Strong DNA binding by covalently linked dimeric Lac headpiece: evidence for the crucial role of the hinge helices

Can molecular dynamics be used to simulate biomolecular recognition?

There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are challenged by the size of systems and the time scales needed to describe relevant motions. In theory, enhanced sampling algorithms can help to overcome some of the limitations of molecular simulations. Here, we discuss a problem in biochemistry that offers a significant challenge for enhanced sampling methods and that could, therefore, serve as a benchmark for comparing approaches that use machine learning to find suitable collective variables. In particular, we study the transitions LacI undergoes upon moving between being non-specifically and specifically bound to DNA. Many degrees of freedom change during this transition and that the transition does not occur reversibly in simulations if only a subset of these degrees of freedom are biased. We also explain why this problem is so important to biologists and the transformative impact that a simulation of it would have on the understanding of DNA regulation.

Ligand-specific changes in conformational flexibility mediate long-range allostery in the lac repressor

Biological regulation ubiquitously depends on protein allostery, but the regulatory mechanisms are incompletely understood, especially in proteins that undergo ligand-induced allostery with few structural changes. Here we used hydrogen-deuterium exchange with mass spectrometry (HDX/MS) to map allosteric effects in a paradigm ligand-responsive transcription factor, the lac repressor (LacI), in different functional states (apo, or bound to inducer, anti-inducer, and/or DNA). Although X-ray crystal structures of the LacI core domain in these states are nearly indistinguishable, HDX/MS experiments reveal widespread differences in flexibility. We integrate these results with modeling of protein-ligand-solvent interactions to propose a revised model for allostery in LacI, where ligand binding allosterically shifts the conformational ensemble as a result of distinct changes in the rigidity of secondary structures in the different states. Our model provides a mechanistic basis for the altered function of distal mutations. More generally, our approach provides a platform for characterizing and engineering protein allostery.

Conformational Change of Transcription Factors from Search to Specific Binding: A lac Repressor Case Study

In a process known as facilitated diffusion, DNA-binding proteins find their target sites by combining three-dimensional diffusion and one-dimensional scanning of the DNA. Following the trade-off between speed and stability, agile exploration of DNA requires loose binding, whereas, at the DNA target site, the searching protein needs to establish tight interactions with the DNA. To enable both efficient search and stable binding, DNA-binding proteins and DNA often switch conformations upon recognition. Here, we study the one-dimensional diffusion and DNA binding of the dimeric lac repressor (LacI), which was reported to adopt two different conformations when binding different conformations of DNA. Using coarse-grained molecular dynamic simulations, we studied the diffusion and the sequence-specific binding of these conformations of LacI, as well as their truncated or monomeric variants, with two DNA conformations: straight and bent. The simulations were compared to experimental observables. This study supports that linear diffusion along DNA combines tight rotation-coupled groove tracking and rotation-decoupled hopping, where the protein briefly dissociates and reassociates just a few base pairs away. Tight groove tracking is crucial for target-site recognition, while hopping speeds up the overall search process. We investigated the diffusion of different LacI conformations on DNA and show how the flexibility of LacI's hinge regions ensures agility on DNA as well as faithful groove tracking. If the hinge regions instead form α-helices at the protein-DNA interface, tight groove tracking is not possible. On the contrary, the helical hinge region is essential for tight binding to bent, specific DNA, for the formation of the specific complex. Based on our study of different encounter complexes, we argue that the conformational change in LacI and DNA bending are somewhat coupled. Our findings underline the importance of two distinct protein conformations for facilitated diffusion and specific binding, respectively.

Substitutions at Nonconserved Rheostat Positions Modulate Function by Rewiring Long-Range, Dynamic Interactions

Amino acid substitutions at nonconserved protein positions can have noncanonical and "long-distance" outcomes on protein function. Such outcomes might arise from changes in the internal protein communication network, which is often accompanied by changes in structural flexibility. To test this, we calculated flexibilities and dynamic coupling for positions in the linker region of the lactose repressor protein. This region contains nonconserved positions for which substitutions alter DNA-binding affinity. We first chose to study 11 substitutions at position 52. In computations, substitutions showed long-range effects on flexibilities of DNA-binding positions, and the degree of flexibility change correlated with experimentally measured changes in DNA binding. Substitutions also altered dynamic coupling to DNA-binding positions in a manner that captured other experimentally determined functional changes. Next, we broadened calculations to consider the dynamic coupling between 17 linker positions and the DNA-binding domain. Experimentally, these linker positions exhibited a wide range of substitution outcomes: Four conserved positions tolerated hardly any substitutions ("toggle"), ten nonconserved positions showed progressive changes from a range of substitutions ("rheostat"), and three nonconserved positions tolerated almost all substitutions ("neutral"). In computations with wild-type lactose repressor protein, the dynamic couplings between the DNA-binding domain and these linker positions showed varied degrees of asymmetry that correlated with the observed toggle/rheostat/neutral substitution outcomes. Thus, we propose that long-range and noncanonical substitutions outcomes at nonconserved positions arise from rewiring long-range communication among functionally important positions. Such calculations might enable predictions for substitution outcomes at a range of nonconserved positions.

DNA immobilization and detection using DNA binding proteins

The immobilization of sensing bioreceptors is a critical feature affecting the final performance of a biosensor. For DNA detection, the (strept)avidin-biotin affinity interaction is often used for the immobilization of biotin-labeled oligonucleotides or PCR amplicons. Herein, DNA binding proteins are proposed as alternative universal anchors for both DNA immobilization and detection, based on the strong and specific affinity interaction between certain DNA binding proteins and their respective dsDNA binding sites. These binding sites can be incorporated in the target DNA molecule during synthesis and by PCR, eliminating the need for post-synthesis chemical modification and resulting in lower costs. When scCro DNA binding protein was immobilized on microplates and nitrocellulose membrane, both ssDNA and dsDNA targets were successfully detected. The detection limits achieved were similar to those obtained with the streptavidin-biotin system. However, the scCro system resulted in higher signals while using less amount of protein. The adsorption properties of scCro were superior to streptavidin's, making scCro a viable alternative as an anchor biomolecule for the development of DNA assays and biosensors. Finally, a nucleic acid lateral flow assay based solely on two different DNA binding proteins, scCro and dHP, was developed for the detection of a PCR amplicon. Overall, the proposed system appears to be very promising and with potential use for multiplex detection using various DNA binding proteins with different sequence specificities. Further work is required to better understand the adsorption properties of these biomolecules on nitrocellulose, optimize the assays comprehensively, and achieve improved sensitivities.

Characterization of nucleosome sediments for protein interaction studies by solid-state NMR spectroscopy

Regulation of DNA-templated processes such as gene transcription and DNA repair depend on the interaction of a wide range of proteins with the nucleosome, the fundamental building block of chromatin. Both solution and solid-state NMR spectroscopy have become an attractive approach to study the dynamics and interactions of nucleosomes, despite their high molecular weight of ~ 200 kDa. For solid-state NMR (ssNMR) studies, dilute solutions of nucleosomes are converted to a dense phase by sedimentation or precipitation. Since nucleosomes are known to self-associate, these dense phases may induce extensive interactions between nucleosomes, which could interfere with protein-binding studies. Here, we characterized the packing of nucleosomes in the dense phase created by sedimentation using NMR and small-angle X-ray scattering (SAXS) experiments. We found that nucleosome sediments are gels with variable degrees of solidity, have nucleosome concentration close to that found in crystals, and are stable for weeks under high-speed magic angle spinning (MAS). Furthermore, SAXS data recorded on recovered sediments indicate that there is no pronounced long-range ordering of nucleosomes in the sediment. Finally, we show that the sedimentation approach can also be used to study low-affinity protein interactions with the nucleosome. Together, our results give new insights into the sample characteristics of nucleosome sediments for ssNMR studies and illustrate the broad applicability of sedimentation-based NMR studies.

Structural basis of a novel repressor, SghR, controlling Agrobacterium infection by cross-talking to plants

Agrobacterium tumefaciens infects various plants and causes crown gall diseases involving temporal expression of virulence factors. SghA is a newly identified virulence factor enzymatically releasing salicylic acid from its glucoside conjugate and controlling plant tumor development. Here, we report the structural basis of SghR, a LacI-type transcription factor highly conserved in Rhizobiaceae family, regulating the expression of SghA and involved in tumorigenesis. We identified and characterized the binding site of SghR on the promoter region of sghA and then determined the crystal structures of apo-SghR, SghR complexed with its operator DNA, and ligand sucrose, respectively. These results provide detailed insights into how SghR recognizes its cognate DNA and shed a mechanistic light on how sucrose attenuates the affinity of SghR with DNA to modulate the expression of SghA. Given the important role of SghR in mediating the signaling cross-talk during Agrobacterium infection, our results pave the way for structure-based inducer analog design, which has potential applications for agricultural industry.

Price of disorder in the lac repressor hinge helix

The Lac system of genes has been pivotal in understanding gene regulation. When the lac repressor protein binds to the correct DNA sequence, the hinge region of the protein goes through a disorder to order transition. The structure of this region of the protein is well understood when it is in this bound conformation, but less so when it is not. Structural studies show that this region is flexible. Our simulations show this region is extremely flexible in solution; however, a high concentration of salt can help kinetically trap the hinge helix. Thermodynamically, disorder is more favorable without the DNA present.

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe-a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.

Lactose repressor hinge domain independently binds DNA

The short 8-10 amino acid "hinge" sequence in lactose repressor (LacI), present in other LacI/GalR family members, links DNA and inducer-binding domains. Structural studies of full-length or truncated LacI-operator DNA complexes demonstrate insertion of the dimeric helical "hinge" structure at the center of the operator sequence. This association bends the DNA ∼40° and aligns flanking semi-symmetric DNA sites for optimal contact by the N-terminal helix-turn-helix (HtH) sequences within each dimer. In contrast, the hinge region remains unfolded when bound to nonspecific DNA sequences. To determine ability of the hinge helix alone to mediate DNA binding, we examined (i) binding of LacI variants with deletion of residues 1-50 to remove the HtH DNA binding domain or residues 1-58 to remove both HtH and hinge domains and (ii) binding of a synthetic peptide corresponding to the hinge sequence with a Val52Cys substitution that allows reversible dimer formation via a disulfide linkage. Binding affinity for DNA is orders of magnitude lower in the absence of the helix-turn-helix domain with its highly positive charge. LacI missing residues 1-50 binds to DNA with ∼4-fold greater affinity for operator than for nonspecific sequences with minimal impact of inducer presence; in contrast, LacI missing residues 1-58 exhibits no detectable affinity for DNA. In oxidized form, the dimeric hinge peptide alone binds to O1 and nonspecific DNA with similarly small difference in affinity; reduction to monomer diminished binding to both O1 and nonspecific targets. These results comport with recent reports regarding LacI hinge interaction with DNA sequences.

Proteins Recognizing DNA: Structural Uniqueness and Versatility of DNA-Binding Domains in Stem Cell Transcription Factors

Proteins in the form of transcription factors (TFs) bind to specific DNA sites that regulate cell growth, differentiation, and cell development. The interactions between proteins and DNA are important toward maintaining and expressing genetic information. Without knowing TFs structures and DNA-binding properties, it is difficult to completely understand the mechanisms by which genetic information is transferred between DNA and proteins. The increasing availability of structural data on protein-DNA complexes and recognition mechanisms provides deeper insights into the nature of protein-DNA interactions and therefore, allows their manipulation. TFs utilize different mechanisms to recognize their cognate DNA (direct and indirect readouts). In this review, we focus on these recognition mechanisms as well as on the analysis of the DNA-binding domains of stem cell TFs, discussing the relative role of various amino acids toward facilitating such interactions. Unveiling such mechanisms will improve our understanding of the molecular pathways through which TFs are involved in repressing and activating gene expression.

Insights into the Structure of Sulfolobus Nucleoid Using Engineered Sac7d Dimers with a Defined Orientation

The structure of Archaeal chromatin or nucleoid is believed to have characteristics similar to that found in both eukaryotes and bacteria. Recent comparative studies have suggested that DNA compaction in Archaea requires a bridging protein (e.g., Alba) along with either a wrapping protein (e.g., a histone) or a bending protein such as Sac7d. While X-ray crystal structures demonstrate that Sac7d binds as a monomer to create a significant kink in duplex DNA, the structure of a multiprotein-DNA complex has not been established. Using cross-linked dimers of Sac7d with a defined orientation, we present evidence that indicates that Sac7d is able to largely coat duplex DNA in vivo by binding in alternating head-to-head and tail-to-tail orientations. Although each Sac7d monomer promotes a significant kink of nearly 70°, coated DNA is expected to be largely extended because of compensation of repetitive kinks with helical symmetry.

Optimized expression and purification of biophysical quantities of Lac repressor and Lac repressor regulatory domain

The recombinant production of Lac repressor (LacI) in Escherichia coli is complicated by its ubiquitous use as a regulatory element in commercially-available expression vectors and host strains. While LacI-regulated expression systems are often used to produce recombinant LacI, the product can be heterogeneous and unsuitable for some studies. Alternative approaches include using unregulated vectors which typically suffer from low yield or vectors with promoters induced by metabolically active sugars which can dilute isotope labels necessary for certain biophysical studies. Here, an optimized expression system and isolation protocol for producing various constructs of LacI is introduced which eliminates these complications. The expression vector is an adaptation of the pASK backbone wherein expression of the lacI gene is regulated by an anhydrotetracyline inducible tetA promoter and the host strain lacks the lacI gene. Typical yields in highly deuterated minimal medium are nearly 2-fold greater than those previously reported. Notably, the new expression system is also able to produce the isolated regulatory domain of LacI without co-expression of the full-length protein and without any defects in cell viability, eliminating the inconvenient requirement for strict monitoring of cell densities during pre-culturing. Typical yields in highly deuterated minimal medium are significantly greater than those previously reported. Characterization by solution NMR shows that LacI constructs produced using this expression system are highly homogenous and functionally active.

The Hinge Region Strengthens the Nonspecific Interaction between Lac-Repressor and DNA: A Computer Simulation Study

LacI is commonly used as a model to study the protein-DNA interaction and gene regulation. The headpiece of the lac-repressor (LacI) protein is an ideal system for investigation of nonspecific binding of the whole LacI protein to DNA. The hinge region of the headpiece has been known to play a key role in the specific binding of LacI to DNA, whereas its role in nonspecific binding process has not been elucidated. Here, we report the results of explicit solvent molecular dynamics simulation and continuum electrostatic calculations suggesting that the hinge region strengthens the nonspecific interaction, accounting for up to 50% of the micro-dissociation free energy of LacI from DNA. Consequently, the rate of microscopic dissociation of LacI from DNA is reduced by 2~3 orders of magnitude in the absence of the hinge region. We find the hinge region makes an important contribution to the electrostatic energy, the salt dependence of electrostatic energy, and the number of salt ions excluded from binding of the LacI-DNA complex.

The Hinge Region Strengthens the Nonspecific Interaction between Lac-Repressor and DNA: A Computer Simulation Study

LacI is commonly used as a model to study the protein-DNA interaction and gene regulation. The headpiece of the lac-repressor (LacI) protein is an ideal system for investigation of nonspecific binding of the whole LacI protein to DNA. The hinge region of the headpiece has been known to play a key role in the specific binding of LacI to DNA, whereas its role in nonspecific binding process has not been elucidated. Here, we report the results of explicit solvent molecular dynamics simulation and continuum electrostatic calculations suggesting that the hinge region strengthens the nonspecific interaction, accounting for up to 50% of the micro-dissociation free energy of LacI from DNA. Consequently, the rate of microscopic dissociation of LacI from DNA is reduced by 2~3 orders of magnitude in the absence of the hinge region. We find the hinge region makes an important contribution to the electrostatic energy, the salt dependence of electrostatic energy, and the number of salt ions excluded from binding of the LacI-DNA complex.

Structure, function, and tethering of DNA-binding domains in σ⁵⁴ transcriptional activators

We compare the structure, activity, and linkage of DNA-binding domains (DBDs) from σ(54) transcriptional activators and discuss how the properties of the DBDs and the linker to the neighboring domain are affected by the overall properties and requirements of the full proteins. These transcriptional activators bind upstream of specific promoters that utilize σ(54)-polymerase. Upon receiving a signal the activators assemble into hexamers, which then, through adenosine triphosphate (ATP) hydrolysis, drive a conformational change in polymerase that enables transcription initiation. We present structures of the DBDs of activators nitrogen regulatory protein C 1 (NtrC1) and Nif-like homolog 2 (Nlh2) from the thermophile Aquifex aeolicus. The structures of these domains and their relationship to other parts of the activators are discussed. These structures are compared with previously determined structures of the DBDs of NtrC4, NtrC, ZraR, and factor for inversion stimulation. The N-terminal linkers that connect the DBDs to the central domains in NtrC1 and Nlh2 were studied and found to be unstructured. Additionally, a crystal structure of full-length NtrC1 was solved, but density of the DBDs was extremely weak, further indicating that the linker between ATPase and DBDs functions as a flexible tether. Flexible linking of ATPase and DBDs is likely necessary to allow assembly of the active hexameric ATPase ring. The comparison of this set of activators also shows clearly that strong dimerization of the DBD only occurs when other domains do not dimerize strongly.

Sliding and target location of DNA-binding proteins: an NMR view of the lac repressor system

In non-specific lac headpiece-DNA complexes selective NMR line broadening is observed that strongly depends on length and composition of the DNA fragments. This broadening involves amide protons found in the non-specific lac-DNA structure to be interacting with the DNA phosphate backbone, and can be ascribed to DNA sliding of the protein along the DNA. This NMR exchange broadening has been used to estimate the 1D diffusion constant for sliding along non-specific DNA. The observed 1D diffusion constant of 4×10(-12) cm(2)/s is two orders of magnitude smaller than derived from previous kinetic experiments, but falls in the range of values determined more recently using single molecule methods. This strongly supports the notion that sliding could play at most a minor role in the association kinetics of binding of lac repressor to lac operator and that other processes such as hopping and intersegment transfer contribute to facilitate the DNA recognition process.

DNA-recognition process described by MD simulations of the lactose repressor protein on a specific and a non-specific DNA sequence

The lactose repressor protein may bind DNA in two possible configurations: a specific one, if the DNA sequence corresponds to a binding site, and a non-specific one otherwise. To find its target sequences, the lactose repressor first binds non-specifically to DNA, and subsequently, it rapidly searches for a binding site. Atomic structures of non-specific and specific complexes are available from crystallographic and nuclear magnetic resonance experiments. However, what remains unknown is a detailed description of the steps that transform the non-specific complex into the specific one. Here, how the protein first recognizes its binding site has been studied using molecular dynamics simulations. The picture that emerges is that of a protein that is as mobile when interacting with non-specific DNA sequences as when free in solution. This high degree of mobility allows the protein to rapidly sample different DNA sequences. In contrast, when the protein encounters a binding site, the configuration ensemble collapses, and the protein sliding movements along the DNA sequence become scarce. The binding energies in the specific and non-specific complexes were analysed using the Molecular Mechanics Poisson Boltzmann Surface Area approach. These results represent a first step towards a throughout characterization of the DNA-recognition process.

Introductory lecture: interpreting and predicting Hofmeister salt ion and solute effects on biopolymer and model processes using the solute partitioning model

Understanding how Hofmeister salt ions and other solutes interact with proteins, nucleic acids, other biopolymers and water and thereby affect protein and nucleic acid processes as well as model processes (e.g. solubility of model compounds) in aqueous solution is a longstanding goal of biophysical research. Empirical Hofmeister salt and solute "m-values" (derivatives of the observed standard free energy change for a model or biopolymer process with respect to solute or salt concentration m3) are equal to differences in chemical potential derivatives: m-value = delta(dmu2/dm3) = delta mu23, which quantify the preferential interactions of the solute or salt with the surface of the biopolymer or model system (component 2) exposed or buried in the process. Using the solute partitioning model (SPM), we dissect mu23 values for interactions of a solute or Hofmeister salt with a set of model compounds displaying the key functional groups of biopolymers to obtain interaction potentials (called alpha-values) that quantify the interaction of the solute or salt per unit area of each functional group or type of surface. Interpreted using the SPM, these alpha-values provide quantitative information about both the hydration of functional groups and the competitive interaction of water and the solute or salt with functional groups. The analysis corroborates and quantifies previous proposals that the Hofmeister anion and cation series for biopolymer processes are determined by ion-specific, mostly unfavorable interactions with hydrocarbon surfaces; the balance between these unfavorable nonpolar interactions and often-favorable interactions of ions with polar functional groups determine the series null points. The placement of urea and glycine betaine (GB) at opposite ends of the corresponding series of nonelectrolytes results from the favorable interactions of urea, and unfavorable interactions of GB, with many (but not all) biopolymer functional groups. Interaction potentials and local-bulk partition coefficients quantifying the distribution of solutes (e.g. urea, glycine betaine) and Hofmeister salt ions in the vicinity of each functional group make good chemical sense when interpreted in terms of competitive noncovalent interactions. These interaction potentials allow solute and Hofmeister (noncoulombic) salt effects on protein and nucleic acid processes to be interpreted or predicted, and allow the use of solutes and salts as probes of

Nuclear magnetic resonance analysis of protein-DNA interactions

Recent methodological and instrumental advances in solution-state nuclear magnetic resonance have opened up the way to investigating challenging problems in structural biology such as large macromolecular complexes. This review focuses on the experimental strategies currently employed to solve structures of protein-DNA complexes and to analyse their dynamics. It highlights how these approaches can help in understanding detailed molecular mechanisms of target recognition.

Specificity and affinity of Lac repressor for the auxiliary operators O2 and O3 are explained by the structures of their protein-DNA complexes

The structures of a dimeric mutant of the Lac repressor DNA-binding domain complexed with the auxiliary operators O2 and O3 have been determined using NMR spectroscopy and compared to the structures of the previously determined Lac-O1 and Lac-nonoperator complexes. Structural analysis of the Lac-O1 and Lac-O2 complexes shows highly similar structures with very similar numbers of specific and nonspecific contacts, in agreement with similar affinities for these two operators. The left monomer of the Lac repressor in the Lac-O3 complex retains most of these specific contacts. However, in the right half-site of the O3 operator, there is a significant loss of protein-DNA contacts, explaining the low affinity of the Lac repressor for the O3 operator. The binding mode in the right half-site resembles that of the nonspecific complex. In contrast to the Lac-nonoperator DNA complex where no hinge helices are formed, the stability of the hinge helices in the weak Lac-O3 complex is the same as in the Lac-O1 and Lac-O2 complexes, as judged from the results of hydrogen/deuterium experiments.

Experimental identification of specificity determinants in the domain linker of a LacI/GalR protein: bioinformatics-based predictions generate true positives and false negatives

In protein families, conserved residues often contribute to a common general function, such as DNA-binding. However, unique attributes for each homolog (e.g. recognition of alternative DNA sequences) must arise from variation in other functionally-important positions. The locations of these "specificity determinant" positions are obscured amongst the background of varied residues that do not make significant contributions to either structure or function. To isolate specificity determinants, a number of bioinformatics algorithms have been developed. When applied to the LacI/GalR family of transcription regulators, several specificity determinants are predicted in the 18 amino acids that link the DNA-binding and regulatory domains. However, results from alternative algorithms are only in partial agreement with each other. Here, we experimentally evaluate these predictions using an engineered repressor comprising the LacI DNA-binding domain, the LacI linker, and the GalR regulatory domain (LLhG). "Wild-type" LLhG has altered DNA specificity and weaker lacO(1) repression compared to LacI or a similar LacI:PurR chimera. Next, predictions of linker specificity determinants were tested, using amino acid substitution and in vivo repression assays to assess functional change. In LLhG, all predicted sites are specificity determinants, as well as three sites not predicted by any algorithm. Strategies are suggested for diminishing the number of false negative predictions. Finally, individual substitutions at LLhG specificity determinants exhibited a broad range of functional changes that are not predicted by bioinformatics algorithms. Results suggest that some variants have altered affinity for DNA, some have altered allosteric response, and some appear to have changed specificity for alternative DNA ligands.

Functional consequences of exchanging domains between LacI and PurR are mediated by the intervening linker sequence

Homologue function can be differentiated by changing residues that affect binding sites or long-range interactions. LacI and PurR are two proteins that represent the LacI/GalR family (>500 members) of bacterial transcription regulators. All members have distinct DNA-binding and regulatory domains linked by approximately 18 amino acids. Each homologue has specificity for different DNA and regulatory effector ligands; LacI and PurR also exhibit differences in allosteric communication between DNA and effector binding sites. A comparative study of LacI and PurR suggested that alterations in the interface between the regulatory domain and linker are important for differentiating their functions. Four residues (equivalent to LacI positions 48, 55, 58, and 61) appear particularly important for creating a unique interface and were predicted to be necessary for allosteric regulation. However, nearby residues in the linker interact with DNA ligand. Thus, differences observed in interactions between linker and regulatory domain may be the cause of altered function or an effect of the two proteins binding different DNA ligands. To separate these possibilities, we created a chimeric protein with the LacI DNA-binding domain/linker and the PurR regulatory domain (LLhP). If the interface requires homologue-specific interactions in order to propagate the signal from effector binding, then LLhP repression should not be allosterically regulated by effector binding. Experiments show that LLhP is capable of repression from lacO1 and, contrary to expectation, allosteric response is intact. Further, restoring the potential for PurR-like interactions via substitutions in the LLhP linker tends to diminish repression. These effects are especially pronounced for residues 58 and 61. Clearly, binding affinity of LLhP for the lacO1 DNA site is sensitive to long-range changes in the linker. This result also raises the possibility that mutations at positions 58 and 61 co-evolved with changes in the DNA-binding site. In addition, repression measured in the absence and presence of effector ligand shows that allosteric response increases for several LLhP variants with substitutions at positions 48 and 55. Thus, while side chain variation at these sites does not generally dictate the presence or absence of allostery, the nature of the amino acid can modulate the response to effector.

Ligand-induced conformational changes and conformational dynamics in the solution structure of the lactose repressor protein

We present here the results of a series of small-angle X-ray scattering studies aimed at understanding the role of conformational changes and structural flexibility in DNA binding and allosteric signaling in a bacterial transcription regulator, lactose repressor protein (LacI). Experiments were designed to detect possible conformational changes that occur when LacI binds either DNA or the inducer IPTG, or both. Our studies included the native LacI dimer of homodimers and a dimeric variant (R3), enabling us to probe conformational changes within the homodimers and distinguish them from those involving changes in the homodimer-homodimer relationships. The scattering data indicate that removal of operator DNA (oDNA) from R3 results in an unfolding and extension of the hinge helix that connects the LacI regulatory and DNA-binding domains. In contrast, only very subtle conformational changes occur in the R3 dimer-oDNA complex upon IPTG binding, indicative of small adjustments in the orientations of domains and/or subdomains within the structure. The binding of IPTG to native (tetrameric) LacI-oDNA complexes also appears to facilitate a modest change in the average homodimer-homodimer disposition. Notably, the crystal structure of the native LacI-oDNA complex differs significantly from the average solution conformation. The solution scattering data are best fit by an ensemble of structures that includes (1) approximately 60% of the V-shaped dimer of homodimers observed in the crystal structure and (2) approximately 40% of molecules with more "open" forms, such as those generated when the homodimers move with respect to each other about the tetramerization domain. In gene regulation, such a flexible LacI would be beneficial for the interaction of its two DNA-binding domains, positioned at the tips of the V, with the required two of three LacI operators needed for full repression.

Radiation-induced oxidative damage to the DNA-binding domain of the lactose repressor

Understanding the cellular effects of radiation-induced oxidation requires the unravelling of key molecular events, particularly damage to proteins with important cellular functions. The Escherichia coli lactose operon is a classical model of gene regulation systems. Its functional mechanism involves the specific binding of a protein, the repressor, to a specific DNA sequence, the operator. We have shown previously that upon irradiation with gamma-rays in solution, the repressor loses its ability to bind the operator. Water radiolysis generates hydroxyl radicals (OH* radicals) which attack the protein. Damage of the repressor DNA-binding domain, called the headpiece, is most likely to be responsible of this loss of function. Using CD, fluorescence spectroscopy and a combination of proteolytic cleavage with MS, we have examined the state of the irradiated headpiece. CD measurements revealed a dose-dependent conformational change involving metastable intermediate states. Fluorescence measurements showed a gradual degradation of tyrosine residues. MS was used to count the number of oxidations in different regions of the headpiece and to narrow down the parts of the sequence bearing oxidized residues. By calculating the relative probabilities of reaction of each amino acid with OH. radicals, we can predict the most probable oxidation targets. By comparing the experimental results with the predictions we conclude that Tyr7, Tyr12, Tyr17, Met42 and Tyr47 are the most likely hotspots of oxidation. The loss of repressor function is thus correlated with chemical modifications and conformational changes of the headpiece.

Flexibility and adaptability in binding of E. coli cytidine repressor to different operators suggests a role in differential gene regulation

Interactions between DNA-bound transcription factors CytR and CRP regulate the promoters of the Escherichia coli CytR regulon. A distinctive feature of the palindromic CytR operators is highly variable length central spacers (0-9 bp). Previously we demonstrated distinct modes of CytR binding to operators that differ in spacer length. These different modes are characterized by opposite enthalpic and entropic contributions at 25 degrees C. Of particular note were radically different negative DeltaCp values suggesting variable contribution from coupled protein folding and/or DNA structural transitions. We proposed that the CytR DNA binding-domain adopts either a more rigid or flexible DNA-bound conformation in response to the different spacer lengths. More recently, similar effects were shown to contribute to discrimination between operator and non-specific DNA binding by LacR, a CytR homolog. Here we have extended the thermodynamic analysis to the remaining natural CytR operators plus a set of synthetic operators designed to isolate spacing as the single variable. The thermodynamic results show a broad and monotonic range of effects that are primarily dependent on spacer length. The magnitude of effects suggests participation by more than the DNA-binding domain. 15N HSQC NMR and CD spectral analyses were employed to characterize the structural basis for these effects. The results indicate that while CytR forms a well-ordered structure in solution, it is highly dynamic. We propose a model in which a large ensemble of native state conformations narrows upon binding, to an extent governed by operator spacing. This in turn is expected to constrain intermolecular interactions in the CytR-CRP-DNA complex, thus generating operator-specific effects on repression and induction of transcription.

Cooperative α-helix unfolding in a protein-DNA complex from hydrogen-deuterium exchange

We present experimental evidence for a cooperative unfolding transition of an alpha-helix in the lac repressor headpiece bound to a symmetric variant of the lac operator, as inferred from hydrogen-deuterium (H-D) exchange experiments monitored by NMR spectroscopy. In the EX1 limit, observed exchange rates become pH-independent and exclusively sensitive to local structure fluctuations that expose the amide proton HN to exchange. Close to this regime, we measured decay rates of individual backbone HN signals in D2O, and of their mutual HN-HN NOE by time-resolved two-dimensional (2D) NMR experiments. The data revealed correlated exchange at the center of the lac headpiece recognition helix, Val20-Val23, and suggested that the correlation breaks down at Val24, at the C terminus of the helix. A lower degree of correlation was observed for the exchange of Val9 and Ala10 at the center of helix 1, while no correlation was observed for Val38 and Glu39 at the center of helix 3. We conclude that HN exchange in the recognition helix and, to some extent, in helix 1 is a cooperative event involving the unfolding of these helices, whereas the HN exchange in helix 3 is dominated by random local structure fluctuations.

Extrinsic interactions dominate helical propensity in coupled binding and folding of the lactose repressor protein hinge helix

A significant number of eukaryotic regulatory proteins are predicted to have disordered regions. Many of these proteins bind DNA, which may serve as a template for protein folding. Similar behavior is seen in the prokaryotic LacI/GalR family of proteins that couple hinge-helix folding with DNA binding. These hinge regions form short alpha-helices when bound to DNA but appear to be disordered in other states. An intriguing question is whether and to what degree intrinsic helix propensity contributes to the function of these proteins. In addition to its interaction with operator DNA, the LacI hinge helix interacts with the hinge helix of the homodimer partner as well as to the surface of the inducer-binding domain. To explore the hierarchy of these interactions, we made a series of substitutions in the LacI hinge helix at position 52, the only site in the helix that does not interact with DNA and/or the inducer-binding domain. The substitutions at V52 have significant effects on operator binding affinity and specificity, and several substitutions also impair functional communication with the inducer-binding domain. Results suggest that helical propensity of amino acids in the hinge region alone does not dominate function; helix-helix packing interactions appear to also contribute. Further, the data demonstrate that variation in operator sequence can overcome side chain effects on hinge-helix folding and/or hinge-hinge interactions. Thus, this system provides a direct example whereby an extrinsic interaction (DNA binding) guides internal events that influence folding and functionality.

Use of urea and glycine betaine to quantify coupled folding and probe the burial of DNA phosphates in lac repressor-lac operator binding

Thermodynamic analysis of urea-biopolymer interactions and effects of urea on folding of proteins and alpha-helical peptides shows that urea interacts primarily with polar amide surface. Urea is therefore predicted to be a quantitative probe of coupled folding, remodeling, and other large-scale changes in the amount of water-accessible polar amide surface in protein processes. A parallel analysis indicates that glycine betaine [N,N,N-trimethylglycine (GB)] can be used to detect burial or exposure of anionic (carboxylate, phosphate) biopolymer surface. To test these predictions, we have investigated the effects of these solutes (0-3 m) on the formation of 1:1 complexes between lac repressor (LacI) and its symmetric operator site (SymL) at a constant KCl molality. Urea reduces the binding constant K(TO) [initial slope dlnK(TO)/dm(urea) = -1.7 +/- 0.2], and GB increases K(TO) [initial slope dlnK(TO)/dm(GB) = 2.1 +/- 0.2]. For both solutes, this derivative decreases with an increase in solute concentration. Analysis of these initial slopes predicts that (1.5 +/- 0.3) x 10(3) A2 of polar amide surface and (4.5 +/- 1.0) x 10(2) A2 of anionic surface are buried in the association process. Analysis of published structural data, together with modeling of unfolded regions of free LacI as extended chains, indicates that 1.5 x 10(3) A2 of polar amide surface and 6.3 x 10(2) A2 of anionic surface are buried in complexation. Quantitative agreement between structural and thermodynamic results is obtained for amide surface (urea); for anionic surface (GB), the experimental value is approximately 70% of the structural value. For LacI-SymL binding, two-thirds of the structurally predicted change in amide surface (1.0 x 10(3) A2) occurs outside the protein-DNA interface in protein-protein interfaces formed by folding of the hinge helices and interactions of the DNA binding domain (DBD) with the core of the repressor. Since urea interacts principally with amide surface, it is particularly well-suited to detect and quantify the extent of coupled folding and other large-scale remodeling events in the steps of protein-nucleic acid interactions and other protein associations.

Altered specificity in DNA binding by the lac repressor: a mutant lac headpiece that mimics the gal repressor

Recognition of the lac operator by the lac repressor involves specific interactions between residues in the repressor's recognition helix and bases in the DNA major groove. Tyr17 and Gln18, at positions 1 and 2 in the lac repressor recognition helix, can be exchanged for other amino acids to generate mutant repressors that display altered specificity. We have solved the solution structure of a protein-DNA complex of an altered-specificity mutant lac headpiece in which Tyr17 and Gln18 were exchanged for valine and alanine, respectively, as found in the recognition helix of the gal repressor. As previously described by Lehming et al. (EMBO J. 1987, 6, 3145-3153), this altered-specificity mutant of the lac repressor recognizes a variant lac operator that is similar to the gal operator Oe. The mutant lac headpiece showed the predicted specificity and is also able to mimic the gal repressor by recognizing and bending the natural gal operator Oe. These structural data show that, while most of the anchoring points that help the lac headpiece to assemble on the lac operator were preserved, a different network of protein-DNA interactions connecting Ala17 and Val18 to bases in the DNA major groove drives the specificity towards the altered operator.

Modification of DNA radiolysis by DNA-binding proteins: structural aspects

Formation of specific complexes between proteins and their cognate DNA modulates the yields and the location of radiation damage on both partners of the complex. The radiolysis of DNA-protein complexes is studied for: (1) the Escherichia coli lactose operator-repressor complex, (2) the complex between DNA bearing an analogue of an abasic site and the repair protein Fpg of Lactococcus lactis. Experimental patterns of DNA damages are presented and compared to predicted damage distribution obtained using an improved version of the stochastic model RADACK. The same method is used for predicting the location of damages on the proteins. At doses lower than a threshold that depends on the system, proteins protect their specific binding site on DNA while at high doses, the studied complexes are disrupted mainly through protein damage. The loss of binding ability is the functional consequence of the amino-acids modification by OH* radicals. Many of the most probably damaged amino acids are essential for the DNA-protein interaction and within a complex are protected by DNA.

Energetic differences between the specific binding of a 40bp DNA duplex and the lac promoter to lac repressor protein

The energetics of LRP binding to a 104 bp lac promoter determined from ITC measurements were compared to the energetics of binding to a shorter 40 bp DNA duplex with the 21 bp promoter binding site sequence. The promoter binding affinity of 2.47 +/- 0.0 1x 10(7) M(-1) was higher than the DNA binding affinity of 1.81 +/- 0.67 x 10(7) M(-1) while the binding enthalpy of -804 +/- 41 kJ mol(-1) was lower than that of the DNA binding enthalpy of -145 +/- 16 kJ mol(-1) at 298.15 K. Both the promoter and DNA binding reactions were exothermic in phosphate buffer but endothermic in Tris buffer that showed the transfer of four protons to LRP in the former reaction but only two in the latter. A more complicated dependence of these parameters on temperature was observed for promoter binding. These energetic differences are attributable to additional LRP-promoter interactions from wrapping of the promoter around the LRP.

Radiation Abolishes Inducer Binding to Lactose Repressor

The lactose operon functions under the control of the repressor-operator system. Binding of the repressor to the operator prevents the expression of the structural genes. This interaction can be destroyed by the binding of an inducer to the repressor. If ionizing radiations damage the partners, a dramatic dysfunction of the regulation system may be expected. We showed previously that gamma irradiation hinders repressor-operator binding through protein damage. Here we show that irradiation of the repressor abolishes the binding of the gratuitous inducer isopropyl-1-beta-D-thiogalactoside (IPTG) to the repressor. The observed lack of release of the repressor from the complex results from the loss of the ability of the inducer to bind to the repressor due to the destruction of the IPTG binding site. Fluorescence measurements show that both tryptophan residues located in or near the IPTG binding site are damaged. Since tryptophan damage is strongly correlated with the loss of IPTG binding ability, we conclude that it plays a critical role in the effect. A model was built that takes into account the kinetic analysis of damage production and the observed protection of its binding site by IPTG. This model satisfactorily accounts for the experimental results and allows us to understand the radiation-induced effects.

Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential

Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the process of recognition, a protein rapidly searches for its specific site on a long DNA molecule and then strongly binds this site. Here we aim to find a mechanism that can provide both a fast search (1-10 s) and high stability of the specific protein-DNA complex (Kd=10(-15)-10(-8) M). Earlier studies have suggested that rapid search involves sliding of the protein along the DNA. Here we consider sliding as a one-dimensional diffusion in a sequence-dependent rough energy landscape. We demonstrate that, despite the landscape's roughness, rapid search can be achieved if one-dimensional sliding is accompanied by three-dimensional diffusion. We estimate the range of the specific and nonspecific DNA-binding energy required for rapid search and suggest experiments that can test our mechanism. We show that optimal search requires a protein to spend half of its time sliding along the DNA and the other half diffusing in three dimensions. We also establish that, paradoxically, realistic energy functions cannot provide both rapid search and strong binding of a rigid protein. To reconcile these two fundamental requirements we propose a search-and-fold mechanism that involves the coupling of protein binding and partial protein folding. The proposed mechanism has several important biological implications for search in the presence of other proteins and nucleosomes, simultaneous search by several proteins, etc. The proposed mechanism also provides a new framework for interpretation of experimental and structural data on protein-DNA interactions.

Allosteric transition pathways in the lactose repressor protein core domains: asymmetric motions in a homodimer

The crystal structures of lactose repressor protein (LacI) provide static endpoint views of the allosteric transition between DNA- and IPTG-bound states. To obtain an atom-by-atom description of the pathway between these two conformations, motions were simulated with targeted molecular dynamics (TMD). Strikingly, this homodimer exhibited asymmetric dynamics. All asymmetries observed in this simulation are reproducible and can begin on either of the two monomers. Asymmetry in the simulation originates around D149 and was traced back to the pre-TMD equilibrations of both conformations. In particular, hydrogen bonds between D149 and S193 adopt a variety of configurations during repetitions of this process. Changes in this region propagate through the structure via noncovalent interactions of three interconnected pathways. The changes of pathway 1 occur first on one monomer. Alterations move from the inducer-binding pocket, through the N-subdomain beta-sheet, to a hydrophobic cluster at the top of this region and then to the same cluster on the second monomer. These motions result in changes at (1) side chains that form an interface with the DNA-binding domains and (2) K84 and K84', which participate in the monomer-monomer interface. Pathway 2 reflects consequent reorganization across this subunit interface, most notably formation of a H74-H74rsquo; pi-stacking intermediate. Pathway 3 extends from the rear of the inducer-binding pocket, across a hydrogen-bond network at the bottom of the pocket, and transverses the monomer-monomer interface via changes in H74 and H74rsquo;. In general, intermediates detected in this study are not apparent in the crystal structures. Observations from the simulations are in good agreement with biochemical data and provide a spatial and sequential framework for interpreting existing genetic data.

Controlled transcriptional regulation in eukaryotes by a novel transcription factor derived from Escherichia coli purine repressor

Unlike the DNA-binding domains (DBD) of most eukaryotic transcription factors, Escherichia coli LacI family transcription factors are unable to bind to specific target DNA sequences without a cofactor-binding domain. In the present study, we reconstructed a novel DBD designated as PurHG, which binds constitutively to a 16bp purine repressor operator, by fusion of the purine repressor (PurR) DBD (residues 1-57) and the GAL4 dimerization domain (DD, residues 42-148). Binding of PurHG to DNA requires the dimerization and a hinge helix of PurR DBD. When the PurHG was expressed as a fusion protein in a form of a transcription activator (PurAD) or an artificial nuclear receptor (PurAPR or PurAER) responding to ligand, such as RU486 or beta-estradiol, it could regulate the expression of the reporter genes in NIH3T3 cells. The prerequisite region of the GAL4 DD for DNA-binding was amino acid residues from 42 to 98 in the form of PurAD, while the amino acid residues from 42 to 75 were sufficient for ligand-dependent regulation in the form of PurAPR. These results suggest that the dimerization function of the progesterone ligand-binding domain could be substituted for region 76-98 of the GAL4 DD. In summary, the fusion of the PurR DBD and the GAL4 DD generates fully active DNA-binding protein, PurHG, in vitro and in vivo, and these results provide the direct evidence of structural predictions that the proximate positioning of PurR hinge helical regions is critical for DNA-binding.

Structure and Flexibility Adaptation in Nonspecific and Specific Protein-DNA Complexes

Interaction of regulatory DNA binding proteins with their target sites is usually preceded by binding to nonspecific DNA. This speeds up the search for the target site by several orders of magnitude. We report the solution structure and dynamics of the complex of a dimeric lac repressor DNA binding domain with nonspecific DNA. The same set of residues can switch roles from a purely electrostatic interaction with the DNA backbone in the nonspecific complex to a highly specific binding mode with the base pairs of the cognate operator sequence. The protein-DNA interface of the nonspecific complex is flexible on biologically relevant time scales that may assist in the rapid and efficient finding of the target site.

DNA radiolysis in DNA-protein complexes: a stochastic simulation of attack by hydroxyl radicals

PURPOSE

To propose an improved version of RADACK, a stochastic simulation of radiolytic attack on DNA, that takes into account the reactivity of each amino acid of a specifically bound protein with hydroxyl radicals. To apply it to the natural lactose operator-repressor complex taking advantage of recently reported structures. To compare the obtained probabilities of DNA strand break induction with those calculated with the previous versions and with an experimental pattern of strand break probabilities.

MATERIALS AND METHODS

Models of complexes close to the natural ones, derived from crystallography- and NMR-based structures recently available in the PDB databank, were used. The specific chemical reactivity of each amino acid was introduced in the new version of RADACK (the reactivity model). The probabilities of strand break induction by the irradiation of the complex were calculated with this new version as well as with previous ones.

RESULTS

The patterns of probabilities of strand break induction calculated with the improved version of RADACK were partially different from those obtained with previous versions. The patterns obtained for both, using putative models of natural complexes, were consistent with the experimental results, but some discrepancies were suggestive of slight differences between these structures and the real natural system. The crystallographic structure agreed best with the experimental results.

CONCLUSIONS

A new version of RADACK was validated that took into account the reactivity of atoms in both DNA and protein. The putative modelled structures of a natural lactose operator-repressor complex were discussed.

Plasticity in protein-DNA recognition: lac repressor interacts with its natural operator 01 through alternative conformations of its DNA-binding domain

The lac repressor-operator system is a model system for understanding protein-DNA interactions and allosteric mechanisms in gene regulation. Despite the wealth of biochemical data provided by extensive mutations of both repressor and operator, the specific recognition mechanism of the natural lac operators by lac repressor has remained elusive. Here we present the first high-resolution structure of a dimer of the DNA-binding domain of lac repressor bound to its natural operator 01. The global positioning of the dimer on the operator is dramatically asymmetric, which results in a different pattern of specific contacts between the two sites. Specific recognition is accomplished by a combination of elongation and twist by 48 degrees of the right lac subunit relative to the left one, significant rearrangement of many side chains as well as sequence-dependent deformability of the DNA. The set of recognition mechanisms involved in the lac repressor-operator system is unique among other protein-DNA complexes and presents a nice example of the adaptability that both proteins and DNA exhibit in the context of their mutual interaction.

Fine-tuning function: correlation of hinge domain interactions with functional distinctions between LacI and PurR

LacI and PurR are highly homologous proteins. Their functional units are homodimers, with an N-terminal DNA binding domain that comprises the helix-turn-helix (HTH), N-linker, and hinge regions from both monomers. Hinge structural changes are known to occur upon DNA dissociation but are difficult to monitor experimentally. The initial steps of hinge unfolding were therefore examined using molecular dynamics simulations, utilizing a truncated, chimeric protein comprising the LacI HTH/N-linker and PurR hinge. A terminal Gly-Cys-Gly was added to allow "dimerization" through disulfide bond formation. Simulations indicate that differences in LacI and PurR hinge primary sequence affect the quaternary structure of the hinge x hinge' interface. However, these alternate hinge orientations would be sterically restricted by the core domain. These results prompted detailed comparison of recently available DNA-bound structures for LacI and truncated LacI(1-62) with the PurR structure. Examination revealed that different N-linker and hinge contacts to the core domain of the partner monomer (which binds effector molecule) affect the juxtapositions of the HTH, N-linker, and hinge regions in the DNA binding domain. In addition, the two full-length repressors exhibit significant differences in the interactions between the core and the C-linker connection to the DNA binding domain. Both linkers and the hinge have been implicated in the allosteric response of these repressors. Intriguingly, one functional difference between these two proteins is that they exhibit opposite allosteric response to effector. Simulations and observed structural distinctions are correlated with mutational analysis and sequence information from the LacI/GalR family to formulate a mechanism for fine-tuning individual repressor function.

Crystallographic analysis of Lac repressor bound to natural operator O1

Previous structures of Lac repressor bound to DNA used a fully symmetric "ideal" operator sequence that is missing the central G-C base-pair present in the three natural operator sequences. Here we have determined the X-ray crystal structure of a dimeric Lac repressor bound to a 22 base-pair DNA with the natural operator O1 sequence and the anti-inducer ONPF, at 4.0 A resolution. The natural operator is bent in the same way as the symmetric sequence, due to the binding of the hinge helices of the repressor to the minor groove at the central GCGG sequence of O1. Comparison of the structures of the repressor bound to the natural and symmetric operators shows very similar overall structures, with only slight rearrangements of the headpiece domains of the repressor. Analysis of crystals with iodinated DNA shows that the operator is uniquely positioned and allows for the sequence registration of the DNA relative to the repressor to be determined. The kink in the operator is centered between the left half-site and the central G-C base-pair of O1. Our results are most consistent with a previously proposed model in which, relative to the complex with the symmetric operator, the repressor accommodates binding to the natural operator sequence by shifting the position of the right headpiece by one base-pair step towards the center of O1.