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BME+321+Homework+3+Solution

BME+321+Homework+3+Solution - Assuming steady state this...

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BME 321 Homework 3 (5 pts) Name: 1. True or False. State reason if false. (0.5 pts each, 1 pt total) (a) In Michaelis-Menten kinetics, for constant [S], reaction rate is proportional to the Km. False. Proportional to Vmax or [E0]. (b) Transition state analog inhibitors work because they looks extremely similar to the natural substrate of the enzyme. False. Shape is complementary in shape and charge to the active site of the enzyme and transition state of the substrate. 2. Find Km and Vmax in the reaction scheme shown on the graph. (0.5 pts each, 1 pt total) Km: 100 μ M Vmax: 1.0 mM/min
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3. Derive an expression for product formation using the pseudo steady state approximation for the following mechanism: (2 pts total) Note that k2 indicates forward reaction (ES -> EP); while k-2 indicates backward reaction (EP <- ES). Velocity definition: V = k3 [EP] Equilibrium 1: d[ES]/dt = k1[E][S] + k-2[EP] – k2[ES] Assuming steady state, this gives [ES] = (k1[E][S] + k-2[EP])/k2 …….. eq1 Equilibrium 2: d[EP]/dt = k2[ES] –k-2[EP] –k3[EP]
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Unformatted text preview: Assuming steady state, this gives [EP] = {k2/(k-2 + k3)}[ES] Then you get: [ES] = {(k-2 + k3)/k2}[EP] Plug into eq 1 and get: {(k-2 + k3)/k2}[EP] = (k1[E][S] + k-2[EP])/k2 [EP] = (k1/k3)[E][S] [E] = {(k3/k1)[EP]}/[S] Mass balance: [E0] = [E] + [ES] + [EP] Plug in to get: [E0] = {(k3/k1)[EP]}/[S] + {(k-2 + k3)/k2}[EP] + [EP] [E0] = [EP] {(k3/k1)/[S] + {(k-2 + k3)/k2} + 1} [E0] = [EP] {(k3/k1) + {(k-2 + k3)/k2}[S] + [S]}/[S] [EP] = [E0][S]/{k3/k1 + [S](1+(k-2 + k3)/k2)} V = k3[EP] = k3[E0][S]/{k3/k1 + [S](1+(k-2 + k3)/k2)} V = Vmax[S]/ {k3/k1 + [S](1+(k-2 + k3)/k2)} 4. Identify apparent Km and Vmax for [I] = 1 if the enzyme concentration was half as what is shown on the plot. (0.5 pts each, 1 pt total) For [I] = 1 X intercept: -0.25 Y intercept: 2.5 Enzyme concentration halved: X intercept: -0.25 Y intercept: 5 Vmax: 1/(Y intercept) = 0.2 Km = -1/(-0.5) = 2 X intercept = -1/[Km(1+[I]/K I )] = -0.25 apparent Km = Km(1++[I]/K I ) = -1/(X intercept) = 4...
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