One way to do an yeast transformation is by using lithium acetate, a single-stranded carrier DNA, and PEG (1). I was wondering why is the polyethylene glycol important for the efficient transformation. How does it affect the take-up of the foreign DNA? Yamakawa et al (2) showed that PEG is essential for the recovery of the cells but I couldn't access that paper to read more about it.
I found this link - it says 'we don't really know'. It says PEG binds DNA, I assume shielding the membrane from its negative charge and allowing internalization to happen.
I would guess that the amphipathic nature of PEG, being partly hydrophobic, also helps soften up the membrane. Interestingly, if you increase the PEG concentration beyond the limits, it decreases the efficiency of the procedure.
I assume it has an analogous function in ligation buffers. There it apparently takes up a large proportion of the volume and thereby increases the chance of interaction between bits of DNA.
In a transformation buffer it should increase the chance of DNA getting into a cell. Unfortunately the only reference I found for this was at Bitesizebio: http://bitesizebio.com/20/5-dna-ligation-tips/