First-principles calculation of DNA looping in tethered particle experiments.
ABSTRACT: We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the 'looping J factor' (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k(B)T, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical 'open' conformation of the LacI tetramer.
Project description:Lac repressor (LacI) binds two operator DNA sites, looping the intervening DNA. DNA molecules containing two lac operators bracketing a sequence-directed bend were previously shown to form hyperstable LacI-looped complexes. Biochemical studies suggested that orienting the operators outward relative to the bend direction (in construct 9C14) stabilizes a positively supercoiled closed form, with a V-shaped LacI, but that the most stable loop construct (11C12) is a more open form. Here, fluorescence resonance energy transfer (FRET) is measured on DNA loops, between fluorescein and TAMRA attached near the two operators, approximately 130 basepairs apart. For 9C14, efficient LacI-induced energy transfer ( approximately 74% based on donor quenching) confirms that the designed DNA shape can force the looped complex into a closed form. From enhanced acceptor emission, correcting for observed donor-dependent quenching of acceptor fluorescence, approximately 52% transfer was observed. Time-resolved FRET suggests that this complex exists in both closed- and open form populations. Less efficient transfer, approximately 10%, was detected for DNA-LacI sandwiches and 11C12-LacI, consistent with an open form loop. This demonstration of long-range FRET in large DNA loops confirms that appropriate DNA design can control loop geometry. LacI flexibility may allow it to maintain looping with other proteins bound or under different intracellular conditions.
Project description:The Escherichia coli lactose repressor protein (LacI) provides a classic model for understanding protein-induced DNA looping. LacI has a C-terminal four-helix bundle tetramerization domain that may act as a flexible hinge. In previous work, several DNA constructs, each containing two lac operators bracketing a sequence-induced bend, were designed to stabilize different possible looping geometries. The resulting hyperstable LacI-DNA loops exist as both a compact "closed" form with a V-shaped repressor and also a more "open" form with an extended hinge. The "9C14" construct was of particular interest because footprinting, electrophoretic mobility shift, and ring closure experiments suggested that it forms both geometries. Previous fluorescence resonance energy transfer (FRET) measurements gave an efficiency of energy transfer (ET) of 70%, confirming the existence of a closed form. These measurements could not determine whether open form or intermediate geometries are populated or the timescale of interconversion. We have now applied single-molecule FRET to Cy3, Cy5 double-labeled LacI-DNA loops diffusing freely in solution. By using multiple excitation wavelengths and by carefully examining the behavior of the zero-ET peak during titration with LacI, we show that the LacI-9C14 loop exists exclusively in a single closed form exhibiting essentially 100% ET.
Project description:Protein-mediated DNA looping, such as that induced by the lactose repressor (LacI) of Escherichia coli, is a well-known gene regulation mechanism. Although researchers have given considerable attention to DNA looping by LacI, many unanswered questions about this mechanism, including the role of protein flexibility, remain. Recent single-molecule observations suggest that the two DNA-binding domains of LacI are capable of splaying open about the tetramerization domain into an extended conformation. We hypothesized that if recent experiments were able to reveal the extended conformation, it is possible that such structures occurred in previous studies as well. In this study, we tested our hypothesis by reevaluating two classic in vitro binding assays using a computational rod model of DNA. The experiments and computations evaluate the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths. The computed energetic minima align well with the experimentally observed interoperator length for optimal loop stability. Of equal importance, the model reveals that the most stable loops for linear DNA occur when LacI adopts the extended conformation. In contrast, for DNA minicircles, optimal stability may arise from either the closed or the extended protein conformation depending on the degree of supercoiling and the interoperator length.
Project description:The tethered particle motion (TPM) allows the direct detection of activity of a variety of biomolecules at the single molecule level. First pioneered for RNA polymerase, it has recently been applied also to other enzymes. In this work we employ TPM for a systematic investigation of the kinetics of DNA looping by wild-type Lac repressor (wt-LacI) and by hinge mutants Q60G and Q60 + 1. We implement a novel method for TPM data analysis to reliably measure the kinetics of loop formation and disruption and to quantify the effects of the protein hinge flexibility and of DNA loop strain on such kinetics. We demonstrate that the flexibility of the protein hinge has a profound effect on the lifetime of the looped state. Our measurements also show that the DNA bending energy plays a minor role on loop disruption kinetics, while a strong effect is seen on the kinetics of loop formation. These observations substantiate the growing number of theoretical studies aimed at characterizing the effects of DNA flexibility, tension and torsion on the kinetics of protein binding and dissociation, strengthening the idea that these mechanical factors in vivo may play an important role in the modulation of gene expression regulation.
Project description:DNA looping mediated by the Lac repressor is an archetypal test case for modeling protein and DNA flexibility. Understanding looping is fundamental to quantitative descriptions of gene expression. Systematic analysis of LacI•DNA looping was carried out using a landscape of DNA constructs with lac operators bracketing an A-tract bend, produced by varying helical phasings between operators and the bend. Fluorophores positioned on either side of both operators allowed direct Förster resonance energy transfer (FRET) detection of parallel (P1) and antiparallel (A1, A2) DNA looping topologies anchored by V-shaped LacI. Combining fluorophore position variant landscapes allows calculation of the P1, A1 and A2 populations from FRET efficiencies and also reveals extended low-FRET loops proposed to form via LacI opening. The addition of isopropyl-?-D-thio-galactoside (IPTG) destabilizes but does not eliminate the loops, and IPTG does not redistribute loops among high-FRET topologies. In some cases, subsequent addition of excess LacI does not reduce FRET further, suggesting that IPTG stabilizes extended or other low-FRET loops. The data align well with rod mechanics models for the energetics of DNA looping topologies. At the peaks of the predicted energy landscape for V-shaped loops, the proposed extended loops are more stable and are observed instead, showing that future models must consider protein flexibility.
Project description:We have measured the bending elasticity of short double-stranded DNA (dsDNA) chains through small-angle x-ray scattering from solutions of dsDNA-linked dimers of gold nanoparticles. This method, which does not require exertion of external forces or binding to a substrate, reports on the equilibrium distribution of bending fluctuations, not just an average value (as in ensemble fluorescence resonance energy transfer) or an extreme value (as in cyclization), and in principle provides a more robust data set for assessing the suitability of theoretical models. Our experimental results for dsDNA comprising 42-94 basepairs are consistent with a simple wormlike chain model of dsDNA elasticity, whose behavior we have determined from Monte Carlo simulations that explicitly represent nanoparticles and their alkane tethers. A persistence length of 50 nm (150 basepairs) gave a favorable comparison, consistent with the results of single-molecule force-extension experiments on much longer dsDNA chains, but in contrast to recent suggestions of enhanced flexibility at these length scales.
Project description:Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here, we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the basepairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.
Project description:Gene expression regulation is a fundamental biological process which deploys specific sets of genomic information depending on physiological or environmental conditions. Several transcription factors (including lac repressor, LacI) are present in the cell at very low copy number and increase their local concentration by binding to multiple sites on DNA and looping the intervening sequence. In this work, we employ single-molecule manipulation to experimentally address the role of DNA supercoiling in the dynamics and stability of LacI-mediated DNA looping. We performed measurements over a range of degrees of supercoiling between -0.026 and +0.026, in the absence of axial stretching forces. A supercoiling-dependent modulation of the lifetimes of both the looped and unlooped states was observed. Our experiments also provide evidence for multiple structural conformations of the LacI-DNA complex, depending on torsional constraints. The supercoiling-dependent modulation demonstrated here adds an important element to the model of the lac operon. In fact, the complex network of proteins acting on the DNA in a living cell constantly modifies its topological and mechanical properties: our observations demonstrate the possibility of establishing a signaling pathway from factors affecting DNA supercoiling to transcription factors responsible for the regulation of specific sets of genes.
Project description:Sequence-dependent intrinsic curvature of DNA influences looping by regulatory proteins such as LacI and NtrC. Curvature can enhance stability and control shape, as observed in LacI loops formed with three designed sequences with operators bracketing an A-tract bend. We explore geometric, topological, and energetic effects of curvature with an analysis of a family of highly bent sequences, using the elastic rod model from previous work. A unifying straight-helical-straight representation uses two phasing parameters to describe sequences composed of two straight segments that flank a common helically supercoiled segment. We exercise the rod model over this two-dimensional space of phasing parameters to evaluate looping behaviors. This design space is found to comprise two subspaces that prefer parallel versus anti-parallel binding topologies. The energetic cost of looping varies from 4 to 12 kT. Molecules can be designed to yield distinct binding topologies as well as hyperstable or hypostable loops and potentially loops that can switch conformations. Loop switching could be a mechanism for control of gene expression. Model predictions for linking numbers and sizes of LacI-DNA loops can be tested using multiple experimental approaches, which coupled with theory could address whether proteins or DNA provide the observed flexibility of protein-DNA loops.
Project description:BACKGROUND:Cyanobacteria are solar-powered prokaryotes useful for sustainable production of valuable molecules, but orthogonal and regulated promoters are lacking. The Lac repressor (LacI) from Escherichia coli is a well-studied transcription factor that is orthogonal to cyanobacteria and represses transcription by binding a primary lac operator (lacO), blocking RNA-polymerase. Repression can be enhanced through DNA-looping, when a LacI-tetramer binds two spatially separated lacO and loops the DNA. Ptrc is a commonly used LacI-repressed promoter that is inefficiently repressed in the cyanobacterium Synechocystis PCC 6803. Ptrc2O, a version of Ptrc with two lacO, is more efficiently repressed, indicating DNA-looping. To investigate the inefficient repression of Ptrc and cyanobacterial DNA-looping, we designed a Ptrc-derived promoter library consisting of single lacO promoters, including a version of Ptrc with a stronger lacO (Ptrc1O-proximal), and dual lacO promoters with varying inter-lacO distances (the Ptrc2O-library). RESULTS:We first characterized artificial constitutive promoters and used one for engineering a LacI-expressing strain of Synechocystis. Using this strain, we observed that Ptrc1O-proximal is similar to Ptrc in being inefficiently repressed. Further, the Ptrc2O-library displays a periodic repression pattern that remains for both non- and induced conditions and decreases with longer inter-lacO distances, in both E. coli and Synechocystis. Repression of Ptrc2O-library promoters with operators out of phase is less efficient in Synechocystis than in E. coli, whereas repression of promoters with lacO in phase is efficient even under induced conditions in Synechocystis. Two well-repressed Ptrc2O promoters were highly active when tested in absence of LacI in Synechocystis. CONCLUSIONS:The artificial constitutive promoters herein characterized can be utilized for expression in cyanobacteria, as demonstrated for LacI. The inefficient repression of Ptrc and Ptrc1O-proximal in Synechocystis, as compared to E. coli, may be due to insufficient LacI expression, or differences in RNAP subunits. DNA-looping works as a transcriptional regulation mechanism similarly as in E. coli. DNA-looping contributes strongly to Ptrc2O-library repression in Synechocystis, even though they contain the weakly-repressed primary lacO of Ptrc1O-proximal and relatively low levels of LacI/cell. Hence, Synechocystis RNAP may be more sensitive to DNA-looping than E. coli RNAP, and/or the chromatin torsion resistance could be lower. Two strong and highly repressed Ptrc2O promoters could be used without induction, or together with an unstable LacI.