  Studies of nanoscale biological transport often use a mean-field
approximation that is exact only when the system is at equilibrium and there
are no interactions between particles on different sites in the network. We
explore the limitations of this approximation to describe many-particle
transport 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 complex
IV of respiration), and a near reversible electron bifurcation network (as in
complex III of respiration and other recently discovered structures). Away from
equilibrium and with typical site-site interactions, we find that the
mean-field approximation adequately describes linear transport chains. However,
the mean-field approximation fails catastrophically to describe
energy-transducing systems, as in the redox coupled proton pump and reversible
electron bifurcation reactions. The mean-field approximation fails to capture
the essential correlations that are needed to prevent slippage events and to
produce efficient energy transduction.
