Question

Turnover number \(\left(k_{\mathrm{ca}}\right)\) A. is a ratio of the rate constants for the formation of ES and of product. B. has units of 1/time. C. is inversely related to how fast the reaction is. D. for a mutant enzyme can change without any change in the \(K_{m}\) of the reaction. E. has units of substrate concentration.

Short answer

Based on the analysis of the given statements: Statement A is false. The turnover number (kca) is a measure of enzyme reaction efficiency, not a ratio of rate constants. Statement B is true. The turnover number (kca) has units of 1/time, indicating the number of substrate molecules converted to product molecules per unit time. Statement C is false. The turnover number (kca) is directly related to the reaction rate, not inversely. Statement D is true. The turnover number (kca) and the Michaelis constant (Km) are independent of each other, so a mutant enzyme could potentially change the turnover number without affecting Km. Statement E is false. The turnover number (kca) has units of 1/time, not substrate concentration.

Step-by-step solution

Statement A:

Is a ratio of the rate constants for the formation of ES and of product. This statement is false. The turnover number \((k_{\mathrm{ca}})\), also known as the catalytic rate constant or \(k_{cat}\), is the maximum number of substrate molecules that an enzyme can convert into product molecules per unit time when the enzyme is fully saturated with substrate. It is not a ratio of rate constants but rather a measure of the enzyme reaction efficiency.

Statement B:

Has units of 1/time. This statement is true. The turnover number \((k_{\mathrm{ca}})\) is expressed in units of reciprocal time (e.g., s\(^{-1}\) or min\(^{-1}\)), indicating the number of substrate molecules converted to product molecules per unit time when the enzyme is fully saturated.

Statement C:

Is inversely related to how fast the reaction is. This statement is false. The turnover number \((k_{\mathrm{ca}})\) is directly related to the reaction rate, not inversely. A higher turnover number indicates that the enzyme converts substrate to product more quickly, whereas a lower turnover number signifies a slower reaction rate.

Statement D:

For a mutant enzyme can change without any change in the \(K_{m}\) of the reaction. This statement is true. \(K_{m}\) (the Michaelis constant) and the turnover number \((k_{\mathrm{ca}})\) are independent of each other. A mutant enzyme could potentially change the turnover number without affecting \(K_{m}\), which is a measure of substrate affinity. This suggests that the enzyme's catalytic efficiency may be altered without impacting its affinity for the substrate.

Statement E:

Has units of substrate concentration. This statement is false. As mentioned earlier, the turnover number \((k_{\mathrm{ca}})\) has units of 1/time, not substrate concentration. It reflects the maximum reaction rate achieved under saturating substrate conditions and gives information about the enzyme's catalytic efficiency.

Key concepts

Catalytic Rate Constant

In biochemistry, the catalytic rate constant, often symbolized as \(k_{cat}\) or the turnover number, is a critical parameter indicating the rate at which an enzyme can catalyze a reaction. It tells us how many substrate molecules one enzyme molecule can convert into product molecules per second under optimal conditions—that is, when the substrate concentration is so high that all enzyme active sites are always occupied.

When we analyze enzymes, knowing their \(k_{cat}\) provides insight into their efficiency. An enzyme with a higher \(k_{cat}\) can process substrates more quickly, denoting a highly efficient enzyme. In contrast, a lower \(k_{cat}\) implies a less efficient enzyme that catalyzes the reaction at a slower pace. It's essential to understand that the \(k_{cat}\) does not vary with substrate concentration once the enzyme is saturated; hence, its value represents the intrinsic turnover rate of the enzyme itself.

Enzyme Saturation

Enzyme saturation occurs when every active site of the enzyme molecules is occupied by substrate molecules. At this point, increasing the substrate concentration further will not increase the reaction rate because there are no free active sites left for additional substrate molecules to bind to.

At saturation, the reaction rate has reached its maximum, termed the maximum velocity (\(V_{max}\)). The relationship between substrate concentration and reaction rate is hyperbolic and is best described by the Michaelis-Menten equation. Enzyme saturation is essential in enzyme kinetics because it ensures that the measurement of \(k_{cat}\) reflects the enzyme's maximum catalytic capacity without interference from limiting substrate availability.

Michaelis Constant (Km)

The Michaelis constant, denoted as \(K_{m}\), is a measure used to describe the affinity of an enzyme for its substrate. It is defined as the substrate concentration at which the reaction rate is half of the maximum velocity (\(V_{max}\)). A low \(K_{m}\) value implies high substrate affinity, meaning the enzyme can achieve \(V_{max}\) even at low substrate concentrations. Conversely, a high \(K_{m}\) suggests low substrate affinity, in that higher substrate concentrations are necessary to reach \(V_{max}\).

Understanding \(K_{m}\) helps in determining the efficiency of enzymes in their natural physiological context where substrate concentrations may vary. The Michaelis constant is crucial when comparing the behavior of wild-type enzymes to mutant forms, as any alteration in \(K_{m}\) could imply changes in the enzyme's interaction with its substrate.

Reaction Rate

The reaction rate in biochemistry refers to the speed at which a reaction occurs. For enzyme-catalyzed reactions, it's specifically the rate at which the enzyme converts substrate molecules into product molecules. The rate can be influenced by several factors, including enzyme and substrate concentration, temperature, pH, and the presence of inhibitors or activators.

Enzymes catalyze reactions by lowering the activation energy required, which increases the reaction rate. The reaction rate is initially proportional to the substrate concentration but levels off as the enzyme becomes saturated, leading to a plateau—the maximum reaction rate (\(V_{max}\)). Understanding the factors that affect reaction rate is fundamental to controlling and predicting the outcomes of biochemical reactions.

Substrate Affinity

Substrate affinity is a term used to describe how strongly an enzyme binds to its substrate. It's an essential concept because it determines how likely a substrate molecule is to find and occupy the active site of an enzyme. The stronger the affinity, the more likely an enzyme is to be occupied by the substrate and catalyze a reaction, even at low substrate concentrations.

Substrate affinity can be quantitatively expressed through the Michaelis constant (\(K_{m}\)). Enzymes with a low \(K_{m}\) have high affinity, as they can achieve half the maximum reaction rate at lower concentrations of substrate. This relationship between \(K_{m}\) and substrate affinity is vital when considering the effectiveness of enzymes under physiological conditions, where the substrate might not always be abundant.