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. 2013 Dec;10(6):066005.
doi: 10.1088/1478-3975/10/6/066005. Epub 2013 Nov 15.

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

James Q Boedicker  1 , Hernan G Garcia, Stephanie Johnson, Rob Phillips
Affiliations

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

James Q Boedicker et al. Phys Biol. 2013 Dec.

Abstract

As the chief informational molecule of life, DNA is subject to extensive physical manipulations. The energy required to deform double-helical DNA depends on sequence, and this mechanical code of DNA influences gene regulation, such as through nucleosome positioning. Here we examine the sequence-dependent flexibility of DNA in bacterial transcription factor-mediated looping, a context for which the role of sequence remains poorly understood. Using a suite of synthetic constructs repressed by the Lac repressor and two well-known sequences that show large flexibility differences in vitro, we make precise statistical mechanical predictions as to how DNA sequence influences loop formation and test these predictions using in vivo transcription and in vitro single-molecule assays. Surprisingly, sequence-dependent flexibility does not affect in vivo gene regulation. By theoretically and experimentally quantifying the relative contributions of sequence and the DNA-bending protein HU to DNA mechanical properties, we reveal that bending by HU dominates DNA mechanics and masks intrinsic sequence-dependent flexibility. Such a quantitative understanding of how mechanical regulatory information is encoded in the genome will be a key step towards a predictive understanding of gene regulation at single-base pair resolution.

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Figures

Figure 1
Figure 1. Loop-mediated repression of gene expression
(A) We have created a suite of synthetic YFP expression constructs, in which the promoter expressing YFP is under negative control by the E. coli Lac repressor. There are two binding sites for the repressor in the vicinity of the promoter: a main operator located at +11 relative to the transcription start site and an auxiliary operator located upstream from the promoter at a variable distance. Lac repressor can bind to both operators simultaneously, looping the intervening DNA. There are four commonly used lac operators, each with a different affinity for Lac repressor. Here we use Oid as the auxiliary operator and O2 as the main operator. The variable region of the loop is derived either from a synthetic, random E8 sequence, or a putatively very flexible TA sequence [30]. The operator distance is defined from the center of each operator. (B) Placing constructs into host strains that do not express Lac repressor results in high expression of the YFP reporter gene. R is the number of repressors per cell. (C) Placing constructs into host strains that express Lac repressor results in loop formation which reduces expression of the reporter gene.
Figure 2
Figure 2. A quantitative model of gene expression predicts how cellular parameters tune the level of repression
(A) The states of the DNA looping constructs, their associated weights, and the rates of transcription from each state used in the thermodynamic model. Refer to text for a description of the different variables. (B) From the statistical mechanical model, an expression for the experimentally measurable quantity repression was derived, Equation 4. This equation quantifies how each “knob” of the system (operator binding energies, number of repressors per cell, loop sequence and length) modulates the reduction of gene expression. We use this expression to predict how repression (Rep) will be influenced by the flexibility of the looping sequence. (C) The two looping sequences used in this work represent the extremes of flexibility observed by [24], as measured by the J-factor of cyclization (a higher J-factor indicates increased flexibility). Here we test the hypothesis that a more flexible looping sequence will increase repression in vivo.
Figure 3
Figure 3. Prediction of repression for a flexible looping sequence
(A) Repression for operator distances between 80.5 and 145.5 bp are shown for the random loop sequence for constructs containing the operators O2 and Oid as main and auxiliary operators, respectively. (B) Using Equation S4, the looping free energy was extracted from the repression data for each operator distance. The data in (A) and (B) were previously reported in [48]. (C) Using the results from (B) as a starting point, repression was found to be sensitive to decreases in the looping energy over the range of looping energies for the random sequence (red shaded region). (D) Predicted repression using Equation 4 when the looping energy is decreased by 1 or 2 kBT for operator distances between 80.5 and 145.5. The previously reported results shown in (A) were used as a basis for the predictions. Shaded regions in (D) represent standard error of the prediction. Error bars correspond to the standard error.
Figure 4
Figure 4. Calculation of the looping energy for the random and flexible DNA sequences from in vitro measurements of looping probability
(A) The tethered particle motion (TPM) assay was used to quantify the in vitro mechanical properties of the random and flexible looping sequences. (B) Results previously reported in [51] show the probability of looping for each sequence as determined by measuring the change in the length of the DNA tether over time in the presence of Lac repressor. (C) Using the previously reported results in (B), the looping energies of each sequence were calculated. The flexible sequence lowers the looping energy by 1–3 kBT at many loop lengths. Error bars correspond to standard errors for looping probabilities and bootstrapped errors for looping energies [51].
Figure 5
Figure 5. In vivo loop-mediated repression
In vivo assay for loop-mediated repression using a fluorescent gene reporter was used to compare repression (A) and looping energies (B) for the random and flexible looping sequences. (C) Plotting the difference in the observed looping energy between the random and flexible sequences at each loop length emphasizes that both sequences have similar propensities to form loops in vivo. In contrast, the in vitro looping free energy of the random sequence can be more than 2 kBT greater than the flexible sequence. The dashed red line corresponds to no difference between the looping energies. Error bars correspond to standard errors.
Figure 6
Figure 6. Deletion of HU restores sequence dependence of loop-mediated repression
(A) Repression in the absence (“ΔHU”) versus presence (“+HU”) of the nonspecific DNA-bending protein HU. Consistent with previous reports [5], deletion of HU decreases repression at all lengths. However, we show here that the presence of HU also masks a sequence dependence to looping that is only detectable when HU is deleted. (B) Comparison of the ratio in repression observed for the random and flexible sequences with and without HU. Error bars are standard errors.
Figure 7
Figure 7. Modeling sequence-dependent buffering by assisted loop formation
(A) A model that incorporates two modes of loop formation adds a new state of assisted looping, state 8, to the model shown in Figure 2A. (B) Given that repression in wild type cells is not dependent on sequence as shown in Figure 5, we assume the assisted looping energies for both the random and flexible sequences are equal. The unassisted looping energy for the flexible sequence is δ kBT greater than the assisted looping energy, and the unassisted looping energy for the random sequence is (δ+σ) kBT greater than the assisted looping energy. (C–D) Using experimental data from Figure 5A as a starting point, when the difference between the unassisted looping energies for the flexible and random sequences, σ, is 2 kBT, the model predicts how repression will change as δ is increased. Calculations use Equations 8 and 9. (C) For δ = 0, the flexible sequence represses more than the random sequence. (D) For δ = 2 kBT, loops containing flexible sequences of DNA repress similarly to loops containing random sequences.
Figure 8
Figure 8. Effect of HU on in vitro loop formation
(A) Probability of looping as a function HU concentration for both the flexible (red squares) and random (black circles) looping sequences. Loop formation in the presence of 100 pM Lac repressor was measured using a tethered particle motion in vitro assay. Dotted lines show the fit of a two-state looping model, in which the loop can form with either 0 or 1 HU molecules in the looping region as shown in the top of (B). Solid lines show the fit of a three-state looping model, in which the loop can form with 0, 1, or 2 HU molecules in the loop as shown in the bottom of (B). For the flexible looping sequence, the fit to the two- and three-state models almost completely overlap. (C) Looping energies ± standard error fit to the in vitro data using either the two-state or three-state looping model. See Supplementary Information for further details. Error bars are standard errors. Broken axis in (A) is used to show the looping probabilities at 0 HU.
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