  Biological processes such as DNA replication, RNA transcription, and protein
translation show remarkable speed and accuracy in selecting the right substrate
from pools of chemically identical molecules. This result is obtained by
nonequilibrium reactions that dissipate chemical energy. It is widely
recognized that there must be a trade-off between speed, error, and dissipation
characterizing these systems. In this paper, we quantify the trade-off between
speed, error, and dissipation using tools from mathematical optimization
theory. We characterize the Pareto optimal front for two paradigmatic models of
biological error correction: Hopfield's kinetic proofreading model and a
ribosome model. We find that error correction processes with more proofreading
steps are characterized by better trade-offs. Furthermore, we identify scaling
relations between speed, accuracy, and dissipation on the Pareto front.
