*Note: this explanation is best understood if you have a Lineweaver-Burke plot and a velocity vs. concentration graph available while reading it.*

When you look at an enzyme reaction, you're really looking at two reactions:

** E+S <--> ES --> E + P **

So in those rxns, E is the enzyme, S is the substrate, and P is the product. You'll notice that substrate binding is reversible, so you *could* say that we're looking at *three* possible reactions. Call the first forward reaction R1. Call the reverse of that reaction R2. Call the release of product from the enzyme R3.

So what happens with the Michaelis constant, Km, is that you make a ratio out of the rates of those three reactions to come up with a ratio for the overall reaction. That ratio is (R2+R3)/R1. So take a look at that ratio, and think about this: R2 and R3 are the two reactions that remove the substrate from the enzyme, and R1 is the reaction that binds the substrate to the enzyme. This means that Km is a ratio of separation:binding. So Km is related to the affinity of the enzyme for the substrate.

Now look at the velocity vs. concentration curve. Km is the substrate concentration at 1/2 of Vmax. Remember that Vmax is the mechanical limit of the enzyme -- it's churning out the product as fast as it possibly can. So look at a pair of enzymes, one with a high Km, and one with a low Km. An enzyme with a low Km reaches 1/2 Vmax at very low concentrations, because the enzyme has a high affinity for the substrate. An enzyme with a high Km, though, doesn't have a strong affinity for the substrate, so it takes a lot more of the substrate to get the enzyme up to 1/2 Vmax.

Now look at the Lineweaver-Burke plot of 1/Vo vs. 1/[substrate], aka the double reciprocal plot. The important things to remember about Lineweaver-Burke plots are the x and y intercepts. The x-intercept = -1/Km, and the y-intercept = 1/Vmax. Just learn these, and I'll help you make sense of them by discussing inhibition.

**Inhibition**The best way to understand these graphs is to look at what happens with different types of inhibition.

First, think about competitive inhibition. You've got another substrate competing for the same enzyme. So what changes? Well, the enzyme suddenly has something else it can bind to, so its affinity for the substrate is reduced. At the same time, if you cram in enough substrate to overwhelm the competition, you can eventually reach Vmax. So in competitive inhibition, Km increases while Vmax remains the same. Look at your V/~~ graph, and the curve will stretch, because it takes a lot more substrate to get that Km at 1/2 Vmax. Look at your Lineweaver-Burke plot. The y-intercept stays the same because Vmax doesn't change. But Km has gone up, which means that -1/Km has gotten closer to zero, increasing the slope of the line and rotating it on the y-axis.~~

Now look at noncompetitive inhibition. In noncompetitive inhibition, you have something binding to another site on the enzyme, changing the structure of the binding site, and thus affecting the amount of enzyme that is able to bind substrate. This means that Vmax is reduced. Km, the affinity of the functional enzyme, remains the same, though. Looking at the V/~~ curve, you simply squish the maximum down. Looking at Lineweaver-Burke, Km is the same, so your x-intercept doesn't move. Vmax is smaller, so 1/Vmax is larger. This means that your line will have a higher slope and rotate on the x axis.~~

There are other conditions possible, but that covers the basics. Oh, and notice I didn't actually mention the Michaelis-Menten equation or the Lineweaver-Burke equation. Questions involving those are memorization w/plug & chug calculation. Understanding what happens on the graphs is much more intuitive.