Understanding Lineweaver burk plots better, please

[arc5005]

So, I have the basics memorized and understood:

a high KM = low affinity
a low KM = high affinity

Vmax is the max rate/velocity
KM is the concentration of substrate where it is 1/2 vmax

competitive inhibitor: KM increases, Vmax stays the same, slope increases. Vmax doesn't change because if the concentration of substrate is high enough, there is very little chance for the competitive inhibitor to bind to the active site. And Km increases because you need a higher substrate concentration.

noncompetitive inhibitor: KM stays the same, Vmax decreases, slope increases. Noncompetitive inhibitor binds an allosteric site, so no change in substrate concentration; however, Vmax decreases, because it binds so strongly that no amount of substrate can remove it. It is as if the enzyme bound to noncompetitive inhibitor is no longer there.

uncompetitive inhibitor: KM & Vmax both decrease, slope increases. Binds to the ES complex, decreasing both Vmax and KM.

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Any suggestions or tweaks on understanding the above concepts any further?

Also, I'm having a hard time understanding the whole inverse y-axis and x-axis thing.

Why are the slopes increasing when an inhibitor is added?

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[Lawpy]

Lineweaver-Burk plots are a way to visualize Michaelis-Menten enzyme kinetics in a simple linear regression model. They’re also called double reciprocal plots because the x and y axes are the reciprocals of substrate concentration and reaction velocity respectively.

You can derive the Lineweaver-Burk equation from Michaelis-Menten equation as follows:

V = (Vmax * S) / (Km + S) —>
1/V = (Km + S) / (Vmax * S) —>
1/V = Km/(Vmax * S) + S/(Vmax * S) —>

1/V = (Km / Vmax) * (1/S) + 1/Vmax

Now the above equation looks complicated but this is simply y = mx + b in disguise, where:

y = 1 / V
m = slope = Km / Vmax
x = 1 / S
b = 1 / Vmax

Now take a look at the slope term. It’s Km / Vmax. In competitive inhibition, Km increases but Vmax is unchanged. So Km / Vmax increases which means the slope increases. In noncompetitive inhibition, Km is unchanged but Vmax decreases. This means Km / Vmax increases (because the denominator is getting smaller), so the slope increases. Uncompetitive inhibition involves Km and Vmax decreasing in similar rates so the Lineweaver-Burk plots are actually parallel lines and thus their slopes are unchanged.

Enzyme Inhibition

10.2: The Equations of Enzyme Kinetics

 

[arc5005]

Lineweaver-Burk plots are a way to visualize Michaelis-Menten enzyme kinetics in a simple linear regression model. They’re also called double reciprocal plots because the x and y axes are the reciprocals of substrate concentration and reaction velocity respectively.

You can derive the Lineweaver-Burk equation from Michaelis-Menten equation as follows:

V = (Vmax * S) / (Km + S) —>
1/V = (Km + S) / (Vmax * S) —>
1/V = Km/(Vmax * S) + S/(Vmax * S) —>

1/V = (Km / Vmax) * (1/S) + 1/Vmax

Now the above equation looks complicated but this is simply y = mx + b in disguise, where:

y = 1 / V
m = slope = Km / Vmax
x = 1 / S
b = 1 / Vmax

Now take a look at the slope term. It’s Km / Vmax. In competitive inhibition, Km increases but Vmax is unchanged. So Km / Vmax increases which means the slope increases. In noncompetitive inhibition, Km is unchanged but Vmax decreases. This means Km / Vmax increases (because the denominator is getting smaller), so the slope increases. Uncompetitive inhibition involves Km and Vmax decreasing in similar rates so the Lineweaver-Burk plots are actually parallel lines and thus their slopes are unchanged.

Enzyme Inhibition

10.2: The Equations of Enzyme Kinetics

thank you. i forgot that it was y = mx + b, and your explanations for the slopes helps a lot. thank you!