Thermodynamics of DNA branching

Leveraging Steric Moieties for Kinetic Control of DNA Strand Displacement Reactions

DNA strand displacement networks are a critical part of dynamic DNA nanotechnology and are proven primitives for implementing chemical reaction networks. Precise kinetic control of these networks is important for their use in a range of applications. Among the better understood and widely leveraged kinetic properties of these networks are toehold sequence, length, composition, and location. While steric hindrance has been recognized as an important factor in such systems, a clear understanding of its impact and role is lacking. Here, a systematic investigation of steric hindrance within a DNA toehold-mediated strand displacement network was performed through tracking kinetic reactions of reporter complexes with incremental concatenation of steric moieties near the toehold. Two subsets of steric moieties were tested with systematic variation of structures and reaction conditions to isolate sterics from electrostatics. Thermodynamic and coarse-grained computational modeling was performed to gain further insight into the impacts of steric hindrance. Steric factors yielded up to 3 orders of magnitude decrease in the reaction rate constant. This pronounced effect demonstrates that steric moieties can be a powerful tool for kinetic control in strand displacement networks while also being more broadly informative of DNA structural assembly in both DNA-based therapeutic and diagnostic applications that possess elements of steric hindrance through DNA functionalization with an assortment of chemistries.

Thermal cycling of DNA devices via associative strand displacement

DNA-based devices often operate through a series of toehold-mediated strand-displacement reactions. To achieve cycling, fluidic mixing can be used to introduce 'recovery' strands to reset the system. However, such mixing can be cumbersome, non-robust, and wasteful of materials. Here we demonstrate mixing-free thermal cycling of DNA devices that operate through associative strand-displacement cascades. These cascades are favored at low temperatures due to the primacy of a net increase in base pairing, whereas rebinding of 'recovery' strands is favored at higher temperatures due to the primacy of a net release of strands. The temperature responses of the devices could be modulated by adjustment of design parameters such as the net increase of base pairs and the concentrations of strands. Degradation of function was not observable even after 500 thermal cycles. We experimentally demonstrated simple digital-logic circuits that evaluate at 35°C and reset after transient heating to 65°C. Thus associative strand displacement enables robust thermal cycling of DNA-based devices in a closed system.

DNA secondary structure formation by DNA shuffling of the conserved domains of the Cry protein of Bacillus thuringiensis

Background

The Cry toxins, or δ-endotoxins, are a diverse group of proteins produced by Bacillus thuringiensis. While DNA secondary structures are biologically relevant, it is unknown if such structures are formed in regions encoding conserved domains of Cry toxins under shuffling conditions. We analyzed 5 holotypes that encode Cry toxins and that grouped into 4 clusters according to their phylogenetic closeness. The mean number of DNA secondary structures that formed and the mean Gibbs free energy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(\overline{\varDelta G}\right) $$\end{document}ΔG¯ were determined by an in silico analysis using different experimental DNA shuffling scenarios. In terms of spontaneity, shuffling efficiency was directly proportional to the formation of secondary structures but inversely proportional to ∆G.

Results

The results showed a shared thermodynamic pattern for each cluster and relationships among sequences that are phylogenetically close at the protein level. The regions of the cry11Aa, Ba and Bb genes that encode domain I showed more spontaneity and thus a greater tendency to form secondary structures (<∆G). In the region of domain III; this tendency was lower (>∆G) in the cry11Ba and Bb genes. Proteins that are phylogenetically closer to Cry11Ba and Cry11Bb, such as Cry2Aa and Cry18Aa, maintained the same thermodynamic pattern. More distant proteins, such as Cry1Aa, Cry1Ab, Cry30Aa and Cry30Ca, featured different thermodynamic patterns in their DNA.

Conclusion

These results suggest the presence of thermodynamic variations associated to the formation of secondary structures and an evolutionary relationship with regions that encode highly conserved domains in Cry proteins. The findings of this study may have a role in the in silico design of cry gene assembly by DNA shuffling techniques.

Availability: A Metric for Nucleic Acid Strand Displacement Systems

DNA strand displacement systems have transformative potential in synthetic biology. While powerful examples have been reported in DNA nanotechnology, such systems are plagued by leakage, which limits network stability, sensitivity, and scalability. An approach to mitigate leakage in DNA nanotechnology, which is applicable to synthetic biology, is to introduce mismatches to complementary fuel sequences at key locations. However, this method overlooks nuances in the secondary structure of the fuel and substrate that impact the leakage reaction kinetics in strand displacement systems. In an effort to quantify the impact of secondary structure on leakage, we introduce the concepts of availability and mutual availability and demonstrate their utility for network analysis. Our approach exposes vulnerable locations on the substrate and quantifies the secondary structure of fuel strands. Using these concepts, a 4-fold reduction in leakage has been achieved. The result is a rational design process that efficiently suppresses leakage and provides new insight into dynamic nucleic acid networks.

Network Formation by Cross-Hybridization of Complementary Strands to Grafted ssDNA

When a low density brush of single-stranded DNA (ssDNA) targets end-grafted to a surface is immersed in a solution of complementary ssDNA probes, a regular brush of DNA duplexes is formed by 1:1 hybridization between probe and target DNA. We suggest that in higher density brushes of ssDNA this process competes with cross-hybridization of a target strand to several neighboring probe strands resulting in the formation of a cross-linked DNA network. We analyze a simple 2D model of a dense DNA brush and use analytic methods and computer simulations to find how the conditions for network formation depend on system size and DNA length. We argue that in 3D brushes cross-hybridization will nearly always lead to network formation and suggest that this may explain some intriguing results on dense DNA brushes. Experiments on DNA monolayers and concentrated DNA solutions that could test our predictions are proposed.

Noncanonical structures and their thermodynamics of DNA and RNA under molecular crowding: beyond the Watson-Crick double helix

How does molecular crowding affect the stability of nucleic acid structures inside cells? Water is the major solvent component in living cells, and the properties of water in the highly crowded media inside cells differ from that in buffered solution. As it is difficult to measure the thermodynamic behavior of nucleic acids in cells directly and quantitatively, we recently developed a cell-mimicking system using cosolutes as crowding reagents. The influences of molecular crowding on the structures and thermodynamics of various nucleic acid sequences have been reported. In this chapter, we discuss how the structures and thermodynamic properties of nucleic acids differ under various conditions such as highly crowded environments, compartment environments, and in the presence of ionic liquids, and the major determinants of the crowding effects on nucleic acids are discussed. The effects of molecular crowding on the activities of ribozymes and riboswitches on noncanonical structures of DNA- and RNA-like quadruplexes that play important roles in transcription and translation are also described.

DNA nanostructures as models for evaluating the role of enthalpy and entropy in polyvalent binding

DNA nanotechnology allows the design and construction of nanoscale objects that have finely tuned dimensions, orientation, and structure with remarkable ease and convenience. Synthetic DNA nanostructures can be precisely engineered to model a variety of molecules and systems, providing the opportunity to probe very subtle biophysical phenomena. In this study, several such synthetic DNA nanostructures were designed to serve as models to study the binding behavior of polyvalent molecules and gain insight into how small changes to the ligand/receptor scaffolds, intended to vary their conformational flexibility, will affect their association equilibrium. This approach has yielded a quantitative identification of the roles of enthalpy and entropy in the affinity of polyvalent DNA nanostructure interactions, which exhibit an intriguing compensating effect.

Nanoengineering with DNA

DNA is a tractable medium for controlling the structure of matter on the nanometer scale. We have explored ligating together stable branched DNA molecules to form geometrical objects. By this means, we have assembled a 3-connected molecule whose helix axes have the connectivity of a cube. The construct is a hexacatenane, each of whose cyclic strands corresponds to a face of the object. Each of its twelve edges contains a unique recognition site for cleavage by a restriction enzyme; these sites are used to demonstrate the assembly of the object. The plectonemic structure of DNA also permits the directed synthesis of molecular knots. Recently, we have constructed trefoil knots from B-DNA and an amphichiral figure-8 knot whose helical domains contain both B-DNA and Z-DNA.

We have developed a solid-support methodology for the synthesis of geometrical objects. This approach provides greater control over products and topological purity, and lends itself better to automation. Branched molecules containing 3–6 double helical arms can be formed from equimolar mixtures of their component strands, thereby enabling the construction of 3–6 connected networks. The goals of this work include the construction of periodic multiply-connected networks of DNA. The aims of these DNA constructions include using them as scaffolding to build periodic macromolecular arrays for diffraction purposes, as well as directing the assembly of molecular electronic devices. There are wellcharacterized molecular transformations of DNA that make nano-scale machines feasible to build in this molecular context. These materials are likely to be useful for understanding crystallization processes and structure-function relationships.

Fluorescence competition and optical melting measurements of RNA three-way multibranch loops provide a revised model for thermodynamic parameters

Three-way multibranch loops (junctions) are common in RNA secondary structures. Computer algorithms such as RNAstructure and MFOLD do not consider the identity of unpaired nucleotides in multibranch loops when predicting secondary structure. There is limited experimental data, however, to parametrize this aspect of these algorithms. In this study, UV optical melting and a fluorescence competition assay are used to measure stabilities of multibranch loops containing up to five unpaired adenosines or uridines or a loop E motif. These results provide a test of our understanding of the factors affecting multibranch loop stability and provide revised parameters for predicting stability. The results should help to improve predictions of RNA secondary structure.

Protocols for self-assembly and imaging of DNA nanostructures

Programed molecular structures allow us to research and make use of physical, chemical, and biological effects at the nanoscale. They are an example of the "bottom-up" approach to nanotechnology, with structures forming through self-assembly. DNA is a particularly useful molecule for this purpose, and some of its advantages include parallel (as opposed to serial) assembly, naturally occurring "tools," such as enzymes and proteins for making modifications and attachments, and structural dependence on base sequence. This allows us to develop one, two, and three dimensional structures that are interesting for their fundamental physical and chemical behavior, and for potential applications such as biosensors, medical diagnostics, molecular electronics, and efficient light-harvesting systems. We describe five techniques that allow one to assemble and image such structures: concentration measurement by ultraviolet absorption, titration gel electrophoresis, thermal annealing, fluorescence microscopy, and atomic force microscopy in fluids.

Experiment and prediction: a productive symbiosis in studies on the thermodynamics of DNA oligomers

Recently, we reported the kinetics of hybridization of cDNA dodecamers (Carrillo-Nava, E., Mejía-Radillo, Y., and Hinz, H.-J. Biochemistry 2008, 47, 13153-13157). In this study, we provide the thermodynamic reaction parameters of those dodecamers as well as a comparison with parameters for 24-mers designed from two identical dodecamers in tandem arrangement. The thermodynamic properties were determined by isothermal titration calorimetry (ITC), differential scanning microcalorimetry (DSC), and UV melting studies. On the basis of the results from our kinetic studies, fitting algorithms of DSC and UV melting profiles employed the two-state assumption for the duplex to a single strand dissociation reaction. The formation of both 12-mer and 24-mer duplexes is strongly enthalpy driven at all temperatures. At identical temperatures, the hybridization enthalpy of the 24-mer is within error limits twice that of the 12-mer. Duplex formation is always associated with a significant negative heat capacity change, ΔC(p), which, on a mass basis, is comparable to that observed for protein folding. Only a small part of the favorable reaction enthalpy appears as a standard Gibbs free energy change due to large compensating negative entropy changes linked to duplex formation. On the basis of the results of the present studies, it appears to be absolutely essential for a proper analysis of thermodynamic parameters of oligonucleotide hybridization reactions to combine low temperature ITC measurements of binding enthalpies with DSC and UV melting studies to obtain an accurate assessment of standard Gibbs energy changes or, equivalently, hybridization constants over a broad temperature range. The experimental thermodynamic parameters were compared with theoretical estimates based on nearest-neighbor approximations employing temperature-independent enthalpies. Good agreement between experimental and predicted ΔG° values is observed at ambient temperatures (20-30 °C), as long as helix formation is associated with small molar heat capacity changes. If the experimental ΔC(p) values determined by ITC are taken into account, significant deviations occur.

Nanomaterials based on DNA

The combination of synthetic stable branched DNA and sticky-ended cohesion has led to the development of structural DNA nanotechnology over the past 30 years. The basis of this enterprise is that it is possible to construct novel DNA-based materials by combining these features in a self-assembly protocol. Thus, simple branched molecules lead directly to the construction of polyhedrons, whose edges consist of double helical DNA and whose vertices correspond to the branch points. Stiffer branched motifs can be used to produce self-assembled two-dimensional and three-dimensional periodic lattices of DNA (crystals). DNA has also been used to make a variety of nanomechanical devices, including molecules that change their shapes and molecules that can walk along a DNA sidewalk. Devices have been incorporated into two-dimensional DNA arrangements; sequence-dependent devices are driven by increases in nucleotide pairing at each step in their machine cycles.

Stabilization of three-way junctions of DNA under molecular crowding conditions

We examined the effects of molecular crowding conditions on the structures and thermodynamics of three-way junctions (TWJs) of DNA. Structural analysis utilizing gel electrophoresis and circular dichroism spectroscopy showed that the designed DNAs folded into TWJ structures in the presence of Na(+) and Mg(2+) under both dilute and molecular crowding conditions with polyethylene glycol 200 (PEG 200). From the thermodynamic parameters evaluated by UV melting techniques in the absence and presence of 5 mM Mg(2+) under dilute and molecular crowding conditions, it was clear that Mg(2+) stabilized all TWJs under the dilute condition, although the extent of stabilization depended on the stacking partners of TWJs. For example, thermodynamic stability (-DeltaG(o) (37)) of A/B-stacked TWJs (A, B, and C are the three helices of TWJ, and among these helices, A and B are stacked together) increased from 3.7 to 5.6 kcal/mol by the addition of 5 mM Mg(2+), while that of A/C-stacked TWJs (A and C are stacked together) increased only from 3.0 to 3.7 kcal/mol. Molecular crowding with PEG 200 destabilized the whole TWJ consisting of a junction point and three helical duplex arms. Crowding agents such as PEG 200 can affect the stability of DNA by modulating its hydration. To explore the crowding effects on the junction point, we evaluated the number of water molecules associated with the whole TWJ as well as the individual arms, and we found that the number of water molecules taken up by the whole TWJ was significantly smaller than the sum of the individual arms. These results show the dehydration from the junction point of the TWJ structure. Therefore, molecular crowding should be favorable for the junction point of TWJ structure and unfavorable for the duplex structure. To prove this concept, we designed truncated TWJ structures that folded into a bimolecular duplex under the dilute condition. With increasing concentrations of PEG 200 from 0 to 30 wt %, the fraction of truncated TWJ structures gradually increased, and that of the bimolecular duplex structure decreased, even in the absence of Mg(2+). We concluded that a cell-mimicking condition, in which the activity of water decreases and hydration becomes less favorable, might facilitate the formation of junction structures in comparison with duplexes.

Folding DNA origami from a double-stranded source of scaffold

Combined heat and chemical denaturation of double-stranded DNA scaffold strands in the presence of staple strands, followed by a sudden temperature drop and then stepwise dialysis to remove the chemical denaturant, leads to self-assembly of two distinct DNA-origami structures.

Thermodynamics of forming a parallel DNA crossover

The process of genetic recombination involves the formation of branched four-stranded DNA structures known as Holliday junctions. The Holliday junction is known to have an antiparallel orientation of its helices, i.e., the crossover occurs between strands of opposite polarity. Some intermediates in this process are known to involve two crossover sites, and these may involve crossovers between strands of identical polarity. Surprisingly, if a crossover occurs at every possible juxtaposition of backbones between parallel DNA double helices, the molecules form a paranemic structure with two helical domains, known as PX-DNA. Model PX-DNA molecules can be constructed from a variety of DNA molecules with five nucleotide pairs in the minor groove and six, seven or eight nucleotide pairs in the major groove. A topoisomer of the PX motif is the juxtaposed JX(1) molecule, wherein one crossover is missing between the two helical domains. The JX(1) molecule offers an outstanding baseline molecule with which to compare the PX molecule, so as to measure the thermodynamic cost of forming a crossover in a parallel molecule. We have made these measurements using calorimetric and ultraviolet hypochromicity methods, as well as denaturing gradient gel electrophoretic methods. The results suggest that in relaxed conditions, a system that meets the pairing requirements for PX-DNA would prefer to form the PX motif relative to juxtaposed molecules, particularly for the 6:5 structure.

Heat capacity changes associated with nucleic acid folding

Whereas heat capacity changes (DeltaCPs) associated with folding transitions are commonplace in the literature of protein folding, they have long been considered a minor energetic contributor in nucleic acid folding. Recent advances in the understanding of nucleic acid folding and improved technology for measuring the energetics of folding transitions have allowed a greater experimental window for measuring these effects. We present in this review a survey of current literature that confronts the issue of DeltaCPs associated with nucleic acid folding transitions. This work helps to gather the molecular insights that can be gleaned from analysis of DeltaCPs and points toward the challenges that will need to be overcome if the energetic contribution of DeltaCP terms are to be put to use in improving free energy calculations for nucleic acid structure prediction.

Spontaneous DNA-DNA interaction of homologous duplexes and factors affecting the result of heteroduplex formation

Mutation detection and mismatch repair investigations based on heteroduplex formation require a linear DNA structure. DNA branching, described previously under physiological conditions, has been analysed in the heteroduplex formation process. Symmetrical chi-structures were detected after heteroduplex formation by gel electrophoresis and electron microscopy. Buffer composition, DNA concentration and duplex end-sequences influence DNA branching. Duplexes with homologous central regions but non-complementary ends do not form hybrid heteroduplexes or hybrid Holliday junctions. Our results explain the requirements for efficient heteroduplex formation, which were previously determined empirically: special solution composition, optimal DNA concentration and GC clamps. This provides the theoretical background for further optimisation of the procedure.

The Thermodynamics of DNA Structural Motifs

DNA secondary structure plays an important role in biology, genotyping diagnostics, a variety of molecular biology techniques, in vitro-selected DNA catalysts, nanotechnology, and DNA-based computing. Accurate prediction of DNA secondary structure and hybridization using dynamic programming algorithms requires a database of thermodynamic parameters for several motifs including Watson-Crick base pairs, internal mismatches, terminal mismatches, terminal dangling ends, hairpins, bulges, internal loops, and multibranched loops. To make the database useful for predictions under a variety of salt conditions, empirical equations for monovalent and magnesium dependence of thermodynamics have been developed. Bimolecular hybridization is often inhibited by competing unimolecular folding of a target or probe DNA. Powerful numerical methods have been developed to solve multistate-coupled equilibria in bimolecular and higher-order complexes. This review presents the current parameter set available for making accurate DNA structure predictions and also points to future directions for improvement.

Interaction of linear homologous DNA duplexes via Holliday junction formation

Interaction of linear homologous DNA duplexes by formation of Holliday junctions was revealed by electrophoresis and confirmed by electron microscopy. The phenomenon was demonstrated using a model of five purified PCR products of different size and sequence. The double-stranded structure of interacting DNA fragments was confirmed using several consecutive purifications, S1-nuclease analysis, and electron microscopy. Formation of Holliday junctions depends on DNA concentration. A thermodynamic equilibrium between duplexes and Holliday junctions was shown. We propose that homologous duplex interaction is initiated by nucleation of several dissociated terminal base pairs of two fragments. This process is followed by branch migration creating a population of Holliday junctions with the branch point at different sites. Finally, Holliday junctions are resolved via branch migration to new or previously existing duplexes. The phenomenon is a new property of DNA. This type of DNA-DNA interaction may contribute to the process of Holliday junction formation in vivo controlled by DNA conformation and DNA-protein interactions. It is of practical significance for optimization of different PCR-based methods of gene analysis, especially those involving heteroduplex formation.

The energetics of HMG box interactions with DNA: thermodynamic description of the target DNA duplexes

The thermal properties and energetics of formation of 10, 12 and 16 bp DNA duplexes, specifically interacting with the HMG box of Sox-5, have been studied by isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). DSC studies show that the partial heat capacity of these short duplexes increases considerably prior to the cooperative process of strand separation. Direct extrapolation of the pre and post-transition heat capacity functions into the cooperative transition zone suggests that unfolding/dissociation of strands results in no apparent heat capacity increment. In contrast, ITC measurements show that the negative enthalpy of complementary strand association increases in magnitude with temperature rise, implying that strand association proceeds with significant decrease of heat capacity. Furthermore, the ITC-measured enthalpy of strand association is significantly smaller in magnitude than the enthalpy of cooperative unfolding measured by DSC. To resolve this paradox, the heat effects upon heating and cooling of the separate DNA strands have been measured by DSC. This showed that cooling of the strands from 100 degrees C to -10 degrees C proceeds with significant heat release associated with the formation of intra and inter-molecular interactions. When the enthalpy of residual structure in the strands and the temperature dependence of the heat capacity of the duplexes and of their unfolded strands have been taken into account, the ITC and DSC results are brought into agreement. The analysis shows that the considerable increase in heat capacity of the duplexes with temperature rise is due to increasing fluctuations of their structure (e.g. end fraying and twisting) and this effect obscures the heat capacity increment resulting from the cooperative separation of strands, which in fact amounts to 200(+/-40) JK(-1) (mol bp)(-1). Using this heat capacity increment, the averaged standard enthalpy, entropy and Gibbs energy of formation of fully folded duplexes from fully unfolded strands have been determined at 25 degrees C as -33(+/-2) kJ (mol bp)(-1), -93(+/-4) J K(-1) (mol bp)(-1) and -5.0(+/-0.5) kJ (mol bp)(-1), respectively.

DNA secondary structure effects on DNA synthesis catalyzed by HIV-1 reverse transcriptase

The effect of DNA secondary structure on polymerization catalyzed by human immunodeficiency virus (HIV-1) reverse transcriptase (RT) was studied using a synthetic 66-nucleotide DNA template containing a stable hairpin structure. Four RT pause sites were identified within the first half of the hairpin stem. Additionally, five weak pause sites within the second half of the stem and the loop of the hairpin were identified at low temperatures. These weak pause sites were relocated to the site of the first few stem base pairs of two new hairpins formed due to a change in DNA secondary structure. Each pause site was correlated with a high free energy barrier of melting the stem base pair. Pre-steady state kinetic analysis of single nucleotide incorporation showed that polymerization at each pause site occurred by both a fast phase (10-20 s-1) and a slow phase (0. 02-0.07 s-1) during a single binding event. The reaction amplitudes of the fast phase were small (4-10% of enzyme sites), whereas the amplitudes of the slow phase were large (14-40%) at the pause sites. In contrast, only a single phase with a large reaction amplitude (32-50%) and a fast nucleotide incorporation rate (33-87 s-1) was observed at the non-pause sites. DNA substrates at all sites had similar dissociation rates (0.14-0.29 s-1) and overall binding affinity (16-86 nM). These results suggest that the DNA substrates at pause sites were bound in both productive and non-productive states at the polymerase site of RT. The non-productively bound DNA was slowly converted into a productive state upon melting of the next stem base pair without dissociation of the DNA from RT.

Sequence dependence of branch migratory minima

The Holliday junction is a central intermediate in the process of genetic recombination. The position of its branch-point can relocate through an isomerization known as branch migration. This migration occurs because the branch-point is flanked by homologous symmetry. All attempts at modeling the kinetics of branch migration have relied on the assumption that branch migration minima are sequence-independent. We have tested that assumption here, using a competition assay based on symmetric immobile branched junctions; these are junctions that cannot undergo branch migration, despite the fact that they are flanked by homology. The assay used is predicated on the non-association of strands displaced in the assay; we have tested this assumption, and have performed our experiments under conditions where we know that it is true. We have measured the free energy of relocating a branched junction from a fixed non-homologous sequence to all possible dimeric symmetric sequences. We find that the assumption of sequence-independence is often valid, but that it is not universally true. We find that the flanking sequences can have a marked effect on the free energy measured, both for extensions of symmetry and for reversals of flanking nucleotides. We have varied the temperature in our experiments, and have derived both enthalpies and entropies for the different sequences. The entropies are largely unfavorable, whereas the enthalpies are largely favorable; regardless of the signs of these quantities, we see that this is another system where enthalpy-entropy compensation is operative.

Thermodynamics of the interactions of lac repressor with variants of the symmetric lac operator: effects of converting a consensus site to a non-specific site

What are the thermodynamic consequences of the stepwise conversion of a highly specific (consensus) protein-DNA interface to one that is nonspecific? How do the magnitudes of key favorable contributions to complex stability (burial of hydrophobic surfaces and reduction of DNA phosphate charge density) change as the DNA sequence of the specific site is detuned? To address these questions we investigated the binding of lac repressor (LacI) to a series of 40 bp fragments carrying symmetric (consensus) and variant operator sequences over a range of temperatures and salt concentrations. Variant DNA sites contained symmetrical single and double base-pair substitutions at positions 4 and/or 5 [sequence: see text] in each 10 bp half site of the symmetric lac operator (Osym). Non-specific interactions were examined using a 40 bp non-operator DNA fragment. Disruption of the consensus interface by a single symmetrical substitution reduces the observed equilibrium association constant (K(obs)) for Osym by three to four orders of magnitude; double symmetrical substitutions approach the six orders in magnitude difference between specific and non-specific binding to a 40 bp fragment. At these adjacent positions in the consensus site, the free energy effects of multiple substitutions are non-additive: the first reduces /deltaG(obs)o/ by 3 to 5 kcal mol(-1), approximately halfway to the non-specific level, whereas the second is less deleterious, reducing /deltaG(obs)o/ by less than 3 kcal mol(-1). Variant-specific dependences of K(obs) on temperature and salt concentration characterize these LacI-operator interactions. In general, binding constants and standard free energies of binding both exhibit characteristic extrema near 290 K. As a consequence, both the enthalpic and entropic contributions to stability of Osym and variant complexes change from positive (i.e. entropy driven) at lower temperatures to negative (i.e. enthalpy driven) at higher temperatures, indicating that the heat capacity change upon binding, deltaC(obs)o, is large and negative. In general, /deltaC(obs)o/ decreases as the specificity and stability of the variant complex decreases. Stabilities of complexes of LacI with Osym and all variant operators are strongly [salt]-dependent. Binding constants for the variant complexes exhibit a power-dependence on [salt] that is larger in magnitude (i.e. more negative) than for Osym, but no obvious trend relates changes in contributions from the polyelectrolyte effect and the observed reductions in stability (delta deltaG(obs)o). These variant-specific thermodynamic signatures provide novel insights into the consequences of converting a consensus interface to a less specific one; such insights are not obtained from comparisons at the level of delta deltaG(obs)o. We propose that this variant-specific behavior arises from a strong effect of operator sequence on the extent of induced conformational changes in the protein (and possibly also in the DNA site) which accompany binding.

Sensing the heat: the application of isothermal titration calorimetry to thermodynamic studies of biomolecular interactions

Biomolecular interactions can be defined by combining thermodynamic data on the energetic properties of the interaction with high-resolution structural data. The development of high sensitivity isothermal titration calorimetric equipment provides a dramatic advance in the gathering of thermodynamic data, and the interactions between biological macromolecules can now be described with unprecedented accuracy.

Xylose-DNA: comparison of the thermodynamic stability of oligo(2'-deoxyxylonucleotide) and oligo(2'-deoxyribonucleotide) duplexes

Measurements of differential scanning calorimetry, ultraviolet absorption and circular dichroism have been performed on two synthetic oligo(2'-deoxyxylonucleotides): (A) d[xA)3-(xT)3-(xA)3-(xT)3-T] and (B) d[(xA-xT)6-T], and on the oligo(2'-deoxyribonucleotide) (C) d[(A)3-(T)3-(A)3-(T)3]. Oligonucleotides having 2'-deoxyxylose instead of 2'-deoxyribose exhibit unusual thermodynamic, optical and structural features. At identical concentrations the transition temperatures of the oligo(2'-deoxyxylooligomers) are higher than those of the oligo(2'-deoxyribooligomers) indicating higher stability. The calorimetric transition enthalpy of (C) is 270 +/- 15 kJ . mol-1, the corresponding van't Hoff value is 280 +/- 15 kJ . (mol of cooperative unit)-1. The ratio of delta HvH/delta Hcal = 1.04 suggests all-or-none behaviour for the transition of the 2'-deoxyribose oligonucleotide. The analogous parameters of (A) are: delta Hcal = 310 +/- 30 kJ . mol-1, delta HvH = 220 +/- 30 kJ.(mol of cooperative unit)-1. The ratio of 0.71 indicates multistate melting for this compound. The sequence dependence of the thermodynamic quantities becomes apparent when the parameters of the alternating oligo(2'-deoxyxylonucleotide) d[(xA-xT)6-T] are compared to those of d[(xA)3-(xT)3-(xA)3-(xT)3-T). The values are delta Hcal = 330 +/- 30 kJ.mol-1; delta HvH = 180 +/- 15 kJ.(mol of cooperative unit)-1 delta HvH/ delta Hcal = 0.55. The transition enthalpy of the alternating oligo(2'-deoxyxylonucleotide) (B) is the highest but the cooperativity of transition is the lowest of the oligonucleotides studied. The circular dichroic spectra of the two oligo(2'-deoxyxylonucleotides) show unusual features in that d[(xA)3-(xT)3-(XA)3-(xT)3-T] exhibits a spectrum that is suggestive of a left-handed double helix, while the spectrum of the alternating oligo(2'-deoxyxylonucleotide) (B) resembles neither that of (C) nor that of (A).

Relative stabilities of DNA three-way, four-way and five-way junctions (multi-helix junction loops): unpaired nucleotides can be stabilizing or destabilizing

Competition binding and UV melting studies of a DNA model system consisting of three, four or five mutually complementary oligonucleotides demonstrate that unpaired bases at the branch point stabilize three- and five-way junction loops but destabilize four-way junctions. The inclusion of unpaired nucleotides permits the assembly of five-way DNA junction complexes (5WJ) having as few as seven basepairs per arm from five mutually complementary oligonucleotides. Previous work showed that 5WJ, having eight basepairs per arm but lacking unpaired bases, could not be assembled [Wang, Y.L., Mueller, J.E., Kemper, B. and Seeman, N.C. (1991) Biochemistry, 30, 5667-5674]. Competition binding experiments demonstrate that four-way junctions (4WJ) are more stable than three-way junctions (3WJ), when no unpaired bases are included at the branch point, but less stable when unpaired bases are present at the junction. 5WJ complexes are in all cases less stable than 4WJ or 3WJ complexes. UV melting curves confirm the relative stabilities of these junctions. These results provide qualitative guidelines for improving the way in which multi-helix junction loops are handled in secondary structure prediction programs, especially for single-stranded nucleic acids having primary sequences that can form alternative structures comprising different types of junctions.

Coaxial stacking of helixes enhances binding of oligoribonucleotides and improves predictions of RNA folding

An RNA model system consisting of an oligomer binding to a 4-nt overhang at the 5' end of a hairpin stem provides thermodynamic parameters for helix-helix interfaces. In a sequence-dependent manner, oligomers bind up to 1000-fold more tightly adjacent to the hairpin stem than predicted for binding to a free tetramer at 37 degrees C. For the interface (/) in [formula: see text] additional free energy change, delta delta G 37 degrees, for binding is roughly the nearest-neighbor delta G 37 degrees for propagation of an uninterrupted helix of equivalent sequence, CGGC. When X and Z are omitted, the delta delta 37 degrees is even more favorable by approximately 1 kcal/mol (1 cal = 4.184J). On average, predictions of 11 RNA secondary structures improve from 67 to 74% accuracy by inclusion of similar stacking contributions.

The thermodynamics of formation of a three-strand, DNA three-way junction complex

Isothermal titration calorimetry (ITC) is used to study the thermodynamics of assembly of the three DNA oligonucleotides S1 (5'-GCCTGCCACCGC), S2 (5'-GCGGTGCGTCCG), and S3AA (5'-CGGACGAAGCAGGC) to form a three-way junction (TWJ) complex consisting of three double-helical arms radiating from a junction region having two unpaired adenosines in one strand (S3AA). The thermodynamics of assembly were measured for three different orders of addition of the component oligonucleotides at four temperatures between 10 and 25 degrees C. At each temperature studied, the overall values of delta H, delta S degrees, and delta G degrees for assembly of the complex from the component single strands were found to be independent of the order of addition. The enthalpy of binding, delta H, was found to be linearly dependent on temperature. From the temperature dependence of delta H, the change in heat capacity delta Cp, for the overall assembly of three strands to form the junction complex was calculated and found to be -1.6 kcal mol-1K-1. This work represents the first attempt to evaluate the thermodynamics of DNA TWJ formation by ITC.

Symmetric immobile DNA branched junctions

Branch migration is an isomerization of Holliday recombination intermediates that arises from their homologous (2-fold) sequence symmetry. This isomerization relocates the branch point in an apparently random fashion and thereby complicates the study of the physical and structural properties of these structures. For the past decade, these properties have been studied in low-symmetry immobile junctions, whose sequence asymmetry eliminates branch migration. The asymmetric findings of many of these studies suggest the need for a system combining both immobility and symmetry. Double-crossover DNA molecules have been used to create molecules with both these properties. Immobility is achieved by flanking one crossover with a symmetric junction and the other crossover with an asymmetric junction. Close torsional coupling between the two junctions renders the symmetric junction immobile. These molecules will enable the characterization of thermodynamic, structural, dynamic, liganding, and substrate properties of symmetric branched DNA molecules in a sequence-specific fashion.

The structure of branched DNA species

Branched DNA molecules provide a challenging set of structural problems. Operationally we define branched DNA species as molecules in which double helical segments are interrupted by abrupt discontinuities, and we draw together a number of different kinds of structure in the class, including helical junctions of different orders, and base bulges (Fig. 1).

DNA double-crossover molecules

DNA molecules containing two crossover sites between helical domains have been suggested as intermediates in recombination processes involving double-strand breaks. We have modeled these double-crossover structures in an oligonucleotide system. Whereas the relative orientations of the helical domains must be specified in designing these molecules, there are two broad classes of the molecules, the parallel, DP, and antiparallel, DA, molecules. The distance between crossover points must be specified as multiples of half-turns, in order to avoid torsional stress in this system; hence, there are two further subdivisions, those double-crossover molecules separated by odd, O, and even, E, numbers of half-turns. In addition, the parallel molecules with odd numbers of half-turns between crossovers must be divided into those with an excess major or wide-groove separation, W, or those with an excess minor- or narrow-groove separation, N. We have constructed models of all five of these classes, DAE, DAO, DPE, DPOW, and DPON. DPE molecules containing 1 and 2 helical turns between crossovers have been constructed; the DAE molecule contains 1 turn between crossovers, and the DAO, DPOW, and DPON molecules contain 1.5 helical turns between crossovers. None of the parallel molecules is well-behaved; the molecules either dissociate or form multimers when visualized on native polyacrylamide gels. In contrast, antiparallel molecules form single bands when assayed in this fashion. Hydroxyl radical autofootprinting analysis of these molecules reveals protection at expected sites of crossover and of occlusion, suggesting that all the complexes contain linear helix axes that are roughly coplanar between crossovers. However, the DPOW molecule and the DPE molecule with 2 turns between crossovers show decreased protection in the portion between crossovers, suggesting that their helices may bow in response to charge repulsion. We conclude that the helices between parallel double crossovers must be shielded from each other or distorted from linearity if they are to participate in recombination. We have analyzed the possibilities of branch migration and crossover isomerization in double-crossover molecules. Parallel molecules need no sequence symmetry beyond homology to branch migrate, but the sequence symmetry requirements for antiparallel molecules restrict migration to directly repetitive segments that iterate the sequence between crossovers. Crossover isomerization appears to be a very complex process in parallel double-crossover molecules, suggesting that it may be catalyzed by topoisomerases if it occurs within the cell.