Biocem 5.3 PDF - Enzyme Kinetics

# Graphical Representations of Enzyme Kinetics ## Introduction The Michaelis-Menten equation can be graphed directly by plotting reaction velocity ($V_o$) as a function of substrate concentration [S]. The Michaelis-Menten parameters may be difficult to discern from this graph, and it is often conve...

# Graphical Representations of Enzyme Kinetics ## Introduction The Michaelis-Menten equation can be graphed directly by plotting reaction velocity ($V_o$) as a function of substrate concentration [S]. The Michaelis-Menten parameters may be difficult to discern from this graph, and it is often convenient to use a Lineweaver-Burk plot instead. This is a double reciprocal plot in which $1/V_o$ is plotted as a function of $1/[S]$ to yield a straight line. Some enzymes do not follow Michaelis-Menten kinetics. Many enzymes exhibit cooperativity and follow Hill kinetics, which yield a sigmoidal (s-shaped) curve rather than a hyperbolic curve. This lesson describes several graphs associated with enzyme kinetics and how these plots can be used to determine important enzyme parameters. ## 5.3.01 Michaelis-Menten Plots To interpret experimental kinetics data, scientists often plot the data on a graph. The Michaelis-Menten plot, which compares reaction velocity $V_o$ on the y-axis against substrate concentration [S] on the x-axis, shares many features with the binding curves introduced in Concept 3.1.03 (Figure 5.13). Both plots are hyperbolic, and both plots feature a rapid rise followed by a plateau as the protein sample becomes saturated. This concept discusses the generation of Michaelis-Menten plots and how they can be used to find the kinetic parameters defined in Lesson 5.2. ## 5.3.02 Lineweaver-Burk Plots Before computers, the fitting of enzyme kinetics data to a Michaelis-Menten curve was difficult. Even with computers, a Michaelis-Menten curve can be difficult to interpret visually because the velocity only ever approaches (but never reaches) $V_{max}$. Several transformations of the Michaelis-Menten equation have been proposed that linearize the data, making the data both easier to fit as well as easier to interpret and analyze (Figure 5.21). The Lineweaver-Burk equation is one of the most common linearizations of the Michaelis-Menten equation. Its corresponding plot results in recognizable data points (i.e., the y- and x-intercepts) that relate to the values of $V_{max}$ and $K_M$, and its slope is related to the $V_{max}/K_M$ ratio. Consequently, many questions on the exam that involve enzyme kinetics data present Lineweaver-Burk plots as opposed to traditional Michaelis-Menten plots. ## 5.3.03 Cooperative Enzymes As discussed in Concept 3.1.04, cooperativity in proteins occurs if the binding of one ligand causes a conformational change that influences the protein's ability to bind subsequent ligands. Enzymes can show cooperativity if the binding of one substrate affects that enzyme's ability to bind a second (or third, or fourth) substrate molecule. Enzymes typically show cooperativity either by binding multiple copies of the same substrate or by binding multiple different substrates at the same time (e.g., a bisubstrate enzyme that forms a ternary complex; see Concept 4.3.05). The exam focuses primarily on binding to multiple copies of the same substrate, so that behavior is the focus of this lesson. Enzymes that bind multiple copies of the same substrate usually have multiple catalytic domains. Typically, this occurs in multimeric complexes (e.g., dimers, trimers). The Michaelis-Menten plots for cooperative enzymes change in ways like those described in Concept 3.1.04. In positive cooperativity (i.e., binding of the first substrate facilitates binding subsequent substrates, Hill coefficient n > 1), the Michaelis-Menten curve becomes sigmoidal (i.e., S-shaped). In negative cooperativity (i.e., binding the first substrate hinders binding to subsequent substrates, 0 < n < 1), the plot shows a sharp initial rise followed by a more gradual increase toward $V_{max}$ (Figure 5.26). The Lineweaver-Burk plot also changes (from linear to nonlinear), although interpretation of cooperativity in Lineweaver-Burk plots is rarely required by the exam.