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 Advice: How to understand a model

Encountering an equation causes the brains of many scientists to freeze. If you are one of these scientists who has trouble thinking about equations, here are some tips to help you understand what an equation means. As an example, let's use the Michaelis-Menten equation that describes enzyme activity as a function of substrate concentration:

Y=Vmax*X/(Km +X)

Tip 1. Make sure you know the meaning and units of X and Y

For this example, Y is enzyme activity which can be expressed in various units, depending on the enzyme. X is the substrate concentration in Molar or micromolar or some other unit of concentration.

Tip 2. Figure out the units of the parameters

In the example equation, the parameter Km is added to X. It only makes sense to add things that are expressed in the same units, so Km must be expressed in the same concentration units as X. This means that the units cancel in the term X/(Km +X), so Vmax must be expressed in the same units of enzyme activity as Y.

Tip 3: Figure out the value of Y at extreme values of X

Since X is concentration, it cannot be negative. But it can be zero. Substitute X=0 into the equation, and you will see that Y is also zero.

Let's also figure out what happens as X gets very large. As X gets large compared to Km, the denominator (X+Km) has a value very similar to X. So the ratio X/(X+Km) approaches 1.0, and Y approaches Vmax. So the graph of the model must level off at Y=Vmax as X gets very large.

Tip 4. Figure out the value of Y at special values of X

Since Km is expressed in the same units as X, you can ask what happens if X equals Km? In that case, the ratio X/(Km + X) equals 0.5, so Y equals half of Vmax. This means the Km is the concentration of substrate that leads to a velocity equal to half the maximum velocity Vmax.

Tip 5. Graph the model with various parameter values

Graphing a family of curves with various values for the parameters can help you visualize what the parameters mean. To do this with Prism, use the analysis "Create a family of theoretical curves".