Table 1.
Naturally occurring and synthetic nucleosome-positioning or nucleosome-repelling sequences used in this study.
Figure 1.
Looping probability as a function of loop length and sequence.
(A) Schematic of the tethered particle motion (TPM) assay for measuring looping. In TPM, a bead is tethered to the surface of a microscope coverslip by a linear DNA. The motion of the bead serves as a readout for the state of the tether: if the DNA tether contains two binding sites for a looping protein such as the Lac repressor, and the looping protein is present and binds both sites simultaneously, forming a loop, the motion of the bead is reduced in a detectable fashion [47]–[50]. The motion of the bead is observed over time, and the looping probability for a particular DNA is defined as the time spent in the looped (reduced motion) state, divided by the total observation time. (B) Schematic of the “no promoter” (left) and “with-promoter” (right) constructs used in this work. “Loop length” is defined as the inner edge-to-edge distance between operators (excluding the operators themselves, but including the promoter, if present). (C) Looping probabilities for the five sequences described in Table 1, without the bacterial lacUV5 promoter sequence as part of the loop. (D) Looping probabilities for the same five sequences but with the promoter sequence in the loop. Righthand panels in (C) and (D) show the same data as lefthand panels, except magnified around loop lengths 100–110 bp. The five sequences do not all share the same maxima of looping (colored arrows), not even the TA and 5S sequences that share similar sequence features (see Figures S1 and S2 in File S1), though each sequence has the same maximum with and without the promoter (as far as can be determined with the current data; note that the with-promoter maximum for the TA sequence could be at 105 or 106, as those points are within error). All E8 and TA data (in particular, those outside of the 101–108 bp range) were previously described in [35].
Figure 2.
Looping J-factors as a function of loop length and sequence.
J-factors for sequences without (closed circles) and with (open circles) the lacUV5 promoter were extracted from the data in Fig. 1 as described in the Methods section. The J-factor is a measure of the free energy of loop formation (and is related to the bending and twisting flexibility of the DNA in the loop): the higher the J-factor, the lower the free energy required to deform the loop region DNA into a loop. As described in [35], the addition of the promoter to the E8 loop sequence does not significantly affect its J-factor, so the J-factor for E8 with the promoter is shown as a reference in all panels (black open points). In contrast to E8, the addition of the promoter does change the J-factors for three of the four other sequences, making the TA-containing loops more flexible, but the 5S and, to a lesser extent, CG sequences less flexible. Interestingly, the poly(dA:dT) sequence, like the E8 sequence, is unchanged with the inclusion of the promoter. We note that because the no-promoter versus with-promoter constructs contain different combinations of repressor binding sites, we can only use J-factors, not looping probabilities, to quantitatively examine the effect of the promoter; the statistical mechanical model of Eqn. 2 allows us to make this comparison.
Figure 3.
Comparison of the likelihood of the “middle” (longer) versus “bottom” (shorter) looped states.
The y-axes indicate the fraction of the total J-factor that is contributed by the middle state (as in Fig. 2, since the with- and without-promoter constructs have different operators, J-factors and not looping probabilities must be compared). That is, when the ratio is unity, indicated by a horizontal black dashed line, only the middle state is observed; when this ratio is zero, again indicated by a horizontal black dashed line, only the bottom state is observed. Closed circles are no-promoter constructs; open circles are with-promoter. E8 and TA data are a subset of those in [35]. Figure S4 in File S1 shows the looping probabilities and J-factors for the two states instead of the relative measures shown here.
Figure 4.
Tether length as a function of loop length, sequence and J-factor.
(A) Sample TPM time trajectory showing the smoothed (i.e. Gaussian-filtered) root-mean-squared motion, , of a single bead. This construct shows an unlooped state and two looped states, the “middle” state around 130 nm, and the “bottom” state around 110 nm. Black horizontal dashed line indicates the average
for this particular tether in the absence of repressor. Due to variability in tether length even in the absence of repressor [35], on the y-axes in (B) and (D) we plot a relative measure of tether length, by normalizing the mean
value for a particular state to the mean
of each tether in the absence of repressor, and then taking the population average of this difference. (B) Tether length as a function of loop length. We observe a modulation of tether length with loop length, with the shortest tether lengths for both the unlooped and looped states occurring near the maximum of looping (indicated for each sequence by the colored arrows at the bottoms of the plots). See Fig. S5 in File S1 for bottom state lengths. (C) Schematic of our proposed model for the observed variations in unlooped tether length as a function of loop length, which we attribute to the phasing of the bends that the repressor creates upon binding the operators. A similar argument can be made for the looped states. Note that to emphasize the effect of bending from the operators, here we have for the most part represented the DNA as straight segments. (D) Tether length as a function of J-factor. Unlooped state tether lengths are plotted versus the total J-factor, whereas middle state tether lengths are plotted versus the J-factor for the middle state. As in (B), in general the length of the tether in both the unlooped and middle looped states is shorter at larger J-factors (that is, more in-phase operators) for a particular sequence. However, this trend is sharper for some sequences than others (see Fig. S6 in File S1 for the other sequences, which generally have more scatter than either the dA or CG sequences).
Figure 5.
Comparing trends in sequence flexibility for looping versus cyclization and nucleosome formation.
(A) Nucleosome formation and cyclization share trends in sequence flexibility, with sequences that have lower energies of nucleosome formation () also having lower energies of cyclization (
). Cloutier and Widom used this correlation to argue that the same mechanical properties, particularly the bendability, of the DNA contributed to nucleosome formation as to cyclization [8]. The energy of cyclization,
, is related to the cyclization J-factor for a particular DNA,
, through the relationship
, where
is the temperature,
is the gas constant and
is an arbitrary reference molecule (see Ref. [8] for details). Adapted from Refs. [8], [77]. (B) Looping J-factors for the no-promoter data do not show the same trends in sequence dependence as do cyclization and nucleosome formation: if anything, a higher cyclization J-factor correlates with a lower looping J-factor. (C) Same as (B) but for with-promoter DNAs. The cyclization J-factors of the poly(dA:dT)-rich and GC-rich sequences that we use here have not been reported, so they are shown as shaded regions whose height reflects the uncertainty in the looping J-factors we measure, and whose width reflect our estimates about what their cyclization behavior should be. In particular, the poly(dA:dT)-rich sequence exhibits very low nucleosome occupancy in vivo [22], [23], and similar sequences have high energies of nucleosome formation in vitro [22], [28], which, according to the logic of (A), should correspond to a low cyclization J-factor, probably lower than that of E8. Some poly(dA:dT)-rich DNAs were in fact recently directly shown to cyclize less readily than random sequences [34]. In contrast, the GC-rich sequence should be a good nucleosome former (though the nucleosome affinity of this particular sequence has not been tested either in vivo or in vitro), and so its cyclization J-factor is probably comparable to that of 5S and TA, the other strong nucleosome-preferring sequences on this plot. Additional details of how this plot was generated can be found in the Methods section.
Figure 6.
Maximum looping J-factor as a function of loop G+C content.
Maximum J-factors for each of the five sequences, with (closed circles) and without (open circles) promoter, are plotted with respect to each sequence's G+C content. For nucleosomes, G+C content strongly correlates with nucleosome occupancy [17]. In contrast, it appears that G+C content and loopability are anticorrelated. Loop lengths plotted here are the same as in Fig. 5.