A Unified Poland-Scheraga Model of Oligo- and Polynucleotide DNA Melting: Salt Effects and Predictive Power

Key biological and nano-technological processes require the partial or complete association and dissociation of complementary DNA strands. We present a variant of the Poland-Scheraga model for DNA melting where we introduce a local, sequence-dependent salt correction of the nearest-neighbor parameters. Furthermore, our formulation accounts for capping and interfacial energies of helical and coiled chain sections. We show that the model reproduces experimental data for melting temperatures over the full experimental range of strand length, strand concentration, and ionic strength of the solution. In particular, we reproduce a phenomenological relation by Frank-Kamenetskii for very long chains using a parameterization based on melting curves for short oligomers. However, we also show that the parameters of the Poland-Scheraga model are still not known with sufficient precision to quantitatively predict the fine structure of melting curves. This formulation of the Poland-Scheraga model opens the possibility to overcome this limitation by optimizing parameters with respect to an extended base of experimental data for short-, medium-, and long-chain melting. We argue that the often-discarded melting data for longer oligomers exhibiting non-two-state transitions could play a particularly important role.     

The Kinetics of Cooperative Cofilin Binding Reveals Two States of the Cofilin-Actin Filament

The interaction of cofilin with actin filaments displays positive cooperativity. The equilibrium binding and associated thermodynamic properties of this interaction are well described by a simple, one-dimensional Ising model with nearest neighbor interactions. Here we evaluate the kinetic contributions to cooperative binding and the ability of this model to account for binding across a wide range of cofilin concentrations. A Monte Carlo-based simulation protocol that allows for nearest-neighbor interactions between adjacent binding sites was used to globally fit time courses of human cofilin binding to human nonmuscle (β-, γ-) actin filaments. Several extensions of the one-dimensional Ising model were tested, and a mechanism that includes isomerization of the actin filament was found to best account for time courses of association as well as irreversible dissociation from a saturated filament. This model predicts two equilibrium states of the cofilin-actin, or cofilactin, filament, and the resulting set of binding parameters are in agreement with equilibrium thermodynamic parameters. We conclude that despite its simplicity, this one-dimensional Ising model is a reliable model for analyzing and interpreting the energetics and kinetics of cooperative cofilin-actin filament interactions. The model predicts that severing activity associated with boundaries between bare and decorated segments will not be linear, but display a transient burst at short times on cofilin activation then dissipate due to a kinetic competition between severing activity and cofilin binding. A second peak of severing activity is predicted to arise from irreversible cofilin dissociation on inactivation. These behaviors predict what we believe to be novel mechanisms of cofilin severing and spatial regulation of actin filament turnover in cells. The methods developed for this system are generally applicable to the kinetic analysis of cooperative ligand binding to linear polymers.     

Lac repressor-operator interaction: DNA length dependence

The interaction of the E. coli lac operon repressor with its operator DNA has been directly examined as a function of the length of operator-containing DNA. The apparent bimolecular association rate constants were calculated as ka = (kd/KD), where the dissociation equilibrium constant, KD and the dissociation rate constant, kd, were measured by nitrocellulose filter adsorption assays. The values obtained for the overall association rate constants are compared with theoretical association rate curves for specific mechanisms. Association of the repressor with short operator containing DNA fragments (less than 70 base pairs) occurs at rates expected of three-dimensional diffusion. Our data also imply that at longer DNA lengths a combination of three-dimensional diffusion with one-dimensional sliding along with hopping and/or intersegment transfer must be involved to facilitate the repressor operator association.     

Influence of base-pair changes and cooperativity parameters on the melting curves of short DNAs

Theoretical melting curves were calculated for four DNA restriction fragments, 157–257 base pairs (bp), and a series of hypothetical block DNAs with sequences d(C_2xA_xC_2x). d(C_2xT_xG_2x), 5 ? x ? 40. These DNAs provided a mixture of A·T/G·C sequence distributions with which to investigate the effects of parameters and base-pair changes on the melting of short DNAs. The sensitivity of DNA melting curves to changes in internal loop melting parameters σ and κ was examined. As Expected, theoretical melting curves of short DNAs with a quasirandom base-pair sequence vary little with changes in internal loop parameters. End melting dominates the transition behaviour of these moleucles. This was also observed for the block DNAs up to x = 22. Beyond this length, melting curves are highly sensitive to the internal loop parameters. Sensitivity is also predicted for a 157-bp fragment with a block distribution of A·T and G·C pairs. These results indicate that accurate evaluation of internal loop parameters is possible with short DNAs (100–200 bp) containing a G·C/A·T/G·C block distribution with at least 22 bp in each block. Duplex-to-single-strands dissociation parameters were reevaluated form experimental melting curve data of eight DNA fragments using a least squares fit approach. This analysis confirmed parameter values previously found with a simplified dissociation model. A Priori predictions are made on the effects of base-pair changes on the melting curves of three characterized DNA restriction fragments. Single base-pair changes are predicted to induce small but measurable changes in the melting curves. The characteristics of the altered melting curves depend on the location of the base-pair change.     

Relaxation kinetics of denaturation of DNA

The one-dimensional Ising model, with nearest-neighbor correlations only, used earlier in equilibrium studies of melting of DNA is extended to study the relaxation kinetics of copolymeric synthetic DNA near the melting temperature. An exponential kinetics, in agreement with the observations, has been found.     

A study of the reversibility of helix-coil transition in DNA.

The reversibility of DNA melting has been thoroughly investigated at different ionic strengths. We concentrated on those stages of the process that do not involve a complete separation of the strands of the double helix. The differential melting curves of pBR 322 DNA and a fragment of T7 phage DNA in a buffer containing 0.02M Na+ have been shown to differ substantially from the differential curves of renaturation. Electron-microscopic mapping of pBR 322 DNA at different degrees of unwinding (by a previously elaborated technique) has shown that the irreversibility of melting under real experimental conditions is connected with the stage of forming new helical regions during renaturation. In a buffer containing 0.2M Na+ the melting curves of the DNAs used (pBR322, a fragment of T7 phage DNA, a fragment of phage Lambda DNA, a fragment of phiX174 phage DNA) coincide with the renaturation curves, i.e. the process is equilibrium. We have carried out a semi-quantitative analysis of the emergence of irreversibility in the melting of a double helix. The problem of comparing theoretical and experimental melting curves is discussed.     

Molecular model of a eucaryotic transcription complex: functions and movements of influenza P proteins during capped RNA-primed transcription

We present a model for the functions and movements of the influenza virus P proteins (PB1, PB2, and PA) as they transcribe the virion RNAs (vRNAs) into messenger RNAs (mRNAs). Using ultraviolet-light-induced crosslinking, we show that the P proteins as a complex move from the 3' ends of the vRNA templates down the elongating mRNAs. PB2 binds the cap 1 structure of heterologous RNAs, which are cleaved to generate capped primer fragments. PB1, initially found at the first residue added onto the primer, moves to the 3' ends of the growing mRNA chains, indicating that it most likely catalyzes each nucleotide addition. PA and PB2 move down the growing chains in concert with PB1. PB2 is also associated with the cap during the first 11-15 nucleotides of chain growth, but then dissociates from the cap as the P protein complex moves further down the mRNA chains.     

Duration time of a one-dimensional random walk as a function of the energies of the intermediate states: application for dissociation and relaxation processes in DNA hybrids.

Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.     

Calculating thermodynamic data for transitions of any molecularity from equilibrium melting curves

In this paper, we derive the general forms of the equations required to extract thermodynamic data from equilibrium transition curves on oligomeric and polymeric nucleic acids of any molecularity. Significantly, since the equations and protocols are general, they also can be used to characterize thermodynamically equilibrium processes in systems other than nucleic acids. We briefly review how the reduced forms of the general equations have been used by many investigators to evaluate mono- and bimolecular transitions, and then explain how these equations can be generalized to calculate thermodynamic parameters from common experimental observables for transitions of higher molecularities. We emphasize the strengths and weaknesses of each method of data analysis so that investigators can select the approach most appropriate for their experimental circumstances. We also describe how to analyze calorimetric heat capacity curves and noncalorimetric differentiated melting curves so as to extract both model-independent and model-dependent thermodynamic data for transitions of any molecularity. The general equations and methods of analysis described in this paper should be of particular interest to laboratories that currently are investigating association and dissociation processes in nucleic acids that exhibit molecularities greater than two.     

Kinetics and thermodynamics of DNA hybridization on gold nanoparticles

Hybridization of single-stranded DNA immobilized on the surface of gold nanoparticles (GNPs) into double stranded DNA and its subsequent dissociation into ssDNA were investigated. Melting curves and rates of dissociation and hybridization were measured using fluorescence detection based on hybridization-induced fluorescence change. Two distribution functions, namely the state distribution and the rate distribution, were proposed in order to take interfacial heterogeneity into account and to quantitatively analyze the data. Reaction and activation enthalpies and entropies of DNA hybridization and dissociation on GNPs were derived and compared with the same quantities in solution. Our results show that the interaction between GNPs and DNA reduces the energetic barrier and accelerates the dissociation of adhered DNA. At low surface densities of ssDNA adhered to GNP surface, the primary reaction pathway is that ssDNA in solution first adsorbs onto the GNP, and then diffuses along the surface until hybridizing with an immobilized DNA. We also found that the secondary structure of a DNA hairpin inhibits the interaction between GNPs and DNA and enhances the stability of the DNA hairpin adhered to GNPs.     

Hybridization and dissociation rates of phosphodiester or modified oligodeoxynucleotides with RNA at near-physiological conditions.

We have used RNase H to study both the rates of oligonucleotide hybridization and dissociation at near-physiological conditions. We have studied the Effects of oligonucleotide length, mismatch, and chemical modifications on oligonucleotide association and dissociation with RNA. Dissociation results were compared with standard thermal melting curves to compare relative stabilities evaluated by the two techniques. Although generally the two techniques correlate for the compounds evaluated, we found several instances where the thermal melting curves failed to reflect the relative stability of different oligonucleotides at 37 degrees C using near-physiological conditions. This study suggests that direct measurement of hybridization and dissociation of an oligomer with RNA more accurately assesses the complicated kinetic scheme at 37 degrees C using near-physiological conditions than thermal melting curves would predict.     

In vitro polyoma DNA synthesis: discontinuous chain growth

Using an in vitro system for polyoma DNA synthesis from polyoma-infected mouse BALB/3T3 cells, we have shown that short pulses of radioactively labeled deoxynucleoside triphosphates are incorporated into viral replicative intermediates. Upon denaturation, the pulse-labeled replicative intermediates yield two size classes of growing DNA chains, namely a heterogeneous long class with S values up to unit viral DNA length (16 S) and a rather discrete short class of 5 S pieces. We have shown that these short fragments are involved as precursors in viral DNA chain elongation and that they can be chased into mature viral DNA. The fragments are found in replicative intermediates at all stages of replication and are therefore presumably not involved in specialized initiation or termination processes. Kinetic analysis of the appearance of radioactivity in short and long chains shows that initially approximately equal amounts are incorporated at a linear rate into the two classes. Subsequently, the rate of incorporation into long chains approximately doubles, while the amount of radioactivity in short chains reaches a plateau. This not only suggests that short chains are precursors to long chains, but that the synthesis of long chains occurs as a separate event and is not simply a result of joining of short fragments. Under the in vitro labeling conditions the time taken for radioactivity in short chains to reach a constant level can be used as a measure of the average lifetime of a 5 S piece. Our analysis indicates that there may be a considerable lag between the completion of a 5 S piece and its joining into longer DNA. Estimates of the self-annealing of the short chains showed approximately 20% self-complementarity. Thus, polyoma synthesis in vitro appears to proceed predominantly by a semi-discontinuous mechanism in which the nascent DNA on one side of the growing fork is elongated continuously, while on the other side of the fork DNA is synthesized discontinuously as 5 S fragments, which are subsequently joined. Both the short and the long chains are synthesized in the 5′ to 3′ direction.A fraction of the pulse-labeled material is found as free 3 to 5 S single-stranded DNA. These pieces are of both viral and cellular origin. A majority of them appear to be involved as precursors in DNA chain elongation.     

DNA as Membrane-Bound Ligand-Receptor Pairs: Duplex Stability Is Tuned by Intermembrane Forces

We use membrane-anchored DNA as model adhesion receptors between lipid vesicles. By studying the thermal stability of DNA duplex formation, which tethers the vesicles into superstructures, we show that the melting temperature of a 10-base DNA sequence is dependent on the lipid composition of the tethered vesicles. We propose a simple model that describes how the intermembrane interactions tilt the free energy landscape for DNA binding. From our model, we estimate the area per DNA in the binding sites between vesicles and also the total area of the adhesion plaques. We find that vesicles containing a small proportion of cationic lipid that are modified with membrane-anchored DNA can be reversibly tethered by specific DNA interactions and that the DNA also induces a small attraction between these membranes, which stabilizes the DNA duplex. By increasing the equilibrium intermembrane distance on binding, we show that intermembrane interactions become negligible for the binding thermodynamics of the DNA and hence the thermal stability of vesicle aggregates becomes independent of lipid composition at large enough intervesicle separations. We discuss the implications of our findings with regards to cell adhesion and fusion receptors, and the programmable self-assembly of nano-structured materials by DNA hybridization.     

Kinetics of irreversible dissociation for proteins bound cooperatively to DNA

We consider the irreversible dissociation kinetics of proteins that bind cooperatively and nonspecifically to DNA. Our model consists of an infinitely long one-dimensional nucleic acid lattice on which are bound protein ligands. A set of adjacent bound proteins forms a cluster of length n. A protein molecule may dissociate from any site within the bound cluster, not only from the ends, as was assumed in a previous model of this process due to Lohman [(1983) Biopolymers 22 , 1697–1713]. By considering this additional pathway, we present a more general treatment of the dissociation kinetics of cooperatively bound ligands. We show that dissociation from the (n?2) internal positions of an n-cluster is an important pathway when the initial fractional saturation of the lattice is close to unity and the co operatively is low. When the fractional saturation is initially equal to 1 and the co operatively is low, our model does not give the zero-order dissociation kinetics predicted by the Lohman model.     

Thermal stability of DNA with interstrand crosslinks

Although many anticancer drugs exert their biological activity by forming DNA interstrand crosslinks (ICLs), the thermodynamics of biologically relevant long crosslinked DNAs has not been intensively studied in contrast to short duplexes. Here, we carry out computer modeling of the shift of melting temperature of long DNAs caused by ICLs taking into account crosslinking effect in itself and concomitant local alterations in the free energy (δG) of the helix-coil transition at sites of ICLs. Depending on δG, DNA interstrand crosslinks at per nucleotide concentration r = 0.05 can change the melting temperature by value from -17 to +47°C, and the influence weakly depends on DNA sequence and GC content. A change in melting temperature caused by introduction of interstrand crosslinking in modified DNA at sites of modifications also depends on δG and varies from 0 to +12°C. Comparison with experiment for the three platinum crosslinking compounds demonstrates utility of the theoretical method for understanding how crosslinking compounds can influence the melting behavior. On the basis of the method, interdependence of local distortions and crosslinking in itself was studied for thermal effect of ICLs. A method for evaluating the nature of the structural alteration that produces a change in thermal stability for short crosslinked DNA is also proposed. The methods can be used for comparative thermodynamic characterization of various DNA crosslinking agents.     

MWC allosteric model explains unusual hemoglobin-oxygen binding curves from sickle cell drug binding

An oxygen-affinity-modifying drug, voxelotor, has very recently been approved by the FDA for treatment of sickle cell disease. The proposed mechanism of action is by preferential binding of the drug to the R quaternary conformation, which cannot copolymerize with the T conformation to form sickle fibers. Here, we report widely different oxygen dissociation and oxygen association curves for normal blood in the presence of voxelotor and interpret the results in terms of the allosteric model of Monod, Wyman, and Changeux with the addition of drug binding. The model does remarkably well in quantitatively explaining a complex data set with just the addition of drug binding and dissociation rates for the R and T conformations. Whereas slow dissociation of the drug from R results in time-independent dissociation curves, the changing association curves result from slow dissociation of the drug from T, as well as extremely slow binding of the drug to T. By calculating true equilibrium curves from the model parameters, we show that there would be a smaller decrease in oxygen delivery from the left shift in the dissociation curve caused by drug binding if drug binding and dissociation for both R and T were rapid. Our application of the Monod, Wyman, and Changeux model demonstrates once more its enormous power in explaining many different kinds of experimental results for hemoglobin. It should also be helpful in analyzing oxygen binding and in vivo delivery in future investigations of oxygen-affinity-modifying drugs for sickle cell disease.     

Consequences of methylation on the amino group of adenine. A proton two-dimensional NMR study of d(GGATATCC) and d(GGm6ATATCC)

A two-dimensional 500-MHz 1H-NMR study of two oligonucleotides, d(GGATATCC) and d(GGm6ATATCC), is presented in which we have investigated the effects of adenine methylation. The two-dimensional nuclear Overhauser spectra (NOESY) show that both oligonucleotides adopt a normal right-handed B-type helix and one-dimensional nuclear Overhauser enhancement (NOE) studies demonstrate that any difference in conformation must be small. However methylation drastically slows down the helix in equilibrium coil exchange which becomes slow on a proton NMR time scale. While d(GGATATCC) fits a two-site exchange model, d(GGm6ATATCC) does not and we invoke the presence of a third species which may be an intermediate in helix formation. NMR and ultraviolet spectroscopy show that methylation destabilizes the helix, measured by the melting temperature and enthalpy of dissociation.     

Single molecule force spectroscopy of salt-dependent bacteriophage T7 gene 2.5 protein binding to single-stranded DNA

The gene 2.5 protein (gp2.5) encoded by bacteriophage T7 binds preferentially to single-stranded DNA. This property is essential for its role in DNA replication and recombination in the phage-infected cell. gp2.5 lowers the phage lambda DNA melting force as measured by single molecule force spectroscopy. T7 gp2.5-Delta26C, lacking 26 acidic C-terminal residues, also reduces the melting force but at considerably lower concentrations. The equilibrium binding constants of these proteins to single-stranded DNA (ssDNA) as a function of salt concentration have been determined, and we found for example that gp2.5 binds with an affinity of (3.5 +/- 0.6) x 10(5) m(-1) in a 50 mm Na(+) solution, whereas the truncated protein binds to ssDNA with a much higher affinity of (7.8 +/- 0.9) x 10(7) m(-1) under the same solution conditions. T7 gp2.5-Delta26C binding to single-stranded DNA also exhibits a stronger salt dependence than the full-length protein. The data are consistent with a model in which a dimeric gp2.5 must dissociate prior to binding to ssDNA, a dissociation that consists of a weak non-electrostatic and a strong electrostatic component.     

Evidence for the reversible binding of paraquat to deoxyribonucleic acid

Evidence for the reversible binding of paraquat to calf thymus DNA has been obtained using equilibrium dialysis and thermal melting point determinations. The data indicated the presence of at least two populations of binding site with affinity constants of 6.2 X 10(4) and 7.1 X 10(3) M-1, respectively. The binding capacities of DNA for paraquat were 66 and 480 nmol/mumol DNA nucleotide, respectively, and were equivalent to one ligand bound per 2 DNA phosphate groups. Putrescine inhibited paraquat binding to the low affinity sites without altering binding to the high affinity sites. Scatchard plots of paraquat binding characteristics indicated the presence of positive cooperativity between the compound and DNA. Thermal melting curves of DNA in the presence of paraquat and the endogenous amines putrescine, spermidine and spermine, provided evidence that paraquat cross-linked to DNA with a similar affinity as spermidine. The thermal melting point data also suggested the presence of positive cooperativity between ligand and macromolecule that possibly resulted from a conformation change in the structure of the DNA molecule. Paraquat competitively inhibited the binding of ethidium bromide to DNA and this effect was reversed by Na+. From the data, it is suggested that paraquat binds primarily to the negatively charged phosphates on the DNA backbone but is displaced into the interbase region occupied by the intercalator ethidium bromide. DNA binding of paraquat may, in part, account for its weak mutagenic activity.