Before revision:  We present a rigorous analytical treatment of the  steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .
After revision:  We present a rigorous analytical treatment of the steady-state kinetic equations including higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs .