R and T conformations in relation to Activators and Inhibitors; Km of reaction in relation to uncompetitive and non-competitive inhibitor
Allosteric inhibitors changes the conformation of enzyme enzyme for preventing the substrate binding, and allosteric activators modify the enzyme conformation so that  substrate binding can take place.

Competitive inhibitors don't change the enzyme conformation, as these inhibitors compete with the substrate to bind at enzyme's active site. 

Non-competitive inhibitors change the enzyme conformation, as they inhibit enzyme activity by binding to site other than active site and prevent the substrate binding by changing the active site's structure so that substrate can not bind to enzyme. 

Uncompetitive inhibitors inhibit enzyme activity by binding to enzyme substrate complex and these inhibitors change the conformation of the enzyme which reduces the affinity of the substrate for the enzyme's active site.

Km decreases in uncompetitive inhibition because inhibitor binds to the enzyme-substrate complex and it becomes incredibly difficult for the substrate to leave the enzyme. This results in increased affinity and Km represents an increase in affinity.

(Via: https://courses.lumenlearning.com/boundless-microbiology/chapter/enzymes/

https://en.wikibooks.org/wiki/Structural_Biochemistry/Enzyme/Reversible_Inhibitors)