The Infamous Hyperbolic Equation in Biochemistry

THE INFAMOUS HYPERBOLIC EQUATION IN BIOCHEMISTRY Hyperbolic equations appear in biochemistry in a number of forms. Here are several forms commonly encountered: Binding of O2 to myoglobin: Mb + O2 W MbO2 Velocity of enzyme-catalyzed reaction: E+S WE@S WE+P Vo % [E@S] at all Eo, So Proportion of myoglobin bound to O2 Y = MbO2 -----------Total Mb Vo = Vmax @So ----------------Km + So So where ratio ---------Km + So = = MbO2 ---------------MbO2 + Mb [ES] ----[Eo] is the proportion of Eo present as ES. At low So, [E@S] % [So] so Vo % [So] At high So, [E@S] is maximum, and Vo = Vmax Proportion of an ionizable functional group in the conjugate base or acid form: Proportion of HA = [H+ ] -----------Ka + [H+ ] = Ka -----------Ka + [H+ ] HA W A- + H+ [HA]T = [HA] + [A-] Proportion [HA] = [HA] -------------[HA] + [A-] Proportion [A-] = [A-] -------------[HA] + [A-] Proportion of free E (not total Eo) bound to an inhibitor - Proportion of A 1/" = KI -------------KI + [I] Hyperbolic Equation in Biochemistry x y = ---------m + bx 0.14 RESPONSE Y 0.09 m = 10 b = 20 0.04 -4.0 -3.0 -2.0 -1.0 -0.01 0.0 1.0 2.0 3.0 -0.06 -0.11 -0.16 VARIABLE X Hyperbolic form of equation used in biochemistry (positive x and y quadrant) for analysis of enzyme kinetics, acid-base behavior, and absorption processes (e. g., binding of O2 to myoglobin) . The double reciprocal plot of data in the positive x and y quadrant, 1/y = m*1/x + b, is used to obtain values of m and b. 4.0