Both connect to some site other than the active site which controls the shape of the active site and causes the enzyme to be less active. So what is the difference?
2 Answers
There Are Two Similar but Distinct Types of Noncompetitive Binding.
Starting from a pharmacological perspective, there are 2 definitions of "noncompetitive" binding that have similar macroscopic effects but differ slightly in their molecular mechanisms. Depending on which definition you use, noncompetitive ligands can bind either orthosterically or allosterically. Aspirin at cyclooxygenase and alanine at pyruvate kinase have both been referred to as "noncompetitive" (see below), despite aspirin binding orthosterically and alanine binding allosterically. Both types of inhibition involve depression of the maximum response, efficacy or enzyme activity. In other words, they reduce $y_{\mathrm{max}}$, $E_{\mathrm{max}}$ or $V_{\mathrm{max}}$. This is described in (Lippincott. (2015). Illustrated Reviews Pharmacology. 6th ed. p. 34). Similarly, (Goodman and Gilman. (2011). The Pharmacological Basis of Therapeutics. 12th ed. p. 46) gives an operational definition of noncompetitive antagonism as that which depresses the maximal response to the agonist but the molecular mechanism of action "really cannot be inferred unequivocally from the effect". The two types of noncompetitive molecular mechanisms are (1) irreversible antagonism and (2) allosteric antagonism. Lippincott claims that both of these mechanisms are "noncompetitive" antagonism. Textbooks trump Wikipedia on credibility so I'm afraid to say that Wikipedia may have been leading people astray for years by saying that noncompetitive ligands can only bind allosterically. Due to this confusion, I think it's better to avoid the term noncompetitive entirely and opt for "insurmountable" inhibitor if the mechanism is unknown, or "irreversible/allosteric inhibitor" if the mechanism is.
Type 1: Irreversible Antagonism
Goodman and Gilmans' definition in the previous paragraph notes that the effect is for "a slowly dissociating antagonist" (i.e. an irreversible antagonist). This is mirrored in (Rang and Dale. (2015). Pharmacology. 8th ed. p. 11) and (Katzung. Basic and Clinical Pharmacology 11th ed. p. 31), which define noncompetitive antagonism as irreversible antagonism. Rang and Dale also makes the point that the term is ambiguous with other meanings of noncompetitive. Rang and Dale claim that aspirin is a noncompetitive antagonist at cyclooxygenase. It may be an irreversible antagonist but it's certainly not an allosteric one, as it modifies the orthosteric binding site. Another "noncompetitive" drug in this class (according to Rang and Dale) is phenelzine, which irreversibly binds MAO.
Type 2: Allosteric Antagonism
Not to be confused with negative allosteric modulators, (Goodman and Gilman. p. 46), (Rang and Dale. p. 17), (Lippincott. p. 34) and (Katzung, p. 32) all give a second definition of noncompetitive antagonism as antagonism at an allosteric site. This antagonism may be reversible or not but as the agonist can't displace the antagonist, it is insurmountable in all cases. Rang and Dale give the example of ketamine at the NMDA receptor, which depresses the maximal response by binding in the channel (an allosteric site) but doesn't bind irreversibly. For ligands relevant to enzymes, alanine and ATP allosterically (yet reversibly) bind pyruvate kinase. So this would cause insurmountable inhibition of pyruvate kinase activity but not irreversible inhibition. Various authors, such as (Mustafa and Hochachka, 1970) refer to this as "noncompetitive" inhibition.
Interestingly, I can't find any exogenous ligand that is both reversible and allosteric. It seems that allosteric antagonists are more relevant to receptors and transporters than enzymes. To make it even more confusing, Katzung claims that benzodiazepines (BDZ) act noncompetitively, since they bind allosterically. But this doesn't fit with any other definition of noncompetitive binding since BDZ is a positive modulator. Also interesting is that hexamethonium at the nAChR fits the definition of "noncompetitive", regardless of which one you use. It is an irreversible blocker at an allosteric site.
Marangoni, on p. 70 of Enzyme Kinetics: A Modern Approach, also points out the difficulty in distinguishing between irreversible orthosteric and reversible allosteric inhibition. Using an irreversible inhibitor is equivalent to removing some enzyme from the system, so $V_{\mathrm{max}}$ drops. But at the same time, an allosteric inhibitor causes insurmountable inhibition (reduces $V_{\mathrm{max}}$). Neither type of inhibition alters the affinity of the substrate for the active site of the enzyme (apart from the irreversibly inhibited enzymes with no affinity) so $K_m$ is left unchanged. The figure below, from (Jahangirvand et al., 2016), shows the antagonism of catalase by cimetidine on a Lineweaver Burke Plot. A glance at this graph tells us that $V_{\mathrm{max}}$ is depressed, while $K_m$ is unchanged, so we could (arguably) call this noncompetitive inhibition. But this would not tell us the molecular mechanism of the inhibition.
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1$\begingroup$ This is a well written and researched answer. Thanks comments are discouraged but this answer deserves credit! $\endgroup$ Dec 27, 2018 at 11:32
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$\begingroup$ Anyone reading this article should note that the IUPHAR published a standardisation of terminology which settles the dispute. I'll change my answer in due course. $\endgroup$– JamApr 1, 2019 at 19:47
For allosteric inhibition, the inhibitor binds to the enzyme and induces a change in the conformation so that the substrate cannot bind anymore. The binding site for the allosteric inhibitor is different from the substrate, see the image for illustration (from here):
In non-competetive inhibition the inhibitor also binds to the enzyme indepently of the substrate (wheter it is bound or not) and does not influence substrate binding. What is influenced is the activity of the enzyme, when the inhibitor is bound, it will not process the substrate. See the figure (from here) for illustration:
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$\begingroup$ So in allosteric inhibition what's changing is the affinity to the substrate, and in non-competitive inhibition what's changing is the ability of the enzyme to carry on with the reaction. Got it. $\endgroup$ Jan 27, 2016 at 20:23
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$\begingroup$ @A.Steiner no. The difference is that in allosteric inhibition, the inhibitor does not bind to the active site but to some other site in the enzyme which, due to change in enzyme structure, leads to change in activity. $\endgroup$– WYSIWYGJan 28, 2016 at 6:54
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$\begingroup$ @A.Steiner No. In allosteric inhibition the conformation of the enzyme is changed so that the substrate cannot bind anymore. In non-competetive inhibition the substrate binding is not affected. $\endgroup$– Chris ♦Jan 28, 2016 at 7:06
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$\begingroup$ @WYSIWYG, I pretty much believe that both of them (allosteric/non-competitive) bind to a regulation site which is not the active site, change the enzyme conformation and lead to change in activity. $\endgroup$ Jan 28, 2016 at 9:18
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$\begingroup$ @Chris, an allosteric regulator changes the conformation of the active site, but with saturation of substrate I know the enzyme suppose to work as there is no regulation at all - changes the affinity to substrate (Km) and not the ability of the enzyme to work (Vmax). in that perspective it's dynamics behave like a competitive inhibitor. In non-competitive inhibition, the enzyme will not work the same no matter how much substrate there is. Meaning the effect is not on affinity, like you said. The enzyme structure must be changed though (CoE/critical amino acids) in order for it not to work. $\endgroup$ Jan 28, 2016 at 9:20