Equation and Equilibrium Potentials

  • Equilibrium Potential ($E_X$): The membrane electrical potential at which the electrostatic force exactly balances the concentration gradient force for a given ion species $X$, resulting in zero net flux across the membrane.

  • General Nernst Equation:         $E_X = \frac{RT}{zF} \ln\left(\frac{[X]_o}{[X]_i}\right)$

    • Where $R$ is the universal gas constant, $T$ is absolute temperature in Kelvin, $z$ is the valence charge of the ion, and $F$ is Faraday's constant.

  • Simplified Nernst Equation (at standard temperature $20\,^\circ\text{C}$):         $E_X = 58 \times \log_{10}\left(\frac{[X]_o}{[X]_i}\right)$

  • Calculated Equilibrium Potentials:

    • $\text{Potassium Equilibrium Potential (E}_K\text{)} = -95\text{ mV}$

    • $\text{Sodium Equilibrium Potential (E}_{Na}\text{)} = +84\text{ mV}$

    • $\text{Chloride Equilibrium Potential (E}_{Cl}\text{)} = -45\text{ mV}$

• Generation and Maintenance of Resting Membrane Potential ($V_{m(rest)}$)

  • Definition: $V_{m(rest)}$ is the baseline steady-state electrical potential across the membrane of an inactive cell (e.g., un-stimulated neuron, non-contracting muscle cell, non-secreting endocrine cell).

  • Typical Value: Ranging between $-85\text{ mV}$ and $-65\text{ mV}$ (intracellular space relative to extracellular ground standard at $0\text{ mV}$).

  • Determinants of $V_{m(rest)}$:

    • Primary Transporters: $Na^+/K^+$ ATPase generates core concentration gradients and an electrogenic $-10\text{ mV}$ contribution.

    • Secondary Transporters: Potassium-Chloride Co-transporter ($KCC$) regulates intracellular $Cl^-$ levels.

    • Leak Channels: Non-voltage-gated baseline channels, notably two-pore domain potassium channels ($K2P$, favoring $E_K = -95\text{ mV}$) and background sodium leak channels ($NALCN$, favoring $E_{Na} = +84\text{ mV}$). Because resting membrane permeability to $K^+$ is substantially higher than to $Na^+$, $V_{m(rest)}$ sits close to $E_K$.

Synaptic Physiology and Post-Synaptic Potentials

• Excitable Tissues and Action Potentials

  • Excitable Tissue Definition: Any tissue composed of cells capable of generating and propagating action potentials ($AP$). Examples include central and peripheral neurons, cardiac/skeletal/smooth muscle cells, certain glial cells, and pancreatic beta cells.

  • Action Potential ($AP$): Rapid transient electrical event initiated by explosive influx of positive sodium cations, causing a total voltage swing of approximately $100\text{ mV}$ (from $-70\text{ mV}$ to $+30\text{ mV}$), followed by slower repolarizing efflux of potassium ions.

• Comparative Bioelectric Voltages

  • Electric organ discharge (Electric eel/ray): $+600\text{ V}$

  • Neuronal Action Potential amplitude: $+100\text{ mV}$

  • Neuronal Resting Membrane Potential ($V_{m(rest)}$): $-70\text{ mV}$

  • Post-Synaptic Potentials ($PSP$): $\pm 1\text{ to }40\text{ mV}$

  • Reference Scale Comparisons: AA/Phone battery $= 3.7\text{ V}$, Car battery $= 12\text{ V}$, Mains electricity $= 240\text{ V}$.

• Post-Synaptic Potentials (PSPs)

  • Synaptic Transmission: Pre-synaptic neurons release neurotransmitters via exocytosis into the synaptic cleft. These ligands bind to Receptor-Operated Channels (ROCs), also termed Ligand-Gated Ion Channels (LGICs), on the post-synaptic membrane.

  • Excitatory Post-Synaptic Potentials (EPSPs):

    • Produce membrane depolarization (shifting membrane voltage positive by $1\text{ to }40\text{ mV}$, closer to $0\text{ mV}$ threshold).

    • Driven by ligand-gated opening of channels permeable to cations ($Na^+$ and $Ca^{2+}$ influx).

  • Inhibitory Post-Synaptic Potentials (IPSPs):

    • Produce membrane hyperpolarization (shifting membrane voltage more negative than $-70\text{ mV}$).

    • Driven by ligand-gated opening of channels permeable to anions ($Cl^-$ influx).

• Receptor-Operated Channels and Neurotransmitters

  • $\text{nAChR (Nicotinic Acetylcholine Receptor):}$ Activated by Acetylcholine (ACh) $\rightarrow$ Mediates $Na^+$ and $Ca^{2+}$ influx (and $K^+$ efflux) $\rightarrow$ Depolarizing EPSP. Essential for neuromuscular junction excitation.

  • $\text{5-HT}_3\text{R:}$ Activated by Serotonin (5-HT) $\rightarrow$ Mediates $Na^+$ and $Ca^{2+}$ influx $\rightarrow$ Depolarizing EPSP.

  • $\text{iGluR (Ionotropic Glutamate Receptor):}$ Activated by Glutamate $\rightarrow$ Mediates $Na^+$ influx or $Na^+/Ca^{2+}$ influx $\rightarrow$ Depolarizing EPSP. Glutamate is the primary excitatory neurotransmitter in the central nervous system.

  • $\text{P2XR:}$ Activated by ATP $\rightarrow$ Mediates $Na^+$ and $Ca^{2+}$ influx $\rightarrow$ Depolarizing EPSP.

  • $\text{GABA}_A\text{R:}$ Activated by $\gamma$-aminobutyric acid (GABA) $\rightarrow$ Mediates $Cl^-$ influx $\rightarrow$ Hyperpolarizing IPSP. GABA is the primary inhibitory neurotransmitter in the brain.

  • $\text{GlycineR:}$ Activated by Glycine $\rightarrow$ Mediates $Cl^-$ influx $\rightarrow$ Hyperpolarizing IPSP.

• Neural Circuit Processing Example: Lateral Inhibition

  • Lateral inhibition uses reciprocal inhibitory interneurons to suppress activation of neighboring channels.

  • Functional Role: Provides spatial edge detection and contrast enhancement in sensory networks (e.g., visual retina).

  • Quantitative Signal Response Profile:

    • Without Lateral Inhibition (True Light Intensity): Uniform bright spatial domain $= 150$ arbitrary response units; Uniform dark spatial domain $= 30$ units.

    • With Lateral Inhibition (Perceived Contrast):

      • Uniform Bright region (Points A, B): Output suppressed to $120$.

      • Bright Edge adjacent to Dark border (Point C): Enhanced output to $132$.

      • Dark Edge adjacent to Bright border (Point D): Suppressed output to $12$.

      • Uniform Dark region (Points E, F): Baseline output maintained at 24$.\n\n\n\n# Biological Bioelectricity: Electroplaques in Electric Organ Output\n\n* **Cellular Structure and Polarized Innervation**\n * Electroplaques are specialized, flattened electric cells found in modified muscle tissue of electric eels (*Electrophorus electricus*) and electric rays (*Torpedo*).\n * **Resting Phase:** Na^+/K^+$ATPase pumps maintain uniform low intracellular$Na^+ and negative resting potential across both faces.\n * **Asymmetric Innervation:** Cholinergic nerve terminals innervate only one smooth face of the electroplaque, populating that specific membrane face with nicotinic acetylcholine receptors (nAChR).\n\n* **Mechanism of Discharge**\n * When the nerve fires, acetylcholine (ACh) is released onto the innervated face.\n * nAChR$ion channels open, permitting massive$Na^+$influx that depolarizes the innervated membrane face from resting potential to$0\text{ mV}.\n * The un-innervated opposite membrane face remains at resting potential (-0.12\text{ V} internal relative to outside).\n * This asymmetry establishes a net trans-cellular potential difference of 0.12\text{ V} across a single electroplaque cell during activation.\n\n* **Voltage Summation in Series Stacks**\n * Electroplaques are arranged physically in long columns arranged in series, containing approximately 5,000 stacked cells.\n * Because the cells are oriented in series like batteries in a flashlight, individual cell voltages add together constructively:\n        \text{Total Discharge Voltage} = 0.12\text{ V/cell} \times 5,000\text{ cells} = 600\text{ V}$$