  New advances in nano sciences open the door for scientists to study
biological processes on a microscopic molecule-by-molecule basis. Recent
single-molecule biophysical experiments on enzyme systems, in particular,
reveal that enzyme molecules behave fundamentally differently from what
classical model predicts. A stochastic network model was previously proposed to
explain the experimental discovery. This paper conducts detailed theoretical
and data analyses of the stochastic network model, focusing on the correlation
structure of the successive reaction times of a single enzyme molecule. We
investigate the correlation of experimental fluorescence intensity and the
correlation of enzymatic reaction times, and examine the role of substrate
concentration in enzymatic reactions. Our study shows that the stochastic
network model is capable of explaining the experimental data in depth.
