Current, Channels, and Membrane Potential

Current is the flow of charges, dependent on force divided by resistance.
Voltage (e.g., 1.5 volts from a battery) acts as the force driving the current.
Current is voltage divided by resistance (Ohm's Law).
$Current = \frac{Voltage}{Resistance}$
Higher voltage leads to a greater current, posing electrical hazards.
Increased wire size increases resistance, reducing current and potentially hindering the function of a device like a light bulb.

Cells maintain a separation of charges across their membranes, creating a voltage.
Cell membranes are semi-permeable, composed of phospholipids.
Hydrophobic substances and gases can pass through the membrane.
Hydrophilic substances like sodium cannot directly pass through.
Ion channels, protein structures in the membrane, allow ions like sodium to pass through.
Sodium channels facilitate the movement of sodium from high to low concentration.
Movement of charged ions, such as sodium, constitutes current (sodium current).
More channels lead to better current.
Electrolytes, when in motion, generate current; sodium and potassium are major cations involved.

Cells have a voltage, approximately one-twentieth of a 1.5-volt battery.
Some membranes are impermeable to ions, exhibiting infinite resistance.
Insertion of a protein channel reduces resistance, allowing ion movement and current.
Each ion has a specific channel.
Besides sodium current, potassium and chloride currents also exist.

Diffusion, driven by the concentration gradient (high to low), is a chemical force.
Ions are also subject to electrical force, where positive and negative charges attract.
Electrochemical gradient is the combination of chemical and electrical forces acting on ions.

Typical ion concentrations:
- Sodium: High outside the cell (140 mM), low inside (14 mM).
- Potassium: High inside the cell (140 mM), low outside (5 mM).
Potassium tends to move from high to low concentration.
Movement is also influenced by electrical forces.

Assume a cell starts neutral, with equal positive and negative charges.
Potassium cannot cross the membrane without a channel.
Introducing potassium leakage channels allows potassium to flow outside.
Potassium movement creates a charge imbalance.
- Outside becomes more positive.
- Inside becomes more negative.
This charge distribution generates an electrical force attracting positive potassium back inside.

Initially, the chemical force (diffusion) drives potassium outward.
Potassium moves out via diffusion, creating a growing electrical charge difference across the membrane.
The electrical force pulls potassium back in.
Eventually, the chemical force equals the electrical force, achieving equilibrium.
At equilibrium, equal numbers of ions move in and out; no net movement, no current.

At equilibrium, a stable charge difference exists across the membrane, known as membrane potential.
This is analogous to the potential energy in a battery.
Equilibrium potential ( $E_K$ ) is the membrane potential at which an ion is at equilibrium, with no net movement.
Each ion has its equilibrium potential (e.g., for sodium, potassium, etc.)
The membrane acts like a small battery, with positive and negative charges separated.

Nernst Equation calculates the equilibrium potential for an ion.
$E<em>{ion} = -60 \frac{mV}{z} \log{\frac{[X]</em>{in}}{[X]_{out}}}$
- $E_{ion}$ = Equilibrium potential of ion X (in millivolts).
- z = Charge of the ion (e.g., +1 for sodium and potassium).
- $[X]_{in}$ = Concentration of ion X inside the cell.
- $[X]_{out}$ = Concentration of ion X outside the cell.
Example: Potassium
- $E_K = -60 \frac{mV}{+1} \log{\frac{140}{5}} \approx -87 mV$
- The negative sign indicates the inside of the cell is negative relative to the outside.
If a voltmeter reads -87 mV, it signifies equilibrium for potassium, with no net potassium current.
A reading other than -87 mV indicates disequilibrium and potassium current flow.

If we add sodium leakage channels, sodium moves into the cell (high to low concentration).
Entry of positive sodium ions makes the inside more positive and the outside more negative.
The electrical force then pulls sodium back out.
Equilibrium is reached when these forces balance, and the membrane potential stabilizes.
- $E_{Na} = -60 \frac{mV}{+1} \log{\frac{14}{140}} = +60 mV$

Cells have a mix of sodium and potassium channels.
Hypothetical scenarios:
- More potassium channels.
- More sodium channels.
- Equal numbers of channels (null hypothesis).
If equal numbers of sodium and potassium channels exist, the membrane potential would be the average of their respective equilibrium potentials.