The use of "curved DNA" confuses me. Is the term "curved DNA" essentially the same as "Circular DNA"?
I never heard of the term until today but a quick search implies that certain DNA sequences are more pliable than others. Most notable is the Widom sequence which binds to Histones. It is also noted that DNA isn't a free floating polymer but that there is also some directionality in its bend. It seems that the concept is bested explored in this review: Curved DNA.
it is not necessarily circular - the transcription factors usually require a curvature that is much greater than what a plasmid will have, and the requirement can show up on eukaryotic proteins as well. DNA binding proteins will cause a local loop or curvature that fit the transcription factor.
The classic picture is for the Gal and Lac repressor proteins which bind 2 strands simultaneously, causing a loop in the DNA.
Reference: see fig 1 in: http://genesdev.cshlp.org/content/3/5/606.full.pdf+html
I'm hardly an authority on this topic, but I distinctly recall an amazing report the mid-1990s of the co-crystal structure the yeast TATA binding protein in complex with DNA. The structure shows that TBP bends the DNA axis by approximately 80 degrees, presumably in order to expose bases and improve recognition. The structure is available at RCSB: http://www.rcsb.org/pdb/explore.do?structureId=1ytb . (Make sure you check out the Jmol view.)
Thermodynamically speaking, bending DNA would require energy. Therefore, DNA that was pre-bent (e.g., due to auxiliary binding proteins or composition bias) would improve binding.
So, I suspect that in the context DNA binding proteins, "curved" refers to the static curvature of unbound DNA or to the bending of DNA upon binding in order to facilitate recognition.