Resting Membrane Potential Simulation

Scapula bone lesson icon: anterior, posterior, and lateral views

Introduction

The resting membrane potential is the electrical potential that exists across the plasma membrane of an excitable cell, such as a neuron or muscle cell, when it is resting and not responding to stimuli.

Typically, the resting membrane potential is around -70 mV (ranging from -60 mV to 90 mV), indicating that the interior of the cell membrane is relatively negative compared to its exterior. This charge imbalance results from an uneven distribution of potassium (K⁺), sodium (Na⁺), chloride (Cl^–), and large anions across the cell membrane.

The resting membrane potential can be measured by placing a reference electrode outside the cell membrane and a recording electrode inside the membrane. The charge difference between the two electrodes, the membrane potential, is measured in millivolts (mV) using a voltmeter.

Question 1: What does a 0 mV membrane potential indicate?

Question 2: What does a +30 mV membrane potential indicate?

Review of Cell Membrane Structure

Basic Components

Like other cells in the body, excitable cells are enclosed by a cell (plasma) membrane mainly consisting of a bilayer of phospholipids and embedded proteins.

Lipid Bilayer

Each phospholipid molecule has a polar head and two neutral fatty acid tails. The polar heads of the phospholipids are hydrophilic, meaning they are attracted to the polar water molecules surrounding the membrane. In contrast, the phospholipids’ neutral tails are hydrophobic and drawn to each other in the middle of the membrane.

The phospholipid bilayer forms a semipermeable barrier, allowing some substances to pass through while restricting others. Lipid-soluble and small, slightly polar molecules can pass through the lipid barrier, while ions and large, polar molecules cannot.

Nonrestricted Substances		Restricted Substances
Small, nonpolar molecules (gases)	Small polar molecules	Small, charged molecules (ions)	Large, polar molecules
Oxygen (O₂)	Water (H₂O)	Sodium (Na⁺)	Proteins
Carbon dioxide (CO₂)	Ethanol (C₆H₆O₆)	Potassium (K⁺)	Sugars
Nitrogen (N₂)	Glycerol (C₃H₈O₃)	Chloride (Cl^–)	Nucleic acids

As a result, the lipid bilayer separates the cell cytoplasm from the surrounding environment, creating extracellular and intracellular fluid compartments.

Membrane Proteins

Channel and pump proteins embedded in excitable cell membranes allow ions to pass through the phospholipid bilayer.

Channel proteins allow ions to move through the plasma membrane along their concentration gradients. Some channels, called leak channels, are continuously open, while others are gated and open only when stimulated. Voltage-gated channels open in response to changes in membrane potential, and ligand-gated channels open when chemicals bind. Other neurons have channels that respond to stimuli such as stretch, changes in temperature, or pressure.

Sodium-potassium pump proteins (or Na⁺/ K⁺ ATPases) actively transport Na⁺ and K⁺ ions through the cell membrane, thereby maintaining their concentration gradients. Each pump protein functions by moving 3 Na⁺ ions out of the cell while simultaneously moving 2 K⁺ ions into the cell.

The pump proteins move the ions by changing conformation (shape) using the energy stored in a molecule of ATP (adenosine triphosphate).

While facing the cell’s interior (cytoplasmic side), the pump protein has a high affinity for Na⁺ and binds with three Na⁺ ions and an ATP molecule. The pump protein then acts as an enzyme and hydrolyzes the ATP to ADP + P, allowing a low-energy phosphate group to bond.

The pump protein then changes conformation to face the cell’s exterior, where its affinity for Na⁺ decreases and its affinity for K⁺ increases. As a result, the three Na+ ions detach and enter the extracellular fluid, and two K⁺ ions attach.

The attachment of the K⁺ ions causes the phosphate to detach, and the pump protein changes conformation to face the cell’s interior again. The repositioning of the pump protein alters its ion affinities, causing it to release the two K⁺ ions and bind three Na⁺ ions, which allows the active transport process to start again.

Factors Affecting the Membrane Potential

Two factors primarily influence the measured value of the resting membrane potential of excitable cells.

The equilibrium potentials of potassium (K+), sodium (Na+), and chloride (Cl^–) ions.
The relative permeabilities of the cell membrane to these same ions.

Note: The sodium-potassium pump proteins (3 Na⁺ out / 2 K⁺ in) and large intracellular anions also slightly affect the resting membrane potential. However, the primary function of the pump proteins is to maintain the concentration gradients of Na⁺ and K⁺ ions.

1. Ion Equilibrium Potentials

An equilibrium potential of an ion (E_M) occurs when an opposing electrical gradient exactly counterbalances its concentration gradient, resulting in no net movement of the ion across the cell membrane.

Let us explore this concept further using K⁺ because the membranes of excitable cells are most permeable to this ion.

The following diagram shows a higher concentration of K+ ions inside the plasma membrane than outside. This distribution produces an outward K⁺ concentration gradient. Due to the addition of negatively charged ions, both sides of the membrane are electrically neutral. Therefore, there is no electrical gradient, and the membrane potential is 0mV. Notably, the diagram does not contain Na⁺ ions because the plasma membranes of excitable cells are not very permeable to this ion.

If potassium leak channels are added to the membrane, they provide a pathway for K⁺ ions to exit the cell along their concentration gradient. The K⁺ ion movement increases the positivity outside the cell while making the cell’s internal environment less positive (or more negative). The difference in charges across the membrane causes an inward electrical gradient to develop.

As the cell’s external environment becomes more positive, the opposing electrical gradient increases, making it more difficult for K⁺ ions to cross the membrane. The increasing positivity outside the membrane repels the K⁺ ions, and the growing negativity inside the membrane attracts the K⁺ ions.

An equilibrium for an ion, such as K⁺, is achieved when the electrical gradient’s inward force balances the concentration gradient’s outward force. The greater the concentration gradient of K⁺, the higher the electrical potential required to counter the outward flow of ions.

The point at which the membrane potential attains equilibrium is the ion’s equilibrium potential. At this stage, ions still move across the membrane, but the exchange is balanced, with no net gain on either side.

The Nernst Equation

If one can determine the ion concentration on both sides of the cell membrane, the Nernst equation can be used to predict the magnitude of the ion equilibrium potential. This equation considers various factors, such as the valence of the ion, the temperature, and the concentration of the ion inside and outside the cell.

E _(ion) = 61 * log ([ion outside] / [ion inside])

Full Nernt Equation

E_(ion) = RT/zF * log([ion outside the cell]/[ion inside of the cell]).

E_(ion) = membrane equilibrium potential for ion.

R = gas constant = 8.314472 J · K-1.

T = temperature (Kelvin) = 310 (body temperature).

F = Faraday’s constant = 9.65 x 104 C mol-1.

Z will be 1 for a monovalent ion such as K⁺.

RT/F can be simplified to 61 at normal body temperature.

By plugging in the values for these variables, one can calculate the equilibrium potential for a specific ion, like K⁺. It is important to note that the Nernst equation assumes that the cell membrane is only permeable to the ion that is being evaluated.

Question 1: Why does the electrical gradient change in proportion to the ion concentration gradient for each equilibrium potential?

Question 2: Why is the direction of the electrical gradient reversed for E_Na and E_Clcompared to E_K?

2. Ion Membrane Permeability

Excitable cell membranes are most permeable to potassium (K⁺) ions. However, they also contain open channels for sodium (Na⁺) and chloride (Cl^–) ions, although the number of open channels for these ions is much less.

Ion	Relative Permeability
Potassium (K⁺)	P_K = 1
Chloride (Cl^–)	P_Cl= 0.3 – 0.5
Sodium (Na⁺)	P_Na = 0.05 – 0.01

Question 1: Based on the figures in the permeability table, how much less permeable is the membrane to Na⁺ ions than to K⁺ ions? Determine your answer using P_K / P_Na.

Question 2: How much less permeable is the membrane to Cl^– ions than to K⁺ ions?

Calculation of the Resting Membrane Potential

The Goldman-Hodgkin-Katz equation (GHK) is a frequently used formula for calculating the resting membrane potential of excitable cells.

V_M = 61 * log

P_K[K_out] + P_Na[Na_out] + P_Cl[Cl_in]
—————————————–
P_K[K_in] + P_Na[Na_in] + P_Cl[Cl_out]

The GHK equation appears similar to the Nernst equation, which calculates the equilibrium potential for a single ion. However, the GHK equation simultaneously considers the equilibrium potentials of K⁺, Na⁺, and Cl^– while incorporating the membrane’s permeability to each ion.

Stated differently, the value produced by the GHK is a weighted compromise (or tug-of-war) between the equilibrium potentials of Na⁺, K⁺, and Cl^– ions. The term “weighted” is used because the GHK equation considers the membrane’s permeability to each ion when the value of the resting membrane potential.

Ion Concentrations and Permeabilities

Ion	Extracellular Fluid (mmol/L)	Intracellular Fluid (mmol/L)	Permeability
K⁺	K_out = 3.5 – 5.5	K_in = 130 – 150	1
Na⁺	Na_out= 135 – 145	Na_in = 5 – 15	0.01 – 0.05
Cl^–	Cl_out = 96 – 106	Cl_in = 4 – 12	0.4 – 0.5

When normal ion concentrations and relative membrane permeabilities are inserted into the GHK equation, it indicates the resting membrane potential of an excitable cell is about -70 mV.

GHK Calculator

Question 1: What would be the resting membrane potential (EM) value if the cell membrane only contained open channels for potassium (K⁺)? To determine the answer, adjust the membrane potentials of the two other ions to 0.0. Closing the membrane to these ions eliminates them from the equation, leaving the value for K⁺.

Question 2: What would be the resting membrane potential value (E_M) if the cell membrane only contained open channels for sodium (Na⁺)?

Question 3: What would be the resting membrane potential (E_M) value if the cell membrane only contained open channels for sodium (Cl^–)?

Question 4: Does removing Cl- from the equation significantly affect the value of the resting membrane potential? Why is this the case?

To summarize, the GHK equation reveals that under normal physiological conditions, the resting membrane potential is mainly influenced by the equilibrium potentials of Na⁺ and K⁺ions and their respective membrane permeabilities. Thus, the inward flow of Na⁺ ions counters the outward leakage of K⁺ ions, producing a resting membrane potential that is more positive than the equilibrium potential of potassium.

Significance of the Resting Membrane Potential

When an excitable cell is at rest, it is quiescent and does not produce action potentials (electrochemical impulses). An action potential is a rapid, short-duration spike (+ 30 mV) in the membrane potential. The process begins when a stimulus causes the membrane to depolarize to a threshold level, typically around -55 mV. The change in membrane potential causes Na⁺ voltage-gated channels to activate (open). Na⁺ ions then enter the cell, and the membrane briefly reverse-polarizes to about +30 mV before the Na⁺ channels inactivate and the membrane returns to a resting state.

Na⁺ Channel Activation States During An Action Potential

Fluctuations in the resting membrane potential alter an excitable cell’s responsiveness to stimuli that trigger action potentials. Changes in ion concentration gradients or membrane permeability impact the membrane potential, making it more or less polarized. If the resting membrane potential becomes more negative (hyperpolarized), higher magnitude stimuli are required to start an action potential. Conversely, lower magnitude stimuli will create an action potential if the resting membrane potential becomes less negative (depolarized).

The resting membrane potential can also affect the availability of Na⁺ ions for membrane depolarization. Following an action potential, the membrane must fully repolarize to reactivate all the Na⁺ channels. If the membrane remains partially depolarized for extended periods, many Na⁺ channels may remain inactive (closed), reducing membrane excitability, muscle weakness, or paralysis.

Question 1: What changes in ion concentration could hyperpolarize the membrane?

Question 2: What changes in membrane permeability could hyperpolarize the membrane?

Question 3: What changes in ion concentration could partially depolarize the membrane?

Question 4: What changes in membrane permeability could partially depolarize the membrane?

Case Study 1: Hyperkalemia and Muscle Fatigue

Background: A 40-year-old marathon runner, Jane, has been training for an upcoming race. She has been participating in endurance exercises, including long-distance running.

Problem: Jane began experiencing muscle weakness and heart arrhythmias after a particularly intense training session. After her transport to the hospital, she was diagnosed with hyperkalemia, a condition characterized by high levels of potassium in the blood.

Usually, the potassium levels in your blood and extracellular fluid are 3.5-5.3 mmol/l. However, Jane’s potassium levels rose to 6.0 mmol/l during her intense training session.

Cause: Endurance exercises like marathons can cause skeletal muscle cell breakdown (rhabdomyolysis) and a shift of potassium from cells into the extracellular fluid that exceeds the capacity of the Na+ / K+ pump.

Treatment: Janes was given 500 ml of a 3% saline (NaCl) solution, which is hypertonic (= more concentrated) to the blood and extracellular fluids. As a result, both Na+ and Cl- levels in her extracellular fluids increased by 20 mmol/l.

Question 1: Why would the level of extracellular K⁺ increase if skeletal muscle cells rupture?

Question 2: How is the Na⁺ / K⁺ pump involved in maintaining the level of extracellular potassium?

Question 3: Jane’s potassium level rose to 6.0 mmol/l. How does the resting membrane change? Use the calculator below.

Question 4: Does the change in resting potential make the skeletal muscle cell membranes more or less polarized?

Question 5: Does the change in polarization initially make the skeletal muscle cell membranes more or less sensitive to stimuli?

Question 6: Why do the skeletal muscle cells eventually become fatigued?

Question 7: Do you think the 3% NaCl solution was an appropriate (= effective) treatment for Jane’s condition? Explain your answer using the calculator below.

References and Attributions

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2. DirectScience – “Membrane Potential.”

3. European Society of Cardiology – “Hyperkalemia, the sodium-potassium pump and the heart.”

4. Hindawi Case Reports in Medicine – “Acute Ascending Muscle Weakness Secondary to Medication-Induced Hyperkalemia.”

5. Journal of the Association of Physicians in India – “Severe Muscle Weakness due to Hyperkalemia.”

6. McGill Medicine and Health Sciences – “Resting Membrane Potential.”

7. Michigan State University Library – “Foundations of Neuroscience.”

8. N. I. H. National Library of Medicine – “Structure of the Plasma Membrane.”

9. N. I. H. National Library of Medicine – “Ion Channels and the Electrical Properties of Membranes.”

10. N. I. H. National Library of Medicine – “Physiology, Resting Potential.”

11. N. I. H. National Library of Medicine – “The Electrophysiology of Hypo- and Hyperkalemia.”

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13. Nursing 2020 Critical Care – “Electrolytes Series: Sodium and Chloride.”

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15. Saudi Journal of Kidney Diseases and Transplantation – “Hyperkalemia Revisited.”

16. ScienceDirect – “Development of models of active ion transport for whole-cell modeling: cardiac sodium-potassium pump as a case study.”

17. ScienceDirect – “Membrane Potential.”

18. ScienceDirect – “Skeletal Muscle Physiology.”

19. University of New Mexico – “Ionic gradients, membrane potential and ionic currents.”

20. University of St. Andrews – “Neurosims.”

21. University of St. Andrews – “The Origin of the Resting Membrane Potential.”