This is one of the key dynamics of cheesemaking. It's what James Aldridge, RIP, talked about at some length on his site.
Let's recap the two key mechanisms by which casein micelles are held together not to each other after rennet addition, but each micelle itself, which is made up of many submicelle structures. One, colloidal calcium phosphate is a "glue" that holds individual submicelles together, acting as a sort of bridge. Two, the submicelles exhibit hydrophobic attraction. When acidity goes up, that calcium phosphate can detach from micelles and go into solution, degrading submicelle bonds and therefore the integrity of the micelle structure. This is very very important to cheese texture.
I've covered rennet action before, and the video I posted does a better job than I did. So I'm going to skip it and focus on the acidity and calcium phosphate relationship.
The pH level of 6.1-6.3 is very deceptive because it's a sort of tipping point. As the acid is produced, it keeps getting "eaten up" by the calcium phosphate. At the beginning, say pH 6.5, the micelles can bond very strongly because the structures are stable and there's a lot of calcium phosphate "glue". As that buffer is diminished, the micelles can't bond as well to each other. This is why when you drain at lower pH levels that 6.0-6.1, the end result of the cheese is crumbly and possibly bitter -- too much acid, too much micelle degradation too fast. Then during proteolysis, the submicelles degrade quickly, leading to too fast of chain reactions during catabolysis. It's also why various cheeses have such different profiles. In an alpine or emmenthaler, you drain at 6.3 or 6.4, and those micelles are mostly in tact and bond to each other. In the finished cheese, the micelles will be in a strong matrix. Ever notice how an emmenthaler is almost rubbery? That's why. Similarly for draining at lower pHs, micelles degrade, cheese becomes crumbly. Sorry getting off track.
If you drain at higher pH, there's more calcium phosphate stuck to the, well, the curd. And that calcium mineral content stays in the cheese. If you drain at lower pH, there's less mineral. When there's more calcium in the cheese, it has to go somewhere, and that tends to form more calcium lactate, or more crystalline amino acids (ie tyrosine). But that's just one of the aspects.
If you drain at lower pH, similarly, the micelles are degrades more. That degradation means the curd sticks together not as well, may form smaller pieces unless put into slabs. The squeak sensation happens at this other tipping point in the curd, which is around 5.4, which represents about the middle point from when micelles are very stable (6.5 ish) and when the have completely lost their charge (4.6). At this point of 5.4ish, the micelles are still bonded to each other and the submicelles still hold, but not to the point where they won't let go. So they physically move over each other, breaking bonds, rebonding, forming long, complex strands, etc. That's a good part of why cheese stretches right at that 5.4 pH, why you make mozz starting at 5.4 and often salt/brine around 5.4. You want that middle ground for proper proteolysis, texture, and flavor. Anyway, when you drain at lower pH than 6.2, it can form an odd situation because the micelles still bond, but they are past the tipping point (about 5.9-6.1, this varies with the milk, not a static number) and would really rather unbond... meaning they're losing their affinity and strength. So you're fighting the natural tendency of the chemistry of the curd and acid development, trying to get the curd bits to fuse in time, and then also to slide over each other for the squeak. So the sensation when munching is a barely perceptible less of a squeak. At least, that's how it always seems to me and that's the explanation I have for it. I haven't done some sort of formal squeak analysis
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Does that make sense? There's some complex biochemistry going on in the background, hope that was clear.