= Carrier-turnover saturation of passive transport
{title2=$J=C(s_e-s_i)/(As_e+D)$}
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>.
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