A single mutation, W220F, in the inducer-binding site of the LacI repressor reduces leakiness [30] The LacI protein belongs to the GalR/LacI family and as a member of this family of transcriptional regulators, LacI contains three domains: a helix-turn-helix motif located in the N terminus, the central domain that binds to LacI sugar ligands, and the C terminal, which comprises the tetramerization domain[19] The crystal structure of the LacI binding site for allosteric effectors has been resolved [31] The importance of the N125 and D149 residues of the N terminal in the recognition of the sugar effector binding site has been determined [31, 32] A mutagenesis-based redesign of LacI enabled functionally compatible labeling with maleimide fluorophores. Three single-cysteine-mutated LacI proteins showed near-wild-type activity, and the cysteine residue at position 281 was retained and determined to be essential for LacI dimerization and DNA binding. It was found that the redesigned LacI retained robust activity in vitro and in vivo [33] Based on a computational rod model of the DNA-LacI complex, the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths was analyzed. Analysis showed that the most stable loops for linear DNA occurred when LacI adopted the extended conformation [34] The importance of architecture for the DNA-binding protein in the DNA repression loop has been determined using high-resolution in vivo protein-mapping techniques with heterologous Nhp6A from Saccharomyces cerevisiae and the E. coli lac promoter [35]. Based on molecular dynamics (MD) simulation, it was determined that the hinge-helix linker region (HH) of LacI is extremely flexible in solution, but a high concentration of salt can help kinetically trap the HH [] A computational analysis suggested that the hinge region of LacI is important for the nonspecific binding to DNA, for which the electrostatic interactions among the LacI protein, DNA, and salt ions are crucial [36] Using a method adapted to high-resolution mapping of protein binding to DNA in living cells, binding of three different DNA loop sizes with the Nhp6A architectural protein was detected for a single sequence in the lac promoter [35]. On the other hand, in an in vivo single-molecule assay, the sliding process for the LacI TF was determined. LacI slides 45 +/- 10 bp on chromosomal DNA, and this can be obstructed by other DNA-bound proteins near the operator. LacI binds to the O1, O2, and O3 operators upstream of the lacZ promoter [37] It slides over its natural lacO1 operator several times before binding (>90% repressor frequency), suggesting a trade-off between a rapid search on nonspecific sequences and fast binding at the specific sequence [38] A 91-bp LacI-mediated, negatively supercoiled DNA loop mimics the DNA loop between the O1 and O3 operators in the lacZp1 promoter [39]. Working with a kinetic model of the lac circuit, it was determined that at least 27 protein molecules are produced no matter how much transcription and translation rates are reduced [40] The stability of DNA topological barriers generated by LacI is proportional to its DNA binding afinity [41] DNA supercoiling is capable of regulating the basal expression of the lac operon [41] Negative supercoiling induces significant looping under any appreciable tension [42] The intracellular mobility and spatial distribution of LacI were studied by using photoactivated localization microscopy combined with single-particle tracking [43] This combined method allowed investigators to determine the relative abundances of specific, near-specific, and nonspecific DNA-binding modes of LacI in vivo [43]