Linear DNA fragments of plasmid pSA580, ∼3.6 kb in length, were used as tethers. The original plasmid had been modified to contain properly arranged hybrid operator sites for oriented binding of the GalR^A16T/GalR^V15T,T322R heterodimers (6). The arrangement of the hybrid operator sites determined the mutual orientation of the active tetramerization interfaces of the operator-bound GalR heterodimers, allowing only either A1- or A2-type loop formation. The resulting plasmids were linearized by digestion with KpnI and SacI. Two ‘tails’ were synthesized with biotin or digoxigenin-labeled nucleotides by PCR of the multiple cloning site of a pBS plasmid comprising the restriction sites for KpnI and SacI. After restriction of these labeled tails, they were ligated to the complementary ends of the linear fragment of interest.

All looping experiments were performed in the presence of 25 nM GalR and 50 nM HU. One end of a single molecule of DNA was attached to the glass surface of a microscope flow-chamber (previously coated with antidigoxigenin) and a paramagnetic bead 2.4 μm in diameter (DYNAL MyOne beads coated with streptavidin) was attached to the other end. A pair of permanent magnets, above the microscope stage were used to gently attract the tethered, magnetic bead and effectively stretch the DNA with molecular-scale forces (14). Furthermore, rotation of the magnets causes synchronous rotation of the bead to enable twisting of the DNA tether, which does not swivel at either the glass or bead surfaces due to multiple attachments. The extension, l = <z>, of the molecule of the DNA was monitored with an error of ∼10 nm with 1 s averaging using 3D, video-rate tracking of the bead (15). The horizontal motion of the bead <▵x²> allowed the determination of the tension in the molecule via the equipartition theorem: F = k_BT l/<▵x²> with 10% accuracy. Mechanical drift in the data was eliminated using differential tracking of a second bead stuck on the surface.

Data were analyzed as described previously (10). In brief: traces with transitions between longer (unlooped) and shorter (looped) lengths were best fitted to the raw data l(t) (filtered using a 1 s window) using a sliding Heaviside (step) function: l_step(t) = sθ(t−t₁) + l₁ defined over a time window of size T_av. In other words, for every data point, t, of the data set, the parameters of the step function, s, t₁ and l₁, were fitted such as to minimize the error (l(t)− l_step(t))² in the time window t₀ < t < t₀ + T_av, where only one transition is expected. Finally, the parameters, that consistently scored best (x²-test), were selected as steps. The time intervals between successive looped and unlooped steps were included in histograms of τ_unlooped (or τ_looped) corresponding to the time spent in the longer (or shorter) state.

Interactions between proteins bound to well-separated sites on a DNA molecule require bending and twisting deformations in the intervening DNA. Double-stranded DNA is a semi-flexible polymer, with a persistence length of ∼50 nm (∼150 bp) (23–25). DNA segments shorter than the persistence length do not easily bend. However, many DNA ‘transactions’ require formation of short DNA loops (150 bp or less).The feasibility of loop formation over distances shorter than its persistence length depends on the intrinsic shape and flexibility of the DNA sequence, the phasing of the binding sites being juxtaposed, supercoiling of the DNA, in concert with the effect of architectural proteins.

In many systems, protein–DNA and protein–protein interactions can produce loops with different geometries. However, not all these geometries are energetically equivalent and loops with a specific DNA trajectory may be preferred (1,8,26–28). For example, in the case of the Gal repressosome, which contains a 113-bp long DNA loop mediated by two Gal repressor dimers and the HU protein, there are four possible DNA trajectories. Two of these trajectories have antiparallel DNA at the entry/exit points (A1 and A2), while two other trajectories have parallel DNA (P1 and P2) (6,8). The DNA exiting an antiparallel loop must curve under tension and therefore formation of this kind of loop would be expected to cause a larger change in the overall end-to-end distance of the molecule (larger ▵l) than formation of a parallel loop where the exiting DNA is straight. However, parallel loops are generally more strained than antiparallel ones (9). Stereochemical models of GalR/HU-DNA loops confirm this and also predict that the A1 loop is much more stable than the A2 loop. In addition, they also predicted that, as a consequence of the 60° angle between the two dimers in the GalR tetramer, the DNA is similarly under-twisted in both conformations (8). These structural predictions might be relevant to in vitro transcription assays, in which the heterodimer and the HU protein repressed transcription from DNA engineered to form A1 but not A2 configurations. Note, however, that these twist calculations were performed on relaxed DNA.

Instead, the magnetic tweezing assays reported here indicate that the A1 and A2 loops formed with similar energies in DNA, which was unwound by an amount similar to that found in the plasmids used in in vitro transcription assays and in vivo (Table 1 and Figure 3a). The two loops had nearly equivalent probabilities of formation, P_loop (Figure 3b), which in all cases studied was about 50% at F ∼0.9 pN (force at which τ_loop ∼ τ_unloop). As expected, the change in free energy for loop formation, ▵G_l,F, rose with increasing force (i.e. tension destabilizes the loop in the DNA). Therefore, there is no thermodynamic reason to expect a functional difference in transcriptional repression between A1 and A2 loops. In fact, the only significant difference is that the A2 loop forms and breaks down more frequently than the A1 loop having shorter loop and unloop lifetimes, at least for tensions above 0.7 pN (Figure 2). With the current understanding of repression, it is difficult to relate this observation to RNA polymerase activity.

Of course, in vitro transcription assays utilize supercoiled plasmids that are not under so much tension. However, it would not be rigorous to extrapolate the experimental lifetime data to zero force given the necessarily small range of forces investigated, the distance from the zero point, and the logarithmic scale of the y-axis of Figure 2. In addition, loop lifetimes in the absence of force may not be relevant. Evidence is accumulating in the literature (29) that DNA is under tension in vivo and several motor enzymes, such as RNA polymerase have been reported to exert large forces on the topologically constrained DNA (30). Furthermore, DNA molecules negatively supercoiled by 6% have a built-in entropic tension of about 0.5 pN (31).

Thermodynamic stability plays a key role in the function of DNA loops that regulate transcription. Formation of a transient DNA loop may accompany transcriptional activation when a distant, DNA-bound transcription factor directly interacts with RNA polymerase to close the DNA loop. For transient loops, different DNA trajectories might support similar levels of transcriptional activation (32). Instead, DNA loops that repress transcription are generally quite stable. Repressors involved in DNA loop closure can inhibit RNA polymerase action directly (33,34) [e.g. sterically hindering RNA polymerase binding (35–37) or contacting the promoter-bound RNA polymerase to inhibit transcription initiation (38)] or indirectly by reducing the effective torsional flexibility of DNA (39,40) as in the case of loop formation. Loop formation by repressors may be enhanced by accessory DNA-binding proteins that bend the DNA at a critical segment or contribute stabilizing protein–protein interactions. Especially for the transcriptionally repressive cases, thermodynamic characterization of the macromolecular complex permits quantitative prediction of the probability of DNA loop formation (40,41), which might therefore also predict transcription efficiency.

However, we found that gal DNA loops with A1 and A2 trajectories form with similar energies and probabilities in the range of forces investigated, when DNA is untwisted to the level found in vivo and in in vitro transcriptional assays. Therefore, the failure of the A2 loop to repress transcription cannot be explained on the basis of thermodynamics alone. Previously it has been proposed that, failure of the A2 trajectory to repress in vitro transcription of naturally supercoiled DNA may result from destabilization of the DNA loop by RNA polymerase (6). Calculations performed on relaxed DNA show that, despite the fact that the A1 and A2 loops have similar overall structure, the direction of local DNA bending is different; the DNA surface that is inside the A1 loop apex is turned halfway outside in the A2 loop. One consequence is that the HU-binding site, which is experimentally observed at position +6.5 in the A1 loop, shifts to −14.5, a structurally equivalent position with respect to the loop apex in the A2 loop [Figure 1a and Figure 6 in (4)]. A structural- instead of a sequence-dependent binding site is consistent with the very high nonspecific binding affinity of HU for DNA. Thus, these calculations suggest that in the A2 trajectory, RNA polymerase may easily transition from closed to open complex, facilitating transcription (40), or evict HU from the −13.5/−14.5 site, which overlaps the −10 promoter element. Our data support this idea. In our experimental conditions, DNA may be already unwound by an amount sufficient to abrogate the energetic difference between the A1 and A2 loop and yet maintain the structural difference between A1 and A2 loops found in (4).

Furthermore, we speculate that, given the similarity between the lifetime and ▵l data relative to the interaction between heterodimer and wt GalR and A1, the A1 trajectory is preferred in the wild-type case. This is also to be expected given the similar transcriptional repression by A1 and wt loops but not by A2 loops.

In summary, our data show unequivocally that thermodynamic probabilities of Gal repressor/HU-induced alternate DNA loops failed to quantitatively predict their physiological effect. Therefore, in order to predict transcription modulations due to different DNA loop trajectories, one must carefully consider not only looping probabilities but also how DNA supercoiling affects the double helix topology and how this may impact the interactions of proteins associated with a given trajectory. Single molecule experiments such as those described here are very useful for the characterization of this effect. Furthermore, they emphasize how local tension in the DNA may alter the formation of repressive loops. A better understanding of this and the effect of supercoiling on macromolecular complex formation is emerging from such work.