Membrane Potential: A Critical Reassessment of Pump Theory and an Electrostatic Adsorption Model

The membrane pump theory (MPT) attributes the resting membrane potential of neurons to ionic diffusion driven by transmembrane concentration gradients, maintained by the Na,K-ATPase. Despite decades of dominance, this model harbours fundamental thermodynamic, kinetic, and geometric inconsistencies that have remained unaddressed in mainstream biophysics. We present a systematic quantitative critique across five independent axes: (1)~the electrostatic force exceeds the diffusive force by $\sim$300-fold under physiological conditions; (2)~the peri-axonal space contains 10--100$\times$ fewer ions than required by channel-based models; (3)~the Na,K-ATPase carries an energy deficit of $\sim$26\% per cycle and operates 5000$\times$ too slowly to compensate measured leak fluxes; (4)~the Nernst and Goldman--Hodgkin--Katz equations are applied outside their domain of validity; and (5)~cell geometry invalidates plane-membrane approximations. In contrast, direct experimental evidence (Tamagawa experiment) demonstrates that a potential of $\approx -40$\,mV arises from fixed negative charges alone, without any ionic gradient. We formalise this result within a Poisson--Boltzmann/Grahame electrostatic framework, supplemented by Ling's ion adsorption model and Manoj's murburn concept, and obtain $\Delta\psi \approx -65$ to $-85$\,mV from first principles. Four specific experimental predictions distinguish the model from MPT.