# How to Calculate KCAT and VMAX

Even the smallest of molecules or organisms with quick reproduction times can take a long time to produce what you want to study. For bacteria in a petri dish, the speed of reaction depends upon how much of the reactant there is as well as the presence of enzymes. Whatever the case may be, you can use equations to determine the speed of these biochemical reactions.

## Enzyme kinematics

In chemistry, ​reaction rates​ are described using ​k values​ that measure how fast a reaction occurs from reactants to products. For reactions that use catalysts, biological compounds that speed up reaction rate, the rate, ​kcat​, lets you determine the maximum speed of the reaction. The ​maximum rate of reaction​, ​Vmax​, tells you how many molecules are converted into the product of the reaction when the enzyme fully dissolves itself.

Enzymes achieve these high speeds by lowering the activation energy of a reaction, the amount of energy required for the reaction to occur. When an enzyme bonds to the substrate, the molecule or compounds you are observing, it forms an enzyme-substrate complex. They don't directly affect how much of the reactant or product compounds you have, and they also depend on other factors like concentration of the enzyme, temperature pH and strength between ionic bonds.

## KCAT Equation

Reaction rate lets you write equations to determine how different amounts of reactants lead to how much products you have. For a basic reaction of ​xA + yB → zC​ (that is, converting ​x​ moles of ​A​ with ​y​ moles of ​B​ yields ​z​ moles of ​C​), the rate equation would be

r=k[A]^m\times[B]^n

for the reaction rate ​r,​ rate constant ​k​ and molar concentrations of ​A​ and ​B​ denoted by the brackets. M and ​n​ are exponents that you determine through experiments that measure how fast a reaction occurs. F

For the specific case of an enzyme-catalyzed reaction the initial velocity ​v0​ is

v_0=\frac{k_{cat}}{K_m}

for initial reaction velocity ​v0​. This velocity tells you the rate of catalysis in this ​kcat​ formula. ​Km​ is the ​Michaelis-Menten constant​, which you can either measure experimentally or calculate as the substrate concentration at half of the maximum velocity.

The constant gets its name from the ​Michaelis-Menten equation

v_0=\frac{v_{max}\times[S]}{K_m+[S]}

for substrate concentration ​[S]​ and maximum velocity ​vmax​ tells you how fast an enzymatic reaction. When you calculate ​kcat​, you can also write

v_0=\frac{k_{cat}\times [E]\times [S]}{K_m}

as a general method of reaction rate for concentrations of enzyme and substrate ​[E]​ and ​[S]​, respectively.

## Other KCAT Equation Methods

These different equations let you use the one most appropriate for whatever purpose you need whether it's the rate of bacteria reproduction or the rate of ignition between fuels and gas. You can even use these equations in combining both experimental observations with theoretical models and calculations. You can learn about the significance of the Michaelis Menten equation methods through these different ways of defining reaction rate.

The ​kcat​ equation serves the basis for creating ​bioreactors​. These are systems that let microorganisms grow in an optimum environment, one that can produce as much product as possible. Bioreactors are even used in making fermented foods in some Asian countries.

It's generally very difficult or impossible to determine the meaning of ​Km​ without more information. Scientists use the ratio ​kcat/Km​ to measure how specifically and efficiently an enzyme bonds with a substrate. This ratio, known as the specificity constant ​kSP​, lets you reform the Michaelis-Menten equation as

v=\frac{k_{SP}[S]}{1+\frac{k_{SP}[S]}{k_{cat}}}

to measure more accurate values of ​kSP​.

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