e104 Nucleic Acids Research, 2008, Vol. 36, No. 16 of the bands we calculate an eﬃciency of 75% for the formation of A+B dimers, and indeed almost all of the RNA is bound to DNA. Achieving a similar eﬃciency in binding long RNAs to DNA using enzymatic ligation would be very challenging because the eﬃciency of these reactions may vary depending on the molecules involved. End-joining of RNA to RNA. As a ﬁnal application, we demonstrate that our method can also be applied to eﬃ- ciently end-join two RNA molecules (Figure 3b). Here, we used our protocol to end-join two 4.2 kb dsRNA mole- cules (A) to create dimers A+A. In lane 2, two distinct bands can be seen, one migrating at 4.2 kb DNA (corre- sponding to molecule A) and one migrating at 8.5 kb DNA, which must correspond to the dimers A+A. We ﬁnd that 20% of the ﬁnal product consists of dimers A+A. As before, we have also performed a control in the absence of STV (Figure 3b, lane 1), and here no dimer formation occurs, as expected. DISCUSSION Having demonstrated several applications of our method, we now analyze in more detail a number of aspects that inﬂuence the overall eﬃciency of dimer formation. Speciﬁcally, we will address the importance of tempera- ture and the role of STV quality in dimer formation, and we explain why our protocol disfavors the formation of multimers. Influence of temperature on homodimer formation We have mentioned above that a low temperature during the second incubation step is important in preventing homodimer formation (see also Supplementary material). The reason for this is that the rate of dissociation of STV is much reduced at a lower temperature, so that the STV dissociates less frequently from the A+STV complex and renders formation of A+A dimers (and also B+B dimers) less likely. Assuming that the dissociation rate of STV at 378C is approximately koﬀ = 10 4 s 1 [estimated from ref. (44)], we expect that after 1 hr about 30% of the STV has dissociated once and reassociated again to form a new complex (either a DNA–STV–DNA dimer or a single DNA–STV complex). At 48C, however, the rate of disso- ciation is approximately three orders of magnitude lower (44), meaning that only 0.03% of the STV molecules would have had time to dissociate once. The formation of unwanted dimers such as A+A and B+B due to STV dissociation is dramatically suppressed, therefore. One could argue that the lower temperature may also require longer incubation times to compensate for slower diﬀusion. A longer incubation time would in turn allow for more dissociation to occur, which could cancel the beneﬁt gained from the lower dissociation rate. However, the rate of diﬀusion is reduced by only about 10% by lowering temperature from 378C to 48C, which is hardly signiﬁcant compared with the three orders of magnitude gained in the stability of the A+STV complex. PAGE 6 OF 8 STV quality and the efficiency of dimer formation We have found that the number of molecules that binds STV but does not form dimers (in other words, A+STV and B+STV complexes) is unaﬀected by either the incu- bation time or the relative concentration of molecules A and B (Supplementary material). Our speculation is that the STV molecules in these single DNA–STV complexes do not have multiple binding sites available for biotin, but only a single one. Presumably, partial degradation of the STV molecules may be the cause of this. We have indeed observed degradation over time in individual stocks of STV: in all cases, the eﬃciency of forming single DNA– STV complexes was not diminished (judged from the observable electrophoretic shift due to STV binding), but the relative amount of (homo- or hetero-) dimers would dramatically reduce over the course of several weeks to months, to the point where dimer formation was no longer observed. Switching to a fresh STV stock would always immediately result again in high eﬃciencies of dimer formation. This observation also rules out any possible inﬂuence of other factors, such as the buﬀers or DNA molecules used. The STV used for the experiments presented here (purchased from Roche Applied Sciences, Almere, The Netherlands) showed the best results: stocks were found to be stable for at least 2 weeks up to several months when stored in ddH2O at 48C. Formation of multimers We have observed almost no formation of DNA trimers and tetramers in our experiments, even though wild-type STV has four binding sites for biotin. This is in accor- dance with earlier reports (29,32), where it was also found that direct incubation of biotinylated DNA with STV would not result in multimer formation, except at certain speciﬁc ratios of STV:DNA. Indeed, in some cases we have also observed the formation of trimers and tetramers when both molecules were incubated directly with STV (in a single incubation rather than our preferred two step approach). Formation of trimers and tetramers becomes more likely when the STV concentra- tion is less than twice that of the DNA molecules, although it probably remains much slower than dimer formation because of steric hindrance (29). Indeed, Monte-Carlo simulations (45) imply that the probability of forming trimers and tetramers under optimized molar concentrations is still orders of magnitude lower than the probability of forming dimers. It is likely that our two-step protocol similarly disfavors the formation of trimers and tetramers. The likelihood of multimer formation in the ﬁrst step of our protocol is reduced signiﬁcantly, due to the very large excess of STV used. This makes it much more likely that all the biotin-groups on the molecules A are rapidly saturated by binding to single STV molecules rather than forming dimers. In the second step, when molecule B is added, it can only bind to A+STV com- plexes. Due to steric constraints, the probability that two molecules B bind to the same A+STV complex is lower than for two molecules B to bind two diﬀerent A+STV complexes. Also, the concentrations of A and B are typi- cally matched so that all B molecules can bind to A+STV