This might give you some background
http://www.elp.manchester.ac.uk/pub_pro ... efault.htm
http://themedicalbiochemistrypage.org/glycogen.html
Basically your total blood volume only contains around 5g glucose at any one time. There's a constant shuffling act between insulin stashing dietary carbs/glucose into store and the glucagon releasing it again, principally from the liver ("liver dump") and as you can see the system only has to be out by around 5g for your BG to double, or to crash through the floor.
This is really stuff they *should* tell you but didn't. Once someone pointed it out to me a lot of things became obvious - one of the things I suffered from was exercise-induced liver dumps principally in the morning, whereas the same exercise in the afternoon would be more likely to drop me low.
Insulin resistance is also a factor, within the control circuit as a different problem from that at the muscle receptors. The sensors don't detect BG levels as such, they detect insulin levels, which in normal people are closely related, but not necessarily for us. This is often a major factor in Type 2 but some Type 1s also suffer, the one who explained this to me probably underwent radiation damage from being at Ground Zero after some of the early nuclear tests and used to suffer from crippling hypos where his liver never woke up and also severe highs for no apparent reason where it dumped all the glucose it could until it was empty. I'm not nearly that extreme but a similar thing seems to happen where the two sides of the system stop communicating.
Carbs provide the greatest insulin release. Protein induces some insulin release but not so much. Fat produces none.
Dawn Phenomenon is a typical example where eating the right amount of carbs and/or protein either at breakfast or the previous night can switch it off.
I had one the other day, for no apparent reason my fasting BG was about 1 point higher than usual and breakfast shot me up about two points above where I should have been. After that my liver calmed down and the rest of the day I never broke through 5.8. There was absolutely no dietary reason for the numbers to be that far out, usually I can eat the same things and predict the results quite accurately.