The lock-and-key model and the induced-fit hypothesis are two potential models for how substrates may bind in the active site of an enzyme.
The lock-and-key model suggests that the substrate is completely complementary in shape to the active site, so that it fits in 'perfectly' - i.e. the way a key (the substrate) fits into a lock (the enzyme). There is no change in shape of the active site when the substrate binds.
It's important to remember that the induced-fit hypothesis is similar to the lock-and-key model, but tweaked slightly. It says that the substrate and active site are not completely complementary, but there is still some complementarity. This is like a glove (the enzyme and it's active site) and a hand (the susbtrate) - they're a similar shape but not an exact match. When the hand goes into the glove, the glove changes shape slightly and moulds itself around the hand so that it fits snugly. In the same way, the active site changes shape to tightly bind the substrate. At the moment, this model is supported by a lot of evidence. For example, some enzymes can catalyse reactions with more than one substrate, but these different substrates are still similar in shape. This is much like how a single glove can fit different hands (as hands are generally similarly shaped!).
INDUCED FIT MODEL
The induced fit model maintains that enzyme substrates are not shaped perfectly to the active sites of their respective enzymes before binding occurs (the opposite was the lock and key model, proposed by a man named Emil Fisher; this model was widely accepted for quite a while, but did not explain the changes that occurred during the process of catalysis).
According to the model, the interactions between the substrates and binding sites are relatively weak at first. The initial binding of the substrate causes change in the conformation of the binding site, causing it to become the correct shape to bind with the rest of the substrate. This is also sometimes called the hand-in-glove model, due to the analogy of a hand changing the shape of a glove as it is put on, progressively making it easier for the hand to fit inside.
LOCK AND KEY
The lock and key model is a model of the relationship between the active site of an enzyme and the substrate of the same. The idea is that the active site, often can be imagined as an invagination of the protein, like a tunnel that is open to the outside (To leave a passage to the substrate). Now, this tunnel is built by the aminoacids of the protein so, it’s not a smooth tunnel, instead it’s more like the opening of a lock; the electronic density of the atoms of the protein are disposed so that only a specific substrate can pass through the tunnel, like only the right key can pass through the opening of a lock.
So, this is how the analogy with the lock and key arise. Now, this model isn’t used very much, because it has some problems. Like:
So, actually, instead of the lock and key model, it’s preferred the glove and the hand model. When the glove is the analogy for the active site of the enzyme and the hand is the analogy for the substrate. In this model, you can see that the active site is pictured as it modify its conformation when it binds to the substrate, but it maintain the specificity for the substrate also when it’s not bound; you cannot wear a glove in your nose, but the glove, when there is no hand around, it’s not shaped perfectly like an hand.