© 2006 Nature Publishing Group http://www.nature.com/naturechemicalbiology Michaelis-Menten is dead, long live Michaelis-Menten! Nils G Walter Modern single-molecule tools, when applied to enzymes, challenge fundamental concepts of catalysis by uncovering mechanistic pathways, intermediates and heterogeneities hidden in the ensemble average. It is thus reassuring that the Michaelis-Menten formalism, a pillar of enzymology, is upheld, if reinterpreted, even when visualizing single turnover events with a microscope focus. The seminal 1913 discovery of Leonor Michaelis and Maud Menten 1 arguably represents the beginning of enzyme kinetics as a system- atic field and remains a pillar of enzymology. Thousands of enzymes have been characterized using the Michaelis-Menten formalism, which describes the rate of multiple enzymatic turn- overs as a function of substrate concentration (Fig. 1). Close to a hundred years of successful, largely undisputed use does not imply, however, that modern insight cannot add exciting new twists. In this issue of Nature Chemical Biology, Sunney Xie and co-workers at Harvard 2 have employed creative single-molecule micros- copy to ask the simple question of whether the Michaelis-Menten formalism is upheld even when visualizing catalysis one substrate molecule at a time. The answer is yes, but the microscopic interpretation changes in light of enzymatic heterogeneity. Michaelis and Menten showed that inver- tase (now known as β-fructofuranosidase), a yeast enzyme central to sugar metabolism that catalyzes the hydrolysis of sucrose into an opti- cally distinct mixture of glucose and fructose (‘invert sugar’), has a characteristic hyperbolic dependence on substrate concentration. Two regimes can be distinguished under condi- tions where substrate is in excess over enzyme (multiple-turnover conditions) (Fig. 1). At limiting (low) substrate concentration, the measured rate constant increases linearly with substrate concentration, indicating that revers- ible substrate binding (k on , k off ) is mostly rate limiting. At saturating (high) substrate concen- tration, the measured rate constant is indepen- dent of substrate concentration and the catalytic turnover (k cat ) becomes fully rate limiting. Applying single-molecule microscopy to β-galactosidase, a bacterial enzyme essential for sugar utilization and a modern enzymological work horse, the Harvard group has now taken a closer look at these two regimes (Fig. 1). A derivative of the enzyme’s lactose substrate yields brief fluorescent bursts upon hydrolytic turnover before the fluorescent product diffuses out of a laser focus. A succession of turnovers by a single immobilized enzyme thus yields a meteor shower of fluorescence bursts. Kinetic information on multiple turnovers by a single enzyme is derived from a large number of wait- ing times between two successive fluorescence bursts. The authors find that the average waiting time of a single enzyme molecule plotted against the inverse of the substrate concentration reca- pitulates the linear Lineweaver-Burke relation- ship observed in an ensemble measurement. This demonstrates that the Michaelis-Menten equation holds even at the single-molecule level. The average waiting time from a large number of single enzyme molecules then is related to the macroscopic turnover rate constant. At low substrate concentration, Xie and co- workers find that a single time constant char- acterizes the waiting times between substrate turnovers of a single enzyme. This implies that the limiting rate constants under these condi- tions, k on and k off , are uniform over long periods of time (Fig. 1). By contrast, at high substrate concentration the waiting times between sub- strate turnovers show an asymmetric probability distribution. This implies that the limiting rate constant under these conditions—the catalytic turnover rate constant, k cat —varies over time for an individual enzyme (Fig. 1). Although the molecular basis for such catalytic heterogeneity is unclear, Xie and co-workers propose that con- formational isomers of the enzyme are the cause. The broad distribution of k cat values (referred to as χ 2 in the context of a single-molecule obser- vation) (Fig. 1) suggests that large numbers of such conformers with highly variable catalytic powers exist for a single enzyme, and intercon- vert only slowly (as compared to the catalytic turnover rate). Such slow interconversion is also referred to as a ‘memory effect’, in the sense that each enzyme molecule has a memory of its conformational state and retains it for some time longer than the turnover time; such single enzymes are described as showing dynamic dis- order, indicating that they display various con- formational states that are not static but slowly interconvert. From the autocorrelation function of the fluorescence bursts observed for single enzymes at high substrate concentration (that is, the correlation of the fluorescence time trace against a time-shifted version of itself), Xie and co-workers were able to extract time constants for these conformational isomerizations, which themselves show a broad distribution ranging from milliseconds to tens of seconds. The good agreement between this distribution and the known range of timescales of conformational fluctuations in proteins 3 further supports the notion that catalytic heterogeneity is caused by (dynamic) conformational heterogeneity. What consequences does all this heterogeneity at the single-enzyme level have for the Michaelis-Menten formalism? The good news is that the Michaelis-Menten equation as a phenomenological description still holds. Yet our interpretation of the extracted k cat rate constant has to be significantly revised. More specifically, the k cat (or, formally, χ 2 ) value derived at saturating substrate concentration turns out to be the weighted harmonic mean of the different catalytic turnover rate con- stants represented in the single enzyme over time. Consequently, the Michaelis constant Nils G. Walter is in the Department of Chemistry at the University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, USA. e-mail: nwalter@umich.edu York, 1999). 5. Gates, K.S., Nooner, T. & Dutta, S. Chem. Res. Toxicol. 17, 839–856 (2004). 6. Lawley, P.D. & Brookes, P. Biochem. J. 89, 127–138 (1963). 7. Takeshita, M., Grollman, A.P., Ohtsubo, E. & Ohtsubo, H. Proc. Natl. Acad. Sci. USA 75, 5983-5987 (1978). 8. Zang, H. & Gates, K.S. Chem. Res. Toxicol. 16, 1539– 1546 (2003). 9. MacLeod, M.C. Carcinogenesis 16, 2009–2014 (1995). 10. Millard, J.T., Spencer, R.J. & Hopkins, P.B. Biochemistry 37, 5211–5219 (1998). 11. Smith, B.L., Bauer, G.B. & Povirk, L.F. J. Biol. Chem. 269, 30587–30594 (1994). 12. Suto, R.K. et al. J. Mol. Biol. 3326, 371–380 (2003). 66 VOLUME 2 NUMBER 2 FEBRUARY 2006 NATURE CHEMICAL BIOLOGY NEWS AND VIEWS