Enzymatic Kinetics
Enzymes are biological macromolecules vital to all life processes because they facilitate specific chemical reactions. They are fascinating molecules for a variety of reasons:
First, enzymes often exibit high specificity to their physiological substrates. Second, the in vivo activity of enzymes can often be finely tuned through various regulation mechanisms such as allosteric control. Third, the rate enhancements by enzymes are incredibly high compared to the un-catalyzed reaction. Most chemical reactions, vital for life, would simply not occur without the catalysis of the corresponding enzymes. Therefore, it is easy to understand why the quest to understand how enzymes work continues to attract the fascination of enzymologists.
It has been well established that it is the dynamic motion (rather than just static structures) of the whole enzyme that contributes to its biological function. While much has been learned from x-ray crystallography and NMR spectroscopy, which provide detailed information about the static geometry of enzymatic active sites, an enzymologist's dream arguably still is a precise movie of enzymatic catalysis.
Recent advances in single-molecule enzymatic assays have profoundly changed how biochemical reactions are studied. Through the removal of ensemble averaging, the distributions and fluctuations of molecular properties can be characterized, transient intermediates identified, and catalytic mechanisms elucidated.
Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revistited
The Michaelis-Menten equation, first reported in 1913, has been an essential tool for understanding enzyme kinetics ever since. It provides a highly satisfactory description for kinetics of large ensembles of enzyme molecules.
 , 
The Michaelis-Menten equation  gives explicitly the hyperbolic dependence of the enzyme velocity v on substrate concentration [ S ] in an ensemble experiment, where KM =(k-1+k2)/k1 is the Michaelis constant, [E]T = [E] + [ES] is the total enzyme concentration, and vmax is the maximum enzyme velocity.
We have re-examined the Michaelis-Menten formalism by observing enzymatic turnover of a ß-galactosidase molecule at the single molecule level, and explored the equation's microscopic underpinnings.
Distinctly different from ensemble experiments, a single-molecule turnover experiment records the stochastic time trace of repetitive reactions of an individual enzyme molecule. We monitor long time traces of enzymatic turnovers for individual b -galactosidase molecules by detecting one fluorescent product at a time (bottom), from which the probability density of the waiting time t for an enzymatic reaction to occur, f (τ), can be determined.
By varying concentrations of substrate molecules, we found that, at high substrate concentrations, short waiting times tend to be followed by short ones, and long by long. Such a molecular memory phenomenon is characterized by clusters of turnover events separated by periods of low activity. The difference 2D histogram (c) between the 2D joint probability distributions of adjacent waiting times (a) and waiting times with a large separation (b) reveals that long waiting times tend to be followed by a long ones, and a short waiting times tend to be followed by short ones (below).
|
