Summary of "FISIOLOGIA Clase3: Potencial de Membrana, Ecuacion de Nernst y Goldman."

Summary of “FISIOLOGIA Clase3: Potencial de Membrana, Ecuacion de Nernst y Goldman”

Main Ideas and Concepts

Membrane Potential Basics

Membrane potential is the electrical potential difference across the membrane of all cells.
At rest, cells have a negative charge inside (approximately -70 to -90 mV) and a positive charge outside.
This polarity arises from the distribution of ions, mainly potassium (K⁺) and sodium (Na⁺), and their respective anions (chloride Cl⁻ outside, proteins inside).
Electrical potential is crucial for cells like neurons and muscle cells that generate and transmit electrical signals.

Chemical and Electrical Gradients

Ions move according to chemical gradients (from high to low concentration).
Potassium concentration: high inside (140 mEq/L), low outside (4 mEq/L).
Sodium concentration: high outside (142 mEq/L), low inside (10 mEq/L).
Each cation (K⁺, Na⁺) is paired with an anion: chloride (Cl⁻) outside and proteins inside.
Electrical gradients arise because ions carry charges; opposite charges attract, like charges repel.
Membrane potential results from the balance between chemical gradients pushing ions across the membrane and electrical gradients pulling them back.

Diffusion Potential and Equilibrium

Potassium tends to leave the cell following its chemical gradient, but large intracellular proteins (anions) cannot follow, creating an electrical imbalance.
As K⁺ leaves, the inside becomes more negative until the electrical gradient opposes further K⁺ exit.
This balance point is the diffusion potential (~ -94 mV for K⁺).
Similarly, sodium tends to enter the cell but is limited by the electrical gradient when the cell becomes too positive (~ +70 mV for Na⁺).
The membrane selectively allows ion movement until an equilibrium is reached.

Nernst Equation

Developed by Walter Nernst, it calculates the electrical potential needed to counteract ion movement.
Simplified formula:

[ E = \pm 61 \times \log \left(\frac{[\text{ion outside}]}{[\text{ion inside}]}\right) ]

The sign depends on ion charge (negative for cations).
Example calculations:
- Potassium: (-61 \times \log(140/4) = -94 \text{ mV})
- Sodium: (-61 \times \log(10/142) = +70 \text{ mV})
Applies only if a single ion species is permeable.

Goldman Equation (Goldman-Hodgkin-Katz Equation)

Extension of Nernst’s equation to multiple ions simultaneously.
Accounts for permeability differences of ions across the membrane.
Main ions considered: Na⁺, K⁺, Cl⁻.
Membrane permeability values:
- K⁺ = 100%
- Na⁺ = 5%
- Cl⁻ = 45%
Conceptual formula:

[ E_m = -61 \times \log \frac{(P_{Na} \times [Na^+]{in}) + (P_K \times [K^+] \times [Cl^-]}) + (P_{Cl{out})}{(P \times [Na^+]{out}) + (P_K \times [K^+] ]}) + (P_{Cl} \times [Cl^-]_{in})

When applied, yields a resting membrane potential around -72 mV, consistent with physiological values.

Contributions to Resting Membrane Potential

Potassium’s tendency to leave creates a strong negative potential (~ -94 mV).
Sodium’s limited entry adds a small positive contribution (~ +8 mV).
Sodium-potassium pump (Na⁺/K⁺-ATPase) actively transports 3 Na⁺ out and 2 K⁺ in, using energy, contributing ~ -4 mV to maintain negativity.
These combined effects maintain the resting membrane potential between -70 and -90 mV.

Physiological Importance

Resting membrane potential is essential for the generation of action potentials.
Cells remain negative inside at rest but can rapidly change polarity during signaling.
The next topic will cover action potentials and how ions move during excitation.

Methodology / Step-by-Step Instructions

Calculating Ion Equilibrium Potential Using Nernst Equation

Identify ion concentrations inside and outside the cell.
Use the formula:

[ E = \pm 61 \times \log \left(\frac{[\text{ion outside}]}{[\text{ion inside}]}\right) ]

Use the negative sign for cations.
Calculate the logarithm of the concentration ratio.
Multiply by 61 (a constant derived from temperature, charge, and Faraday constant).
Interpret the result as the voltage at which ion movement stops.

Calculating Resting Membrane Potential Using Goldman Equation

Gather concentrations of Na⁺, K⁺, and Cl⁻ inside and outside the cell.
Determine membrane permeability for each ion (K⁺: 1, Na⁺: 0.05, Cl⁻: 0.45).
Apply the Goldman formula:

[ E_m = -61 \times \log \frac{(P_{Na} \times [Na^+]{in}) + (P_K \times [K^+] \times [Cl^-]}) + (P_{Cl{out})}{(P \times [Na^+]{out}) + (P_K \times [K^+] ]}) + (P_{Cl} \times [Cl^-]_{in})

Calculate numerator and denominator separately.
Divide numerator by denominator.
Take the logarithm of the result.
Multiply by -61 to get membrane potential in mV.

Speakers / Sources Featured

Primary Speaker: Unnamed instructor/lecturer presenting the physiology class.
Historical Figures Referenced:
- Walter Nernst (German physicist and chemist, developer of Nernst equation)
- Goldman, Hodgkin, Katz (scientists who extended the Nernst equation into the Goldman equation)
Personified Ions: Potassium, Sodium, and Sodium-Potassium Pump (used as teaching aids for explanation)

This summary captures the key physiological concepts about membrane potential, the role of ion gradients, and the mathematical tools (Nernst and Goldman equations) used to quantify these electrical phenomena in cells.