Figure 2. Single molecule enzymology. The most obvious feature of biochemical processes is their stochastic nature. This implies that any biochemical kinetics usually studied in bulk experiments on a large ensemble of molecules can also be cast in terms of probabilities.39 Here, we give a quick overview of the information contained in such statistical distributions. (A) Three examples of statistical distributions (experimental histograms and corresponding probability density functions) obtained for typical bio-chemical processes. From left to right: 1) Single exponential distribution characteristic of one single limiting step with a rate k1. 2) Two-dimensional exponential characteristic of two rate-limiting steps with rate k1 and k2 respectively. 3) Gaussian-like distribution characteristic of several limiting steps with comparable rates (from k1 to kn with k1 ≈k2 ≈… ≈kn). In a typical experiment, hundreds of events (i.e. hundred of single-molecule traces) are needed to build such histograms and get a reliable description of the bio-chemical reactions. (B) Left panel: A theoretical single-molecule extension vs. time trace (e.g DNA extension vs. time trace). This example shows two different events (different DNA extensions) with two different characteristic times t1 and t2. Right panel: The time distribution for t1 (that would be obtained from different molecules) shows a two-dimensional profile. Changing the substrate concentration (e.g., ATP) dramatically affects the shape of the distribution (different colors corresponding to four different substrate concentrations). This behavior is typical of a Michaelis-Menten kinetic.40 In contrast, the distribution of time t2 shows a Gaussian-like behavior that does not depend on the substrate concentration. Such a distribution could be obtained when the transition from two enzymatic forms (say E and E’) occurs through a large number of irreversible rate-limiting steps.