equilibrium position and enzymes, help me reconcile these theories

[getsome111]

Ok, so we all know that an enzyme/catalyst does not change the place of equilibrium in a chemical reaction. We also know that the definition of equilibrium pertaining to a chemical reaction means that the rate of the forward reaction = the rate of the reverse reaction.

I recall from biochemistry that an enzyme can have a lower km for substrate than its product. does this not mean that the speed of the forward reaction is increased? If this is the case then how is the rate of the reverse reaction increased as well? If I am correct about the km's then where is the compensating factor for the reverse rate? is the enzymes vmax somehow increased for the reverse reaction?

Am I just thinking of enzymes that use some other driving force (ex; atp hydrolysis) to induce a shape change which drives a reaction? this is my best guess

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[Blueprint MCAT Tutor]

I'll confess that I'm not entirely sure I understand your question. You assert the following:

1. Equilibrium = the point in a reaction in which rates of forward and reverse reactions are equal. Okay, so that's certainly true.

2. The speed of the forward reaction is increased for a catalyzed reaction. That's also true, if the reaction is moving forward. If the reaction is currently moving backwards, that reverse reaction will also be faster. Since enzymes lower the activation energy for both forward and reverse, both will go faster.

Maybe the confusion comes from the idea that if you currently have a reaction that's AT equilibrium, what happens when you drop an enzyme in? That'd be a typical MCAT question and the answer would just be: nothing.

You seem really hung up about Km. You're unlikely to get any hugely in-depth questions about it. Here's the entirety of the AAMC outline on Enzymes:

MOLECULAR BIOLOGY: ENZYMES AND METABOLISM

1. Enzyme Structure and Function
   
   1. Function of enzymes in catalyzing biological reactions
      
      
   2. Reduction of activation energy
      
      
   3. Substrates and enzyme specificity
      
2. Control of Enzyme Activity
   
   1. Feedback inhibition
      
      
   2. Competitive inhibition
      
      
   3. Noncompetitive inhibition
      
3. Basic Metabolism
   
   
   1. Glycolysis (anaerobic and aerobic, substrates and products)
      
      
   2. Krebs cycle (substrates and products, general features of the pathway)
      
      
   3. Electron transport chain and oxidative phosphorylation (substrates and products, general features
      
      of the pathway)
      
      
   4. Metabolism of fats and proteins

Literally that's it. Notice what's missing? No mention of MM equation, no mention of Km, etc.

So what do you need to know about Km? I'd suggest you could sum it up with just this:

1. Km is the [substrate] that's 1/2 of Vmax
2. The lower the Km, the stronger the affinity the enz. has for the subs.
3. Competitive inhibition = higher Km but same Vmax
4. Noncompetitive inhibition = lower Vmax, but usually same Km