Sodium Influx and the Positive Charge Inside a Membrane During an Action Potential

Understanding the Core of Neuronal Excitability

During an action potential, one of the most fundamental transformations occurs in the neurons: the reversal of the cell's membrane potential from negative to positive, driven by the influx of sodium ions (Na ). This process is crucial for the transmission of signals throughout the nervous system.

Resting Membrane Potential

Before an action potential, the neuron maintains its resting membrane potential at about -70 millivolts (mV). This stable state is maintained by the sodium-potassium pump (Na /K ATPase), which transports three sodium ions outside the cell for every two potassium ions inside, along with the selective permeability of the membrane to specific ions.

Depolarization Phase

Depolarization, or the phase when the neuron becomes less negative, initiates when a sufficient stimulus causes voltage-gated sodium channels to open. Sodium ions inflow into the cell, which results in a rapid rise in the membrane potential. Initially, the membrane potential may rise to around -55 mV, marking the beginning of the depolarization phase.

Further Depolarization

As more voltage-gated sodium channels open and sodium continues to flood into the cell, the membrane potential can rise rapidly, often reaching a peak of around 30 mV. This peak marks the peak of the action potential, during which the neuron is at a positive charge.

Repolarization and Hyperpolarization Phases

After reaching the peak, the sodium channels actively close, and voltage-gated potassium channels open, allowing potassium ions (K ) to flow out of the cell. This repolarizes the membrane, bringing it back to its resting state at about -70 mV.

If the efflux of potassium ions continues, the membrane potential can become more negative than the resting potential, a phenomenon referred to as hyperpolarization.

The Cable Theory: For a deeper dive into the mathematical models and cable theory that underlie these processes, one can explore the Neuronal Cable Theory. Key to understanding the mathematical calculations is the equation that describes the propagation of electrical signals through axons, which often involves complex interactions between membrane potential and ionic currents.

Cable Theory Equation: The fundamental equation used in cable theory, often referred to as the cable equation, can be described as:

τV/t L2V/x2 R0V

Here, τ is the time constant, L2 is the axial resistance, and R0 is the resistance across the membrane. For more detailed studies, exploring resources like Nrn_LN3.pdf can provide valuable insights.

In conclusion, the positive charge inside the membrane during an action potential is primarily due to the influx of sodium ions through voltage-gated channels, which shifts the membrane potential from negative to positive.

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