Table 1 Reaction and rate equations of the biphasic two-step conformational change model

From: A cysteine-less and ultra-fast split intein rationally engineered from being aggregation-prone to highly efficient in protein trans-splicing

Reaction

Rate equation

\(\left[N\right]+[C]\begin{array}{c}{k}_{a}\\ \rightleftharpoons \\ {k}_{d}\end{array}\left[N\cdot C\right]\begin{array}{c}{k}_{f}\\ \rightleftharpoons \\ {k}_{u}\end{array}[{NC}]\)

\(\left[C\right]=\left[{C}_{0}\right]-\left[{N\cdot C}\right]-[{NC}]\)

\(\frac{d[{N\cdot C}]}{{dt}}={k}_{a}C\left[{C}_{0}\right]-\left({k}_{a}C-{k}_{d}-{k}_{f}\right)\left[{N\cdot C}\right]-({k}_{a}C-{k}_{u})[{NC}]\)

\(\frac{d[{NC}]}{{dt}}={k}_{f}\left[{N\cdot C}\right]-{k}_{u}[{NC}]\)