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In chemistry, turnover number (TON) refers to the average number of cycles a catalyst can perform before decomposition. TON is inversely proportional to catalyst loading; lower TON means more catalyst is required to transform a given amount of substrate.

For fans of statistics and probability, determining the distribution of molecular turnover numbers among the entire ensemble of catalyst molecules is an interesting and non-trivial problem. An average over all the molecular TONs must give the macroscopically observed TON, but it's extremely unlikely that every single catalyst molecule performs exactly the macroscopically observed number of turnovers then just dies. There is some distribution of molecular turnovers with its mean at the macroscopically observed TON. But what is the shape of this distribution? Is it time-dependent? What factors govern its shape? Questions abound.

To the crudest approximation, the macroscopic TON depends in some way on the relative rates of catalyst decomposition and turnover. Catalysts that have extremely low rates of decomposition, like enzymes, have massive turnover numbers. Similarly, catalysts that perform their cycles quickly (relative to the rates of any decomposition pathways) also have large TONs. Catalysts with multiple decomposition pathways, on the other hand, often have low turnover numbers. Transitional metal catalysts exhibit a range of TONs that extends over multiple orders of magnitude: numbers from 20 to 2,000,000 and beyond have been reported.

In biochemstry, the use of "turnover number" is slightly different- it is the amount of substrate that an enzyme can convert to product per unit time.

Turnover number is notated as kcat.  It can be calculated with the formula kcat=Vmax/[E], where [E] is the concentration of enzyme, and Vmax is the maximum rate of conversion (generally found when [S] >>> [E]).  kcat has units of inverse seconds (s-1); a certain enzyme that has a kcat value of 10,000 means that each enzyme can convert 10,000 molecules of substrate per second.

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