I'm reading Medical Physiology by Boron and Boulpaep (a really terrific book). In the chapter Electrophysiology of the Cell Membrane, section Membrane Potential Is Generated by Ion Gradients, Not Directly by Ion Pumps, the text reads:
It may seem that the inside negative Vm originates from the continuous pumping of positive charges out of the cell by the electrogenic Na-K pump. The resting potential of large cells -- whose surface-to-volume ratio is so large that ion gradients run down slowly -- is maintained for a long time even when metabolic poisons block ATP-dependent energy metabolism. This finding implies that an ATP-dependent pump is not the immediate energy source underlying the membrane potential.
I totally get the main takeaway, that Vm results from the net accumulation of ion gradients, rather than the immediate consequences of the ion pumps. But I'm unclear on the phrase large cells -- whose surface-to-volume is so large that ion gradients run down slowly.
Presumably a cell with a large surface-to-volume ratio, like a long thin neuron, would have many ion channels which leak constitutively. So I'd expect the net ion conductance to be high, and gradients would run down quickly. But that contradicts the book's run down slowly point, so I'm confused.
Does passive diffusion play a role here? A long, thin cell would have slow passive ion diffusion, so is that why Vm would run down slowly?
Am I overthinking this?
What is the authors' point here?