The Resting Membrane Potential and the Nernst Equation 2024 PDF

1.2 The resting membrane potential and the Nernst Equation Dr. Veronica Campanucci Objectives for Section 1.2: To understand the Nernst Equation and its relationship with ion fluxes. Readings: From Boron: The resting membrane potential and the Nernst Equation Chapter 5 Chapter...

1.2 The resting membrane potential and the Nernst Equation Dr. Veronica Campanucci Objectives for Section 1.2: To understand the Nernst Equation and its relationship with ion fluxes. Readings: From Boron: The resting membrane potential and the Nernst Equation Chapter 5 Chapter 6 From Kandel: Membrane potential and the passive electrical properties of the neuron Chapter 9 How can an ionic gradient and a semi- permeable membrane generate a membrane potential? The membrane potential results from a separation of positive and negative charges across the cell 5 nm membrane. The excess of positive charges (red circles) outside the membrane and negative charges (blue circles) inside the membrane of a nerve cell at rest represents a small fraction of the total number of ions inside and outside the cell. Figure 9-1 Taken from Kandel, ER. et al. Principles of Neural Science, 6th ed. Separation of charges is an effect at the plasma membrane Changing the membrane voltage requires a tiny movement of ions! In a 50 m cell with an internal K+ concentration of 100 mM, it requires a movement of only 0.00001 mM of K+ to take the cell from 0 mV to -80 mV. Meaning that when K+ ions flow out to reach equilibrium, the internal K+ concentration goes from 100mM to 99.99999 mM, a negligible drop in concentration. The bulk of the cytoplasm and the bulk of the extracellular fluid are electroneutral. How do ionic gradients contribute to the membrane potential? No single ion species is distributed equally across the membrane: - outside: high Na+ and Cl- - inside: high K+ and organic anions (A-, primarily amino acids and proteins) The membrane potential always depends on the permeabilities of physiological ions and will always stay within the limits of their equilibrium potentials Ion flux is determined by both, concentration and the electrical potential A B Figure 9-3 A. In a cell only permeable to K, the resting potential is generated by the efflux of K down its gradient. B. The efflux of K builds up positive charges on the outside of the cell, and leaves behind on the inside an excess of negative charge. This buildup of charge leads to a potential difference across the membrane that impedes the further efflux of K. At equilibrium potential: the electrical and chemical driving forces are equal and opposite, and as many K ions move in as move out. Thus, no net change. Taken from Kandel, ER. et al. Principles of Neural Science, 6th ed. The Nernst Equation (simplified form) at 20ºC: 58 mV [X]o EX = log10 z [X]i Ex = equilibrium potential for a particular ion X z = valence of the ion [X]o = extracellular concentration of the ion [X]i = intracellular concentration of the ion Describes the equilibrium potential for any ion species, which is the electrical potential necessary to balance an ionic concentration gradient across a membrane so that the net flux of the ion is zero. The Nernst Equation - RT [X]i EX = ln zF [X]o EX = equilibrium potential for a particular ion X R = the gas constant T = absolute temperature F = the Faraday constant: electric charge per mole of electrons z = valence of the ion [X]o = extracellular concentration of the ion [X]i = intracellular concentration of the ion Nernst calculations per ion species (+) RT/F value? (+) experimental (2+) body temp. (-) The Nernst Equation (simplified form) at 20ºC: 58 mV [X]o EX = log10 z [X]i Ex = equilibrium potential for a particular ion X z = valence of the ion [X]o = extracellular concentration of the ion [X]i = intracellular concentration of the ion Note that all that you need to know to be able to calculate the Nernst potential for a given ion is its charge (valence) and the internal and external concentrations! Calculation of the Nernst potential for K+ using physiological concentrations: 58 mV [X]o EX = log10 z [X]i 4 mM EX = 58 mV x log10 = -91 mV 155 mM EK = Nernst equilibrium potential for K+ z = +1 [X]o = 4 mM [X]i = 155 mM  Equilibrium Potential (mV) +63 -91 +121 -85 37oC 20oC Recommended: Play around with concentrations and calculate Nernst eq. potentials. What happens to the Nernst Eq. potential for Na when you decrease the extracellular Na concertation by 10 times? Calculate EK by changing [K]o The Nernst equation is able to give a value of voltage that must exist across the membrane to balance a chemical gradient that exists for the ion in question. A plot of log10 of the K concentration (x axis) against membrane potential, gives a straight line (is a linear function) for a membrane permeable to potassium ions. The slope of the line has a value of 58 mV for a 10-fold concentration difference at room temperature (20oC). [K]o (mM) EK (mV) 1 -127 4 -92 10 -69 40 -34 100 -11 400 24 What determines the direction and rate of ion flow? At the equilibrium potential of a given ion there is no net flow of that ion. Ion flow increases as the membrane potential moves farther away from the equilibrium potential. The “driving force” for an ion is defined as the difference between the membrane potential and the equilibrium potential for that ion (i.e. Vm - EX). The current passing through channels permeable to that ion is defined by Ohm’s Law: IX = GX(Vm - EX) Current through an open channel varies with voltage Note that this experiment was performed with identical solutions on both sides of the membrane, so ionic gradients were not a factor. Current through an open channel varies with voltage Current through an open channel varies with voltage and behaves like a resistor that follows Ohm’s Law. Ions always flow through an open channel in the direction that will tend to move the cell toward the equilibrium potential for that ion. If there is only one type of open channel, the membrane potential will move toward and eventually reach the equilibrium potential for that ion. If multiple channel types are open, the membrane potential will depend on the relative permeabilities of the relevant ions. Summary The movement of ions through biological membranes depends both on chemical gradients and electrical potentials. When these two forces are evenly balanced, there is no net flow of that ion and the ion is said to be at its equilibrium potential. The equilibrium potential can be calculated from the internal and external concentrations using the Nernst equation. The resting membrane potential of a cell can be calculated from the internal and external concentrations of all permeant ions and the relative permeability of those ions using the Goldman equation. Self-testing questions 1) What is the origin of the membrane potential? 2) Why is the membrane potential considered solely as a “membrane effect”? 3) Explain what is the Nernst equilibrium potential. 4) What would be the effect on EX of changing the concentration of ion X by 10-fold?