I got all the answers correct this time all on the first attempt!
Notice $ V_{max} $ doesn't change - this is a characteristic for competitive inhibition. $ V_{max} $ does not change because the inhibition is done by competing with enzyme with the substrate, once the substrate concentration increase the inhibition will eventually give way to the substrate and therefore $ V_{max} $ stay constant.
This is Noncompetitive - it is confusing because we have uncompetitive and noncompetitive. Uncompetitive means the inhibitor does not compete with the substrate for the enzyme, instead, it binds to the substrate enzyme complex to inhibit the reaction by not allowing the enzyme substrate complex to turn into product. In that case the lines would be parallel. Noncompetitive is confusing because it is actually competiting, but it is competing and also blocking the enzyme substrate complex to turn into product, to the point that $ k_m $ is identical with the enzyme not inhibited.
Strange name - I have to say, a non-competitive inhibition is actually using the competitive mechanism.
A noncompetitive inhibitor is a special case, where apparent $ k_m $ is the same as for the enzyme without the inhibitor, while the $ V_{max} is decreased. In the mathematical expression above, the value of $ \alpha $ is equal to the value of $ \alpha '$
Remember for competitive inhibitor the line have the same $ y $ intercept and bigger slope, therefore $ \frac{1}{k_m} $ is smaller, therefore $ k_m $ is larger.
It increase the apparent $ k_m $ of the enzyme
It binds the enzyme complex in its active site.
This is similar to the above, because the line is parallel, uncompetitive inhibitor decreases $ k_m $ and $ v_{max} $
It decreases the apparent $ k_m $ of the enzyme.
It binds the enzyme-substrate complex.
The above equation represents the Lineweaver-Burk equation for an enzyme with a mixed inhibitor.
This is so because we have two alphas.
Note that the slope of the equation does not change, it is the parallel line case.
The above equation represents the Lineweaver-Burk equation for an enzyme with an uncompetitive inhibitor.
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