  Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical
processes aided by enzymes. Performance of these enzymes is usually
characterized in terms of their average error rate and speed. However, because
of thermal fluctuations in these single-molecule processes, both error and
speed are inherently stochastic quantities. In this paper, we study
fluctuations of error and speed in biopolymer synthesis and show that they are
in general correlated. This means that, under equal conditions, polymers that
are synthesized faster due to a fluctuation tend to have either better or worse
errors than the average. The error-correction mechanism implemented by the
enzyme determines which of the two cases holds. For example, discrimination in
the forward reaction rates tends to grant smaller errors to polymers with
faster synthesis. The opposite occurs for discrimination in monomer rejection
rates. Our results provide an experimentally feasible way to identify
error-correction mechanisms by measuring the error-speed correlations.
