I am learning membrane transport and learnt that there are 2 gradients that determine passive and active transport.

If the concentration of a cation is higher in the cytoplasm side (hence ions should flow out of the cell passively), but there is higher electrochemical potential in the extracellular side (hence ions should flow into the cell), which side should that ion flow if there is only passive transport?

I know there is Nernst equation for electrochemical potential, but I would like to ask whether there are equations for calculating potential caused by the concentration gradient? Since my thought is by comparing which has the higher potential difference, and deduce which gradient is dominant, eventually deduce the direction of the net passive flow of that ion.

Thank you


All you need is the Nernst equation and the voltage across the membrane.

The answer you get from Nernst is the equilibrium potential for the ion of interest. This is the potential at which the concentration and electrical gradients are exactly equal for that ion. If the voltage across a membrane is at the Nerst potential there is no net passive flow of the ion.

If the voltage is different then the Nernst potential, then the ion moves in the direction that would tend to move the voltage towards the Nernst potential. If the Nernst potential is -90 mV, the membrane potential is -60 mV, and you have a positive charged ion, the ion will tend to move out of the cell because this is what would move it closer to -90 mV.

You can't separate the chemical and electrical gradients and sum them up or anything, the specific way to combine them is given by the Nernst equation. The Nernst equation is not for calculating the electrical potential separately of concentration gradient, it's for calculating the combined result of electrical and chemical gradients. The way to know which way an ion flows is the way I've described it, not by determining which is "dominant".


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