Biochemistry 5.2 Michaelis-Menten Parameters PDF

Michaelis-Menten Parameters Introduction In addition to its dependent and independent variables (ie, V0 and [S], respectively), the Michaelis-Menten equation involves two parameters that are constant within an experiment: Vmax and KM. As described in Concept 5.1.02, Vmax is related to the catalytic...

Michaelis-Menten Parameters Introduction In addition to its dependent and independent variables (ie, V0 and [S], respectively), the Michaelis-Menten equation involves two parameters that are constant within an experiment: Vmax and KM. As described in Concept 5.1.02, Vmax is related to the catalytic rate constant kcat, and kcat can be further combined with KM to form a new constant that describes an enzyme's intrinsic catalytic efficiency. This lesson explains the Michaelis-Menten parameters, their derived constants, and what these values reveal about an enzyme's properties. 5.2.01 The Michaelis Constant (KM) Kd and KM are both constants that have units of concentration (eg, millimolar [mM]). Although the Michaelis constant KM is not a true binding constant, it can be used to describe the affinity of an enzyme for its substrate. Just as Kd indicates the ligand concentration at which half the proteins in a solution are bound, analysis of the Michaelis-Menten equation demonstrates that if the substrate concentration [S] equals the KM value, then the reaction proceeds at half-maximal velocity (ie, ½Vmax): 𝑉max [S] 𝑉0 = 𝐾M + [S] Given: [S] = KM 𝑉max ⋅ 𝐾M 𝑉0,[S]=𝐾M = 𝐾 M + 𝐾M 𝑉max ⋅ 𝐾M = 2𝐾M 𝑉max = 2 1 𝑉0,[S]=𝐾M = 𝑉max 2 An extension of this relationship can estimate V0 as a percentage of Vmax by expressing [S] as a multiple (n) of KM: Given: [S] = n⋅KM 𝑉0,[S]=𝑛𝐾𝑀 𝑉max ⋅ 𝑛𝐾 M = 𝐾M + 𝑛𝐾 M 𝑉max ⋅ 𝑛𝐾 M = (1 + 𝑛) 𝐾M 𝑉max ⋅ 𝑛 = 1+𝑛 𝑉0,[S]=𝑛𝐾𝑀 𝑛 = ⋅𝑉 𝑛 + 1 max  Chapter 5: Enzyme Kinetics Such that when 1 [S] = 1 𝐾 M, 𝑉 0 = 𝑉max 2 2 [S] = 2 𝐾 M, 𝑉 0 = 𝑉max 3 3 [S] = 3 𝐾 M, 𝑉 0 = 𝑉max 4 Because reaction velocity is proportional to the amount of enzyme bound to substrate, this also means that half the enzymes in solution are bound to substrate under experimental conditions when [S] = KM, and two thirds of the enzymes in solution are bound when [S] = 2 KM. As [S] approaches infinity, the enzymes become fully bound (ie, saturated), and V0 approaches Vmax. The relationship between the KM value and affinity is inverse. A small KM value means that only a small concentration of substrate is needed to reach half-maximal velocity, and therefore the enzyme has a high affinity for its substrate. In contrast, a large KM value means a large concentration of substrate is needed to reach half-maximal velocity, and therefore the enzyme has a low affinity for its substrate (Figure 5.8). This definition of KM—that it equals the substrate concentration that corresponds to half-maximal velocity—is used even for enzymes that do not follow conventional Michaelis-Menten kinetics (eg, cooperative enzymes; see Concept 5.3.03). 210  Chapter 5: Enzyme Kinetics Figure 5.8 KM is a measure of an enzyme's affinity for its substrate. 5.2.02 Turnover Number (kcat) and Maximum Reaction Velocity (Vmax) Maximal Reaction Velocity (Vmax) Vmax is the maximal reaction velocity that a given amount of enzyme can achieve within a set of experimental conditions. It is measured in units of concentration of product produced per unit time (eg, micromolar per minute [μM/min]). This velocity is only achieved if the enzyme is saturated with substrate. In other words, if an enzyme is operating at its Vmax, then all enzyme active sites are bound to (and acting on) substrate (Figure 5.9). 211  Chapter 5: Enzyme Kinetics Figure 5.9 Vmax is achieved when all enzyme molecules are bound to substrate (ie, enzyme is saturated). Experiments can be performed to determine Vmax. However, Vmax is also an extensive property, which means that it depends on the amount of enzyme used in an experiment. An increased enzyme concentration corresponds to an increased Vmax. Despite this, scientists often want to describe enzyme properties in ways that are intrinsic to the enzyme itself and not dependent on the amount used in an experiment. Therefore, the measured Vmax is often converted into the intensive variable kcat. Turnover Number (kcat) As described in Lesson 5.1, the reaction velocity (ie, reaction rate) can be described as a rate law that multiplies the concentration of the enzyme-substrate complex by the catalytic rate constant: 𝑉0 = 𝑘cat [ES] Because maximal reaction velocity is reached when all enzyme molecules (ie, Etot) are saturated with substrate (ie, [ES] = [Etot]), kcat can be related to the measured Vmax parameter through the equation: 𝑉max = 𝑘 cat[Etot ] Rearranging this equation to solve for kcat yields: 𝑉max 𝑘cat = [Etot ] Like other first-order rate constants, kcat has units of reciprocal time (eg, min−1, s−1). The catalytic rate constant kcat describes how many substrate molecules an enzyme can convert to product (or "turn over") per unit time, assuming the enzyme is in saturating substrate conditions. For this reason, kcat is also known as the enzyme's turnover number (Figure 5.10). 212  Chapter 5: Enzyme Kinetics Figure 5.10 The turnover number (kcat) is the number of reactions catalyzed per enzyme per unit time. 5.2.03 Catalytic Efficiency (kcat/KM) Catalytic Efficiency The Michaelis constant (KM) and the turnover number (kcat) provide two separate intensive parameters to describe an enzyme's ability to catalyze chemical reactions. To facilitate the comparison of different isozymes (ie, different enzymes that catalyze the same reaction), these parameters can be combined into a single constant called the enzyme's catalytic efficiency, also sometimes known as the specificity constant. The catalytic efficiency of an enzyme is calculated by dividing the enzyme's kcat value by its KM value. As kcat increases (meaning an enzyme converts more substrates per unit time when saturated), the catalytic efficiency also increases. As KM decreases (meaning less substrate is needed to reach half-maximal velocity), catalytic efficiency also increases (Figure 5.11). Because of these characteristics, catalytic efficiency is a succinct way to describe the combined effects of both kinetic parameters with one value. Figure 5.11 The catalytic efficiency of an enzyme. The catalytic efficiency can also be thought of as being similar to a rate constant when substrate concentrations are well below the KM value. If [S]