M. K. Raghuraman
The principle: A non-replicating DNA circle is created in vivo by site-specific pop-out recombination. This non-replicating fragment is then used as an internal control to measure the two-fold ncrease in copy number of replicating chromosomal sequences between the start and end of S phase.
1. Grow the cells in minimal medium with 1% Na-acetate or 3% glycerol as the carbon source, aiming for about 20 ml cells per time point. (Raffinose has not worked well for me, so I avoid it.)
2. Arrest the culture with alpha factor (200 nM final concentration for bar1 strains) when the OD660 is about 0.2-0.25.
3. When the cells have arrested (more than 95% unbudded), remove 20 ml for the "Uninduced" control, and add dry galactose (2% w/v final concentration) to the remainder of the culture.
4. Allow the induction to proceed for 2.5 hr (R-KT-DIR) or 4 hr (R-Zeo-DIR), then add dry glucose (2% w/v final concentration). Thirty minutes later, shift the culture to the 37o bath.
5. Once the culture has reached 37oC (it takes 10-15 min), add Pronase (0.01-0.05 mg/ml final conc) to release the cells from the alpha factor block. [You can add dry Pronase. I usually dissolve the Pronase in 5 ml of minimal medium, just to avoid having the dry Pronase stick to the sides of the flask.]
6. Hold at 37oC for 90-120 min (until budded cells accumulate). Remove one sample (t = 0), then swirl the flask in ice-water and return it to 23oC. Continue to collect samples every 4 min (until t = 80 min or more). I usually take two 0-min samples, and take samples every 4 min from t=8 through t=56, then take t=64, 72, and 80 min samples--19 samples in all.
The ice-water treatment is to quick-chill the culture to 23oC, and is usually for ~1 min. You can empirically determine how long it takes to bring your desired volume of medium from 37o to 23oC.
Collecting samples: Freeze 8 ml of 0.1% NaN3, 0.2 M EDTA in "50 ml" Oakridge-type plastic, screw-capped centrifuge tubes (frozen slanted to maximize the surface area). During the experiment, mix 20 ml of cells with 1/50 volume of 10% NaN3 in a 35 ml Corex tube (on ice) and immediately transfer the mix to a tube of frozen EDTA/NaN3. Alternatively, squirt the 10% azide on the frozen azide/EDTA and immediately add the cell sample. Vortex or shake the tube vigorously to chill the sample and break up the frozen EDTA. Spin down the cells in a chilled centrifuge, wash with 1 ml cold water per sample in Eppendorf tubes and freeze the pellets at -20oC.
7. Extract the DNA (smash-&-grab with glass beads); digest 1/4 to 1/3 of it with the enzyme of choice in 40-60 microliters (EcoRI works well, as it cuts the ARS-less circle just once). Split each digest in two or three to run in duplicate (or triplicate) gels. It helps to make wide, well-separated wells. Blot the gels as usual.
8. Hybridize simultaneously with probes for the ARS-less circle, an early marker, a late marker, and the sequence of interest. Quantitation comes out best if the fragments to be probed are in the 2 kb-8kb range. Sometimes the fragments just don't work out (i.e., two fragments are too close for comfort), in which case you'll have to strip the blots and re-probe. If so, I usually include the ARS-less circle probe for each hybridization.
9. Quantitation: we use a Molecular Dynamics PhosphorImager or a Packard InstantImager. The values obtained for the two t=0 samples are combined and used as the zero time point (to be used for normalization of the later samples).

Here's a typical plot showing replication of ARS1 and R14 (a fragment near the right end of chromosome V):
Pronase: We use Calbiochem's Pronase (catalog #53702), which seems pretty clean--i.e., plates spread after Pronase treatment aren't contaminated--but I heard from someone who'd used Sigma's Pronase and had massive growth of Streptomyces.