Inferring the in vivo looping properties of DNA

Abstract

The free energy of looping DNA by proteins and protein complexes determines to what extent distal DNA sites can affect each other. We inferred its in vivo value through a combined computational-experimental approach for different lengths of the loop and found that, in addition to the intrinsic periodicity of the DNA double helix, the free energy has an oscillatory component of about half the helical period. Moreover, the oscillations have such an amplitude that the effects of regulatory molecules become strongly dependent on their precise DNA positioning and yet easily tunable by their cooperative interactions. These unexpected results can confer to the physical properties of DNA a more prominent role at shaping the properties of gene regulation than previously thought.

Fig. 1.

Schematic representation of the five possible states for lac repressor binding to two operators for the lac constructs used in the analyzed experiments from Muller et al. (7). The lac Z gene, downstream the main operator, is repressed when the lac repressor (in gray with black contour line) is bound to the main operator (states iii, iv, and v); and unrepressed when the main operator is unoccupied (states i and ii). The thick black line represents the DNA, and the two lac operators are shown as white (auxiliary operator) and highlighted (main operator) boxes. The thick dotted line indicates the different lengths of the spacer DNA between operators.

Fig. 2.

Cartoon of the lac repressor (in gray with black contour line) bound simultaneously to the main (O1) and one auxiliary operator (Oid, with the sequence of the ideal operator), which are represented by white rectangles. Binding of the repressor to O1 represses the lac Z gene in the experiments (7). The simultaneous binding to O1 and Oid with free energies ΔG_O1 and ΔG_Oid, respectively, competes with the unfavorable process of forming a loop (ΔG_l). By using this type of lac constructs, Muller et al. (7) measured the in vivo repression of the lac Z gene as a function of the distance between the centers of the O1 and Oid operators.

Fig. 3.

From enzyme content of E. coli populations to in vivo DNA looping free energies. (a) Measured repression levels, R_loop, as a function of the distance between operators from Muller et al. (7). (b) Inferred free energies of looping using Eq. 1 and R_loop as in a, with R_noloop = 135 and [N] = 75 nM (7). (c) Fourier analysis of the operator distance dependence of the free energy. (d) Behavior of the two main periodic components of the free energy of looping: ΔG_l(l) = 8.79 – 0.68sin(2π l/10.9 – 0.94) – 0.30sin(2π l/5.6 – 2.32), where l is the distance between operators.

Fig. 4.

Corroboration of the main results. (a) Measured repression levels, R_loop, as a function of the distance between operators from figure 4a of Becker et al. (21). (b) Inferred free energies of looping ΔG_l(l), using Eq. 1 and R_loop as in a, with R_noloop = 5 and [N] = 15 nM. (c) Fourier analysis of the operator distance dependence of the free energy. (d) Behavior of the two main periodic components of the free energy of looping: ΔG_l(l) = 9.58 – 0.72sin(2π l/11.6 – 3.08) – 0.28sin(2π l/5.2 – 3.31), where l is the distance between operators.