I am a high school student and I am little confused about the uses of restriction endonucleases. Why do hydrogen bonds(base pairing) break when restriction endonucleases produce sticky ends? If they only break phosphodiester bond, should hydrogen bonds not break on their own? I searched it on few sites but didn't find any discussion.
The short answer is heat. Compared to the covalent phosphodiester bonds, hydrogen bonds (H-bonds) are very weak, and they're much easier to break and re-form. A long enough piece of double-stranded DNA will stick together at physiological temperature because it contains thousands of highly coordinated hydrogen bonds. But even long pieces of double-stranded DNA can easily be denature into single-stranded DNA by heating them up to ~95°C. The handful of H-bonds on a sticky end will spontaneously disassociate quite easily at the restriction enzyme's optimal temperature (usually ~37°C).
A good way to think about this is to imagine the sticky ends as PCR primers. When I'm planning a PCR reaction, I first need to calculate the melting temperature (Tm) of my primers (the single-stranded oligonucleotides that form duplex DNA on a reverse-complimentary sequence of a strand of template DNA). Tm is the temperature at which half of the duplexed DNA primers will disassociate and become single strands. As the temperature increases above the Tm, an even greater proportion of those primers will disassociate into single-stranded DNA.
If I take EcoR1 as an example, the sticky end sequence is AATT. Just four bases with 2 H-bonds per base, for a total of 8 H-bonds (A-T pairs have two H-bonds, G-C pairs have three). When I plug this sequence into a primer Tm calculator like OligoCalc, I get a Tm of 8°C. Meaning, if you kept this reaction at 8°C, half of your sticky ends would become unstuck. This is why the ligation of sticky ends is often performed at a much cooler temperature than the restriction digestion (either room-temperature, or 4-8°C).