Modeling the Lac repressor-operator assembly: the influence of DNA looping on Lac repressor conformation

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model's ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.

emDNA - A Tool for Modeling Protein-decorated DNA Loops and Minicircles at the Base-pair Step Level

Computational modeling of nucleic acids plays an important role in molecular biology, enhancing our general understanding of the relationship between structure and function. Biophysical studies have provided a wealth of information on how double-helical DNA responds to proteins and other molecules in its local environment but far less understanding of the larger scale structural responses found in protein-decorated loops and minicircles. Current computational models of DNA range from detailed all-atom molecular dynamics studies, which produce rich time and spatially dependent depictions of small DNA fragments, to coarse-grained simulations, which sacrifice detailed physical and chemical information to treat larger scale systems. The treatment of DNA used here, at the base-pair step level with rigid-body parameters, allows one to develop quality models hundreds of base pairs long from local, sequence-specific features found from experiment. The emDNA software takes advantage of this framework, producing elastically optimized models of DNA at thermal equilibrium with built-in or user-generated elastic models. This versatile program, in combination with case studies included in this article, allows users of any skill level to develop and investigate mesoscale models of their own design. The functionality of emDNA includes a tool to incorporate experiment-specific configurations, e.g. protein-bound and/or melted DNA from known high-resolution structures, within higher-order 3D models by fixing the orientation and position of user-specified base pairs. The software provides a new avenue into multiscale genetic modeling, giving a wide range of users a deeper understanding of DNA mesoscale organization and the opportunity to pose new questions in genetic research. The publicly available emDNA software, including build instructions and usage information, is available on GitHub (https://nicocvn.github.io/emDNA/).

Construction of an AI-2 quorum sensing induced heterologous protein expression system in Escherichia coli

Background

The pET expression system based on T7 promoter which is induced by isopropyl-β-D-1-thiogalactopyranoside (IPTG) is by far the most commonly used system for production of heterogeneous proteins in Escherichia coli. However, this system was limited by obvious drawbacks including the host toxicity and metabolic burden imposed by the presence of IPTG.

Methods

In this study, we incorporated the autoinducer-2 (AI-2) quorum sensing system to realize autoinduction of the pET expression system. The autoinduction expression vector pXWZ1 was constructed by inserting the lsr promoter regions into the pET28a(+) vector. The expression efficiency of the reporter genes gfpuv and lacZ by the pXWZ1 and pET28a(+) vectors were compared.

Results

The results showed that the expression levels of the both report genes in the cells transformed with pXWZ1 without any addition of exogenous inducer were higher than that transformed with pET28a(+) vectors by the induction of IPTG.

Conclusion

This new auto-induction system will exclude the limitations of the IPTG induction including toxic to host and increasing formation of inclusion body and will become a more economical and convenient tool for recombinant protein expression.

Characterization of Gene Repression by Designed Transcription Activator-like Effector Dimer Proteins

Gene regulation by control of transcription initiation is a fundamental property of living cells. Much of our understanding of gene repression originated from studies of the Escherichia coli lac operon switch, in which DNA looping plays an essential role. To validate and generalize principles from lac for practical applications, we previously described artificial DNA looping driven by designed transcription activator-like effector dimer (TALED) proteins. Because TALE monomers bind the idealized symmetrical lac operator sequence in two orientations, our prior studies detected repression due to multiple DNA loops. We now quantitatively characterize gene repression in living E. coli by a collection of individual TALED loops with systematic loop length variation. Fitting of a thermodynamic model allows unequivocal demonstration of looping and comparison of the engineered TALED repression system with the natural lac repressor system.

Biophysical Reviews' "Meet the Editors Series"-a profile of Wilma K. Olson

As one of the five Executive Editors of Biophysical Reviews I have been asked to provide this short biographical sketch for the readers of the journal. I have been a member of the Editorial Board since the inception of the journal in 2008 and an Executive Editor since 2014. I hold a B.S. degree in Chemistry from the University of Delaware and a Ph.D. in Physical Chemistry from Stanford University. Except for a year as a Damon Runyon Postdoctoral Fellow at Columbia University, I have spent my entire professional career at Rutgers, the State University of New Jersey, where I am currently the Mary I. Bunting Professor of Chemistry and Chemical Biology. I served for many years as Founding Director of the Rutgers University Center for Molecular Biophysics and Biophysical Chemistry, and have trained undergraduate, graduate, and postdoctoral students from a variety of academic disciplines.

Parallels between DNA and collagen - comparing elastic models of the double and triple helix

Multi-stranded helices are widespread in nature. The interplay of polymeric properties with biological function is seldom discussed. This study probes analogies between structural and mechanical properties of collagen and DNA. We modeled collagen with Eulerian rotational and translational parameters of adjacent rungs in the triple-helix ladder and developed statistical potentials by extracting the dispersion of the parameters from a database of atomic-resolution structures. The resulting elastic model provides a common quantitative way to describe collagen deformations upon interacting with integrins or matrix metalloproteinase and DNA deformations upon protein binding. On a larger scale, deformations in Type I collagen vary with a periodicity consistent with the D-periodic banding of higher-order fibers assemblies. This indicates that morphologies of natural higher-order collagen packing might be rooted in the characteristic deformation patterns.

Transcription control engineering and applications in synthetic biology

In synthetic biology, researchers assemble biological components in new ways to produce systems with practical applications. One of these practical applications is control of the flow of genetic information (from nucleic acid to protein), a.k.a. gene regulation. Regulation is critical for optimizing protein (and therefore activity) levels and the subsequent levels of metabolites and other cellular properties. The central dogma of molecular biology posits that information flow commences with transcription, and accordingly, regulatory tools targeting transcription have received the most attention in synthetic biology. In this mini-review, we highlight many past successes and summarize the lessons learned in developing tools for controlling transcription. In particular, we focus on engineering studies where promoters and transcription terminators (cis-factors) were directly engineered and/or isolated from DNA libraries. We also review several well-characterized transcription regulators (trans-factors), giving examples of how cis- and trans-acting factors have been combined to create digital and analogue switches for regulating transcription in response to various signals. Last, we provide examples of how engineered transcription control systems have been used in metabolic engineering and more complicated genetic circuits. While most of our mini-review focuses on the well-characterized bacterium Escherichia coli, we also provide several examples of the use of transcription control engineering in non-model organisms. Similar approaches have been applied outside the bacterial kingdom indicating that the lessons learned from bacterial studies may be generalized for other organisms.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

DNA-Endonuclease Complex Dynamics by Simultaneous FRET and Fluorophore Intensity in Evanescent Field

The single-molecule Förster resonance energy transfer (FRET) is a powerful tool to study interactions and conformational changes of biological molecules in the distance range from a few to 10 nm. In this study, we demonstrate a method to augment this range with longer distances. The method is based on the intensity changes of a tethered fluorophore, diffusing in the exponentially decaying evanescent excitation field. In combination with FRET it allowed us to reveal and characterize the dynamics of what had been inaccessible conformations of the DNA-protein complex. Our model system, restriction enzyme Ecl18kI, interacts with a FRET pair-labeled DNA fragment to form two different DNA loop conformations. The DNA-protein interaction geometry is such that the efficient FRET is expected for one of these conformations-"antiparallel" loop. In the alternative "parallel" loop, the expected distance between the dyes is outside the range accessible by FRET. Therefore, "antiparallel" looping is observed in a single-molecule time trajectory as discrete transitions to a state of high FRET efficiency. At the same time, transitions to a high-intensity state of the directly excited acceptor fluorophore on a DNA tether are due to a change of its average position in the evanescent field of excitation and can be associated with a loop of either "parallel" or "antiparallel" configuration. Simultaneous analysis of FRET and acceptor intensity trajectories then allows us to discriminate different DNA loop conformations and access the average lifetimes of different states.

Simulation of DNA Supercoil Relaxation

Several recent single-molecule experiments observe the response of supercoiled DNA to nicking endonucleases and topoisomerases. Typically in these experiments, indirect measurements of supercoil relaxation are obtained by observing the motion of a large micron-sized bead. The bead, which also serves to manipulate DNA, experiences significant drag and thereby obscures supercoil dynamics. Here we employ our discrete wormlike chain model to bypass experimental limitations and simulate the dynamic response of supercoiled DNA to a single strand nick. From our simulations, we make three major observations. First, extension is a poor dynamic measure of supercoil relaxation; in fact, the linking number relaxes so fast that it cannot have much impact on extension. Second, the rate of linking number relaxation depends upon its initial partitioning into twist and writhe as determined by tension. Third, the extensional response strongly depends upon the initial position of plectonemes.

Protein-induced DNA linking number change by sequence-specific DNA binding proteins and its biological effects

Sequence-specific DNA-binding proteins play essential roles in many fundamental biological events such as DNA replication, recombination, and transcription. One common feature of sequence-specific DNA-binding proteins is to introduce structural changes to their DNA recognition sites including DNA-bending and DNA linking number change (ΔLk). In this article, I review recent progress in studying protein-induced ΔLk by several sequence-specific DNA-binding proteins, such as E. coli cAMP receptor protein (CRP) and lactose repressor (LacI). It was demonstrated recently that protein-induced ΔLk is an intrinsic property for sequence-specific DNA-binding proteins and does not correlate to protein-induced other structural changes, such as DNA bending. For instance, although CRP bends its DNA recognition site by 90°, it was not able to introduce a ΔLk to it. However, LacI was able to simultaneously bend and introduce a ΔLk to its DNA binding sites. Intriguingly, LacI also constrained superhelicity within LacI-lac O1 complexes if (-) supercoiled DNA templates were provided. I also discuss how protein-induced ΔLk help sequence-specific DNA-binding proteins regulate their biological functions. For example, it was shown recently that LacI utilizes the constrained superhelicity (ΔLk) in LacI-lac O1 complexes and serves as a topological barrier to constrain free, unconstrained (-) supercoils within the 401-bp DNA loop. These constrained (-) supercoils enhance LacI's binding affinity and therefore the repression of the lac promoter. Other biological functions include how DNA replication initiators λ O and DnaA use the induced ΔLk to open/melt bacterial DNA replication origins.

Contributions of Sequence to the Higher-Order Structures of DNA

One of the critical unanswered questions in genome biophysics is how the primary sequence of DNA bases influences the global properties of very-long-chain molecules. The local sequence-dependent features of DNA found in high-resolution structures introduce irregularities in the disposition of adjacent residues that facilitate the specific binding of proteins and modulate the global folding and interactions of double helices with hundreds of basepairs. These features also determine the positions of nucleosomes on DNA and the lengths of the interspersed DNA linkers. Like the patterns of basepair association within DNA, the arrangements of nucleosomes in chromatin modulate the properties of longer polymers. The intrachromosomal loops detected in genomic studies contain hundreds of nucleosomes, and given that the simulated configurations of chromatin depend on the lengths of linker DNA, the formation of these loops may reflect sequence-dependent information encoded within the positioning of the nucleosomes. With knowledge of the positions of nucleosomes on a given genome, methods are now at hand to estimate the looping propensities of chromatin in terms of the spacing of nucleosomes and to make a direct connection between the DNA base sequence and larger-scale chromatin folding.

Protein/DNA interactions in complex DNA topologies: expect the unexpected

DNA supercoiling results in compacted DNA structures that can bring distal sites into close proximity. It also changes the local structure of the DNA, which can in turn influence the way it is recognised by drugs, other nucleic acids and proteins. Here, we discuss how DNA supercoiling and the formation of complex DNA topologies can affect the thermodynamics of DNA recognition. We then speculate on the implications for transcriptional control and the three-dimensional organisation of the genetic material, using examples from our own simulations and from the literature. We introduce and discuss the concept of coupling between the multiple length-scales associated with hierarchical nuclear structural organisation through DNA supercoiling and topology.

Insights into Genome Architecture Deduced from the Properties of Short Lac Repressor-mediated DNA Loops

Genomic DNA is vastly longer than the space allotted to it in a cell. The molecule must fold with a level of organization that satisfies the imposed spatial constraints as well as allows for the processing of genetic information. Key players in this organization include the negative supercoiling of DNA, which facilitates the unwinding of the double-helical molecule, and the associations of DNA with proteins, which partition the DNA into isolated loops, or domains. In order to gain insight into the principles of genome organization and to visualize the folding of spatially constrained DNA, we have developed new computational methods to identify the preferred three-dimensional pathways of protein-mediated DNA loops and to characterize the topological properties of these structures. Here we focus on the levels of supercoiling and the spatial arrangements of DNA in model nucleoprotein systems with two topological domains. We construct these systems by anchoring DNA loops in opposing orientations on a common protein-DNA assembly, namely the Lac repressor protein with two bound DNA operators. The linked pieces of DNA form a covalently closed circle such that the protein attaches to two widely spaced sites along the DNA. We examine the effects of operator spacing, loop orientation, and long-range contacts on overall chain configuration and topology and discuss our findings in the context of classic experiments on the effects of supercoiling and operator spacing on Lac repressor-mediated looping and recent work on the role of proteins as barriers that divide genomes into independent topological domains.

Protein/DNA interactions in complex DNA topologies: expect the unexpected

DNA supercoiling results in compacted DNA structures that can bring distal sites into close proximity. It also changes the local structure of the DNA, which can in turn influence the way it is recognised by drugs, other nucleic acids and proteins. Here, we discuss how DNA supercoiling and the formation of complex DNA topologies can affect the thermodynamics of DNA recognition. We then speculate on the implications for transcriptional control and the three-dimensional organisation of the genetic material, using examples from our own simulations and from the literature. We introduce and discuss the concept of coupling between the multiple length-scales associated with hierarchical nuclear structural organisation through DNA supercoiling and topology.

Protein-induced DNA linking number change by sequence-specific DNA binding proteins and its biological effects

Sequence-specific DNA-binding proteins play essential roles in many fundamental biological events such as DNA replication, recombination, and transcription. One common feature of sequence-specific DNA-binding proteins is to introduce structural changes to their DNA recognition sites including DNA-bending and DNA linking number change (ΔLk). In this article, I review recent progress in studying protein-induced ΔLk by several sequence-specific DNA-binding proteins, such as E. coli cAMP receptor protein (CRP) and lactose repressor (LacI). It was demonstrated recently that protein-induced ΔLk is an intrinsic property for sequence-specific DNA-binding proteins and does not correlate to protein-induced other structural changes, such as DNA bending. For instance, although CRP bends its DNA recognition site by 90°, it was not able to introduce a ΔLk to it. However, LacI was able to simultaneously bend and introduce a ΔLk to its DNA binding sites. Intriguingly, LacI also constrained superhelicity within LacI-lac O1 complexes if (-) supercoiled DNA templates were provided. I also discuss how protein-induced ΔLk help sequence-specific DNA-binding proteins regulate their biological functions. For example, it was shown recently that LacI utilizes the constrained superhelicity (ΔLk) in LacI-lac O1 complexes and serves as a topological barrier to constrain free, unconstrained (-) supercoils within the 401-bp DNA loop. These constrained (-) supercoils enhance LacI's binding affinity and therefore the repression of the lac promoter. Other biological functions include how DNA replication initiators λ O and DnaA use the induced ΔLk to open/melt bacterial DNA replication origins.

The solution configurations of inactive and activated DntR have implications for the sliding dimer mechanism of LysR transcription factors

LysR Type Transcriptional Regulators (LTTRs) regulate basic metabolic pathways or virulence gene expression in prokaryotes. Evidence suggests that the activation of LTTRs involves a conformational change from an inactive compact apo- configuration that represses transcription to an active, expanded holo- form that promotes it. However, no LTTR has yet been observed to adopt both configurations. Here, we report the results of structural studies of various forms of the LTTR DntR. Crystal structures of apo-DntR and of a partially autoinducing mutant H169T-DntR suggest that active and inactive DntR maintain a compact homotetrameric configuration. However, Small Angle X-ray Scattering (SAXS) studies on solutions of apo-, H169T- and inducer-bound holo-DntR indicate a different behaviour, suggesting that while apo-DntR maintains a compact configuration in solution both H169T- and holo-DntR adopt an expanded conformation. Models of the SAXS-obtained solution conformations of apo- and holo-DntR homotetramers in complex with promoter-operator region DNA are consistent with previous observations of a shifting of LTTR DNA binding sites upon activation and a consequent relaxation in the bend of the promoter-operator region DNA. Our results thus provide clear evidence at the molecular level which strongly supports the 'sliding dimer' hypothesis concerning LTTR activation mechanisms.

Exploring LacI-DNA dynamics by multiscale simulations using the SIRAH force field

The lac repressor protein (LacI) together with its target regulatory sequence are a common model for studying DNA looping and its implications on transcriptional control in bacteria. Owing to the molecular size of this system, standard all-atom (AA) simulations are prohibitive for achieving relevant biological time scales. As an alternative, multiscale models, which combine AA descriptions at particular regions with coarse-grained (CG) representations of the remaining components, were used to address this computational challenge while preserving the relevant details of the system. In this work, we implement a new multiscale approach based on the SIRAH force field to gain deeper insights into the dynamics of the LacI-DNA system. Our methodology allows for a dual resolution treatment of the solute and solvent, explicitly representing the protein, DNA, and solvent environment without compromising the AA region. Starting from the P1 loop configuration in an undertwisted conformation, we were able to observe the transition to the more stable overtwisted state. Additionally, a detailed characterization of the conformational space sampled by the DNA loop was done. In agreement with experimental and theoretical evidence, we observed the transient formation of kinks at the loop, which were stabilized by the presence of counterions at the minor groove. We also show that the loop's intrinsic flexibility can account for reported FRET measurements and bent conformations required to bind the CAP transcription factor.

DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

For much of the last three decades, Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequence-dependent bends or inhomogeneous bending flexibility. Within the last 10 years approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum. However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length, the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, kB T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size

The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.

DNA topology confers sequence specificity to nonspecific architectural proteins

Topological constraints placed on short fragments of DNA change the disorder found in chain molecules randomly decorated by nonspecific, architectural proteins into tightly organized 3D structures. The bacterial heat-unstable (HU) protein builds up, counter to expectations, in greater quantities and at particular sites along simulated DNA minicircles and loops. Moreover, the placement of HU along loops with the "wild-type" spacing found in the Escherichia coli lactose (lac) and galactose (gal) operons precludes access to key recognition elements on DNA. The HU protein introduces a unique spatial pathway in the DNA upon closure. The many ways in which the protein induces nearly the same closed circular configuration point to the statistical advantage of its nonspecificity. The rotational settings imposed on DNA by the repressor proteins, by contrast, introduce sequential specificity in HU placement, with the nonspecific protein accumulating at particular loci on the constrained duplex. Thus, an architectural protein with no discernible DNA sequence-recognizing features becomes site-specific and potentially assumes a functional role upon loop formation. The locations of HU on the closed DNA reflect long-range mechanical correlations. The protein responds to DNA shape and deformability—the stiff, naturally straight double-helical structure—rather than to the unique features of the constituent base pairs. The structures of the simulated loops suggest that HU architecture, like nucleosomal architecture, which modulates the ability of regulatory proteins to recognize their binding sites in the context of chromatin, may influence repressor-operator interactions in the context of the bacterial nucleoid.

What controls DNA looping?

The looping of DNA provides a means of communication between sequentially distant genomic sites that operate in tandem to express, copy, and repair the information encoded in the DNA base sequence. The short loops implicated in the expression of bacterial genes suggest that molecular factors other than the naturally stiff double helix are involved in bringing the interacting sites into close spatial proximity. New computational techniques that take direct account of the three-dimensional structures and fluctuations of protein and DNA allow us to examine the likely means of enhancing such communication. Here, we describe the application of these approaches to the looping of a 92 base-pair DNA segment between the headpieces of the tetrameric Escherichia coli Lac repressor protein. The distortions of the double helix induced by a second protein--the nonspecific nucleoid protein HU--increase the computed likelihood of looping by several orders of magnitude over that of DNA alone. Large-scale deformations of the repressor, sequence-dependent features in the DNA loop, and deformability of the DNA operators also enhance looping, although to lesser degrees. The correspondence between the predicted looping propensities and the ease of looping derived from gene-expression and single-molecule measurements lends credence to the derived structural picture.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA–protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein–nucleic acid interactions.

Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor.

Weak operator binding enhances simulated Lac repressor-mediated DNA looping

The 50th anniversary of Biopolymers coincides closely with the like celebration of the discovery of the Escherichia coli (lac) lactose operon, a classic genetic system long used to illustrate the influence of biomolecular structure on function. The looping of DNA induced by the binding of the Lac repressor protein to sequentially distant operator sites on DNA continues to serve as a paradigm for understanding long-range genomic communication. Advances in analyses of DNA structures and in incorporation of proteins in computer simulations of DNA looping allow us to address long-standing questions about the role of protein-mediated DNA loop formation in transcriptional control. Here we report insights gained from studies of the sequence-dependent contributions of the natural lac operators to Lac repressor-mediated DNA looping. Novel superposition of the ensembles of protein-bound operator structures derived from NMR measurements reveals variations in DNA folding missed in conventional structural alignments. The changes in folding affect the predicted ease with which the repressor induces loop formation and the ways that DNA closes between the protein headpieces. The peeling of the auxiliary operators away from the repressor enhances the formation of loops with the 92-bp wildtype spacing and hints of a structural reason behind their weak binding.

Reliable prediction of complex phenotypes from a modular design in free energy space: an extensive exploration of the lac operon

The basic methodology for designing, altering, and constructing biological systems is increasingly relying on well-established engineering principles to move forward from trial and error approaches to reliably predicting the system behavior from the properties of the components and their interactions. The inherent complexity of even the simplest biological systems, however, often precludes achieving such predictive power. A prototypical example is the lac operon, one of the best-characterized genetic systems, which still poses serious challenges for understanding the results of combining its parts into novel setups. The reason is the pervasive complex hierarchy of events involved in gene regulation that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. Here, we integrate such complexity into a few-parameter model to accurately predict gene expression from a few simple rules to connect the parts. The model accurately reproduces the observed transcriptional activity of the lac operon over a 10,000-fold range for 21 different operator setups, different repressor concentrations, and tetrameric and dimeric forms of the repressor. Incorporation of the calibrated model into more complex scenarios accurately captures the induction curves for key operator configurations and the temporal evolution of the β-galactosidase activity of cell populations.

Poly(dA:dT)-rich DNAs are highly flexible in the context of DNA looping

Large-scale DNA deformation is ubiquitous in transcriptional regulation in prokaryotes and eukaryotes alike. Though much is known about how transcription factors and constellations of binding sites dictate where and how gene regulation will occur, less is known about the role played by the intervening DNA. In this work we explore the effect of sequence flexibility on transcription factor-mediated DNA looping, by drawing on sequences identified in nucleosome formation and ligase-mediated cyclization assays as being especially favorable for or resistant to large deformations. We examine a poly(dA:dT)-rich, nucleosome-repelling sequence that is often thought to belong to a class of highly inflexible DNAs; two strong nucleosome positioning sequences that share a set of particular sequence features common to nucleosome-preferring DNAs; and a CG-rich sequence representative of high G+C-content genomic regions that correlate with high nucleosome occupancy in vivo. To measure the flexibility of these sequences in the context of DNA looping, we combine the in vitro single-molecule tethered particle motion assay, a canonical looping protein, and a statistical mechanical model that allows us to quantitatively relate the looping probability to the looping free energy. We show that, in contrast to the case of nucleosome occupancy, G+C content does not positively correlate with looping probability, and that despite sharing sequence features that are thought to determine nucleosome affinity, the two strong nucleosome positioning sequences behave markedly dissimilarly in the context of looping. Most surprisingly, the poly(dA:dT)-rich DNA that is often characterized as highly inflexible in fact exhibits one of the highest propensities for looping that we have measured. These results argue for a need to revisit our understanding of the mechanical properties of DNA in a way that will provide a basis for understanding DNA deformation over the entire range of biologically relevant scenarios that are impacted by DNA deformability.

Rationally designed coiled-coil DNA looping peptides control DNA topology

Artificial DNA looping peptides were engineered to study the roles of protein and DNA flexibility in controlling the geometry and stability of protein-mediated DNA loops. These LZD (leucine zipper dual-binding) peptides were derived by fusing a second, C-terminal, DNA-binding region onto the GCN4 bZip peptide. Two variants with different coiled-coil lengths were designed to control the relative orientations of DNA bound at each end. Electrophoretic mobility shift assays verified formation of a sandwich complex containing two DNAs and one peptide. Ring closure experiments demonstrated that looping requires a DNA-binding site separation of 310 bp, much longer than the length needed for natural loops. Systematic variation of binding site separation over a series of 10 constructs that cyclize to form 862-bp minicircles yielded positive and negative topoisomers because of two possible writhed geometries. Periodic variation in topoisomer abundance could be modeled using canonical DNA persistence length and torsional modulus values. The results confirm that the LZD peptides are stiffer than natural DNA looping proteins, and they suggest that formation of short DNA loops requires protein flexibility, not unusual DNA bendability. Small, stable, tunable looping peptides may be useful as synthetic transcriptional regulators or components of protein–DNA nanostructures.

Analyzing and building nucleic acid structures with 3DNA

The 3DNA software package is a popular and versatile bioinformatics tool with capabilities to analyze, construct, and visualize three-dimensional nucleic acid structures. This article presents detailed protocols for a subset of new and popular features available in 3DNA, applicable to both individual structures and ensembles of related structures. Protocol 1 lists the set of instructions needed to download and install the software. This is followed, in Protocol 2, by the analysis of a nucleic acid structure, including the assignment of base pairs and the determination of rigid-body parameters that describe the structure and, in Protocol 3, by a description of the reconstruction of an atomic model of a structure from its rigid-body parameters. The most recent version of 3DNA, version 2.1, has new features for the analysis and manipulation of ensembles of structures, such as those deduced from nuclear magnetic resonance (NMR) measurements and molecular dynamic (MD) simulations; these features are presented in Protocols 4 and 5. In addition to the 3DNA stand-alone software package, the w3DNA web server, located at http://w3dna.rutgers.edu, provides a user-friendly interface to selected features of the software. Protocol 6 demonstrates a novel feature of the site for building models of long DNA molecules decorated with bound proteins at user-specified locations.

Structural insights into the role of architectural proteins in DNA looping deduced from computer simulations

Bacterial gene expression is regulated by DNA elements that often lie far apart along the genomic sequence, but come close together during genetic processing. The intervening residues form loops, which are organized by the binding of various proteins. For example, the Escherichia coli Lac repressor protein binds DNA operators, separated by 92 or 401 bp, and suppresses the formation of gene products involved in the metabolism of lactose. The system also includes several highly abundant architectural proteins, such as the histone-like (heat-unstable) HU protein, which severely deform the double helix upon binding. In order to gain a better understanding of how the naturally stiff DNA double helix forms the short loops detected in vivo, we have developed new computational methods to study the effects of various non-specific binding proteins on the three-dimensional configurational properties of DNA sequences. The present article surveys the approach that we use to generate ensembles of spatially constrained protein-decorated DNA structures (minicircles and Lac repressor-mediated loops) and presents some of the insights gained from the correspondence between computation and experiment about the potential contributions of architectural and regulatory proteins to DNA looping and gene expression.

Interplay of protein and DNA structure revealed in simulations of the lac operon

The E. coli Lac repressor is the classic textbook example of a protein that attaches to widely spaced sites along a genome and forces the intervening DNA into a loop. The short loops implicated in the regulation of the lac operon suggest the involvement of factors other than DNA and repressor in gene control. The molecular simulations presented here examine two likely structural contributions to the in-vivo looping of bacterial DNA: the distortions of the double helix introduced upon association of the highly abundant, nonspecific nucleoid protein HU and the large-scale deformations of the repressor detected in low-resolution experiments. The computations take account of the three-dimensional arrangements of nucleotides and amino acids found in crystal structures of DNA with the two proteins, the natural rest state and deformational properties of protein-free DNA, and the constraints on looping imposed by the conformation of the repressor and the orientation of bound DNA. The predicted looping propensities capture the complex, chain-length-dependent variation in repression efficacy extracted from gene expression studies and in vitro experiments and reveal unexpected chain-length-dependent variations in the uptake of HU, the deformation of repressor, and the folding of DNA. Both the opening of repressor and the presence of HU, at levels approximating those found in vivo, enhance the probability of loop formation. HU affects the global organization of the repressor and the opening of repressor influences the levels of HU binding to DNA. The length of the loop determines whether the DNA adopts antiparallel or parallel orientations on the repressor, whether the repressor is opened or closed, and how many HU molecules bind to the loop. The collective behavior of proteins and DNA is greater than the sum of the parts and hints of ways in which multiple proteins may coordinate the packaging and processing of genetic information.

Theoretical and experimental dissection of DNA loop-mediated repression

Transcriptional networks across all domains of life feature a wide range of regulatory architectures. Theoretical models now make clear predictions about how key parameters describing those architectures modulate gene expression, and the ability to construct genetic circuits with tunable parameters enables precise tests of such models. We dissect gene regulation through DNA looping by tuning network parameters such as repressor copy number, DNA binding strengths, and loop length in both thermodynamic models and experiments. Our results help clarify the short-length mechanical properties of DNA.

DNA looping in prokaryotes: experimental and theoretical approaches

Transcriptional regulation is at the heart of biological functions such as adaptation to a changing environment or to new carbon sources. One of the mechanisms which has been found to modulate transcription, either positively (activation) or negatively (repression), involves the formation of DNA loops. A DNA loop occurs when a protein or a complex of proteins simultaneously binds to two different sites on DNA with looping out of the intervening DNA. This simple mechanism is central to the regulation of several operons in the genome of the bacterium Escherichia coli, like the lac operon, one of the paradigms of genetic regulation. The aim of this review is to gather and discuss concepts and ideas from experimental biology and theoretical physics concerning DNA looping in genetic regulation. We first describe experimental techniques designed to show the formation of a DNA loop. We then present the benefits that can or could be derived from a mechanism involving DNA looping. Some of these are already experimentally proven, but others are theoretical predictions and merit experimental investigation. Then, we try to identify other genetic systems that could be regulated by a DNA looping mechanism in the genome of Escherichia coli. We found many operons that, according to our set of criteria, have a good chance to be regulated with a DNA loop. Finally, we discuss the proposition recently made by both biologists and physicists that this mechanism could also act at the genomic scale and play a crucial role in the spatial organization of genomes.

Insights into Gene Expression and Packaging from Computer Simulations

Within the nucleus of each cell lies DNA - an unfathomably long, twisted, and intricately coiled molecule - segments of which make up the genes that provide the instructions that a cell needs to operate. As we near the 60(th) anniversary of the discovery of the DNA double helix, crucial questions remain about how the physical arrangement of the DNA in cells affects how genes work. For example, how a cell stores the genetic information inside the nucleus is complicated by the necessity of maintaining accessibility to DNA for genetic processing. In order to gain insight into the roles played by various proteins in reading and compacting the genome, we have developed new methodologies to simulate the dynamic, three-dimensional structures of long, fluctuating, protein-decorated strands of DNA. Our a priori approach to the problem allows us to determine the effects of individual proteins and their chemical modifications on overall DNA structure and function. Here we present our recent treatment of the communication between regulatory proteins attached to precisely constructed stretches of chromatin. Our simulations account for the enhancement in communication detected experimentally on chromatin compared to protein-free DNA of the same chain length as well as the critical roles played by the cationic 'tails' of the histone proteins in this signaling. The states of chromatin captured in the simulations offer new insights into the ways that the DNA, histones, and regulatory proteins contribute to long-range communication along the genome.

Bullied no more: when and how DNA shoves proteins around

The predominant protein-centric perspective in protein-DNA-binding studies assumes that the protein drives the interaction. Research focuses on protein structural motifs, electrostatic surfaces and contact potentials, while DNA is often ignored as a passive polymer to be manipulated. Recent studies of DNA topology, the supercoiling, knotting, and linking of the helices, have shown that DNA has the capability to be an active participant in its transactions. DNA topology-induced structural and geometric changes can drive, or at least strongly influence, the interactions between protein and DNA. Deformations of the B-form structure arise from both the considerable elastic energy arising from supercoiling and from the electrostatic energy. Here, we discuss how these energies are harnessed for topology-driven, sequence-specific deformations that can allow DNA to direct its own metabolism.

DNA information: from digital code to analogue structure

The digital linear coding carried by the base pairs in the DNA double helix is now known to have an important component that acts by altering, along its length, the natural shape and stiffness of the molecule. In this way, one region of DNA is structurally distinguished from another, constituting an additional form of encoded information manifest in three-dimensional space. These shape and stiffness variations help in guiding and facilitating the DNA during its three-dimensional spatial interactions. Such interactions with itself allow communication between genes and enhanced wrapping and histone-octamer binding within the nucleosome core particle. Meanwhile, interactions with proteins can have a reduced entropic binding penalty owing to advantageous sequence-dependent bending anisotropy. Sequence periodicity within the DNA, giving a corresponding structural periodicity of shape and stiffness, also influences the supercoiling of the molecule, which, in turn, plays an important facilitating role. In effect, the super-helical density acts as an analogue regulatory mode in contrast to the more commonly acknowledged purely digital mode. Many of these ideas are still poorly understood, and represent a fundamental and outstanding biological question. This review gives an overview of very recent developments, and hopefully identifies promising future lines of enquiry.

Sequence dependence of transcription factor-mediated DNA looping

DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes and DNA looping in transcriptional regulation in both prokaryotes and eukaryotes. These kinds of regulatory problems are now becoming amenable to systematic quantitative dissection with a powerful dialogue between theory and experiment. Here, we use a single-molecule experiment in conjunction with a statistical mechanical model to test quantitative predictions for the behavior of DNA looping at short length scales and to determine how DNA sequence affects looping at these lengths. We calculate and measure how such looping depends upon four key biological parameters: the strength of the transcription factor binding sites, the concentration of the transcription factor, and the length and sequence of the DNA loop. Our studies lead to the surprising insight that sequences that are thought to be especially favorable for nucleosome formation because of high flexibility lead to no systematically detectable effect of sequence on looping, and begin to provide a picture of the distinctions between the short length scale mechanics of nucleosome formation and looping.

The physics of protein-DNA interaction networks in the control of gene expression

Protein-DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein-DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.

DNA looping by FokI: the impact of twisting and bending rigidity on protein-induced looping dynamics

Protein-induced DNA looping is crucial for many genetic processes such as transcription, gene regulation and DNA replication. Here, we use tethered-particle motion to examine the impact of DNA bending and twisting rigidity on loop capture and release, using the restriction endonuclease FokI as a test system. To cleave DNA efficiently, FokI bridges two copies of an asymmetric sequence, invariably aligning the sites in parallel. On account of the fixed alignment, the topology of the DNA loop is set by the orientation of the sites along the DNA. We show that both the separation of the FokI sites and their orientation, altering, respectively, the twisting and the bending of the DNA needed to juxtapose the sites, have profound effects on the dynamics of the looping interaction. Surprisingly, the presence of a nick within the loop does not affect the observed rigidity of the DNA. In contrast, the introduction of a 4-nt gap fully relaxes all of the torque present in the system but does not necessarily enhance loop stability. FokI therefore employs torque to stabilise its DNA-looping interaction by acting as a ‘torsional’ catch bond.

DNA looping by FokI: the impact of synapse geometry on loop topology at varied site orientations

Most restriction endonucleases, including FokI, interact with two copies of their recognition sequence before cutting DNA. On DNA with two sites they act in cis looping out the intervening DNA. While many restriction enzymes operate symmetrically at palindromic sites, FokI acts asymmetrically at a non-palindromic site. The directionality of its sequence means that two FokI sites can be bridged in either parallel or anti-parallel alignments. Here we show by biochemical and single-molecule biophysical methods that FokI aligns two recognition sites on separate DNA molecules in parallel and that the parallel arrangement holds for sites in the same DNA regardless of whether they are in inverted or repeated orientations. The parallel arrangement dictates the topology of the loop trapped between sites in cis: the loop from inverted sites has a simple 180° bend, while that with repeated sites has a convoluted 360° turn. The ability of FokI to act at asymmetric sites thus enabled us to identify the synapse geometry for sites in trans and in cis, which in turn revealed the relationship between synapse geometry and loop topology.

Influence of mobile DNA-protein-DNA bridges on DNA configurations: coarse-grained Monte-Carlo simulations

A large literature exists on modeling the influence of sequence-specific DNA-binding proteins on the shape of the DNA double helix in terms of one or a few fixed constraints. This approach is inadequate for the many proteins that bind DNA sequence independently, and that are present in very large quantities rather than as a few copies, such as the nucleoid proteins in bacterial cells. The influence of such proteins on DNA configurations is better modeled in terms of a great number of mobile constraints on the DNA. Types of constraints that mimic the influence of various known non-specifically DNA binding proteins include DNA bending, wrapping, and bridging. Using Monte-Carlo simulations, we here investigate the influence of (non-interacting) mobile DNA-protein-DNA bridges on the configurations of a 1000 bp piece of linear DNA, for both homogeneous DNA and DNA with an intrinsic planar bend. Results are compared to experimental data on the bacterial nucleoid protein H-NS that forms DNA-protein-DNA bridges. In agreement with data on H-NS, we find very strong positioning of DNA-protein-DNA bridges in the vicinity of planar bends. H-NS binds to DNA very cooperatively, but for non-interacting bridges we only find a moderate DNA-induced clustering. Finally, it has been suggested that H-NS is an important contributor to the extreme condensation of bacterial DNA into a nucleoid structure, but we find only a moderate compaction of DNA coils with increasing numbers of non-interacting bridges. Our results illustrate the importance of quantifying the various effects on DNA configurations that have been proposed for proteins that bind DNA sequence independently.

FRET studies of a landscape of Lac repressor-mediated DNA loops

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-β-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.

DNA modeling reveals an extended lac repressor conformation in classic in vitro binding assays

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.

FLEXIBILITY AND CONTROL OF PROTEIN–DNA LOOPS

Protein–DNA loops are essential for efficient transcriptional repression and activation. The geometry and stability of the archetypal Lac repressor tetramer (LacI)–DNA loop were investigated using designed hyperstable loops containing lac operators bracketing a sequence-directed bend. Electrophoretic mobility shift assays, DNA cyclization, and bulk and single-molecule fluorescence resonance energy transfer (FRET) demonstrate that the DNA sequence controls whether the LacI–DNA loop forms a compact loop with positive writhe or an open loop with little writhe. Monte Carlo methods for simulation of DNA ring closure were extended to DNA loops, including treatment of variable protein hinge angles. The observed distribution of topoisomer products upon cyclization provides a strong constraint on possible models. The experiments and modeling imply that LacI–DNA can adopt a wide range of geometries but has a strong intrinsic preference for an open form. The flexibility of LacI helps explain in vivo observations that DNA looping is less sensitive to DNA length and shape than that expected from the physical properties of DNA. While DNA cyclization suggests two pools of precursor loops for the 9C14 construct, single-molecule FRET demonstrates a single population. This discrepancy suggests that the LacI–DNA structure is strongly influenced by flanking DNA.

Building enhancers from the ground up: a synthetic biology approach

A challenge of the synthetic biology approach is to use our understanding of a system to recreate a biological function with specific properties. We have applied this framework to bacterial enhancers, combining a driver, transcription factor binding sites, and a poised polymerase to create synthetic modular enhancers. Our findings suggest that enhancer-based transcriptional control depends critically and quantitatively on DNA looping, leading to complex regulatory effects when the enhancer cassettes contain additional transcription factor binding sites for TetR, a bacterial transcription factor. We show through a systematic interplay of experiment and thermodynamic modeling that the level of gene expression can be modulated to convert a variable inducer concentration input into discrete or step-like output expression levels. Finally, using a different DNA-binding protein (TraR), we show that the regulatory output is not a particular feature of the specific DNA-binding protein used for the enhancer but a general property of synthetic bacterial enhancers.

A multiscale dynamic model of DNA supercoil relaxation by topoisomerase IB

In this study, we report what we believe to be the first multiscale simulation of the dynamic relaxation of DNA supercoils by human topoisomerase IB (topo IB). We leverage our previous molecular dynamics calculations of the free energy landscape describing the interaction between a short DNA fragment and topo IB. Herein, this landscape is used to prescribe boundary conditions for a computational, elastodynamic continuum rod model of a long length of supercoiled DNA. The rod model, which accounts for the nonlinear bending, twisting, and electrostatic interaction of the (negatively charged) DNA backbone, is extended to include the hydrodynamic drag induced by the surrounding physiological buffer. Simulations for a 200-bp-long DNA supercoil in complex with topo IB reveal a relaxation timescale of ∼0.1-1.0 μs. The relaxation follows a sequence of cascading reductions in the supercoil linking number (Lk), twist (Tw), and writhe (Wr) that follow companion cascading reductions in the supercoil elastic and electrostatic energies. The novel (to our knowledge) multiscale modeling method may enable simulations of the entire experimental setup that measures DNA supercoiling and relaxation via single molecule magnetic trapping.