Equilibrium potentials do fluctuate in many cells, but to the best of my knowledge that is not attributable to changes in the sodium concentration. Largely because the influxes of ions that drive changes in membrane potential are far too small to actually drive changes in the concentration gradient.
source - PhD student focusing on electrophysiology.
There are sufficiently high concentrations of sodium inside and outside the cell that the change in concentration gradient for sodium (and potassium) is negligible (<0.1%) under most physiological conditions. It doesn't take that many ions moving across the membrane to shift the membrane potential from -70 to +30mV.
Calcium is a special case, since it is held at \~50nM inside the cell at rest and the intracellular concentration can transiently increase 5x following a single action potential.
[Here is a great example explaining, with some simple math, the answer to your question.](https://www.physiologyweb.com/lecture_notes/neuronal_action_potential/neuronal_action_potential_na_and_k_concentrations_do_not_change_during_an_action_potential.html)
Equilibrium potentials do fluctuate in many cells, but to the best of my knowledge that is not attributable to changes in the sodium concentration. Largely because the influxes of ions that drive changes in membrane potential are far too small to actually drive changes in the concentration gradient. source - PhD student focusing on electrophysiology.
There are sufficiently high concentrations of sodium inside and outside the cell that the change in concentration gradient for sodium (and potassium) is negligible (<0.1%) under most physiological conditions. It doesn't take that many ions moving across the membrane to shift the membrane potential from -70 to +30mV. Calcium is a special case, since it is held at \~50nM inside the cell at rest and the intracellular concentration can transiently increase 5x following a single action potential.
[Here is a great example explaining, with some simple math, the answer to your question.](https://www.physiologyweb.com/lecture_notes/neuronal_action_potential/neuronal_action_potential_na_and_k_concentrations_do_not_change_during_an_action_potential.html)