If we are to comment on the models of Li and coworkers and others, it is necessary first to be able to reproduce, at least qualitatively, in vivo results such as those of Oehler and coworkers [93, 94].
So far, however, we have not done that: we have foundin vitro that theO3 operator has no effect on looping, and that the three-operator construct behaves the same as a two-operator derivative with O1 and O2 only. We speculated that either nonspecific bending proteins such as HU, or specific bending proteins such as the CAP activator, might enhance looping in vivoand cause the discrepancy between the in vivo and in vitro results. We therefore asked from both a theoretical and an experimental perspective what the effects of proteins like HU and/or CAP might have on this three-operator system. (Other cellular factors such as the supercoiled state of the DNA could also be contributing to this in vivo-in vitro discrepancy; in fact it has been shown in vitro that supercoiling greatly stabilizes the loop between O1 and the auxiliary operators [175, 176]. These other potential contributing factors also need to be considered, though we will have not done so here
100-15 10-13 10-11 10-9 10-7 10-5 0.2
0.4 0.6 0.8 1
LacI Concentration (M)
Looping Probability
100-15 10-13 10-11 10-9 10-7 10-5 0.2
0.4 0.6 0.8 1
LacI Concentration (M)
Looping Probability
+ + + All six states
(A) With HU (B) With CAP
O2 O1 O3
O2 O1 O3
Figure 6.5: Predictions of effect of nonspecific or specific bending proteins such as HU or CAP on looping by the Lac repressor in the presence of three operators. The legend in the center shows schematics for which states of Fig. 6.2 are plotted; looped states versus states with a loop and the third operator bound by a separate repressor are probably not distinguishable in our assay and so are plotted together. They are not equally likely, however: for example, in (A), at repressor concentrations where theO3-O2 loop forms,O1 will also be bound (that is, the state with anO3-O2loop withoutO1also bound separately has zero looping probability at all concentrations). (A)Predictions of the model of Fig. 6.2 for the probabilities of the various looped states in the presence of some amount of HU, if we assume that HU does not change the repressor-operator dissociation constants but only increases all of the J-factors by some amount (here, we assume it increases all J-factors by a factor of 4, consistent with the results presented in the text here in the presence of 500 nM HU; see also [143], where HU increases looping for 60–100 bp loops by a factor of up to 6in vivo).
The amount by which HU increases a loop’s J-factor may actually depend on length, such that, for example, longer loops would on average have more HU molecules bound and so would increase more in apparent flexibility, but we neglect such potential effects here. In these predictions we have usedK3=5 nM to make the trends more noticeable.
(B)Predictions of the model of Fig. 6.2 for the probabilities of the various looped states in the presence of some amount of CAP, if we assume that CAP increases the J-factor for theO1-O3 loop alone by a factor of 10, a value consistent with the -1.4kBT to -2.4kBT stabilization found by biochemical assays [174]. Unlike the addition of HU as shown in (A), the addition of CAP to the TPM assay could bring ourin vitroresults into better alignment with vivoresults in whichO3is an essential component of the system, particularly ifK3is closer to 5 nM than the 15 nM used here. It is also possible that CAP increases the J-factor of theO2-O3 loop as well, but given the data in [93], in which repression in the absence ofO1 (but the presence of the other two operators) is negligible, it is reasonable to assume that CAP stabilizes only theO1-O3 loop. Of course it is likely thatin vivoboth HU and CAP influence looping in thelacoperon.
in these preliminary results.)
HU is known from bothin vitro[177] andin vivo[19] studies to increase the flexibility of DNA, and to enhance DNA looping by the Lac repressor in vivo [19] and by the Gal repressor in vitro [122, 178]. Other nucleoid-associated proteins like IHF have also been shown to enhance looping by the Lac repressorin vitro, at least in some regimes [179]. As will be discussed in more detail in Chapter 7, more rigorousin vitrostudies with HU and the Lac repressor must be done to precisely quantify the effects of HU on looping by the Lac repressor. However, Fig. 6.5(A) shows the prediction of our model for the simplest effect HU might have on looping, in which we assume that HU increases the J-factors for the three loops, leaving the dissociation constants unchanged. The result is that for reasonable values of the amount by which the J-factors might increase in the presence of HU (based
on the literature cited in the figure caption and on our results presented below), the effect of theO3 operator are still negligible.
On the other hand, the CAP protein, which as noted above bends the DNA between the O1
and O3 operators [168] and stabilizes the loop between these two operators [174], might enhance looping between theO1 and O3 operators but not between the other operators, leading to a larger contribution of theO1-O3loop relative to the othersin vitro. Fig. 6.5(B) shows the predictions of our model for the effect CAP might have on our TPM results, again assuming that CAP increases the J-factor for theO1-O3 loop by an amount consistent with literature values, leaving the dissociation constants unchanged. The value of K3 in that prediction is the relatively conservative value of 15 nM; particularly ifK3is closer to 5 nM, CAP could make the stability of theO1-O3loop comparable to that ofO1-O2 at high repressor concentrations, potentially bringing the TPM results into better qualitative agreement with in vivo work where O3 and O2 are both important to the wild-type function of the system.
HU and CAP have both been purified and used in in vitrostudies before (e.g., [122, 168, 177]), and so it should be feasible to add HU and/or CAP to our TPM assay and ask what their effects on looping with the wild-type three-operator lac system and its two-operator derivatives are. In Fig. 6.6 we show preliminary experimental results of the effect of adding HU to a TPM Lac repressor looping assay.3 HU alone compacts the DNA tethers, as has been observed previously using magnetic tweezers [177] (Fig. 6.6(A)); and, as we expect fromin vivoassays [19], HU increases looping by the Lac repressor when both HU and Lac are present (compare Figure 6.4 and Fig. 6.6(B–E)). We can quantify the amount by which HU increases looping by the Lac repressor, again assuming that HU affects only the J-factor and not dissociation constants, by thresholding the traces from the data set represented by Fig. 6.6(B) (the two-operators-only construct that is missingO3) to obtain a looping probability at 1 nM Lac repressor and 500 nM HU of 0.59±0.3. This looping probability corresponds to a J-factor for theO1-O2loop that is roughly 4 times higher than the J-factor determined without
3Purified HU was a kind gift from Remus Dame at Leiden University in the Netherlands, and was sent in a buffer of 25 mM Tris (pH 8.0), 200 mM NaCl, 1 mM EDTA, 5 mM β-mercaptoethanol, and 10% glycerol. The stock concentration is 94µM, so 500 nM HU, the concentration used in our assays, is only a 100- to 200-fold dilution into the Lac repressor buffer. Future work with HU and the Lac repressor should ensure that the small but significant amount of this HU buffer, particularly the glycerol, does not alter the activity of the Lac repressor.
127
(B) No O3, 500 nM HU, 1 nM Lac
(C) No O3, 500 nM HU, 10 nM Lac
0 1000 2000 3000 4000 5000 6000 7000
80 120 160 200 240
Time (sec)
<R> (nm)
0 0.08 0.15
Probability
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80 120 160 200 240
120322_WTnoO3_newscope_500nMHU_1nMlac_area2_discprev_Bead5
Time (sec)
<R> (nm)
0 0.04 0.08
Probability
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120322_WTnoO3_oldscope_slide2_500nMHU_10nMSJlac_area2_Bead7
Time (sec)
<R> (nm)
0 0.08 0.15
Probability 0 1000 2000 3000 4000 5000
80 120 160 200 240
120322_WTnoO3_oldscope_slide2_500nMHU_10nMSJlac_area2_Bead3
Time (sec)
<R> (nm)
0 0.09 0.18
Probability
(D) WT, 500 nM HU,
1 nM Lac 800 1000 2000 3000 4000 5000 120
160 200 240
120306_WTLac_newscope_500nMHU_1nMSJlac_area2_Bead15
Time (sec)
<R> (nm)
0 0.05 0.10
Probability 0 1000 2000 3000 4000 5000
80 120 160 200 240
120306_WTLac_newscope_500nMHU_1nMSJlac_area2_Bead12
Time (sec)
<R> (nm)
0 0.04 0.08
Probability
0 1000 2000 3000 4000 5000 6000 7000
80 120 160 200 240
120306_WTLac_newscope_500nMHU_1nMSJlac_area1_Bead2
Time (sec)
<R> (nm)
0 0.06 0.12
Probability 0 1000 2000 3000 4000 5000
80 120 160 200 240
120306_WTLac_newscope_500nMHU_1nMSJlac_area2_Bead1
Time (sec)
<R> (nm)
0 0.03 0.06
Probability
0 1000 2000 3000 4000 5000
80 120 160 200 240
120306_WTLac_newscope_slide2_500nMHU_10nMSJlac_area1_Bead6
Time (sec)
<R> (nm)
0 0.04 0.09
Probability
(E) WT, 500 nM HU,
10 nM Lac 800 1000 2000 3000 4000 5000
120 160 200 240
120306_WTLac_newscope_slide2_500nMHU_10nMSJlac_area2_Bead9
Time (sec)
<R> (nm)
0 0.05 0.10
Probability
0 1000 2000 3000 4000 5000
80 120 160 200 240
120306_WTLac_newscope_slide2_500nMHU_10nMSJlac_area1_Bead9
Time (sec)
<R> (nm)
0 0.08 0.16
Probability 0 1000 2000 3000 4000 5000
80 120 160 200 240
120306_WTLac_newscope_slide2_500nMHU_10nMSJlac_area2_Bead11
Time (sec)
<R> (nm)
0 0.07 0.13
Probability S
L I DE 115 bp 380 bp
O1 BE A D O2
198 bp CAP
lacI Plac
S L DI E 115 bp380 bp
O1 B E A D O2
198 bp CAP
lacI Plac
S LI D
E 115 bp380 bp 106 bp O1
B E AD O3 O2
71 bp CAP lacI Plac
S LI D
E 115 bp380 bp 106 bp O1
B E AD O3 O2
71 bp CAP lacI Plac
0 0.2 0.4 0.6 0.8 1
110 120 130 140 150 160
HU concentration ( µM)
<R> (nm)
(A) Compaction of DNA by HU
Figure 6.6: The DNA-bending protein HU increases looping by the Lac repressor and may lead to an observable effect from theO3 operatorin vitro. The format for the sample traces in (B–E) is the same as in Fig. 6.4, which shows representative traces for the constructs shown here but in the absence of HU.(A)The RMS motion of a tether in the absence of Lac repressor decreases with increasing HU. This result is comparable to that of [177], especially given the difference in salt concentrations between the two experiments (HU is sensitive to salt). Note that these data are for a shorter construct that in (B–E).(B)Sample trajectories with the construct that contains only theO1 and O2 operators (same construct as the red data of Fig. 6.3), in the presence of 500 nM HU and 1 nM Lac repressor.
Stretches of long dwells as in the top trace are rare without the third operator, but do occur. The bottom trace is more representative of this data set, especially in that it looks like there might be more than two looped states.
It is unclear if this is a real result or an artifact (two operators should yield only two looped states, according to the results of preceding chapters, though if these two looped states are superpositions of the four underlying loop topologies of Fig. 4.3, it is possible that HU changes how many different tether lengths the four states collapse into.
Some traces without HU for this construct may also exhibit more than two looped states, though without HU the looping probability is so low as to make distinguishing looped states difficult. It is also possible that the deletion of O3was incomplete, as is probably the case for the deletion ofO1(see caption to Fig. 6.4)). The black dashed line in this and (C–E) represents the length of the particular tether in the absence of both HU and Lac repressor; note the compaction of the tether in the presence of HU, in that the unlooped state of the blue data is well below the black dashed line.(C)Sample trajectories with the construct that contains only theO1andO2operators, in the presence of 500 nM HU and 10 nM Lac repressor. (D)Sample trajectories with the full three-operator construct (black data in Fig. 6.3), in the presence of 500 nM HU and 1 nM Lac repressor. The top two traces are the most representative of this data set and are not obviously different than those in (B) that lack the third operator; however the bottom two traces show long dwells in one or more looped states that are more common than in the data set in (B), and may indicate the formation of theO2-O3 loop. (E)Sample trajectories with the full three-operator construct in the presence of 500 nM HU and 10 nM Lac repressor. The top trajectories show the long dwells that are common at this repressor concentration, and are suggestive of both theO1-O2 andO2-O3 loops forming (and, interestingly, possibly directly interconverting). The bottom two traces look similar to those in (C) that lack the third operator.
HU (see Fig. 6.3(B)). As shown in Fig. 6.5(A), even ifK3is as low as 5 nM, an increase in J-factors for all of the loops by a factor of 4 should still not allow us to reliably detect loops with O3, nor should we observe a difference between the full three operator construct versus the one that lacks O3.
As suggested by the examples in Fig. 6.6(B–E), there is a large bead-to-bead variation in looping behavior in the presence of HU, especially when all three operators are present, and so more data will be necessary to differentiate spurious behavior from real results before conclusions can be drawn about the effect of HU on this three-operator system. More importantly, a quantitative analysis and objective state identification is crucial, which we believe will be best accomplished by the hidden Markov model analysis discussed in the previous chapter. However, from the trajectories in Figs. 6.4 and 6.6(B–E) it does appear that the presence of the O3 operator, with HU in the sample, alters the dynamics of looping: with HU and O3, long dwells in one or more looped states are observed, some of whose lengths are suggestive of the formation of the O2-O3 loop, and possibly its direct interconversion with theO1-O2 loop. Some traces also appear to have states at RMS values that would correspond to the O1-O3 loop. It will be exciting to see if these trends hold with more data and a more rigorous analysis.