The turnover number, symbolized as $k_{cat}$, is a fundamental property in biochemistry used to compare the efficiency of different enzymes. It is a rate constant that describes the maximum number of chemical conversions an enzyme can execute. Calculating $k_{cat}$ requires the precise measurement of two experimental values: the maximum reaction velocity and the total concentration of active enzyme molecules.
Defining the Turnover Number
The turnover number, or $k_{cat}$, conceptually represents the maximum number of substrate molecules that a single active site on an enzyme can convert into product per unit of time. This intrinsic rate constant reflects the speed of the chemical conversion step within the overall catalytic cycle. It is a value independent of the amount of enzyme present, providing a true measure of the enzyme’s inherent effectiveness.
When an enzyme is saturated with substrate, the reaction proceeds at its fastest possible rate. The $k_{cat}$ value quantifies this maximum activity at the molecular level. For example, a $k_{cat}$ of $100\,s^{-1}$ indicates that each enzyme molecule is converting 100 substrate molecules to product every second. This value is typically expressed in units of inverse time, such as $s^{-1}$ (per second) or $\min^{-1}$ (per minute).
The magnitude of the turnover number can vary dramatically across different enzymes, reflecting their diverse roles in metabolism. Enzymes involved in highly rapid, non-regulatory processes, like carbonic anhydrase, can boast $k_{cat}$ values exceeding $10^5\,s^{-1}$. Understanding this value provides insight into the speed of the rate-limiting step, which is the slowest step in the enzyme’s catalytic cycle.
Finding Maximum Reaction Velocity
The first experimental value needed to determine the turnover number is the maximum reaction velocity, known as $V_{max}$. This value represents the fastest rate at which a specific amount of enzyme can convert substrate to product when the enzyme is fully saturated. $V_{max}$ is typically measured in units like $\text{moles per minute}$ or $\text{micromoles per second}$.
To find $V_{max}$, a series of initial rate experiments are performed by setting up multiple reaction mixtures, each containing the same concentration of enzyme but increasing concentrations of the substrate. The reaction is started, and the initial velocity ($v_0$) is measured by monitoring the formation of product or the disappearance of substrate over a short period of time. Measuring the initial rate ensures that the substrate concentration has not significantly decreased and that the reverse reaction has not begun.
When the measured initial velocities are plotted against the corresponding substrate concentrations, the resulting graph displays a characteristic hyperbolic curve. As the substrate concentration continues to increase, the curve begins to plateau because nearly all of the enzyme’s active sites are occupied. This plateau represents $V_{max}$, the theoretical maximum velocity that the enzyme can achieve. $V_{max}$ is mathematically extrapolated from the experimental data, often by fitting the data to the Michaelis-Menten equation or by using linear transformations like the Lineweaver-Burk plot.
Measuring Total Active Enzyme Concentration
The second critical component for calculating the turnover number is the total concentration of active enzyme molecules, symbolized as $[E]_T$. This value is the denominator in the $k_{cat}$ equation and is measured in molar units, such as moles per liter ($\text{M}$) or micromolar ($\mu \text{M}$). Simply knowing the total protein concentration is insufficient because not every protein molecule may possess a functional active site.
Accurately determining the concentration of only the active enzyme sites is often the most challenging step in a kinetic study. One common and precise method is active site titration, which uses a specialized molecule known as a tight-binding or suicide inhibitor. This inhibitor is designed to react irreversibly with the enzyme’s active site in a one-to-one stoichiometric ratio. By measuring the amount of inhibitor required to completely stop the enzyme’s activity, researchers can directly determine the number of functional active sites present in the sample.
Another method for enzyme quantification involves spectrophotometric techniques, which relate the enzyme’s concentration to its ability to absorb light at a specific wavelength. Methods like Bradford or UV-Vis spectroscopy can estimate the total protein concentration, which is then often assumed to be the active enzyme concentration for highly purified samples. Regardless of the technique used, the concentration must be expressed in molar units to represent the number of catalytic units available.
Calculating the Final Turnover Number and Interpretation
With the two necessary experimental values—the maximum reaction velocity ($V_{max}$) and the total active enzyme concentration ($[E]_T$)—the turnover number ($k_{cat}$) can be calculated using a straightforward ratio: $k_{cat} = V_{max} / [E]_T$. When $V_{max}$ (concentration per time) is divided by $[E]_T$ (concentration), the concentration units cancel out, leaving the final $k_{cat}$ value in units of inverse time, such as $s^{-1}$.
For example, if an experiment yields a $V_{max}$ of $100\,\mu \text{M/s}$ and the total active enzyme concentration is measured to be $1\,\mu \text{M}$, the $k_{cat}$ is $100\,s^{-1}$. This final result provides a clear, interpretable number: each enzyme molecule is converting 100 substrate molecules every second.
A high $k_{cat}$ value indicates an enzyme that is a very fast catalyst, efficiently converting substrate to product once it is bound to the active site. Conversely, a low $k_{cat}$ suggests that the rate-limiting step in the catalytic cycle is slow, perhaps due to a slow chemical transformation or a slow release of the product. The turnover number is also integrated into a more comprehensive measure of enzyme efficiency known as the specificity constant, which is the ratio of $k_{cat}$ to the Michaelis constant ($K_M$). This ratio, $k_{cat}/K_M$, is often considered the best measure of an enzyme’s overall performance, as it accounts for both the catalytic speed ($k_{cat}$) and the enzyme’s affinity for its substrate ($K_M$).