Alternating-access carrier transport

In an alternating-access model a protein binding site faces either side of a membrane; both empty and substrate-bound carriers can switch orientation. Mass-action binding on each side and conformational transition rates give a four-state carrier cycle coupled to two free-substrate pools. Conservation counts all four carrier states as one protein each and counts bound substrate with the free-substrate pools. Equal source and sink fluxes preserve the total substrate while maintaining throughput.

With fixed interior substrate and finite carrier protein, symmetric alternating-access kinetics produce a monotone concave transport curve of the displayed form, with $A,C,D>0$. The flux reverses at equal free concentrations and approaches the finite limit $C/A$ for abundant exterior substrate. Its plateau reflects finite carrier abundance and finite turnover, rather than unlimited transport proportional to the concentration difference. The protein total multiplying the flux is distinct from the total substrate.