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During the transcription elongation cycle (TEC), RNA polymerases (RNAPs) recognize the template DNA and catalyse the chemical reaction to add the incoming nucleotide to the growing RNA chain. Additionally, RNAPs maintain fidelity via proofreading, which include backtracking and cleavage of the misincorporated nucleotides. This chapter discusses the atomistic mechanism and kinetics at each step of the TEC and proofreading of various RNA polymerases, i.e. viral, bacterial, and eukaryotic, examined by computer simulation at the quantum and classical mechanics level. It also covers the construction of a kinetic network model of the entire TEC, which combines the results of these kinetic studies.

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