Answered Essay: The Michaelis-Menten equation models the hyperbolic relationship between [S] and the initial

The Michaelis-Menten equation models the hyperbolic relationship between [S] and the initial reaction rate (V0) for an enzyme catalyzed, single substrate reaction: E S ES E P. The model can be more readily understood when comparing three conditions: [S]Km. Match each statement with the condition that it describes. Note: “Rate” refers to initial velocity (V0) where steady state conditions are assumed; [Etotal] refers to the total enzyme concentration, and [Efree] refers to the concentration of free enzyme.

Map Sapling Learning macmillan learning The Michaelis-Menten equation models the hyperbolic relationship between [S] and the initial reaction rate (Vo) for an enzyme catalyzed, single substrate reaction: E + S → ES → E + P. The model can be more readily understood when comparing three conditions: [S]<CKm, [S] = Km, and [S]>>Km. Match each statement with the condition that it describes. Note: Rate refers to initial velocity (Vo) where steady state conditions are assumed: [Etotal refers to the total enzyme concentration, and [Efree] refers to the concentration of free enzyme. [S] = Km Not true for any of these conditions rate is directly proportional to [S] ES] is much lower than [Etreel half of the active sites almost all active sites will be fille are filled with S this condition rarely occurs for most in vivo enzymes

I’m uncertain about which condition rarely occurs for most in vivo enzymes. I suspected low substrate concentrations relative to Km, because this would lower the enzyme’s efficiency and why synthesize more enzyme than one needs? Additionally, many in vivo enzymes are rate-limited by diffusion (catalytic perfection), so this also leads me to suspect that most enzymes operate near saturation.

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Answer

Ans. All options, except “this condition rarely occurs in vivo enzymes”, are placed correctly in respective boxes.

Change in [S], say glucose, is one of the most import factor affecting rate of catalysis. I could not find Km value for hexokinase, the enzyme that catalyzes the first reaction of glycolysis.

Consider [glucose] in cells, it’s maintained almost to a fixed range through homeostasis.

However, there may be several enzymes for which [S] have regulatory roles.

For example, hormones and neurotransmitters are generally present in micro-molar or even nano-molar concentrations. Still they efficiently bind to their cognate protein or enzyme and trigger the physiological activity.

Consider another example. Normal concentration of hormone human chorionic gonadotropin, [hCG] is below 5 mIU/ mL in a normal, non-pregnant female. Around 7-8th week of fertilization, [hCG] increases to around 3.0 x 105 mIU/ mL– the [hCG] increased around 60000 times ! Though hCG in NOT a true substrate to any enzyme, it an effector molecule, the scenario is put to present the range of [S] that can vary in body.

Increase in [S] for various enzymes may substantially also increase after the meal, or in case of starving or prolonged starving. Both very high and very low [S] may old true for ‘regulatory’ enzymes. In fact, difference in [S] from Km seems to be the key regulatory factor that may orchestrate with other metabolic pathways. For example, depletion of [glucose] after prolonged starvation may trigger glycogenesis.

Since all enzymes in body directly or indirectly regulate some other metabolic pathways, they may face very high or low [S] as key regulatory factors. So, [S]>>Km and [S]<<Km cases shall be relatively more common under normal physiological conditions.

However, [S]= Km appears to be a rare condition in body under normal physiological conditions. If [S]=Km, no enzyme would reach its Vmax under physiological conditions. Consider [glucose] after a meal. [S] would be higher than Km for initial few hours, there would also be several hours when [S] >> Km (say, due to escaping lunch), but only a transient point when [S]=Km.

So, the option “this condition rarely occurs for most in vivo enzymes” shall be placed in “[S] = Km” box.

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