Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

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, θ_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 θ_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.     

Thermodynamics of DNA target site recognition by homing endonucleases

The thermodynamic profiles of target site recognition have been surveyed for homing endonucleases from various structural families. Similar to DNA-binding proteins that recognize shorter target sites, homing endonucleases display a narrow range of binding free energies and affinities, mediated by structural interactions that balance the magnitude of enthalpic and entropic forces. While the balance of ΔH and TΔS are not strongly correlated with the overall extent of DNA bending, unfavorable ΔH_binding is associated with unstacking of individual base steps in the target site. The effects of deleterious basepair substitutions in the optimal target sites of two LAGLIDADG homing endonucleases, and the subsequent effect of redesigning one of those endonucleases to accommodate that DNA sequence change, were also measured. The substitution of base-specific hydrogen bonds in a wild-type endonuclease/DNA complex with hydrophobic van der Waals contacts in a redesigned complex reduced the ability to discriminate between sites, due to nonspecific ΔS_binding.     

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.     

Equilibrium and Kinetics of DNA Overstretching Modeled with a Quartic Energy Landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ≈ 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.     

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.     

Cy3-DNA stacking interactions strongly depend on the identity of the terminal basepair

We characterized the effect of the first basepair on the conformational dynamics of the fluorescent dye Cy3 attached to the 5′ end of double-stranded DNA using Gaussian-mixture adaptive umbrella sampling simulations. In the simulations, the sampling of all five dihedral angles along the linker was enhanced, so that both stacked and unstacked states were sampled. The affinity of Cy3 for a T·A basepair (with the dye attached to T) was found to be significantly less than for the other basepairs. This was verified experimentally by measuring the activation energies for cis-trans isomerization of the dye. The simulation and experimental results indicate the existence of partially unstacked conformations amenable to photoisomerization. The simulations also showed that stacking of Cy3 straightens the DNA while stabilizing the first basepair. Our findings indicate that fluorescence is modulated by Cy3-DNA interactions in a sequence-dependent manner.     

DNA sequence and methylation prescribe the inside-out conformational dynamics and bending energetics of DNA minicircles

Eukaryotic genome and methylome encode DNA fragments’ propensity to form nucleosome particles. Although the mechanical properties of DNA possibly orchestrate such encoding, the definite link between ‘omics’ and DNA energetics has remained elusive. Here, we bridge the divide by examining the sequence-dependent energetics of highly bent DNA. Molecular dynamics simulations of 42 intact DNA minicircles reveal that each DNA minicircle undergoes inside-out conformational transitions with the most likely configuration uniquely prescribed by the nucleotide sequence and methylation of DNA. The minicircles’ local geometry consists of straight segments connected by sharp bends compressing the DNA’s inward-facing major groove. Such an uneven distribution of the bending stress favors minimum free energy configurations that avoid stiff base pair sequences at inward-facing major grooves. Analysis of the minicircles’ inside-out free energy landscapes yields a discrete worm-like chain model of bent DNA energetics that accurately account for its nucleotide sequence and methylation. Experimentally measuring the dependence of the DNA looping time on the DNA sequence validates the model. When applied to a nucleosome-like DNA configuration, the model quantitatively reproduces yeast and human genomes’ nucleosome occupancy. Further analyses of the genome-wide chromatin structure data suggest that DNA bending energetics is a fundamental determinant of genome architecture.     

Equilibrium and Kinetics of DNA Overstretching Modeled with a Quartic Energy Landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ≈ 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.     

Free-Energy Landscape and Characteristic Forces for the Initiation of DNA Unzipping

DNA unzipping, the separation of its double helix into single strands, is crucial in modulating a host of genetic processes. Although the large-scale separation of double-stranded DNA has been studied with a variety of theoretical and experimental techniques, the minute details of the very first steps of unzipping are still unclear. Here, we use atomistic molecular-dynamics simulations, coarse-grained simulations, and a statistical-mechanical model to study the initiation of DNA unzipping by an external force. Calculation of the potential of mean force profiles for the initial separation of the first few terminal basepairs in a DNA oligomer revealed that forces ranging between 130 and 230 pN are needed to disrupt the first basepair, and these values are an order of magnitude larger than those needed to disrupt basepairs in partially unzipped DNA. The force peak has an echo of ∼50 pN at the distance that unzips the second basepair. We show that the high peak needed to initiate unzipping derives from a free-energy basin that is distinct from the basins of subsequent basepairs because of entropic contributions, and we highlight the microscopic origin of the peak. To our knowledge, our results suggest a new window of exploration for single-molecule experiments.     

Energetic signatures of single base bulges: thermodynamic consequences and biological implications

DNA bulges are biologically consequential defects that can arise from template-primer misalignments during replication and pose challenges to the cellular DNA repair machinery. Calorimetric and spectroscopic characterizations of defect-containing duplexes reveal systematic patterns of sequence-context dependent bulge-induced destabilizations. These distinguishing energetic signatures are manifest in three coupled characteristics, namely: the magnitude of the bulge-induced duplex destabilization (ΔΔG_Bulge); the thermodynamic origins of ΔΔG_Bulge (i.e. enthalpic versus entropic); and, the cooperativity of the duplex melting transition (i.e. two-state versus non-two state). We find moderately destabilized duplexes undergo two-state dissociation and exhibit ΔΔG_Bulge values consistent with localized, nearest neighbor perturbations arising from unfavorable entropic contributions. Conversely, strongly destabilized duplexes melt in a non-two-state manner and exhibit ΔΔG_Bulge values consistent with perturbations exceeding nearest-neighbor expectations that are enthalpic in origin. Significantly, our data reveal an intriguing correlation in which the energetic impact of a single bulge base centered in one strand portends the impact of the corresponding complementary bulge base embedded in the opposite strand. We discuss potential correlations between these bulge-specific differential energetic profiles and their overall biological implications in terms of DNA recognition, repair and replication.     

Sequence effects of aminofluorene-modified DNA duplexes: thermodynamic and circular dichroism properties

Circular dichroism (CD) and UV-melting experiments were conducted with 16 oligodeoxynucleotides modified by the carcinogen 2-aminofluorene, whose sequence around the lesion was varied systematically [d(CTTCTNG[AF]NCCTC), N = G, A, C, T], to gain insight into the factors that determine the equilibrium between base-displaced stacked (S) and external B-type (B) duplex conformers. Differing stabilities among the duplexes can be attributed to different populations of S and B conformers. The AF modification always resulted in sequence-dependent thermal (T_m) and thermodynamic (−ΔG°) destabilization. The population of B-type conformers derived from eight selected duplexes (i.e. -AG*N- and -CG*N-) was inversely proportional to the −ΔG° and T_m values, which highlights the importance of carcinogen/base stacking in duplex stabilization even in the face of disrupted Watson–Crick base pairing in S-conformation. CD studies showed that the extent of the adduct-induced negative ellipticities in the 290–350 nm range is correlated linearly with −ΔG° and T_m, but inversely with the population of B-type conformations. Taken together, these results revealed a unique interplay between the extent of carcinogenic interaction with neighboring base pairs and the thermodynamic properties of the AF-modified duplexes. The sequence-dependent S/B heterogeneities have important implications in understanding how arylamine–DNA adducts are recognized in nucleotide excision repair.     

New insights into DNA triplexes: residual twist and radial difference as measures of base triplet non-isomorphism and their implication to sequence-dependent non-uniform DNA triplex

DNA triplexes are formed by both isomorphic (structurally alike) and non-isomorphic (structurally dissimilar) base triplets. It is espoused here that (i) the base triplet non-isomorphism may be articulated in structural terms by a residual twist (Δt°), the angle formed by line joining the C1′…C1′ atoms of the adjacent Hoogsteen or reverse Hoogsteen (RH) base pairs and the difference in base triplet radius (Δr Å), and (ii) their influence on DNA triplex is largely mechanistic, leading to the prediction of a high (t + Δt)° and low (t − Δt)° twist at the successive steps of Hoogsteen or RH duplex of a parallel or antiparallel triplex. Efficacy of this concept is corroborated by molecular dynamics (MD) simulation of an antiparallel DNA triplex comprising alternating non-isomorphic G*GC and T*AT triplets. Conformational changes necessitated by base triplet non-isomorphism are found to induce an alternating (i) high anti and anti glycosyl and (ii) BII and an unusual BIII conformation resulting in a zigzag backbone for the RH strand. Thus, base triplet non-isomorphism causes DNA triplexes into exhibiting sequence-dependent non-uniform conformation. Such structural variations may be relevant in deciphering the specificity of interaction with DNA triplex binding proteins. Seemingly then, residual twist (Δt°) and radial difference (Δr Å) suffice as indices to define and monitor the effect of base triplet non-isomorphism in nucleic acid triplexes.     

Hydration of short DNA, RNA and 2'-OMe oligonucleotides determined by osmotic stressing

Studies on hydration are important for better understanding of structure and function of nucleic acids. We compared the hydration of self-complementary DNA, RNA and 2′-O-methyl (2′-OMe) oligonucleotides GCGAAUUCGC, (UA)₆ and (CG)₃ using the osmotic stressing method. The number of water molecules released upon melting of oligonucleotide duplexes, Δn_W, was calculated from the dependence of melting temperature on water activity and the enthalpy, both measured with UV thermal melting experiments. The water activity was changed by addition of ethylene glycol, glycerol and acetamide as small organic co-solutes. The Δn_W was 3–4 for RNA duplexes and 2–3 for DNA and 2′-OMe duplexes. Thus, the RNA duplexes were hydrated more than the DNA and the 2′-OMe oligonucleotide duplexes by approximately one to two water molecules depending on the sequence. Consistent with previous studies, GC base pairs were hydrated more than AU pairs in RNA, whereas in DNA and 2′-OMe oligonucleotides the difference in hydration between these two base pairs was relatively small. Our data suggest that the better hydration of RNA contributes to the increased enthalpic stability of RNA duplexes compared with DNA duplexes.     

Sequence-dependent cost for Z-form shapes the torsion-driven B–Z transition via close interplay of Z-DNA and DNA bubble

Despite recent genome-wide investigations of functional DNA elements, the mechanistic details about their actions remain elusive. One intriguing possibility is that DNA sequences with special patterns play biological roles, adopting non-B-DNA conformations. Here we investigated dynamics of thymine-guanine (TG) repeats, microsatellite sequences and recurrently found in promoters, as well as cytosine–guanine (CG) repeats, best-known Z-DNA forming sequence, in the aspect of Z-DNA formation. We measured the energy barriers of the B–Z transition with those repeats and discovered the sequence-dependent penalty for Z-DNA generates distinctive thermodynamic and kinetic features in the torque-induced transition. Due to the higher torsional stress required for Z-form in TG repeats, a bubble could be induced more easily, suppressing Z-DNA induction, but facilitate the B–Z interconversion kinetically at the transition midpoint. Thus, the Z-form by TG repeats has advantages as a torsion buffer and bubble selector while the Z-form by CG repeats likely behaves as torsion absorber. Our statistical physics model supports quantitatively the populations of Z-DNA and reveals the pivotal roles of bubbles in state dynamics. All taken together, a quantitative picture for the transition was deduced within the close interplay among bubbles, plectonemes and Z-DNA.     

Statistical Mechanical Approach for Predicting the Transition to Non-B DNA Structures in Supercoiled DNA

Abstract

Supercoiling causes global twist of DNA structure and the supercoiled state has wide influence on conformational transition. A statistical mechanical approach was made for prediction of the transition probability to non-B DNA structures under torsional stress. A conditional partition function was defined as the sum over all possible states of the DNA sequence with basepair 1 and basepair n being in B-form helix and a recurrence formula was developed which expressed the partition function for basepair n with those for less number of pairs. This new definition permits a quick enumeration of every configuration of secondary structures. Energetic parameters of all conformations concerned, involving B-form, interior loop, cruciform and Z-form, were included in the equation. The probability of transition to each non-B conformation could be derived from these conditional partition functions. For treatment of effects of superhelicity, supercoiling energy was considered, and a twist of each conformation was determined to minimize the supercoiling energy. As the twist itself affects the transition probability, the whole scheme of equations was solved by renormalization technique. The present method permits a simultaneous treatment of serveral types of conformations under a common torsional stress.

A set of energetic parameters of DNA secondary structures has been chosen for calculation. Some DNA sequences were submitted to the calculation, and all the sequences that we submitted gave stable convergence. Some of them have been investigated the critical supercoil density for the transition to non-B DNA structures. Even though the reliability of the set of parameters was not enough, the prediction of secondary structure transition showed good agreement with reported observation. Hence, the present algorithm can estimate the probability of local conformational change of DNA under a given supercoil density, and also be employed to predict some specific sequences in which conformational change is sensitive to superhelicity.