# Two important consequences from the mm equation i km

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Unformatted text preview: nten equation, The basic equation of enzyme kinetics. Two important consequences from the MM equation: (i) KM is the substrate concentration at which the reaction velocity is half maximal. (ii) When [S]<<KM: vo = Vmax[S]/KM Summary of special positions on the Michaelis-Menten graph vo = Vmax[S]/(Km + [S]) (The “MM Equation”) KM and Vmax are the quantities of interest which capture the character of the catalysis of substrate S by enzyme E Lehninger f06.12, 4th ed. Lineweaver-Burk plot Start from: Invert the MM eqn: vo = Vmax[S]/(KM + [S]) (I.e. the MM Eqn = VVP 12-25) 1/vo = (KM/Vmax)(1/[S]) + 1/Vmax Then, this is the Lineweaver-Burk plot (VVP Eq. 12-29) with ● 1/[S] as the independent variable, and ● 1/vo as the dependent variable. This equation describes a straight line with: ● Slope: (KM/Vmax) ● Intercept on the y-axis : 1/Vmax ● Intercept on the 1/[S] axis: -1/KM. vo VVP Fig 12-3 Michaelis-Menten Graph VVP Fig 12-4 Lineweaver-Burk Plot Michaelis-Menten and Lineweaver-Burk Equations # 1 (No inhibitor present) Competitive Inhibition Inhibitor and Substrate compete for the Active Site KI is the quantity of interest: it captures the inhibition power of inhibitor I for the particular reaction catalyzed by enzyme E. Ki = [E][I] / [EI] (VVP Eq. 12-30) Hence: the SMALLER the Ki, the BETTER the inhibitor! Here: I = Competitive Inhibitor EI = Enzyme-Inhibitor Complex S = Substrate E = Enzyme P = Product ES = Michaelis complex Competitive Inhibition MM equation: vo = Vmax[S]/(αKM + [S]) Where: α = 1 + [I]/KI and KI = ([E][I])/[EI] LB equation: 1/v0 = (αKM /Vmax) (1/ [S]) + 1/ Vmax VVP4e Fig 12-7 Michaelis-Menten Graph Measure data for increasing values of [I] You don’t know α yet…. You get α from the intercept in the LB plot on the right VVP4e Fig 12-8 Lineweaver-Burk Plot Intercept on x-axis: 1/[S] = -1/(αKM) Since KM is known, α can be calculated. Then with the definition of α and the known [I], KI can be calculated. Michaelis-Menten and Lineweaver-Burk Equations # 2 Competitive Inhib...
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