Enzymes are biological catalysts that accelerate chemical reactions necessary for life. Scientists study their performance using enzyme kinetics, which aims to understand how fast an enzyme converts its specific starting material, known as a substrate, into a product. Among the metrics used, $k_{cat}$ is a widely used measure for quantifying an enzyme’s catalytic speed.
Defining the Turnover Number
The parameter $k_{cat}$, formally known as the turnover number, measures an enzyme’s intrinsic speed. It represents the maximum number of substrate molecules that a single enzyme molecule can convert into product per unit of time, typically per second. This measurement is taken when the enzyme is completely saturated with substrate, meaning every active site is constantly occupied and working at full capacity.
A high $k_{cat}$ value signifies a fast-working enzyme. For example, the enzyme carbonic anhydrase, which helps manage carbon dioxide in the body, has a $k_{cat}$ of about $10^6$ per second, meaning it can process one million molecules of substrate every second. Conversely, a low $k_{cat}$ suggests a slower, more deliberate enzyme.
The mathematical definition of $k_{cat}$ is the maximum reaction velocity ($V_{max}$) divided by the total concentration of active enzyme sites ($[E]_t$): $k_{cat} = V_{max} / [E]_t$. Because the total enzyme concentration is in the denominator, $k_{cat}$ is independent of the amount of enzyme used in the experiment, providing a standardized constant. The resulting unit for $k_{cat}$ is inverse time, such as $s^{-1}$.
How $k_{cat}$ is Determined
Calculating $k_{cat}$ requires accurately measuring the maximum reaction velocity ($V_{max}$) and the total active enzyme concentration ($[E]_t$). Determining $V_{max}$ involves running the enzyme reaction at a series of increasing substrate concentrations while keeping the enzyme concentration constant. The reaction rate increases until it reaches a plateau, indicating the enzyme’s active sites are completely saturated.
This data is then plotted on a graph of initial reaction velocity versus substrate concentration, resulting in a curve that asymptotically approaches $V_{max}$. $V_{max}$ represents the maximum rate of product formation extrapolated from this curve. Separately, $[E]_t$ must be precisely determined, which is often the most challenging step.
Researchers typically use specialized techniques like spectrophotometry or mass quantification to measure the concentration of the purified enzyme sample. It is also important to account for the number of active sites per enzyme molecule. For example, a dimeric enzyme with two active sites has an active site concentration double the molar concentration of the enzyme molecule itself. Only when the concentration of these active sites is known can $V_{max}$ be normalized to yield an accurate $k_{cat}$ value.
Contextualizing Enzyme Efficiency
While $k_{cat}$ measures the intrinsic speed of an enzyme when saturated, it does not provide a complete picture of the enzyme’s real-world performance, as most enzymes in a living cell are not saturated with substrate. To understand the enzyme’s true efficiency, scientists combine $k_{cat}$ with another kinetic constant, the Michaelis constant ($K_m$). $K_m$ is the substrate concentration required for the enzyme to reach half of its maximum velocity, and it serves as an inverse measure of the enzyme’s affinity for its substrate.
The ratio of these two constants, $k_{cat}/K_m$, is known as catalytic efficiency or the specificity constant. This ratio measures how effectively an enzyme converts substrate to product when substrate concentrations are low. A high catalytic efficiency is achieved by having a large $k_{cat}$ (fast turnover) and a small $K_m$ (high substrate affinity), meaning the enzyme is both fast and requires very little substrate to operate near its maximum capacity. The catalytic efficiency is considered a better measure of enzyme performance under physiological conditions where substrate is often scarce.
For some enzymes, the $k_{cat}/K_m$ ratio is so high, approaching $10^8$ to $10^9$ per molar per second, that they are deemed “catalytically perfect” or diffusion-limited enzymes. For these enzymes, the chemical conversion step is so rapid that the only factor limiting the reaction rate is how quickly the substrate molecules can physically diffuse through the solution to encounter the enzyme’s active site. Enzymes like triose phosphate isomerase and superoxide dismutase operate at this physical limit, processing the substrate almost every time they encounter it. Understanding this combined ratio is essential for comparing different enzymes or assessing an enzyme’s preference for various substrates, providing a complete picture of its biological function.