Statistical mechanics of sequence-dependent circular DNA and its application for DNA cyclization

A molecular mechanism for the "digital" response of p53 to stress

The tumor suppressor protein p53 accumulates in response to cellular stress and consequently orchestrates the expression of multiple genes in a p53-level and time-dependent manner to overcome stress consequences, for which a molecular mechanism is currently unknown. Previously, we reported that DNA torsional flexibility distinguishes among p53 response elements (REs) and that transactivation at basal p53 levels is correlated with p53 REs flexibility. Here, we calculated the flexibility of ~200 p53 REs. By connecting functional outcomes of p53-target genes' activation to the calculated flexibility of their REs, we show that genes known to belong to pathways that are activated rapidly upon stress contain REs that are significantly more flexible relative to REs of genes known to be involved in pathways that are activated later in the response to stress. The global structural properties of several p53 REs belonging to different pathways were experimentally validated. Additionally, reporter-gene expression driven by flexible p53 REs occurred at lower p53 levels and with faster rates than expression from rigid REs. Furthermore, analysis of published endogenous mRNA levels of p53-target genes as a function of REs' flexibility showed that early versus late genes differ significantly in their flexibility properties of their REs and that highly flexible p53 REs enable high-activation level exclusively to early-response genes. Overall, we demonstrate that DNA flexibility of p53 REs contributes significantly to functional selectivity in the p53 system by facilitating the initial steps of p53-dependent target-genes expression, thereby contributing to survival versus death decisions in the p53 system.

Surprising Twists in Nucleosomal DNA with Implication for Higher-order Folding

While nucleosomes are dynamic entities that must undergo structural deformations to perform their functions, the general view from available high-resolution structures is a largely static one. Even though numerous examples of twist defects have been documented, the DNA wrapped around the histone core is generally thought to be overtwisted. Analysis of available high-resolution structures from the Protein Data Bank reveals a heterogeneous distribution of twist along the nucleosomal DNA, with clear patterns that are consistent with the literature, and a significant fraction of structures that are undertwisted. The subtle differences in nucleosomal DNA folding, which extend beyond twist, have implications for nucleosome disassembly and modeled higher-order structures. Simulations of oligonucleosome arrays built with undertwisted models behave very differently from those constructed from overtwisted models, in terms of compaction and inter-nucleosome contacts, introducing configurational changes equivalent to those associated with 2-3 base-pair changes in nucleosome spacing. Differences in the nucleosomal DNA pathway, which underlie the way that DNA enters and exits the nucleosome, give rise to different nucleosome-decorated minicircles and affect the topological mix of configurational states.

The complex architecture of p53 binding sites

Sequence-specific protein-DNA interactions are at the heart of the response of the tumor-suppressor p53 to numerous physiological and stress-related signals. Large variability has been previously reported in p53 binding to and transactivating from p53 response elements (REs) due, at least in part, to changes in direct (base) and indirect (shape) readouts of p53 REs. Here, we dissect p53 REs to decipher the mechanism by which p53 optimizes this highly regulated variable level of interaction with its DNA binding sites. We show that hemi-specific binding is more prevalent in p53 REs than previously envisioned. We reveal that sequences flanking the REs modulate p53 binding and activity and show that these effects extend to 4–5 bp from the REs. Moreover, we show here that the arrangement of p53 half-sites within its REs, relative to transcription direction, has been fine-tuned by selection pressure to optimize and regulate the response levels from p53 REs. This directionality in the REs arrangement is at least partly encoded in the structural properties of the REs. Furthermore, we show here that in the p21-5′ RE the orientation of the half-sites is such that the effect of the flanking sequences is minimized and we discuss its advantages.

Three-dimensional nonlinear dynamics of prestressed active filaments: Flapping, swirling, and flipping

Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.

Determinants of cyclization-decyclization kinetics of short DNA with sticky ends

Cyclization of DNA with sticky ends is commonly used to measure DNA bendability as a function of length and sequence, but how its kinetics depend on the rotational positioning of the sticky ends around the helical axis is less clear. Here, we measured cyclization (looping) and decyclization (unlooping) rates (k_loop and k_unloop) of DNA with sticky ends over three helical periods (100-130 bp) using single-molecule fluorescence resonance energy transfer (FRET). k_loop showed a nontrivial undulation as a function of DNA length whereas k_unloop showed a clear oscillation with a period close to the helical turn of DNA (∼10.5 bp). The oscillation of k_unloop was almost completely suppressed in the presence of gaps around the sticky ends. We explain these findings by modeling double-helical DNA as a twisted wormlike chain with a finite width, intrinsic curvature, and stacking interaction between the end base pairs. We also discuss technical issues for converting the FRET-based cyclization/decyclization rates to an equilibrium quantity known as the J factor that is widely used to characterize DNA bending mechanics.

Identifying Physical Causes of Apparent Enhanced Cyclization of Short DNA Molecules with a Coarse-Grained Model

DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart—with the deviation larger for shorter molecules—because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.

Quantifying the impact of simple DNA parameters on the cyclization J-factor for single-basepair-addition families

We use Monte Carlo simulation to quantify the change in cyclization J-factor within a dramatically simplified model of DNA that involves parameters for uniform stiffnesses, intrinsic twist, and intrinsic bending (including nonplanar bending). Plots of J versus DNA length over multiple periods of helical repeat are fit to a simple functional form in order to project the behavior of J over a broad range of these model parameters. In some instances, this process allows us to find families of DNA molecules (within our model) with quite different material properties, but very similar plots of J versus length, so similar as to likely to be indistinguishable by experiments. This effect is seen both for the parameter-pair of bend angle and stiffness scaling, as well as for the parameter-trio of helical repeat, bend angle, and bend non-planarity.

Diverse p53/DNA binding modes expand the repertoire of p53 response elements

The tumor suppressor protein p53 acts as a transcription factor, binding sequence-specifically to defined DNA sites, thereby activating the expression of genes leading to diverse cellular outcomes. Canonical p53 response elements (REs) are made of two decameric half-sites separated by a variable number of base pairs (spacers). Fifty percent of all validated p53 REs contain spacers between 1 and 18 bp; however, their functional significance is unclear at present. Here, we show that p53 forms two different tetrameric complexes with consensus or natural REs, both with long spacers: a fully specific complex where two p53 dimers bind to two specific half-sites, and a hemispecific complex where one dimer binds to a specific half-site and the second binds to an adjacent spacer sequence. The two types of complexes have comparable binding affinity and specificity, as judged from binding competition against bulk genomic DNA. Structural analysis of the p53 REs in solution shows that these sites are not bent in both their free and p53-bound states when the two half-sites are either abutting or separated by spacers. Cell-based assay supports the physiological relevance of our findings. We propose that p53 REs with long spacers comprise separate specific half-sites that can lead to several different tetrameric complexes. This finding expands the universe of p53 binding sites and demonstrates that even isolated p53 half-sites can form tetrameric complexes. Moreover, it explains the manner in which p53 binds to clusters of more than one canonical binding site, common in many natural REs.

Evaluating the role of coherent delocalized phonon-like modes in DNA cyclization

The innate flexibility of a DNA sequence is quantified by the Jacobson-Stockmayer's J-factor, which measures the propensity for DNA loop formation. Recent studies of ultra-short DNA sequences revealed a discrepancy of up to six orders of magnitude between experimentally measured and theoretically predicted J-factors. These large differences suggest that, in addition to the elastic moduli of the double helix, other factors contribute to loop formation. Here, we develop a new theoretical model that explores how coherent delocalized phonon-like modes in DNA provide single-stranded "flexible hinges" to assist in loop formation. We combine the Czapla-Swigon-Olson structural model of DNA with our extended Peyrard-Bishop-Dauxois model and, without changing any of the parameters of the two models, apply this new computational framework to 86 experimentally characterized DNA sequences. Our results demonstrate that the new computational framework can predict J-factors within an order of magnitude of experimental measurements for most ultra-short DNA sequences, while continuing to accurately describe the J-factors of longer sequences. Further, we demonstrate that our computational framework can be used to describe the cyclization of DNA sequences that contain a base pair mismatch. Overall, our results support the conclusion that coherent delocalized phonon-like modes play an important role in DNA cyclization.

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.

Computational 3D Assembling Methods for DNA: A Survey

DNA encodes the genetic information of most living beings, except viruses that use RNA. Unlike other types of molecules, DNA is not usually described by its atomic structure being instead usually described by its base-pair sequence, i.e., the textual sequence of its subsidiary molecules known as nucleotides ( adenine (A), cytosine (C), guanine (G), and thymine (T)). The three-dimensional assembling of DNA molecules based on its base-pair sequence has been, for decades, a topic of interest for many research groups all over the world. In this paper, we survey the major methods found in the literature to assemble and visualize DNA molecules from their base-pair sequences. We divided these methods into three categories: predictive methods, adaptive methods, and thermodynamic methods . Predictive methods aim to predict a conformation of the DNA from its base pair sequence, while the goal of adaptive methods is to assemble DNA base-pairs sequences along previously known conformations, as needed in scenarios such as DNA Monte Carlo simulations. Unlike these two geometric methods, thermodynamic methods are energy-based and aim to predict secondary structural motifs of DNA in cases where hydrogen bonds between base pairs might be broken because of temperature changes. We also present the major software tools that implements predictive, adaptive, and thermodynamic methods.

The role of structural parameters in DNA cyclization

BACKGROUND

The intrinsic bendability of DNA plays an important role with relevance for myriad of essential cellular mechanisms. The flexibility of a DNA fragment can be experimentally and computationally examined by its propensity for cyclization, quantified by the Jacobson-Stockmayer J factor. In this study, we use a well-established coarse-grained three-dimensional model of DNA and seven distinct sets of experimentally and computationally derived conformational parameters of the double helix to evaluate the role of structural parameters in calculating DNA cyclization.

RESULTS

We calculate the cyclization rates of 86 DNA sequences with previously measured J factors and lengths between 57 and 325 bp as well as of 20,000 randomly generated DNA sequences with lengths between 350 and 4000 bp. Our comparison with experimental data is complemented with analysis of simulated data.

CONCLUSIONS

Our data demonstrate that all sets of parameters yield very similar results for longer DNA fragments, regardless of the nucleotide sequence, which are in agreement with experimental measurements. However, for DNA fragments shorter than 100 bp, all sets of parameters performed poorly yielding results with several orders of magnitude difference from the experimental measurements. Our data show that DNA cyclization rates calculated using conformational parameters based on nucleosome packaging data are most similar to the experimental measurements. Overall, our study provides a comprehensive large-scale assessment of the role of structural parameters in calculating DNA cyclization rates.

Hybrid simulation approach incorporating microscopic interaction along with rigid body degrees of freedom for stacking between base pairs

Stacking interaction between the aromatic heterocyclic bases plays an important role in the double helical structures of nucleic acids. Considering the base as rigid body, there are total of 18 degrees of freedom of a dinucleotide step. Some of these parameters show sequence preferences, indicating that the detailed atomic interactions are important in the stacking. Large variants of non-canonical base pairs have been seen in the crystallographic structures of RNA. However, their stacking preferences are not thoroughly deciphered yet from experimental results. The current theoretical approaches use either the rigid body degrees of freedom where the atomic information are lost or computationally expensive all atom simulations. We have used a hybrid simulation approach incorporating Monte-Carlo Metropolis sampling in the hyperspace of 18 stacking parameters where the interaction energies using AMBER-parm99bsc0 and CHARMM-36 force-fields were calculated from atomic positions. We have also performed stacking energy calculations for structures from Monte-Carlo ensemble by Dispersion corrected density functional theory. The available experimental data with Watson-Crick base pairs are compared to establish the validity of the method. Stacking interaction involving A:U and G:C base pairs with non-canonical G:U base pairs also were calculated and showed that these structures were also sequence dependent. This approach could be useful to generate multiscale modeling of nucleic acids in terms of coarse-grained parameters where the atomic interactions are preserved. This method would also be useful to predict structure and dynamics of different base pair steps containing non Watson-Crick base pairs, as found often in the non-coding RNA structures. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 212-226, 2016.

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.

A statistical thermodynamic model for investigating the stability of DNA sequences from oligonucleotides to genomes

We describe the development and testing of a simple statistical mechanics methodology for duplex DNA applicable to sequences of any composition and extensible to genomes. The microstates of a DNA sequence are modeled in terms of blocks of basepairs that are assumed to be fully closed (paired) or open. This approach generates an ensemble of bubblelike microstates that are used to calculate the corresponding partition function. The energies of the microstates are calculated as additive contributions from hydrogen bonding, basepair stacking, and solvation terms parameterized from a comprehensive series of molecular dynamics simulations including solvent and ions. Thermodynamic properties and nucleotide stability constants for DNA sequences follow directly from the partition function. The methodology was tested by comparing computed free energies per basepair with the experimental melting temperatures of 60 oligonucleotides, yielding a correlation coefficient of -0.96. The thermodynamic stability of genic/nongenic regions was tested in terms of nucleotide stability constants versus sequence for the Escherichia coli K-12 genome. It showed clear differentiation of the genes from promoters and captures genic regions with a sensitivity of 0.94. The statistical thermodynamic model presented here provides a seemingly new handle on the challenging problem of interpreting genomic sequences.

Small circular DNA molecules act as rigid motifs to build DNA nanotubes

Small circular DNA molecules with designed lengths, for example 64 and 96 nucleotides (nt), after hybridization with a few 32-nt staple strands respectively, can act as rigid motifs for the construction of DNA nanotubes with excellent uniformity in ring diameter. Unlike most native DNA nanotubes, which consist of longitudinal double helices, nanotubes assembled from circular DNAs are constructed from lateral double helices. Of the five types of DNA nanotubes designed here, four are built by alternating two different rings of the same ring size, while one is composed of all the same 96-nt rings. Nanotubes constructed from the same 96-nt rings are 10-100 times shorter than those constructed from two different 96-nt rings, because there are fewer hinge joints on the rings.

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.

Measuring shape-dependent looping probability of DNA

Recently, several studies have shown that short doubled-stranded DNA (dsDNA) loops more readily than the wormlike chain model predicts. In most of these experiments, the intrinsic bendedness of dsDNA, which in theory can dramatically influence looping dynamics, was either avoided or unaccounted for. To investigate the effect of the shape of dsDNA on looping dynamics, we characterized the shapes of several synthetic dsDNA molecules of equal length but different sequences using gel electrophoresis. We then measured their looping rates using a FRET (Förster resonance energy transfer)-based assay and extracted the looping probability density known as the J factor (jM). We also used, for comparison, several dinucleotide angular parameter sets derived from the observed electrophoretic mobility to compute the jM predicted by the wormlike chain model. Although we found a strong correlation between curvature and jM, the measured jM was higher than most dinucleotide model predictions. This result suggests that it is difficult to reconcile the looping probability with the observed gel mobility within the wormlike chain model and underscores the importance of determining the intrinsic shape of dsDNA for proper theoretical analysis.

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

As the chief informational molecule of life, DNA is subject to extensive physical manipulations. The energy required to deform double-helical DNA depends on sequence, and this mechanical code of DNA influences gene regulation, such as through nucleosome positioning. Here we examine the sequence-dependent flexibility of DNA in bacterial transcription factor-mediated looping, a context for which the role of sequence remains poorly understood. Using a suite of synthetic constructs repressed by the Lac repressor and two well-known sequences that show large flexibility differences in vitro, we make precise statistical mechanical predictions as to how DNA sequence influences loop formation and test these predictions using in vivo transcription and in vitro single-molecule assays. Surprisingly, sequence-dependent flexibility does not affect in vivo gene regulation. By theoretically and experimentally quantifying the relative contributions of sequence and the DNA-bending protein HU to DNA mechanical properties, we reveal that bending by HU dominates DNA mechanics and masks intrinsic sequence-dependent flexibility. Such a quantitative understanding of how mechanical regulatory information is encoded in the genome will be a key step towards a predictive understanding of gene regulation at single-base pair resolution.

Block decoys: transcription-factor decoys designed for in vitro gene regulation studies

Transcription-factor decoys are short synthetic oligodeoxynucleotides that sequester cognate transcription factors and prevent their binding at target promoters. Current methods of decoy formation have primarily been optimized for potential therapeutic applications. However, they are not ideally suited to in vitro investigations into multi-transcription factor-mediated processes that may require multiple regulatory elements to be inhibited in varying combinations. In this study we describe a novel method for chimeric decoy formation in which blocks containing discrete transcription factor binding sites are combined into circular molecules. Unlike currently available methods, block decoys allow rapid construction of chimeric decoys targeting multiple regulatory elements. Further, they enable fine-tuning of binding-site copy ratios within chimeras, allowing sophisticated control of the cellular transcriptional landscape. We show that block decoys are exonuclease-resistant and specifically inhibit expression from target binding sites. The potential of block decoys to inhibit multiple elements simultaneously was demonstrated using a chimeric decoy containing molar optimized ratios of three regulatory elements, NF-κB-RE, CRE, and E-box. The chimeric decoy inhibited expression from all three elements simultaneously at equivalent levels. The primary intended use of block decoys is in vitro gene regulation studies in which bespoke chimeras can be rapidly constructed and utilized to determine a promoter's functional regulation.

The thermodynamics of DNA loop formation, from J to Z

The formation of DNA loops is a ubiquitous theme in biological processes, including DNA replication, recombination and repair, and gene regulation. These loops are mediated by proteins bound at specific sites along the contour of a single DNA molecule, in some cases many thousands of base pairs apart. Loop formation incurs a thermodynamic cost that is a sensitive function of the length of looped DNA as well as the geometry and elastic properties of the DNA-bound protein. The free energy of DNA looping is logarithmically related to a generalization of the Jacobson-Stockmayer factor for DNA cyclization, termed the J factor. In the present article, we review the thermodynamic origins of this quantity, discuss how it is measured experimentally and connect the macroscopic interpretation of the J factor with a statistical-mechanical description of DNA looping and cyclization.

DNA Bending through Roll Angles Is Independent of Adjacent Base Pairs

We have studied DNA bending for a wide range of DNA sequences by two-dimensional adaptive umbrella sampling simulations on adjacent roll angles. Calculated free energy surfaces are largely additive and can be well approximated by the sum of the one-dimensional free energy surfaces. Cooperativity between adjacent roll angles was found to be negligible: less than 1.0 kcal/mol and a small fraction of the overall bending energy. Our calculations validate the assumptions underlying many popular coarse-grained models for DNA bending, and demonstrate their theoretical validity for investigating DNA bending.

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.

On binding of DNA-bending proteins to DNA minicircles

We present a theoretical study of binding of DNA-bending proteins to circular DNA, using computer simulations of the wormlike chain model of DNA. We find that the binding affinity is affected by the bending elasticity and the conformational entropy of the polymer and that while protein adsorption is identical on open and closed long DNA molecules, there is significant enhancement of binding on DNA minicircles, compared to their linear counterparts. We also find that the ratio of the radii of gyration of open and closed chains depends on protein concentration for short DNA molecules. Experimental tests of our predictions are proposed.

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.

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.

Theory on the dynamic memory in the transcription-factor-mediated transcription activation

We develop a theory to explain the origin of the static and dynamical memory effects in transcription-factor-mediated transcription activation. Our results suggest that the following inequality conditions should be satisfied to observe such memory effects: (a) τ(L)≫max(τ(R),τ(E)), (b) τ(LT)≫τ(T), and (c) τ(I)≥(τ(EL)+τ(TR)) where τ(L) is the average time required for the looping-mediated spatial interactions of enhancer-transcription-factor complex with the corresponding promoter--RNA-polymerase or eukaryotic RNA polymerase type II (PolII in eukaryotes) complex that is located L base pairs away from the cis-acting element, (τ(R),τ(E)) are respectively the search times required for the site-specific binding of the RNA polymerase and the transcription factor with the respective promoter and the cis-regulatory module, τ(LT) is the time associated with the relaxation of the looped-out segment of DNA that connects the cis-acting site and promoter, τ(T) is the time required to generate a complete transcript, τ(I) is the transcription initiation time, τ(EL) is the elongation time, and τ(TR) is the termination time. We have theoretically derived the expressions for the various searching, looping, and loop-relaxation time components. Using the experimentally determined values of various time components we further show that the dynamical memory effects cannot be experimentally observed whenever the segment of DNA that connects the cis-regulatory element with the promoter is not loaded with bulky histone bodies. Our analysis suggests that the presence of histone-mediated compaction of the connecting segment of DNA can result in higher values of looping and loop-relaxation times, which is the origin of the static memory in the transcription activation that is mediated by the memory gene loops in eukaryotes.

Transition between two regimes describing internal fluctuation of DNA in a nanochannel

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.

Transition between two regimes describing internal fluctuation of DNA in a nanochannel

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.

Sequence-dependent cooperative binding of p53 to DNA targets and its relationship to the structural properties of the DNA targets

The prime mechanism by which p53 acts as a tumor suppressor is as a transcription factor regulating the expression of diverse downstream genes. The DNA-binding domain of p53 (p53DBD) interacts with defined DNA sites and is the main target for mutations in human primary tumors. Here, we show that the CWWG motif, found in the center of each consensus p53 half-site, is a key player in p53/DNA interactions. Gel-mobility-shift assays provide a unique opportunity to directly observe the various oligomeric complexes formed between p53DBD and its target sites. We demonstrate that p53DBD binds to p53 consensus sites containing CATG with relatively low cooperativity, as both dimers and tetramers, and with even lower cooperativity to such sites containing spacer sequences. p53DBD binds to sites containing CAAG and CTAG with measurable affinity only when imbedded in two contiguous p53 half-sites and only as tetramers (with very high cooperativity). There are three orders-of-magnitude difference in the cooperativity of interaction between sites differing in their non-contacted step, and further two orders-of-magnitude difference as a function of spacer sequences. By experimentally measuring the global structural properties of these sites, by cyclization kinetics of DNA minicircles, we correlate these differences with the torsional flexibility of the binding sites.

Looping probabilities of elastic chains: a path integral approach

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.

Sequence dependence of DNA bending rigidity

For many aspects of DNA-protein interaction, it is vital to know how DNA bending rigidity (or persistence length, a) depends on its sequence. We addressed this problem using the method based on cyclization of short DNA fragments, which allows very accurate determination of a. Our approach was based on assigning specific values of a to each of 10 distinct dinucleotide steps. We prepared DNA fragments, each about 200 bp in length, with various quasi-periodic sequences, measured their cyclization efficiencies (j factors), and fitted the data by the theoretical equation to obtain the values of a for each fragment. From these data, we obtained a set of a for the dinucleotide steps. To test this set, we used it to design DNA sequences that should correspond to very low and very high values of a, prepared the corresponding fragments, and determined their values of a experimentally. The measured and calculated values of a were very close to one another, confirming that we have found the correct solution to this long-standing problem. The same experimental data also allowed us to determine the sequence dependence of DNA helical repeat.

HIV-1 nucleocapsid protein bends double-stranded nucleic acids

The human immunodeficiency virus type-1 (HIV-1) nucleocapsid (NC) protein is believed to be unique among the nucleic acid (NA) binding proteins encoded by this retrovirus in being highly multifunctional and relatively nonsequence-specific. Underlying many of NC's putative functions, including for example its chaperon-like activity for various steps of HIV-1 reverse transcription, is NC's ability to partially melt short double-stranded regions of structured NAs, which is essentially a consequence of NC's general binding preference for single-stranded bases. Herein we report a different, previously undiscovered, mode of NC/NA interaction, i.e., NC-induced sharp bending of short segments of fully duplexed DNA/DNA and DNA/RNA. We use single-molecule fluorescence resonance energy transfer (SM-FRET) in vitro to probe NC-induced NA bending and associated heterogeneous conformational dynamics for model NC/NA complexes. NC-induced NA bending may have important biological roles in the previously reported NC-mediated condensation of duplex proviral DNA in the HIV-1 life cycle.

First-principles calculation of DNA looping in tethered particle experiments

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.

Elastic energy driven polymerization

We present a molecular system where polymerization is controlled externally by tuning the elastic energy of the monomers. The elastic energy, provided by a DNA molecular spring, destabilizes the monomer state through a process analogous to domain swapping. This energy can be large (of approximately 10 kT) and thus drive polymerization at relatively low monomer concentrations. The monomer-dimer equilibrium provides a measurement of the elastic energy of the monomer, which in this construction appears limited by kink formation in the DNA molecular spring, in accord with previous theoretical and experimental investigations of the elasticity of sharply bent DNA.

Theoretical analysis of disruptions in DNA minicircles

Under sufficient bending stress, which appears in DNA minicircles and small DNA loops, the double helix experiences local disruptions of its regular structure. We developed a statistical-mechanical treatment of the disruptions in DNA minicircles, studied experimentally by Du et al. The model of disruptions used in our Monte Carlo simulation of minicircle conformations specifies these conformations by three parameters: DNA bend angle at the disruption, theta(d); local DNA unwinding caused by the disruption; and the free energy associated with the disruption in the unstressed double helix, G(d). The model is applicable to any structural type of disruption, kinks or opening of single basepairs. The simulation shows that accounting for both torsional and bending deformation associated with the disruptions is very important for proper analysis. We obtained a relationship between values of G(d) and theta(d) under which the simulation results are compatible with the experimental data. The relationship suggests that the free energy of basepair opening, which includes flipping out both bases, is significantly higher than the generally accepted value. The model is also applied to the analysis of j-factors of very short DNA fragments.

Computational analysis of looping of a large family of highly bent DNA by LacI

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.

Mesoscale modeling of multi-protein-DNA assemblies: the role of the catabolic activator protein in Lac-repressor-mediated looping

DNA looping plays a key role in the regulation of the lac operon in Escherichia coli. The presence of a tightly bent loop (between sequentially distant sites of Lac repressor protein binding) purportedly hinders the binding of RNA polymerase and subsequent transcription of the genetic message. The unexpectedly favorable binding interaction of this protein-DNA assembly with the catabolic activator protein (CAP), a protein that also bends DNA and paradoxically facilitates the binding of RNA polymerase, stimulated extension of our base-pair level theory of DNA elasticity to the treatment of DNA loops formed in the presence of several proteins. Here we describe in detail a procedure to determine the structures and free energies of multi-protein-DNA assemblies and illustrate the predicted effects of CAP binding on the configurations of the wild-type 92-bp Lac repressor-mediated O3-O1 DNA loop. We show that the DNA loop adopts an antiparallel orientation in the most likely structure and that this loop accounts for the published experimental observation that, when CAP is bound to the loop, one of the arms of LacR binds to an alternative site that is displaced from the original site by 5 bp.

Effect of bending anisotropy on the 3D conformation of short DNA loops

The equilibrium three dimensional shape of relatively short loops of DNA is studied using an elastic model that takes into account anisotropy in bending rigidities. Using a reasonable estimate for the anisotropy, it is found that cyclized DNA with lengths that are not integer multiples of the pitch take on nontrivial shapes that involve bending out of planes and formation of kinks. The effect of sequence inhomogeneity on the shape of DNA is addressed, and shown to enhance the geometrical features. These findings could shed some light on the role of DNA conformation in protein-DNA interactions.