Resting Membrane Potential Simulation

Background Information

Introduction

A resting membrane potential occurs when ions are distributed unevenly across a cell membrane, resulting in an electrostatic charge differential. The resting membrane potential of excitable cells, such as neurons and muscle cells, is typically around -70 millivolts (mV). Excitable cells can generate electrical signals, called action potentials, in response to various stimuli.

Basic Membrane Structure

Like other cells in the body, excitable cells are enveloped by a plasma membrane consisting primarily of a framework of phospholipids arranged in a bilayer. Proteins embedded in the membrane regulate the entry and exit of charged substances (ions), creating a selectively permeable barrier that separates the cytoplasm from the surrounding environment.

Fluid Compartments

The plasma membranes of excitable cells are surrounded by dilute aqueous (water) environments containing dissolved ions, primarily sodium (Na+), potassium (K+), and chloride (Cl-).

The polar, hydrophilic heads of the membrane phospholipids are attracted to aqueous environments. In contrast, the hydrophobic tails of the phospholipids are drawn to each other in the middle of the membrane.

The lipid tails create a barrier separating a neuron’s inner and outer regions into extracellular (ECF) and intracellular fluid (ICF) compartments. Lipid-soluble and small, slightly polar molecules can pass through the lipid barrier, while ions and large, polar molecules cannot.

Ion Channels and Pump Proteins

Proteins embedded in excitable cell membranes act as channels or pumps, allowing ions to pass through the phospholipid bilayer.

Channel proteins allow ions to move freely 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. Additionally, other types of neurons have channels that respond to stimuli such as stretch, changes in temperature, and pressure.

Pump proteins require energy in the form of ATP to move ions through the plasma membrane against their concentration gradients.

Ion Concentration Gradients

Sodium-potassium pump proteins (Na+ / K+ ATPase), embedded in the plasma membrane of excitable cells, are responsible for forming and maintaining the concentration gradients for Na+ and K+. A pump protein works by moving 3 Na+ ions out of the cell in exchange for 2 K+ ions moved into the cell. The pumping process moves the ions against their concentration gradients.

A pump protein moves 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+ 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.

Unlike Na+ and K+ ions, the concentration gradient of Cl- ions builds passively. Cl- ions move freely through open channels and disperse according to the resting membrane potential. Since the extracellular environment in resting cells is relatively positive, more negatively charged Cl- ions accumulate outside the plasma membrane than inside.

Factors that Determine the Resting Membrane Potential

The resting membrane potential is the charge difference across the plasma membrane of a resting (non-signaling) neuron. Several factors determine the resting membrane potential of a cell.

1. Ion Concentration Gradients: The difference in concentration of ions inside and outside the cell plays a significant role. 
2. Membrane Permeability: The cell membrane’s permeability to different ions also affects the resting potential. 
3. Electrochemical Gradient: This is a combination of the concentration gradient and the electrical gradient for an ion across the membrane. 
4. Active Transport Mechanisms: These mechanisms, like the sodium-potassium pump, maintain the concentration gradients of different ions across the membrane.
5. Intracellular Anions: These negatively charged molecules, such as phosphates and proteins, contribute to a negative charge within the cell.

When excitable cells are at rest, their internal environment has a negative charge compared to the external environment due to the uneven distribution of certain types of ions. Sodium (Na+) and chloride (Cl-) ions are more abundant outside the membrane, while potassium (K+) ions and various large anions (such as phosphates and proteins) are more abundant inside the membrane. The uneven distribution also creates concentration gradients for these ions across the plasma membrane.

Ion	ECF (mmol/l)	ICF (mmol/l)
Na+	145 (High)	15 (Low)
Cl-	150 (High)	13 (Low)
K+	5 (Low)	150 (High)

The charge difference across the plasma membrane can be measured using electrodes and a voltmeter. A reference electrode is placed outside the membrane of an excitable cell, and a recording electrode is inserted into the cell’s interior. The charge difference between the two electrodes, the membrane potential, is determined by a voltmeter. Typically, the resting membrane potential is around -70 mV.

Equilibrium Potentials

An equilibrium potential (E_M) occurs when an ion’s electrical gradient is balanced by its concentration gradient, resulting in no net movement of the ion.

Let’s use K+ ions to illustrate the concept’s underlying principles because this ion most influences the resting membrane potential in excitable cells. 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 while at rest.

Potassium leak channels added to the membrane provide a passageway for K+ ions to move along their concentration gradient and exit the cell. The K+ ion movement increases the positivity outside the cell while making the cell’s internal environment less positive (or more negative), creating an inward electrical gradient across the membrane.

As the cell’s external environment becomes more positive, the 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.

Calculation of Ion Equilibrium Potentials

If you know the ion concentration on both sides of the cell membrane, you can use the Nernst equation to predict the size of the ion equilibrium potential. It considers factors like the temperature (in the body), the valence of the ion, and the concentration of the ion inside and outside the cell.

E _(ion) = 61 / 1 * log (ion _outside / ion _inside)

It’s important to note that the Nernst equation assumes that the cell membrane is only permeable to a single ion.

Factors that Determine the Resting Membrane Potential

The resting potential of an excitable cell is mainly influenced by the concentration gradients of potassium (K+), sodium (Na+), and chloride (Cl-) ions, as well as the permeability of the cell’s membrane to these ions. Under normal physiological conditions, the concentrations of these ions inside and outside the cell remain stable due in large part to the Na+/K+ pump proteins. Therefore, the ion permeabilities of the membrane become the most significant factor in determining the value of the resting membrane potential.

If the cell membrane of an excitable cell only contained open channels for potassium (K+), then its resting membrane potential (E_M) would tend to equal the equilibrium potential of potassium (E_K), which is approximately -90 mV. Instead, the resting membrane potential is closer to -70 mV (or less positive). This decrease occurs because excitable cell membranes have open channels for sodium (Na+) and chloride (Cl-). However, there are about half as many open chloride channels and about 20 to 100 times fewer open sodium channels.

Therefore, the resting membrane potential is a weighted compromise (tug of war) between the equilibrium potentials of Na+, K+, and Cl- ions. The effect of Cl- is often excluded from consideration because its equilibrium potential is about the same as the membrane potential. Thus, the equilibrium potentials of K+ and Na+ ions mainly determine the resting potential. The inward movement of Na+ ions partially counteracts the outward leakage of K+ ions, which results in a more positive (or less negative) resting membrane potential than the equilibrium potential of potassium.

Additionally, the unequal distribution of ions resulting from the sodium-potassium pump proteins (3 Na+ out / 2 K+ in) and large intracellular anions contribute slightly to the resting membrane potential.

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. While similar in form to the Nernst Equation, the GHK equation considers the equilibrium potentials of the three most involved ions (K+, Na+, and Cl-) and their respective membrane permeabilities (i.e., the number of open channels).

Ion Concentrations and Permeabilities

Ion	Extracellular Fluid (mmol/L)	Intracellular Fluid (mmol/L)	Permeability
K+	3.5-5.5	120-150	1
Na+	135-145	5-15	0.01-0.05
Cl-	96-110	4-12	0.4-0.5

Significance of the Resting Membrane Potential

Excitable cells generate rapid, short-duration spikes in potential called action potentials. These occur when the membrane potential depolarizes to a threshold level, causing Na⁺ voltage-gated channels to activate (open) and Na+ ions to enter the cell. As a result, the membrane briefly reverse-polarizes.

The process of generating an action potential can either be facilitated or impeded by changes in the resting membrane potential value. If the resting potential becomes more negative, the membrane becomes less sensitive to stimuli, making it harder to create an action potential. Conversely, if the resting potential becomes less negative (more positive), the membrane becomes more susceptible to stimuli, making it easier to generate an action potential.

The resting membrane potential can also affect how many Na⁺ are available for membrane depolarization. If the membrane remains partially depolarized for long periods, Na+ channels can become increasingly inactive, resulting in decreased membrane excitability and muscle weakness or paralysis. (5, 10)

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, during her intense training session, Jane’s potassium levels rose to 7.0 mmol/L.

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: How does the resting membrane change if the blood potassium level is 7.0 mmol/L? 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

1. Advances in Physiology Education – “Generation of resting membrane potential.”

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.”

12. ResearchGate – “Implications of active lifestyles and environmental factors for water needs and consequences of failure to meet those needs.”

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

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

15. ScienceDirect – “Membrane Potential.”

16. ScienceDirect – “Skeletal Muscle Physiology.”

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

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

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