Negative power-law correlation
between kcat,C and kcat,C/KC is not supported by the
extended data set. In the model diagrammed
in panel A, CO2-specific Rubiscos have low barriers to
enolization and CO2 addition (first effective carboxylation
barrier ΔG1,C), but lowering the
first effective barrier necessarily increases the second effective
barrier (ΔG2,C), reducing kcat,C. In this view, stabilizing the first carboxylation
TS also enhances selectivity but also slows carboxylation (Figure S2). ΔG1,C and ΔG2,C should be negatively
correlated, which would manifest as negative power-law correlation
between kcat,C and kcat,C/KC under certain assumptions
(Supporting Information). (B) The extended
data set does not evidence the expected correlation (for Form I enzymes, R = 0.02 and p = 0.8). While previous analyses
gave an R of approximately −0.9,6 the 95% confidence interval for R now includes 0.0. Restricting our focus to particular physiologies
like C3 plants does not result in the expected correlation.