Polymerases are protein enzymes that move along nucleic acid chains and
catalyze template-based polymerization reactions during gene transcription and
replication. The polymerases also substantially improve transcription or
replication fidelity through the non-equilibrium enzymatic cycles. We briefly
review computational efforts that have been made toward understanding
mechano-chemical coupling and fidelity control mechanisms of the polymerase
elongation. The polymerases are regarded as molecular information motors during
the elongation process. It requires a full spectrum of computational approaches
from multiple time and length scales to understand the full polymerase
functional cycle. We keep away from quantum mechanics based approaches to the
polymerase catalysis due to abundant former surveys, while address only
statistical physics modeling approach and all-atom molecular dynamics
simulation approach. We organize this review around our own modeling and
simulation practices on a single-subunit T7 RNA polymerase, and summarize
commensurate studies on structurally similar DNA polymerases. For multi-subunit
RNA polymerases that have been intensively studied in recent years, we leave
detailed discussions on the simulation achievements to other computational
chemical surveys, while only introduce very recently published representative
studies, including our own preliminary work on structure-based modeling on
yeast RNA polymerase II. In the end, we quickly go through kinetic modeling on
elongation pauses and backtracking activities. We emphasize the fluctuation and
control mechanisms of the polymerase actions, highlight the non-equilibrium
physical nature of the system, and try to bring some perspectives toward
understanding replication and transcription regulation from single molecular
details to a genome-wide scale
