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Studies of nanoscale biological transport often use a mean-fieldapproximation that is exact only when the system is at equilibrium and thereare no interactions between particles on different sites in the network. Weexplore the limitations of this approximation to describe many-particletransport in the context of enzyme function and biological transport networks.Our focus is on three bioenergetic networks: a linear electron transfer chain(as found in bacterial nanowires), a redox-coupled proton pump (as in complexIV of respiration), and a near reversible electron bifurcation network (as incomplex III of respiration and other recently discovered structures). Away fromequilibrium and with typical site-site interactions, we find that themean-field approximation adequately describes linear transport chains. However,the mean-field approximation fails catastrophically to describeenergy-transducing systems, as in the redox coupled proton pump and reversibleelectron bifurcation reactions. The mean-field approximation fails to capturethe essential correlations that are needed to prevent slippage events and toproduce efficient energy transduction.

Biological free energy transduction is an Achilles heel of mean-field transport theory