The effect of nonspecific binding of lambda repressor on DNA looping dynamics

Abstract

The λ repressor (CI) protein-induced DNA loop maintains stable lysogeny, yet allows efficient switching to lysis. Herein, the kinetics of loop formation and breakdown has been characterized at various concentrations of protein using tethered particle microscopy and a novel, to our knowledge, method of analysis. Our results show that a broad distribution of rate constants and complex kinetics underlie loop formation and breakdown. In addition, comparison of the kinetics of looping in wild-type DNA and DNA with mutated o3 operators showed that these sites may trigger nucleation of nonspecific binding at the closure of the loop. The average activation energy calculated from the rate constant distribution is consistent with a model in which nonspecific binding of CI between the operators shortens their effective separation, thereby lowering the energy barrier for loop formation and broadening the rate constant distribution for looping. Similarly, nonspecific binding affects the kinetics of loop breakdown by increasing the number of loop-securing protein interactions, and broadens the rate constant distribution for this reaction. Therefore, simultaneous increase of the rate constant for loop formation and reduction of that for loop breakdown stabilizes lysogeny. Given these simultaneous changes, the frequency of transitions between the looped and the unlooped state remains nearly constant. Although the loop becomes more stable thermodynamically with increasing CI concentration, it still opens periodically, conferring sensitivity to environmental changes, which may require switching to lytic conditions.

Figure 1

Different phases of a TPM measurement. (A and B) TPM setup. The centroid of a diffusing bead tethered by a DNA molecule to the glass surface of a flow chamber is tracked in time. Topological modifications of the DNA tether, such as looping, shorten the tether, limiting the excursion of the bead. (C and D) Time traces of a 3477 bp-long wt DNA fragment in the absence (C) and in the presence of 20 nM CI protein (D). The overlaid segments show the results of the cp routine. Although many different levels were obtained by the cp analysis, clustering via the EM routine determined one level in the absence (C) and two levels in the presence of CI (D). The final reconstructed traces are schematically depicted and have been shifted above the trace for clarity. (E and F) Histograms of the ρ traces normalized to the bin width and the total number of events. The histograms represented with empty bins (E and F) correspond to the fraction of the trace identified as the high (unloop) and low (loop) amplitude level, respectively.

Figure 2

Effect of CI concentration on DNA length. (A) Mean values of ρ obtained for the unlooped wt, unlooped o3-, looped wt, looped o3-, and oL-oR- DNA fragments at different CI concentrations (20, 40, 80, or 170 nM). Lines represent mean values of ρ obtained for a 3477 and a 1100 bp DNA fragment in the absence of CI protein. The right y axis represents the effective DNA contour length calculated according to the calibration curve (18) for a persistence length of 46 nm. (B) Effective loop length obtained for wt and o3- at various CI concentrations from a calibration curve (18). The upper line represents the λ loop length (2317 bp). The right y axis represents the difference in energy associated with loop formation calculated as described in the Supporting Material.

Figure 3

Kinetics of loop formation and breakdown. (A and B) Distribution of dwell times spent in the unlooped (A) and looped (B) state for wt (upper panels) and o3- (lower panels) λ DNA at 80 nM CI concentration. Each data set was fitted with the probability distribution function described in Eq. 2 (A) and Eq. 3 (B) as well as with single exponential, double exponential and, only for panel A, with a first passage time distribution. (C and D) Schematic representations of the distribution of rate constants used to fit the unlooped (C) and looped (D) dwell time histograms for the wt and o3- λ DNA.

Figure 4

Rate constants of looping kinetics and consecutive dwell times correlation. (A) The concentration dependence of the rate constants for loop formation k_L associated with bare DNA for the wt (solid squares) and the o3- (solid squares) λ DNA, respectively. The open circles represent the rate constants for loop formation k_f calculated as described in the text. The associated difference in activation energy is reported on the right y axis. (B) Concentration dependence of the rate constants for loop breakdown. The values obtained for k₁ for both types of DNA are represented by the solid squares on the upper part of the plot, whereas the k₃ values, obtained only for wt λ DNA, are represented by the solid squares on the lower part of the plot. These rates are associated with the octamer- and octamer+tetramer-mediated loop, respectively. Dashed lines represent the mean values of k₁ and k₃. The open circles represent the average rate constants for loop breakdown, k_b, calculated as described in the text, for wt and o3- λ DNA. The associated difference in activation energy, calculated as described in the Supporting Material, is reported on the right y axis. (C and D) Log-log scatter plot of the duration of the dwell time in the looped state versus the duration of the previous dwell time in the unlooped state for wt (C) and o3- λ DNA (D) at 80 nM CI concentration. The superimposed solid circles depict the average loop dwell time corresponding to logarithmically binned unloop dwell times.

Figure 5

Energy landscape and mechanism of looping. (A) Schematic energy barrier landscape for loop formation and breakdown in species containing nonspecifically bound CI (open circles). As the CI concentration is increased, more unlooped species are progressively populated, which have higher energy (dashed lines on the left) and more looped species are formed with lower energy (dashed lines on the right). Therefore, the average energy barrier for loop formation is reduced, whereas that for loop breakdown is increased. (B) Free energies of looping for the octamer- (upper solid squares) and octamer+tetramer-mediated loop (lower squares) calculated for wt and o3- λ DNA. The open circles represent the averaged free energy (see the Supporting Material). The associated fraction of time spent in the looped configuration is reported on the right y axis. (C) Schematic representations of the effects of concentration dependent variations of the rate constant for loop formation, k_f, and breakdown, k_b. Left: reducing k_b, while keeping constant k_f, as CI concentration increases, increases the time spent in the loop state but reduces the number of looped and unlooped events per unit time. Right: Opposite changes of both average rate constants (decreasing k_b and increasing k_f) with increasing CI stabilizes the loop while keeping constant the number of looped and unlooped events per unit time. (D) Average number of cycles (from one state to the other and back) per second for wt and o3- λ DNA at the investigated CI concentrations. Opposite variations of k_f and k_b keep the frequency of transitions much higher than it would be if k_f was constant and k_b decreased enough to achieve the ratio of rate constants found experimentally (continuous lines).