Kinetic proofreading fidelity-throughput tradeoff ($F=\frac{a+m}{b+m}\frac{c+V}{d+V}$)

In a generic two-stage selection model with correct and incorrect dissociation rates $a<b$ and $c<d$, the displayed error ratio increases with either common forward rate. Slow forward transitions allow rejection at both stages, approaching discrimination $(a/b)(c/d)$, but zero forward rate gives zero output. A high-yield window can instead lie between well-separated correct and incorrect rejection rates. A finite useful optimum needs a throughput or yield objective as well as an error ratio.