It first introduces the ions and currents and moves quickly towards the dynamics of Hodgkin-Huxley model. So basically electrical activity in neurons are propagated via ionic currents through neural membranes. There are three positive currents and one negative ionic current.

Positive Ionic current

• sodium Na+
• potassium K+
• calcium Ca2+

Negative Ionic current

• chloride Cl-

The concentration of these ions are different inside and different outside which is the major driving force for neural activity.

The extracellular medium has high conc of Na+ and Cl- and relatively high conc of Ca2+. Whereas in intracellular medium there is high conc of K+ and negative charged molecules denoted by A-.

The cell membrane has large protein molecules forming channels through which ions (but not A-) can flow according to their electrochemical gradient. The flow of Na+ and Ca2+ ions is not significant at least at rest but the flow of K+ and Cl- ions is.

Through this description it refers to the selective membrane permeability and the fundamental mechanism that maintains ionic concentration gradient across cell membranes despite ion flow through the channels.
The protein channels mentioned are ion selective channels that allow specific ions to pass through according to their electrochemical gradient. While K+ and Cl- ions can flow relatively freely through their respective channels at rest, Na+ and Ca2+ flow is minimal due to either closed channels or very low permeability.
The concentration asymmetry persists despite this ion flow for two key reasons:

1. Active transport mechanism
The Na+/K+-ATPase pump actively maintains concentration gradient by continuously pumping ions against their electrochemical gradient using ATP energy. This pump moves 3 Na+ ions out and 2 K+ ions in for each ATP molecule consumed, countering the passive flow through leak channels.

2. Electrochemical Equilibrium
The flow of ions creates an electrical gradient that opposes further ion movement. As K+ ions leave the cell down their conc gradient, the interior becomes more negative, which then attracts K+ ions back in the cell. This creates an electrochemical equilibrium where the electrical force balances the conc gradient preventing complete equilibration.

Additionally, large organic anions A- mentioned cannot cross the membrane, creating a permanent negative charge inside the cell that contributes to the electrical gradient. This impermeant anion pool helps maintain the overall charge separation across the membrane.

The result is a stable resting membrane potential (typically around -70mV) where ion concentration remains asymmetric despite selective permeability because active transport continually works against passive leak current and electrochemical forces reach a dynamic equilibrium.

The Neuron Cycle: From Rest to Action and Back

1. Resting state (starting point: -70mV)

   • Inside is negative relative to outside
   • Na+/K+ pump maintains concentration gradient
   • K+ leak channels allow some K+ to flow out, keeping interior negative
   • Na+ channels mostly closed - minimal Na+ enters

2. Stimulus / Threshold (-55mV)

   • A stimulus makes the membrane slightly less negative
   • Once it reaches threshold (around -55mV), voltage gated Na+ channels open

3. Depolarization phase (-55mV -> +30mV)

   • Massive Na+ influx through open voltage gated Na+ channels
   • Interior becomes rapidly more positive
   • Membrane potential shoots from -70mV to +30mV
   • This is the upstroke of the action potential

4. Peak and Na+ channel Inactivation (+30mV)

   • Na+ channels automatically inactivate (close and won't reopen until reset)
   • Voltage gated K+ channels open with a slight delay

5. Repolarization phase (+30mV -> -70mV)

   • K+ rushes out through opened voltage gated K+ channels
   • Membrane potential rapidly returns towards negative
   • Interior becomes negative again

6. Hyperpolarization (-70mV -> -80mV)

   • K+ channels stay open briefly too long
   • Membrane becomes more negative than resting (around -80mV)
   • This prevents immediate refiring

7. Return to rest (-80mV -> -70mV)

   • K+ channels close
   • Na+/K+ pump restores original ion distributions
   • Membrane returns to -70mV resting potential

Key point: It's not neutral The neuron never goes to neutral (0mV) during normal function. It oscillates between negative at rest (-70mV) and briefly positive during action potential (+30mV). The "neutral" state would only occur if all the ion gradients were lost, which would mean cell death.

Nerst potential

There are two forces that drive each ion species thioght the membrance channel: concentration and electric potential griadent first this ion difues down the ceontentration gradient. fow example eht k+ ion depiceted diffues out of the cell because of k+ ceoncentration inside is higher thatn that outsize. while exiting the cell k+ ions there by producing the outward current the positive ahd negfative charges accumulate on the opposite side of the membrane surface creating an electicl potential gradient accross the membrande - transmembrane poteintial or membrane volage the potential show he diffusion of k+ since k+ ions are attracted to the negatively chareged interior and repelled from the positvely charges exterior of the membrane. At some point an equlibrium is achived/: the ceonecntration gradient and the eletric potential gradient exet equal and opposit forces that conterbalance each other and the net cross membra current is zero the value of such an equlibrium potential depends on the ionic species and it is give by the nerst equation

More simplifyied:

The Nernst equation is a fundamental formula in neuroscience that calculates the equilibrium potential for a specific ion across a cell membrane. This equation is crucial for understanding how neurons generate and maintain electrical signals.[1][2][3]

What is the Nernst Equation?

The Nernst equation defines the electrical potential that must exist across a membrane to exactly balance the concentration gradient of a particular ion. In mathematical form:[4]

E = (RT/zF) × ln([ion]out/[ion]in)

Where:

• E = equilibrium potential (in volts)
• R = universal gas constant (8.314 J·K⁻¹·mol⁻¹)[5]
• T = temperature in Kelvin[5]
• z = valence (charge) of the ion (+1 for Na⁺, +2 for Ca²⁺, -1 for Cl⁻)[5]
• F = Faraday's constant (96,485 C·mol⁻¹)[5]
• [ion]out = concentration outside the cell[5]
• [ion]in = concentration inside the cell[5]

Simplified Version for Human Neurons

At body temperature (37°C), the equation simplifies to:[6]

Ev = -58.0 × Log([in]/[out])

For negative ions like chloride (Cl⁻), the inside and outside concentrations are switched in the equation.[6]

What Does Equilibrium Potential Mean?

The equilibrium potential is the membrane voltage at which there is no net movement of a particular ion across the membrane. At this point, two forces are perfectly balanced:[7][8]

1. Concentration gradient - the tendency for ions to move from areas of high concentration to low concentration
2. Electrical gradient - the tendency for charged particles to move toward areas of opposite charge[8]

When these forces are equal but opposite, the ion stops moving and reaches equilibrium.[8]

Real-World Example: Potassium

Let's consider potassium (K⁺) ions, which are highly concentrated inside neurons:

• Inside concentration: ~140 mM[1]
• Outside concentration: ~5 mM[1]

Using the Nernst equation, potassium's equilibrium potential is approximately -90 mV. This means that when the membrane potential reaches -90 mV, potassium ions stop flowing despite the large concentration gradient.[1]

Why the Nernst Equation Matters in Neuroscience

1. Resting Membrane Potential

The resting potential of neurons (typically around -70 mV) is heavily influenced by potassium's equilibrium potential since the membrane is most permeable to K⁺ at rest.[2][9]

2. Action Potential Dynamics

During action potentials, different ions become dominant:

• Sodium equilibrium potential: ~+60 mV[10]
• Calcium equilibrium potential: varies with concentration[1]

3. Predicting Ion Movement

By comparing the current membrane potential to an ion's equilibrium potential, we can predict which direction that ion will flow:[10]

• If membrane potential is more negative than equilibrium potential → ion moves into cell
• If membrane potential is more positive than equilibrium potential → ion moves out of cell

Electrochemical Driving Force

When the membrane potential differs from an ion's equilibrium potential, there's an electrochemical driving force:[11]

ΔV = Vmem - Erev

This driving force determines the strength and direction of ion flow across the membrane.[11]

Limitations and Extensions

Goldman-Hodgkin-Katz Equation

While the Nernst equation works for single ions, real neurons have multiple permeable ions. The Goldman equation extends this concept by considering all permeable ions simultaneously:[6][5]

Em = (RT/F) × ln((PK[K⁺]out + PNa[Na⁺]out + PCl[Cl⁻]in)/(PK[K⁺]in + PNa[Na⁺]in + PCl[Cl⁻]out))

Where P represents the permeability of each ion.[6]

Active Transport

The Nernst equation assumes passive diffusion only. In reality, active transporters like the sodium-potassium pump also influence membrane potential by moving ions against their concentration gradients.[12][6]

Practical Applications

The Nernst equation helps neuroscientists:

• Calculate reversal potentials for synaptic currents[3]
• Predict drug effects on ion channels
• Understand disease states where ion concentrations are altered
• Design experiments involving ion substitution

The Nernst equation is therefore essential for understanding how neurons generate electrical signals, maintain resting potentials, and respond to stimuli - making it one of the most important equations in neuroscience.[9]