Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor. © 2014 Biton et al

Calculated values characterizing looping probabilities.

<p>Calculated values of -factors, and optimized values of binding constants , , and the open loop ratio for the three cases described in the text: <b>A</b> (900 bp DNA with 326 bp loop and 245 nm bead), <b>B</b> (1632 bp DNA with 600 bp loop and 160 nm bead), and <b>C</b> (1632 bp DNA with 900 bp loop and 160 nm bead). The dissociation constants , , and the ratio were obtained by performing an optimized nonlinear fit between the experimental results and theoretical joint distribution as function of [LacI] (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0092475#pone.0092475.e220" target="_blank">equation (26)</a>) as described in the text. For the case <b>A</b> we used experimental results shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0092475#pone-0092475-g003" target="_blank">Figure 3</a> of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0092475#pone.0092475-Han1" target="_blank">[19]</a>.</p

Probability density functions for RMS values of the projected distances.

<p>The probability density functions for RMS values of the projected distance calculated for the loop topologies, P1, P2, A1, A2, the loop associated with the open conformation of the Lac repressor, an unlooped DNA with one or both sites occupied, and the free DNA. (<b>A</b>) 900 bp DNA attached to a bead with radius = 245 nm; loop length is 326 bp. (<b>B</b>) 1632 bp DNA attached to a bead with radius = 160 nm; loop length is 600 bp. (<b>C</b>) 1632 bp DNA attached to a bead with radius = 160 nm; loop length is 900 bp. Each graph shows the distribution of values (in nm), computed from distributions in order to mimick the window averaging of traces during the processing of TPM traces (see text).</p

An illustrations of the Lac repressor in its possible conformations.

<p>A space filling model of the Lac repressor tetramer in its stiff V-shaped conformation (right) and a schematic representation of our assumed model of the open (extended) conformation of the Lac repressor (left). To simulate the open conformation, we assumed that the two dimeric arms of the Lac repressor are connected by a spherical joint that permits them to rotated freely about the joint. Thus, the three degrees of freedom characterizing the relative orientation between the two arms can attain any feasible value in the configurational space with no energetic cost for the conformational change of the Lac repressor.</p

Experimental and simulated probability density of the projected distance for the 1632 bp DNA.

<p>The probability density of the projected distance between attached DNA end and bead center, as measured in our TPM experiments (blue bars) and computed by numerical simulation (green curve). The 1632 bp tethered DNA molecule is unlooped for the duration of this experiment. The bead radius is 160 nm.</p

Kinematical variables.

<p>Schematic representations of the kinematical variables that describe the relative orientation and displacement of consecutive base pairs. Each drawing illustrates a case in which one of the kinematical variables has a positive value and the others (with the exception of ) are set equal to zero.</p

Calibration curves of the projected RMS distance (center of bead to attached end) for five bead radii.

<p>For each bead radius, a curve based on the numerical fit given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0092475#pone.0092475-Nelson1" target="_blank">[26]</a> is shown (marked with circles) together with our calculated curve. Our model is based on homogeneous DNA segments with persistence length of 476 .</p

Base-pair step.

<p>A schematic drawing of the two adjacent base pairs forming the -th step of DNA. Each nucleotide base in the -th base pair is covalently bonded at its darkened corner to one of the two sugar phosphate backbone chains. The direction of that oriented chain is indicated by a light-face arrow; the chain itself is not shown. The gray-shaded long edges are in the minor groove of the DNA.</p