Nerve lecture 1: The-Resting-Membrane-Potential-donan and equilibrium potentials.

The-Resting-Membrane-Potential-donan and equilibrium potentials.

1. The Resting Membrane Potential: The Nerve Cell at Rest Before a neuron can fire a signal, it must first establish a state of readiness. This state is an electrical potential difference, or voltage, across its membrane, known as the Resting Membrane Potential (RMP) . Think of it as a charged battery, storing potential energy that can be rapidly converted into a nerve impulse. In this chapter, we will perform a deep dive into the electrochemical principles and mathematical models that explain how this potential is generated and maintained, focusing on the unequal distribution of ions, the influence of impermeable molecules, and the selective permeability of the neuronal membrane.

2. 2.1 Ion Distribution Across the Neuronal Membrane . The fluid inside a neuron (intracellular fluid, or ICF) and the fluid outside it (extracellular fluid, or ECF) have vastly different ionic compositions. This imbalance is the first critical ingredient for the RMP.

3. 2.2 The Gibbs-Donnan Equilibrium: The Effect of Trapped Ions Inside every neuron are large proteins and organic phosphates that carry a net negative charge. These molecules are too big to leave the cell, making them impermeable anions (A⁻). The presence of these "trapped" negative charges has a powerful influence on the distribution of all the other, smaller ions that can move across the membrane, like potassium (K⁺) and chloride (Cl⁻). This predictable redistribution of mobile ions in the presence of immobile ones is known as the Gibbs-Donnan Equilibrium.

4. Impact of Trapped Anions (A⁻) In our neuron, the high concentration of A⁻ inside the cell creates a strong negative charge. To maintain overall electroneutrality inside the cell, two things happen: Positive Ions Drawn In Positively charged permeable ions (like K⁺) are drawn into the cell. Negative Ions Pushed Out Negatively charged permeable ions (like Cl⁻) are pushed out of the cell. This leads to an unequal distribution of K⁺ and Cl⁻ that is directly influenced by the trapped A⁻. This unequal distribution of charged particles is a primary reason why an electrical potential—the membrane potential—must exist across the membrane at equilibrium.

5. The Gibbs-Donnan Principle The principle states that in the presence of a non-diffusible charged ion on one side of a semipermeable membrane, the diffusible ions will redistribute themselves to satisfy two conditions at equilibrium: Unequal Concentration The concentration of permeable ions will be unequal across the membrane. Product Equality The product of the concentrations of the diffusible cations and anions on one side will equal the product of their concentrations on the other side. (e.g., [K⁺]in * [Cl⁻]in = [K⁺]out * [Cl⁻]out).

6. Key Ions and Their Distribution Potassium (K⁺) Concentration is much higher inside (~140 mM) than outside (~4 mM). Sodium (Na⁺) Concentration is much higher outside (~145 mM) than inside (~14 mM). Chloride (Cl⁻) Concentration is much higher outside (~110 mM) than inside (~10 mM). Anionic Proteins (A⁻) Large, negatively charged proteins and organic phosphates are trapped inside the neuron, unable to cross the membrane. This distribution creates powerful concentration gradients (chemical forces) that would drive ions to move from an area of high concentration to an area of low concentration, if they were permitted to do so.

7. The Balancing Act This electrical shuffling leads to a new situation: a high concentration of K⁺ builds up inside the cell, and a high concentration of Cl⁻ builds up outside. Now, a second force comes into play: the chemical force of the concentration gradient, which pushes K⁺ back out and Cl⁻ back in. The Gibbs-Donnan equilibrium is reached when these two opposing forces—the electrical force pulling/pushing and the chemical force pushing back—find a perfect balance for each permeable ion.

8. The Two Major Consequences of this Equilibrium This balancing act has two unavoidable and critical consequences: Creation of an Electrical Potential Because the mobile ions have been distributed asymmetrically (more K⁺ inside, more Cl⁻ outside), there is a net separation of charge across the membrane. The inside of the cell becomes negatively charged relative to the outside. This electrical potential, created by the interplay of trapped anions and mobile ions, is a primary reason the Resting Membrane Potential exists. Creation of an Osmotic Problem The side of the membrane with the trapped anions (the inside of the cell) ends up with more total dissolved particles. It has the A⁻ plus the extra K⁺ that was pulled in. This higher total solute concentration creates an osmotic force that continuously pulls water into the cell.

9. Diagram 2.1: The Gibbs-Donnan Effect in a Neuron Gibbs-Donnan Effect in a Neuron Impermeable Anions Fixed A- inside the neuron K+ Redistribution More K+ accumulates inside Cl- Redistribution Cl- shifts outward across membrane Electrical Potential Inside becomes negatively charged

10. Because of charged proteins (Prot–) in cells, there are more osmotically active particles in cells than in interstitial fluid osmosis would make them swell and eventually rupture Na, K ATPase pumping ions back out of cells. Thus, normal cell volume and pressure depend on Na, K ATPase.

11. Resting Membrane Potential (RMP) The Electrical Foundation of Neural Communication

12. Defining the Resting Membrane Potential (RMP) Resting membrane potential (RMP): It is the difference in electrical potential between the inner and outer surface of the membrane under rest measured in millivolt. The ions primarily responsible for the generation of the membrane potential are Na+ , K+ A- (large, negatively charged intracellular proteins). The magnitude of the potential depends on the number of opposite charges separated: the greater the number of charges separated the larger the potential.

13. Ion Distribution and Potential Magnitude Ion ECF (millimoles/Liter) ICF (millimoles/Liter) Relative Permeability Na+ 140 14 1 K+ 4 140 100 Magnitude of RMP The magnitude of RMP equal: -70 mv in medium sized neurons. -90 mv in large nerve fibers and in large skeletal muscle fibers. -20 to -40 in non- excitable cell.

14. Cathode ray oscilloscope

15. Membrane potential Inside is negative with respect to the outside This is measured using microelectrodes and oscilloscope This is about -70 to -90 mV

16. Causes of RMP 1. Ion Leak Channels (Selective Permeability) The neuronal membrane at rest contains "leak" channels that are always open, allowing ions to diffuse passively across the membrane down their electrochemical gradients. Crucially, the resting membrane has many more K ⁺ leak channels than Na ⁺ leak channels. High Permeability to Potassium (K ⁺ ): Due to the abundance of K ⁺ leak channels, K ⁺ ions are driven by their steep concentration gradient to diffuse out of the cell. Low Permeability to Sodium (Na ⁺ ): There are very few Na ⁺ leak channels, so the influx of Na ⁺ into the cell is minimal. The outward movement of K ⁺ continues until the electrical gradient (the negative charge inside the cell pulling the positive K ⁺ back in) becomes strong enough to balance the chemical gradient (the concentration difference pushing K ⁺ out). This balance point for a single ion is called its equilibrium potential . The RMP of a typical neuron is about -70mV , which is very close to the equilibrium potential for K ⁺ .

17. Causes of RMP Causes of RMP (ionic basis of RMP) This unequal distribution of ions is determined mainly by: Membrane potential is directly generated by Na+-K+ pump, which is initially responsible for the Na+ and K+ concentration differences across the membrane, and it also maintains these differences. The passive diffusion of K+ and Na+ down concentration gradients. This passive diffusion occurs through a leakage channels that are non-gated channels always opened specific for them, (at resting potential in a nerve cell the membrane is about 100 times more permeable to K+ than to Na+ )

18. Contribution of the Sodium-Potassium Pump Let’s see how ion fluxes and Na+ -K+ - pump contributes to RMP: Contribution of the sodium-potassium pump to resting membrane potential: All cell membranes of the body have Na+ -K+ pump that continually transports 3 sodium ions to the outside of the cell and 2 potassium ions to the inside. The Na⁺/K⁺ pump has two vital functions: Maintains Concentration Gradients: Its primary role is to continuously counteract the passive ion leaks, ensuring that the high concentration of K⁺ inside and Na⁺ outside is maintained over time. It is the single most important factor in maintaining the RMP. Electrogenic Activity: Because the pump moves more positive charges out (3 Na⁺) than in (2 K⁺), it creates a net outward positive current. This direct contribution to the membrane potential is small (only a few millivolts) but helps make the inside of the cell even more negative. This causes a negative potential inside the cell membrane of about -4mv.

19. Diffusion and Equilibrium Potentials Unraveling the Electrical Basis of Life How can the passive diffusion of ions, like potassium and sodium, lead to the development of a negative membrane potential?

20. Defining the Diffusion Potential The initial spark of cellular electrophysiology lies in the concept of the diffusion potential, a foundational principle for understanding membrane voltage. Potential Difference A diffusion potential is the electrical potential difference generated across a membrane. Concentration Gradient This potential arises directly from a concentration difference of a permeable ion between the two sides of the membrane (inside vs. outside). Selective Permeability Crucially, this potential can only be generated if the membrane is selectively permeable to that specific ion, allowing it to move down its chemical gradient.

21. The Principle of Equilibrium Potential (EP) The Equilibrium Potential (EP) represents a specific voltage where the forces acting on an ion are perfectly balanced, leading to a dynamic steady state. Matching Strength The EP is the voltage at which the strength of the concentration gradient (chemical force) for a particular ion is precisely matched and opposed by the electrical gradient (electrical force). Zero Net Movement At this potential, there is no net movement of the ion in or out of the cell. Individual ions still move, but the flux inward equals the flux outward. Theoretical Voltage The potential that would exist at this equilibrium is the equilibrium potential . It dictates the theoretical maximum potential an ion can generate across a permeable membrane.

22. K+ Equilibrium Potential (EK+) Concentration Gradient K+ concentration is high inside (140 mEq/l) and low outside (4 mEq/l), creating a strong outward diffusion tendency. Electrical Charge As K+ diffuses out, it carries positive charge, making the outside electro-positive and the inside electro-negative (due to large, non-diffusible anions). Equilibrium Point The outward concentration gradient is exactly counterbalanced by the inward electrical gradient (diffusion potential).

23. Calculating EK+: The Nernst Potential The Equilibrium Potential (EP) for K+ is calculated using the Nernst equation, reflecting the point where no further net movement occurs. Using the concentrations (140 mEq/l inside, 4 mEq/l outside): If potassium ions were the only factor causing the resting potential, the resting potential inside the fiber would be equal to -94 mV. Key K+ Values Inside K+: 140 mEq/l Outside K+: 4 mEq/l EK+: -94 mV

24. Na+ Equilibrium Potential (ENa+) The movement of Sodium ions (Na+) alone creates an opposite polarity due to their concentration gradient. High Outside Na+ Na+ concentration is high outside (140 mEq/l) and low inside (14 mEq/l). Na+ diffuses inward. Polarity Reversal Inward Na+ movement makes the inside positive and the outside negative (Cl- ions remain outside). Equilibrium Reached The outward electrical gradient balances the inward concentration gradient, halting net Na+ movement.

25. Calculating ENa+: The Nernst Potential Key Na+ Values Inside Na+: 14 mEq/l Outside Na+: 140 mEq/l ENa+: +61 mV Using the Nernst equation for Na+ concentrations (14 mEq/l inside, 140 mEq/l outside): If Na+ ions were the only factor causing the resting potential, the resting potential inside the fiber would be equal to +61 mV.

26. The Reality: Multiple Ions Contribute In real cells, the resting potential is not equal to the equilibrium potential of any single ion. Most cells at rest have selective channels for K+, Na+, and Cl−. K+ Channels High permeability, driving potential toward -94 mV. Na+ Channels Lower permeability, driving potential toward +61 mV. Cl- Channels Also contribute significantly to the overall resting potential. The combined effect of these ions determines the final membrane potential.

27. The Goldman-Hodgkin-Katz (GHK) Equation When a membrane is permeable to several different ions, the diffusion potential is calculated using the GHK equation, which accounts for three critical factors: Polarity of Charge Membrane Permeability (P) Ion Concentrations (C) The GHK equation calculates the potential when two univalent positive ions (Na+, K+) and one univalent negative ion (Cl-) are involved.

28. GHK Equation Formula The full GHK equation incorporates the concentration (C) and permeability (P) for each ion (Na+, K+, Cl-) on both the inside (in) and outside (out) of the membrane. The degree of importance of each ion in determining the voltage is directly proportional to the membrane permeability for that ion.

29. The Calculated Resting Potential Applying typical values to the GHK equation yields a potential closer to the K+ equilibrium potential, reflecting the higher resting permeability to potassium. -94mV EK+ (Nernst) The potential K+ alone would create. +61mV ENa+ (Nernst) The potential Na+ alone would create. -86mV GHK Value Calculated potential considering K+, Na+, and Cl- permeability. The GHK value of -86 mV is much nearer to the K+ diffusing potential (-94 mV).

30. Final Resting Membrane Potential in Nerves The final resting membrane potential is determined by the GHK potential plus the contribution of the Na-K pump. GHK Potential -86 mV Na-K Pump Contribution -4 mV Total Resting Potential -90 mV The Na-K pump actively transports ions, adding a small hyperpolarizing effect to reach the final resting potential of -90 mV in large nerve fibers.