Lac repressor hinge flexibility and DNA looping: single molecule kinetics by tethered particle motion

Abstract

The tethered particle motion (TPM) allows the direct detection of activity of a variety of biomolecules at the single molecule level. First pioneered for RNA polymerase, it has recently been applied also to other enzymes. In this work we employ TPM for a systematic investigation of the kinetics of DNA looping by wild-type Lac repressor (wt-LacI) and by hinge mutants Q60G and Q60 + 1. We implement a novel method for TPM data analysis to reliably measure the kinetics of loop formation and disruption and to quantify the effects of the protein hinge flexibility and of DNA loop strain on such kinetics. We demonstrate that the flexibility of the protein hinge has a profound effect on the lifetime of the looped state. Our measurements also show that the DNA bending energy plays a minor role on loop disruption kinetics, while a strong effect is seen on the kinetics of loop formation. These observations substantiate the growing number of theoretical studies aimed at characterizing the effects of DNA flexibility, tension and torsion on the kinetics of protein binding and dissociation, strengthening the idea that these mechanical factors in vivo may play an important role in the modulation of gene expression regulation.

Figure 1

The TPM experiment. The DNA molecule is shown in black, with the two operators highlighted by the black boxes. The Lac repressor tetramer (LacI) is schematically drawn as a V-shaped molecule. The microsphere is shown in gray and the range of diffusion allowed to the sphere by the DNA tether is shown as a dashed line. The upper panel shows unlooped DNA, the lower panel shows the same molecule looped by the binding of a Lac repressor tetramer to the two operators. The drawing is not to scale.

Figure 2

Examples of TPM experimental recordings obtained with wild-type LacI. The left panels show time courses of the average radius of microsphere mobility, 〈R(t)〉 (calculated as described in the Materials and Methods section, choosing a Gaussian filter with cutoff frequency of 0.066 Hz) obtained with LacI at a concentration of 100 pM (a), 20 pM (c), and 4 pM (e). The right panels show the distributions of 〈R(t)〉 corresponding to each of the recordings shown on the left. The lines represent the best fit of the sum of two Gaussians (see Materials and Methods) to the histogram. The fitted parameters are shown in the insets.

Figure 3

Examples of TPM experimental recordings obtained with LacI mutants Q60G and Q60 + 1. The left panels show time courses of the average radius of mobility, 〈R(t)〉 (calculated as in Figure 2), obtained with Q60G (a) and Q60 + 1 (c) at a concentration of 100 pM. Histograms (shown on the right) are fitted with two Gaussians as described in Figure 2.

Figure 4

Distributions of dwell-times of wild-type LacI. The histograms are distributions of the loop (left) and unloop (right) dwell-times measured on TPM recordings obtained with wild-type LacI at concentrations of 100 pM (a: loop; b: unloop), 20 pM (c: loop; d: unloop) and 4 pM (e: loop; f: unloop). The dwell-times were measured after filtering the 〈R(t)〉 data, as described in text, with a Gaussian filter with a cutoff frequency of 0.033 Hz, characterized by a dead time of 5.4 s. Only events with durations longer than twice the dead time are plotted. The lines in the left panels represent fit to the data using a mono-exponential function $N\left(t\right)=\left(w{N}_{\text{tot}}/\tau \right)\text{exp}\left[-\left(t-t_0\right)/\tau \right]$, where N_tot is the total number of events observed, w is the histogram bin width, and t₀ is the shortest plotted duration (10.8 s). The insets report the value of the fitted parameter τ and the reduced χ². The lines in the right panels represent fit to the data using a double-exponential function $N\left(t\right)=w{N}_{\text{tot}}\left[\left(a/{\tau }_1\right)\text{exp}\right(-t/{\tau }_1)+(\left(1-a\right)/{\tau }_2)\text{exp}\left(-t/{\tau }_2)\right]/\left[a\text{exp}\left(-t_0/{\tau }_1\right)+\left(1-a\right)\text{exp}\left(-t_0/{\tau }_2\right)\right]$.

Figure 5

Distributions of dwell-times of the LacI mutants Q60G and Q60 + 1. The histograms are distributions of the loop (left) and unloop (right) dwell-times measured on TPM recordings obtained with Q60G (a: loop; b: unloop) and Q60 + 1 (c: loop; d: unloop) at a concentration of 100 pM. The histogram and the fit in the left panels were obtained as described in Figure 4.

Figure 6

Scheme of the biochemical states corresponding to the loop and unloop states as measured with TPM. O and R represent the operator sequence and the Lac repressor tetramer, respectively. k_a and k_d are the association and dissociation rate constants of LacI for a single operator. J_m and α are defined in the text. The segment between the two operators represents the intervening (305 bp long) DNA sequence.

Figure 7

Choice of filter and measured looped and unlooped lifetimes. The measured average lifetimes are reported as a function of the filter dead time (T_d). (a): the average loop (filled symbols) and unloop lifetimes (empty symbols) are shown for wt-LacI at 100 pM (squares), 20 pM (triangles) and 4 pM (circles). (b): the average loop (filled symbols) and unloop lifetimes (empty symbols) are shown for wild-type LacI (squares), Q60G (triangles) and Q60 + 1 (circles), all at a concentration of 100 pM.