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 computationalexperimental 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.computational modeling ͉ DNA looping ͉ gene expression ͉ lac operon ͉ regulation T he cell is a densely packed dynamic structure made of thousands of different molecular species that orchestrate their interactions to form a functional unit. Such complexity poses a strong barrier for experimentally characterizing the cellular components: not only the properties of the components can change when studied in vitro outside the cell, but also the in vivo probing of the cell can perturb the process under study (1). Here we use computational modeling to obtain the properties of the in vivo unperturbed components at the molecular level from physiological measurements at the cellular level. Explicitly, we infer the in vivo free energies of DNA looping from enzyme production in the lac operon (2).The formation of DNA loops by the binding of proteins at distal DNA sites plays a fundamental role in many cellular processes, such as transcription, recombination, and replication (3-5). In gene regulation, proteins bound far away from the genes they regulate can be brought to the initiation of transcription region by looping the intervening DNA. The free energy cost of this process determines how easily DNA can loop and therefore the extent to which distal DNA sites can affect each other (5).In the lac operon, there is a repressor molecule that regulates transcription by binding specifically to DNA sites known as operators and preventing the RNA polymerase from transcribing the genes. DNA looping allows the repressor to bind to two operators simultaneously, leading to an increase in repression of transcription. This increase, characterized by the repression level, can be connected to the free energy of looping DNA by a recent model for transcription regulation by the lac repressor (6). The distance between operators determines the length of the DNA loop and affects the repression level through the changes in the free energy of looping. For interoperator distances from 57.5 to 98.5 bp, Muller et al. (7) systematically varied the distance between two operators in increments of 1 bp and measured the in vivo repression levels under conditions similar to wild type. These physiological measurements of enzyme production in Escherichia coli cell populations allowed us to ...