Statistical mechanical theory of melting transition in supercoiled DNA

The melting curve for a covalently closed circular DNA has been analyzed on the basis of an expression for the supercoiling energy derived in terms of the elastic parameters of the macromolecule, treated as a homopolymer. The result obtained by applying the usual methods of statistical mechanics indicate close agreement with the available experimental data. It is found that the elevation of the melting temperature, as compared to that of the nicked circular or linear DNA, is a natural consequence of the fact that the supercoiled molecule is constrained by an invariant linking number. The flattening of the melting curve, on the other hand, arises as the closed circular duplex melts into a loose helix rather than random coils.     

Fine structure of DNA melting curves.

Theoretical calculations predict that the differential melting curves for random polynucleotide sequences having lengths up to several tens of thousands of base pairs have a clear-cut fine structure. This structure appears in the form of multiple narrow peaks 0.3–0.4°C wide on the bell shaped main curve. The differential melting curves have different shapes for different specific sequences. The theory also predicts the disappearance of the fine structure when the length of the sequence increases and when circular, covalently closed DNA is considered instead of the open structure. The predictions of the theory were confirmed by the measurements of differential melting curves for open and covalently closed circular forms of DNA for PM2 phage (N = 10⁴ base pairs) and also for other phage DNA's of different length: T7 (N = 3.8 × 10⁴); S_D (N = 9.2 × 10⁴); T2 (N = 17 × 10⁴). It was shown that the effect of fine structure results mainly from the cooperative melting out of DNA regions 300–500 base pairs long.     

Determination of melting temperature and temperature melting range for DNA with multi-peak differential melting curves

Many factors that change the temperature position and interval of the DNA helix–coil transition often also alter the shape of multi-peak differential melting curves (DMCs). For DNAs with a multi-peak DMC, there is no agreement on the most useful definition for the melting temperature, T_m, and temperature melting width, ΔT, of the entire DNA transition. Changes in T_m and ΔT can reflect unstable variation of the shape of the DMC as well as alterations in DNA thermal stability and heterogeneity. Here, experiments and computer modeling for DNA multi-peak DMCs varying under different factors allowed testing of several methods of defining T_m and ΔT. Indeed, some of the methods give unreasonable “jagged” T_m and ΔT dependences on varying relative concentration of DNA chemical modifications (r_b), [Na⁺], and GC content. At the same time, T_m determined as the helix–coil transition average temperature, and ΔT, which is proportional to the average absolute temperature deviation from this temperature, are suitable to characterize multi-peak DMCs. They give smoothly varying theoretical and experimental dependences of T_m and ΔT on r_b, [Na⁺], and GC content. For multi-peak DMCs, T_m value determined in this way is the closest to the thermodynamic melting temperature (the helix–coil transition enthalpy/entropy ratio).     

DNA sequencing and helix-coil transition. I. Theory of DNA melting

An explicit analytic formula accurately describing the melting of a natural DNA is derived. For phage ?X-174 and virus SV-40, the nucleotide sequences of which are known, the formula fits experimental data for the differential melting curve almost within the experimental accuracy.     

Statistical thermodynamics of nucleic acid melting transitions with coupled binding equilibria

Equations are developed to describe the shift in the temperature of the helix–coil transition when small molecules bind to nucleic acids. Included are high polymers, oligonucleotides, and oligomer–polymer interactions. The equations prescribe simple ways of plotting experimental data to evaluate transition and binding parameters.     

Statistical mechanical equilibrium theory of selective ion channels.

A rigorous statistical mechanical formulation of the equilibrium properties of selective ion channels is developed, incorporating the influence of the membrane potential, multiple occupancy, and saturation effects. The theory provides a framework for discussing familiar quantities and concepts in the context of detailed microscopic models. Statistical mechanical expressions for the free energy profile along the channel axis, the cross-sectional area of the pore, and probability of occupancy are given and discussed. In particular, the influence of the membrane voltage, the significance of the electric distance, and traditional assumptions concerning the linearity of the membrane electric field along the channel axis are examined. Important findings are: 1) the equilibrium probabilities of occupancy of multiply occupied channels have the familiar algebraic form of saturation properties which is obtained from kinetic models with discrete states of denumerable ion occupancy (although this does not prove the existence of specific binding sites; 2) the total free energy profile of an ion along the channel axis can be separated into an intrinsic ion-pore free energy potential of mean force, independent of the transmembrane potential, and other contributions that arise from the interfacial polarization; 3) the transmembrane potential calculated numerically for a detailed atomic configuration of the gramicidin A channel embedded in a bilayer membrane with explicit lipid molecules is shown to be closely linear over a distance of 25 A along the channel axis. Therefore, the present analysis provides some support for the constant membrane potential field approximation, a concept that has played a central role in the interpretation of flux data based on traditional models of ion permeation. It is hoped that this formulation will provide a sound physical basis for developing nonequilibrium theories of ion transport in selective biological channels.     

Theory of DNA melting curves

Exact algorithms for the calculation of melting curves of heterogeneous DNA with N base pairs apparently require computer time proportional to N². However, it is shown that a decomposition of the loop entropy factor into a sum of I exponential functions (1) gives an extremely accurate approximation to the loop entropy factor for small values of I and (2) makes the computer time for the exact algorithms proportional to I·N. In effect, exact results for melting curves and lengths of helix or coil stretches are obtained with computer time comparable to that required for the Frank-Kamenetskii approximation. The remarkable accuracy of the latter for the fraction of helical content (errors of 0.01–0.05) is confirmed, but appreciably larger errors are found for the lengths of helix or coil stretches (typical errors of 30–100%).     

Intramolecular DNA melting between stable helical segments: melting theory and metastable states.

Melting of DNA in a segment bounded at both ends by regions of greater stability during electrophoresis in denaturing gradient gels show complex properties, not accommodated with standard melting theory. Compact bands of some DNA molecules become anomalously broadened at the retardation level in a denaturing gradient, or double bands may appear in a uniform denaturant concentration. These properties are associated only with molecules for which the distribution of stability calculated by the Poland-Fixman-Freire algorithms indicates that the region of lowest stability does not extend to an end of the molecule. Retention of helicity at the ends is shown by the difference in the effect of base substitution in the end domains and in the least stable domain. Both the appearance of double bands and band broadening can be explained by invoking a hypothetical metastable intermediate in melting, which is converted into the equilibrium melted form at a relatively slow rate, depending on both denaturant concentration and field strength. A kinetic model permits plausible rate constants to be inferred from the patterns. Despite the increased band width, sequence variants with base changes in the least stable domain result in readily detectable band shifts in the gradient.     

Hyperfine structure in melting profile of bacteriophage lambda DNA.

A high-resolution plotter of differential melting profiles of DNA, RNA, or related biopolymers with an on-line mini-computer is described. With this device, more than 15 transition steps were identified in the thermal melting profile of DNA from bacteriophage lambda. These fine structures were found to be reproducible, and some of them disappear in the deletion mutant. To Examine the melting profile, computer simulations for several hypothetical polynucleotide sequences were performed, and compared with experimental data. The sharp peaks that appeared in the differential melting profile of λ DNA may come from some homogeneous sequences of 500 bases or longer.     

Preparation and melting of single strand circular DNA loops.

A method for preparation of single strand DNA circles of almost arbitrary sequence is described. By ligating two sticky ended hairpins together a linear duplex is formed, closed at both ends by single stranded loops. The melting characteristics of such loops are investigated using optical absorbance and NMR. It is shown by comparison with the corresponding linear sequence (closed circle minus the end loops) that the effects of end fraying and the strand concentration dependence of the melting temperature are eliminated in the circular form. Over the concentration range examined (0.5 to 2.0 micromolar strands), the circular DNA has a monophasic melting curve, while the linear duplex is biphasic, probably due to hairpin formation. Since effects of duplex to single strands dissociation do not contribute to melting of the circular molecules (dumbells), these DNAs present a realistic experimental model for examining local thermal stability in DNA.     

Theoretical melting profiles and denaturation maps of DNA with known sequence: fdDNA.

Differential melting profiles and denaturation maps are calculated for fdDNA whose sequence of nucleotides has been determined recently. The melting profiles for the total DNA and a number of its restriction fragments are compared with experimental data taken from literature. The comparison enables one to correlate a number of peaks on experimental melting profiles with the melting out of concrete regions of the nucleotide sequence. For three fragments very strong end effects are demonstrated on both theoretical and experimental profiles. These anomalous end effects are shown to be connected with a region highly enriched with AT-pairs. A possible influence of the heterogeneity of stacking interaction on the results obtained is discussed in detail.     

Cooperative lengths of DNA during melting

The mean cooperative length of domains of DNA, determined from the variance in (G + C) content in derivative melting curves of large bacterial DNAs, varies from 230 base pairs (bp) for (A ? T)-rich domains to 580 bp for (G ? C) domains. These values correspond to values for the cooperativity parameter of 2(±2) × 10^?5 and 3(±2) × 10^?6, respectively, and to +7.2 and +9.6 kcal for the free energy of helix interruption in those regions.     

Interaction of 2-chloro-N10-substituted phenoxazine with DNA and effect on DNA melting

Five N10-substituted phenoxazines having different R groups and -Cl substitution at C-2 were found to bind to calf -thymus DNA and plasmid DNA with high affinity as seen from by UV and CD spectroscopy. The effect of phenoxazines on DNA were studied using DNA-ethidium bromide complexes. Upon addition of phenoxazines, the ethidium bromide dissociated from the complex with DNA. The binding of phenoxazines to plasmid PUC18 reduced ethidium bromide binding as seen from the agarose gel electrophoresis. Butyl, and propyl substituted phenoxazines were able to release more ethidium bromide compared with that of acetyl substitution. Addition of phenoxazines also enhanced melting temperature of DNA.     

The DNA melting transition in aqueous magnesium salt solutions.

The melting transition of the magnesium salt of DNA has been systematically examined in the presence of various types of anions. The addition of ClO4- to a concentration of 3.0 N results in the biphasic optical transition, with the first phase exhibiting rapid reversibility and independence of the DNA concentration. This subtransition, which is interpreted as an intramolecular condensation to a collapsed form of DNA, is followed by a DNA concentration-dependent aggregation reaction. The aggregation can be reversed by increasing the ClO4- concentration to 6.0 N while elevating the temperature to post-transition levels. Alternatively, both the collapse and the aggregation can be prevented by melting in the presence of trichloroacetate, the most strongly chaotropic solvent for DNA which has been reported (K. Hamaguchi and E. P. Geiduschek (1962), J. Am. Chem. Soc. 84, 1329). The forces responsible for mediating both the collapse and the aggregation are superficially similar to those involved in maintaining duplex stability. The collapsed form, in particular, possibly possesses features in common with the condensed structures which can be produced in aqueous solution of certain polymers, such as polyethylene glycol (Lerman, L.S. (1971), Proc. Natl. Acad. Sci. U.S.A. 68, 1886).     

Force-induced melting of the DNA double helix 1. Thermodynamic analysis

The highly cooperative elongation of a single B-DNA molecule to almost twice its contour length upon application of a stretching force is interpreted as force-induced DNA melting. This interpretation is based on the similarity between experimental and calculated stretching profiles, when the force-dependent free energy of melting is obtained directly from the experimental force versus extension curves of double- and single-stranded DNA. The high cooperativity of the overstretching transition is consistent with a melting interpretation. The ability of nicked DNA to withstand forces greater than that at the transition midpoint is explained as a result of the one-dimensional nature of the melting transition, which leads to alternating zones of melted and unmelted DNA even substantially above the melting midpoint. We discuss the relationship between force-induced melting and the B-to-S transition suggested by other authors. The recently measured effect on T7 DNA polymerase activity of the force applied to a ssDNA template is interpreted in terms of preferential stabilization of dsDNA by weak forces approximately equal to 7 pN.     

91 Kinetics of DNA overstretching: melting vs. B-to-S transition

Single B-form DNA molecules undergo an overstretching transition at force F_ov to a ～1.7-fold longer form when stretched. The nature of overstretched DNA has been debated for over 10?years. Either peeled (PL DNA), internally melted (M DNA), or unwound double-helical (S DNA) forms of overstretched DNA have been suggested. Here, we characterize the kinetics of the overstretching transition in polymeric torsionally unconstrained double-stranded (ds) DNA molecules. We pull ～50?Kbp λ–DNA molecules using optical tweezers with rates ν ～10?nm/s to 5?×?10⁴?nm/s, (overstretching time between 0.2 and 10³?s). The F_ov(ν, [Na⁺]) dependence measured over a broad range of rates and solution ionic strength suggests the existence of all three forms of the overstretched DNA. Thus, at [Na⁺]?>?50?mM and the stretching time >>1?s, internal melting dominates overstretching. This B-to-M transition is highly cooperative (involves ～100?bp), and slow (on/off time ～1000?s). Faster overstretching during ?1?s leads to B-to-S DNA transition, which is less cooperative (involves ～10?bp) and faster (on/off time ～1?s). In contrast, in lower salt ([Na⁺]?<?50?mM), the overstretching during >1?s leads to DNA peeling. However, on the faster time scale of 0.2–1?s, even in low salt, the DNA overstretches into S DNA, as peeling becomes kinetically prohibited. Our conclusions are supported by several independent lines of evidence, including the salt and rate dependence of both the slope of the overstretched DNA force-extension curve and the value of the second transition force (from M or PL DNA into S DNA).