# Membrane Potential

The membrane potential is the difference in electric charge between the interior and the exterior of a cell. All living cells maintain a potential difference across the membrane thanks to the insulating properties of their plasma membranes (PMs) and the selective transport of ions across this membrane by transporters. There are 3 types of potential: resting membrane potential, equilibrium potential, and action potential. Membrane potential helps to generate action potential, and these action potentials act as carry-and-relay signals to the CNS and brain for performing a specific movement or action.

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Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

## Overview

• Most cells in the human body hold a membrane potential.
• The lipid bilayer of the plasma membrane (PM) insulates the inside of the cell from the outside and does not allow the free diffusion of ions.
• Selective ion channels and transporters allow for increases in concentration of charged ions inside and/or outside the PM.
• Most cells have an electric potential across their PM.
• The inside of the cell is slightly more negative than the outside.
• In some cells, this charge can equalize or even reverse rapidly in response to stimuli.
• Types of potential
• Resting membrane potential
• Equilibrium potential
• Nerve action potential

## Equilibrium Potential

### Overview

• Also known as the reversal potential or “isoelectric state“
• Transmembrane potential voltage at which there is no net flow Flow Blood flows through the heart, arteries, capillaries, and veins in a closed, continuous circuit. Flow is the movement of volume per unit of time. Flow is affected by the pressure gradient and the resistance fluid encounters between 2 points. Vascular resistance is the opposition to flow, which is caused primarily by blood friction against vessel walls. Vascular Resistance, Flow, and Mean Arterial Pressure of ions across a PM
• Ions diffuse along their concentration gradient as well as to neutralize their electrical charges (e.g., negatively charged ions wish to travel toward positively charged areas).
• May act together to push ions in 1 direction or can contrast each other

### Nernst equation

Used to calculate the equilibrium potential at a given concentration difference of a permeable ion across the cell membrane Cell Membrane A cell membrane (also known as the plasma membrane or plasmalemma) is a biological membrane that separates the cell contents from the outside environment. A cell membrane is composed of a phospholipid bilayer and proteins that function to protect cellular DNA and mediate the exchange of ions and molecules. The Cell: Cell Membrane.

$$V_{eq}= \left ( RT/zF \right )ln\left ( X_{o} /X_{i}\right )$$

Veq = equilibrium potential for the ion X
R = gas constant (8.314 joules per kelvin per mole)
T = temperature in kelvin (K = °C + 273.15)
z = charge on the ion (+1 for Na+, +2 for Ca2+, −1 for Cl−)
F = Faraday constant (96,485 Coulombs per mole)
Xi = intracellular concentration (mM)
Xo = extracellular concentration (mM)

## Resting Membrane Potential

### Overview

• Potential that cells have across their membranes at their baseline state
• Excitable cells (neurons, cardiac muscle, etc) return to this resting potential between action potentials
• Non-excitable cells remain constantly at their resting potential.
• Result of the movement of several different ion species through various ion channels and transporters (uniporters, cotransporters, and pumps) in the PM
• Diffusion potential depends on
• The charge of the ions (primarily Na, K, and Cl-)
• The difference in concentration of ions inside vs. outside the cell
• The permeability of the PM to the ions
• Resting membrane potential of various tissues:
• Neuron -70mV
• Skeletal muscle -90mV
• Cardiac -90mV
• Restless membrane potential
• Unstable potential
• Oscillates between -60mV and -40mV
• Seen in pacemaker tissues
• Sinoatrial (SA) node in cardiovascular system (CVS)
• Cajal cells in GI tract
• Pre-Bötzinger complex in the respiratory system

### Goldman equation

The resting membrane potential can be considered the average of the equilibrium potentials of all the ions that permeate in and out of a cell, modified by the relative permeability of a cell to those ions.

$$E_{m}=\frac{RT}{F}ln\left ( \frac{P_{K}\left [ K^{+} \right ]_{out}+P_{Na}\left [ Na \right ]^{+}_{out}+P_{Cl}\left [ Cl^{-} \right ]_{in}}{P_{K}\left [ K^{+} \right ]_{in}+P_{Na}\left [ Na^{+} \right ]_{in}+P_{Cl}\left [ Cl^{-} \right ]_{out}} \right )$$

Em: the membrane potential (in volts, equivalent to joules per coulomb)
Pion: the selectivity for that ion (in meters per second)
[ion]out: the extracellular concentration of that ion (in moles per cubic meter, to match the other International System of Units (SI))
[ion]in: the intracellular concentration of that ion (in moles per cubic meter)
R: the ideal gas constant (joules per kelvin per mole)
T: the temperature in kelvins
F: Faraday constant (coulombs per mole)

## Action Potential

### Overview

• Seen in excitable cells (primarily neurons)
• While at resting membrane potential, ion channels open and lead to rapid flux of ions across the PM along their concentration gradient.
• Leads to rapid changes in voltage across the PM (depolarization)
• Changes are localized to the area around the open ion channels.
• Voltage-sensitive ion channels in adjacent areas open in response to the change in membrane potential, allowing ion influx.
• The potential is thus propagated over the entire surface of the cell membrane Cell Membrane A cell membrane (also known as the plasma membrane or plasmalemma) is a biological membrane that separates the cell contents from the outside environment. A cell membrane is composed of a phospholipid bilayer and proteins that function to protect cellular DNA and mediate the exchange of ions and molecules. The Cell: Cell Membrane.

### Phases of a nerve action potential

• Resting membrane potential in a neuron
• At baseline -70mV
• Reflects the equilibrium potential of K+ due to its high conductance across the PM (from inside to outside)
• In a resting neuron: high concentration of Na+ in the extracellular fluid (ECF) and high concentration of K+ in the intracellular fluid (ICF)
• K leak channels are open while Na channels are closed.
• Leads to an outflow of K+ ions from inside the cell, generating the negative resting membrane potential
• Latent period
• When a stimulus is given, a response doesn’t occur immediately.
• Time gap between stimulus and response
• Upstroke of action potential or depolarization
• Depolarization occurs, which causes the opening of voltage-gated Na channels
• Leads to rapid Na ion influx into the cell along its concentration gradient
• Na+ conductance > K+ conductance
• This causes membrane potential to approach the equilibrium potential of Na+ (+65mV).
• Membrane potential remains positive for a brief period of time.
• Repolarization
• Depolarization causes the following changes
• Closes the inactivation gates of Na+ channels
• Slowly opens K+ channels, causing an increase K+ conductance more than the resting membrane potential
• K+ conductance > Na+ conductance, causing repolarization
• Repolarization occurs mainly due to K+ efflux
• Overshoot or hyperpolarization
• The Na+ channel closes.
• K+ conductance remains higher than the resting membrane potential at rest for some time.
• The membrane potential reaches close to the equilibrium potential of K+, which is -90mV.

### Refractory periods

• Absolute refractory period
• From firing to ⅓ of repolarization
• During this period, a 2nd stimulus, however large, cannot initiate another action potential.
• Relative refractory period
• From the end of absolute refractory period until membrane potential reaches its resting level
• During this period, action potential can be elicited if a larger stimulus is provided.

## Clinical Relevance

• Cardiac action potentials and pacemaker potential: the cells of the heart transmit action potentials that are different from those seen in neurons. The peak phases of the action potentials last longer than those seen with neurons due to the activity of slower calcium (Ca) channels, which open and hold the action potential longer. In addition, a group of special cells in the SA node is characterized as having a pacemaker potential. This action potential is automatically generated at the tail end of the previous, giving the process a repetitive automatic pattern that regulates the heartbeat.
• Brugada syndrome: a genetic condition leading to cardiac arrhythmias due to inherited mutations in the Na channels in cardiac muscle, which lead to aberrant action potential conduction, arrhythmia, and sudden cardiac arrest Cardiac arrest Cardiac arrest is the sudden, complete cessation of cardiac output with hemodynamic collapse. Patients present as pulseless, unresponsive, and apneic. Rhythms associated with cardiac arrest are ventricular fibrillation/tachycardia, asystole, or pulseless electrical activity. Cardiac Arrest. Patients are treated with implanted cardiac defibrillators that can detect aberrant rhythms and deliver a shock Shock Shock is a life-threatening condition associated with impaired circulation that results in tissue hypoxia. The different types of shock are based on the underlying cause: distributive (↑ cardiac output (CO), ↓ systemic vascular resistance (SVR)), cardiogenic (↓ CO, ↑ SVR), hypovolemic (↓ CO, ↑ SVR), obstructive (↓ CO), and mixed. Types of Shock to the heart to reset the action potential.

## References

1. Costanzo, Linda S. (2019). Physiology. Open WorldCat. http://brs.lwwhealthlibrary.com/book.aspx?bookid=2385
2. Chrysafides, Steven M, et al. (Eds.). (2021). Physiology, resting potential. StatPearls. http://www.ncbi.nlm.nih.gov/books/NBK538338/
3. Chen, I, & Forshing, L. (2021). Neuroanatomy, neuron action potential. StatPearls. http://www.ncbi.nlm.nih.gov/books/NBK546639/
4. Hall, JE. (2016). In Guyton and Hall Textbook of Medical Physiology. (13th Ed.) Elsevier.
5. Zaydman, MA, et al. (2012). Ion channel–associated diseases: Overview of molecular mechanisms. Chemical Reviews. 112(12), 6319–6333. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3586387/

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