Kcat Equation: A Simple Guide to Measuring Enzyme Efficiency

In the world of biochemistry, knowing that a reaction is “fast” isn’t quite enough. To truly understand a biological catalyst, we need to know exactly how hard a single molecule of that enzyme is working. That is where the K_cat equation comes in.

K_cat is a parameter that measures an enzyme’s catalytic efficiency. The K_cat value represents the number of substrate molecules an enzyme can convert into a product per unit of time when fully saturated with substrates. K_cat is also referred to as the turnover number or catalytic constant.

How to calculate Kcat

To calculate K_cat, two other parameters are needed: V_max and [E]. V_max is the maximum velocity of the enzyme-catalyzed reaction when the enzyme is saturated with substrates, while [E] represents the total concentration of active enzyme.

$$Kcat = {{Vmax} \over [Et]}$$

Kcat units:  S^-1

V_max can be determined experimentally by plotting the initial velocity (v) of the reaction against the substrate concentration ([S]) and finding the asymptotic value on the y-axis. Alternatively, Vmax can be calculated using the Michaelis-Menten equation, which describes the relationship between V, [S], V_max, and K_m.

Km is another parameter that measures the enzyme’s affinity for its substrate. The Michaelis-Menten equation is:

$$v = {{Vmax [S]} \over Km+[S]}$$

By rearranging the equation, we can solve for V_max:
$$Vmax = {{v(Km+[S])} \over [S]}$$
Once we have V_max, we can plug it into the K_cat equation and obtain the value of K_cat.

Why Kcat is important

K_cat is crucial as it indicates the enzyme’s inherent catalytic ability, regardless of enzyme concentration, unlike V_max, which varies with enzyme quantity. Thus, K_cat is a more dependable and standardized measure of enzyme efficiency.

Kcat can also be used to calculate the catalytic efficiency of the enzyme, which is defined as the ratio of K_cat to K_m:
$$Catalytic efficiency = {{Kcat} \over Km}$$
This efficiency shows how effectively the enzyme uses its substrate at low concentrations. A higher catalytic efficiency allows the enzyme to achieve a high reaction rate with minimal substrate, which is ideal for many biological processes.

Examples of Kcat values

Different enzymes have different K_cat values depending on their structure, function, and substrate specificity. Some examples of Kcat values for various enzymes are:

• Carbonic anhydrase: 10⁶ s^-1
• Acetylcholinesterase: 10⁴ s^-1
• Hexokinase: 10² s^-1
• DNA polymerase: 10 s^-1

In this example, the values demonstrate that carbonic anhydrase is the fastest enzyme, converting one million carbon dioxide molecules into bicarbonate per second. DNA polymerase is the slowest, converting only 10 nucleotides into DNA per second.

Reference:

1. Eisenthal, R., Danson, M. J., & Hough, D. W. (2007). Catalytic efficiency and kcat/KM: a useful comparator? Trends in Biotechnology, 25(6), 247–249. https://doi.org/10.1016/j.tibtech.2007.03.010
2. Bauer, C., Osman (2001). A unified theory of enzyme kinetics based upon the systematic analysis of the variations of kcat, KM, and kcat/KM and the relevant ΔG0≠ values. Biochemical Pharmacology, 61(9), 1049–1055. https://doi.org/10.1016/s0006-2952(01)00579-2
3. https://www.nature.com/articles/s41929-022-00798-z
4. Biorender