Melting of Cross-Linked DNA IV. Methods for Computer Modeling of Total Influence on DNA Melting of Monofunctional Adducts,Intrastrand and Interstrand Cross-Links Formed by Molecules of an Antitumor Drug

Abstract

A theoretical method is developed for calculation of melting curves of covalent complexes of DNA with antitumor drugs. The method takes into account all the types of chemical modifications of the double helix caused by platinum compounds and DNA alkylating agents: 1) monofunctional adducts bound to one nucleotide; 2) intrastrand cross-links which appear due to bidentate binding of a drug molecule to two nucleotides that are included into the same DNA strand; 3) interstrand cross-links caused by bidentate binding of a molecule to two nucleotides of different strands. The developed calculation method takes into account the following double helix alterations at sites of chemical modifications: 1) a change in stability of chemically modified base pairs and neighboring ones, that is caused by all the types of chemical modifications; 2) a change in the energy of boundaries between helical and melted regions at sites of chemical modification (local alteration of the factor of cooperativity of DNA melting), that is caused by all the types of chemical modifications, too; 3) a change in the loop entropy factor of melted regions that include interstrand cross-links; 4) the prohibition of divergence of DNA strands in completely melted DNA molecules, which is caused by interstrand cross-links only. General equations are derived, and three calculation methods are proposed to calculate DNA melting curves and the parameters that characterize the helix-coil transition.     

Melting of cross-linked DNA IV. Methods for computer modeling of total influence on DNA melting of monofunctional adducts, intrastrand and interstrand cross-links formed by molecules of an antitumor drug

A theoretical method is developed for calculation of melting curves of covalent complexes of DNA with antitumor drugs. The method takes into account all the types of chemical modifications of the double helix caused by platinum compounds and DNA alkylating agents: 1) monofunctional adducts bound to one nucleotide; 2) intrastrand cross-links which appear due to bidentate binding of a drug molecule to two nucleotides that are included into the same DNA strand; 3) interstrand cross-links caused by bidentate binding of a molecule to two nucleotides of different strands. The developed calculation method takes into account the following double helix alterations at sites of chemical modifications: 1) a change in stability of chemically modified base pairs and neighboring ones, that is caused by all the types of chemical modifications; 2) a change in the energy of boundaries between helical and melted regions at sites of chemical modification (local alteration of the factor of cooperativity of DNA melting), that is caused by all the types of chemical modifications, too; 3) a change in the loop entropy factor of melted regions that include interstrand cross-links; 4) the prohibition of divergence of DNA strands in completely melted DNA molecules, which is caused by interstrand cross-links only. General equations are derived, and three calculation methods are proposed to calculate DNA melting curves and the parameters that characterize the helix-coil transition.     

Relationship between helix-coil transition and gene organization of ColE1 plasmid DNA. Differential scanning calorimetric and theoretical studies

Differential scanning calorimetry (DSC) was carried out to analyze the transition of helix to coil state of DNA, using ColE1 DNA molecules digested with EcoRI. The DSC curves showed multimodal transition, consisting of nine to 11 peaks over a temperature range, depending on the ionic strength of the DNA solution. These DSC curves were essentially in good agreement with the optical melting curves of ColE1 DNA. The theoretical melting profiles of ColE1 DNA were predicted from calculations based on the helix-coil transition theory and the nucleotide sequence of the DNA. These profiles resembled the DSC curves and made it possible to assign the peaks seen in the DSC curves to the helix-coil transition of particular regions of the nucleotide sequence of ColE1. The helix-coil transition of each of the small genes gave rise to a single peak in the DSC curve, while the helix-coil transition of large genes contributed to two or more peaks in the DSC curve. This multimodal transition within a single coding region might correspond to the melting of individual segments encoding the different domains of the proteins. The helix-coil transition at the specific sites including ori, the origin of replication of ColE1, was also found to occur in a particular temperature range. DSC, a simple method, is thus useful for analyzing the multimodal helix-coil transition of DNA, and for providing information on the genetic organization of DNA.     

Influence of ligands characteristic of selective binding to a certain type of base pairs on DNA helix-coil transition I. Model. Theory

The DNA helix-coil transition in the presence of ligands interacting selectively with a certain type or types of base pairs has been considered. A calculation method for estimation the influence of lignads on the melting process for which the knowledge of DNA primary structure is not required was proposed. It has been shown that the reverse temperature shift caused by ligands bound to a given type of base pairs at given kind of regions (helix or coli) is in direct proportion to the fist derivative with respect to the degree of helicity from ratio beta ji/n, where beta ji--number of nitrogen bases of i-type at the regions of j-kind; N--total number of DNA base pairs. It was assumed earlier that this shift was in direct proportion to beta ji/Nj, where Nj--number of base pairs in DNA regions of j-kind. The specificity of lignads interaction with given kinds of bases alters the manner of the melting process of the heteropolynucleotide in comparison with homopolynucleotide only in the case when the DNA primary structure has a strong influence on the position of helix and coli regions along the DNA chain. Only when this conditions is fulfilled the inversion of thermostability of AT- and GC-pairs may affect the shape of the melting curve.     

A study of DNA denaturation in the ultracentrifuge

The melting transition of DNA in alkaline CsCl can be followed in the analytical ultracentrifuge. Equilibrium partially denatured states can be observed. These partially denatured DNA bands have bandwidths of up to several times those of native DNA. Less stable molecules melt early and are found at heavier densities in the melting region. An idealized ultracentrifuge melting transition is described. The melting transition of singly nicked PM-2 DNA resembles the idealized curve. The DNA profile is a Gaussian band at all points in the melt. DNA's from mouse, D. Melanogaster, M. lysodeikticus, T4, and T7 also show equilibrium bands at partially denatured densities, some of which are highly asymmetric. Simple sequence satellite DNA shows an all-or-none transition with no equilibrium bands at partially denatured densities. The temperature at which a DNA denatures is an increasing function of the (G + C) content of the DNA. The T_m does not show a molecular-weight dependence in the range 1.2 × 10⁶–1.5 × 10⁷ daltons (single strand) for mouse, M. lysodeikticus, or T4 DNA. The mouse DNA partially denatured bands do not change shape as a function of molecular weight. The T4 DNA intermediate band develops a late-melting tail at low molecular weight. M. lysodeikticus DNA bands at partially denatured densities become broader as the molecular weight is decreased. Mouse DNA is resolved into six Gaussian components at each point in the melting transition.     

Denaturation and renaturation of DNA. I. Equilibrium statistics of copolymeric DNA

The one-dimensional Ising model, with nearest neighbor correlation only, suitably modified, is used to explain the observed linear dependence of melting temperature of copolymeric DNA with GC content. Transition curves are plotted for regular, random, and Markoff distribution of base pairs for various values of a correlation parameter U between nearest neighbor bonds. Exact analytic formulas are given for fraction of bonds intact at a particular temperature for various regular distributions for all U and approximate ones for random and Markoff distributions for small U. A scheme is indicated for further improvement. The model, in principle, makes it possible to estimate the statistical distribution of base pairs from the detailed shape of the transition curve.     

Theoretical calculations of the helix–coil transition of DNA in the presence of large,cooperatively binding ligands

Theoretical calculations are conducted on the helix–coil transition of DNA, in the presence of large, cooperatively binding ligands modeled after the DNA-binding proteins of current biological interest. The ligands are allowed to bind both to helx and to coil, to cover up any number of bases or base pairs in the complex, and to interact cooperatively with their nearest neighbors. The DNA is treated in the infinite homogeneous Ising model approximation, and all calculations are done by Lifson's method of sequence-generating functions. DNA melting curves are calculated by computer in order to expolore the effects on the transition of ligand size, binding constant, free activity, and ligand–ligand cooperativity. The calculations indicate that (1) at the same intrinsic free energy change per base pair of the complexes, small ligands, for purely entropic reasons, are more effective than are large ligands in shifting the DNA melting temperature; (2) the response of the DNA melting temperature to increased ligand binding constant K and/or free ligand activity L is adequately represented at high values of KL (but not at low KL) by a simple independent site model; (3) if curves are calculated with the total amount of added ligand remaining constant and the free ligand activity allowed to vary throughout the transition, biphasic melting curves can be obtained in the complete absence of ligand–ligand cooperativity. In an Appendix, the denaturation of poly[d(A-T)] in the presence of the drug, netropsin, is used to verify some features of the theory and to illustrate how the theory can be used to obtain numerical estimates of the ligand binding parameters from the experimental melting curves.     

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.     

The transmission of stability or instability from site specific protein-DNA complexes.

Theoretical calculations were made to determine the influence of side specific 'melting' and 'stabilizing' proteins on the thermal stability of nearby base pairs (bp). A DNA sequence 999bp. long containing the 123 bp. lactose operon control region in the center was examined. Melting curves of base pairs near the binding sites of the catabolite activator protein, CAP, the lactose repressor, and RNA polymerase were calculated in the absence and presence of each protein. The empirical loop entropy model of the helix-coil transition of DNA was employed. Calculations show that melting and stabilizing proteins alter the tm of base pairs 20 to 100 bp-away. The magnitude and range of the effect is strongly influenced by the base pair composition and sequence of the protein site and the immediately adjacent DNA regions.     

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.     

Estimation of the diversity between DNA calorimetric profiles,differential melting curves and corresponding melting temperatures

The Poland–Fixman–Freire formalism was adapted for modeling of calorimetric DNA melting profiles, and applied to plasmid pBR 322 and long random sequences. We studied the influence of the difference (H_GC?H_AT) between the helix‐coil transition enthalpies of AT and GC base pairs on the calorimetric melting profile and on normalized calorimetric melting profile. A strong alteration of DNA calorimetrical profile with H_GC?H_AT was demonstrated. In contrast, there is a relatively slight change in the normalized profiles and in corresponding ordinary (optical) normalized differential melting curves (DMCs). For fixed H_GC?H_AT, the average relative deviation (S) between DMC and normalized calorimetric profile, and the difference between their melting temperatures (T_cal?T_m) are weakly dependent on peculiarities of the multipeak fine structure of DMCs. At the same time, both the deviation S and difference (T_cal?T_m) enlarge with the temperature melting range of the helix‐coil transition. It is shown that the local deviation between DMC and normalized calorimetric profile increases in regions of narrow peaks distant from the melting temperature.     

Melting of Cross-Linked DNA V. Cross-Linking Effect Caused by Local Stabilization of the Double Helix

Abstract

DNA interstrand cross-links are usually formed due to bidentate covalent or coordination binding of a cross-linking agent to nucleotides of different strands. However interstrand linkages can be also caused by any type of chemical modification that gives rise to a strong local stabilization of the double helix. These stabilized sites conserve their helical structure and prevent local and total strand separation at temperatures above the melting of ordinary AT and GC base pairs. This local stabilization makes DNA melting fully reversible and independent of strand concentration like ordinary covalent interstrand cross-links. The stabilization can be caused by all the types of chemical modifications (interstrand cross-links, intrastrand cross-links or monofunctional adducts) if they give rise to a strong enough local stabilization of the double helix. Our calculation demonstrates that an increase in stability by 25 to 30 kcal in the free energy of a single base pair of the double helix is sufficient for this “cross-linking effect” (i.e. conserving the helicity of this base pair and preventing strand separation after melting of ordinary base pairs). For the situation where there is more then one stabilized site in a DNA duplex (e.g., 1 stabilized site per 1000 bp), a lower stabilization per site is sufficient for the “cross-linking effect” (18–20 kcal). A substantial increase in DNA stability was found in various experimental studies for some metal-based anti-tumor compounds. These compounds may give rise to the effect described above. If ligand induced stabilization is distributed among several neighboring base pairs, a much lower minimum increase per stabilized base pair is sufficient to produce the cross-linking effect (1 bp- 24.4 kcal; 5 bp- 5.3 kcal; 10 bp- 2.9 kcal, 25 bp- 1.4 kcal; 50 bp- 1.0 kcal). The relatively weak non-covalent binding of histones or protamines that cover long regions of DNA (20–40 bp) can also cause this effect if the salt concentration of the solution is sufficiently low to cause strong local stabilization of the double helix. Stretches of GC pairs more than 25 bp in length inserted into poly(AT) DNA also exhibit properties of stabilizing interstrand cross-links.     

Melting of cross-linked DNA v. cross-linking effect caused by local stabilization of the double helix

DNA interstrand cross-links are usually formed due to bidentate covalent or coordination binding of a cross-linking agent to nucleotides of different strands. However interstrand linkages can be also caused by any type of chemical modification that gives rise to a strong local stabilization of the double helix. These stabilized sites conserve their helical structure and prevent local and total strand separation at temperatures above the melting of ordinary AT and GC base pairs. This local stabilization makes DNA melting fully reversible and independent of strand concentration like ordinary covalent interstrand cross-links. The stabilization can be caused by all the types of chemical modifications (interstrand cross-links, intrastrand cross-links or monofunctional adducts) if they give rise to a strong enough local stabilization of the double helix. Our calculation demonstrates that an increase in stability by 25 to 30 kcal in the free energy of a single base pair of the double helix is sufficient for this "cross-linking effect" (i.e. conserving the helicity of this base pair and preventing strand separation after melting of ordinary base pairs). For the situation where there is more then one stabilized site in a DNA duplex (e.g., 1 stabilized site per 1000 bp), a lower stabilization per site is sufficient for the "cross-linking effect" (18 - 20 kcal). A substantial increase in DNA stability was found in various experimental studies for some metal-based anti-tumor compounds. These compounds may give rise to the effect described above. If ligand induced stabilization is distributed among several neighboring base pairs, a much lower minimum increase per stabilized base pair is sufficient to produce the cross-linking effect (1 bp- 24.4 kcal; 5 bp- 5.3 kcal; 10 bp- 2.9 kcal, 25 bp- 1.4 kcal; 50 bp- 1.0 kcal). The relatively weak non-covalent binding of histones or protamines that cover long regions of DNA (20- 40 bp) can also cause this effect if the salt concentration of the solution is sufficiently low to cause strong local stabilization of the double helix. Stretches of GC pairs more than 25 bp in length inserted into poly(AT) DNA also exhibit properties of stabilizing interstrand cross-links.     

Pressure dependence of the helix-coil transition temperature for polynucleic acid helices

Thermal denaturation of DNA's and the corresponding helix–coil transformation of artificial polyribonucleic and polydeoxyribonucleic acids have been studied extensively both theoretically^1–13 and experimentally. ^14–30 Much less work has been carried out on the properties of these polynucleic acids at high pressure, and in particular, on the presure dependence of the helix–coil transition temperature.^31–33 Light-scattering techniques have been used in this study to measure the pressure dependence of the helix–coil transition temperature of the two- and three-stranded helices of polyriboadenylic and polyribouridilic acids and of calf thymus DNA. From the slopes of the transition temperature vs. pressure curves and heats of transition obtained from the literature,^20,34 the following volume changes from these helix–coil transitions have been obtained: (a) ?0.96 cc/mole of nucleotide base pairs for the poly (A + U) transition, (b) +0.35 cc/mole of nucleotide base trios for the poly (A + 2U) transition, and (c) +2.7 cc/mole of nucleotide base pairs for the DNA transition. The relative magnitudes and signs of these volume changes which show that poly (A + U) is destabilized by increased pressure, whereas poly (A + 2U) and calf thymus DNA are stabilized by increased pressure, indicates that further development of the helix–coil transition theory for polynucleotides is needed.     

Counterintuitive DNA Sequence Dependence in Supercoiling-Induced DNA Melting

The metabolism of DNA in cells relies on the balance between hybridized double-stranded DNA (dsDNA) and local de-hybridized regions of ssDNA that provide access to binding proteins. Traditional melting experiments, in which short pieces of dsDNA are heated up until the point of melting into ssDNA, have determined that AT-rich sequences have a lower binding energy than GC-rich sequences. In cells, however, the double-stranded backbone of DNA is destabilized by negative supercoiling, and not by temperature. To investigate what the effect of GC content is on DNA melting induced by negative supercoiling, we studied DNA molecules with a GC content ranging from 38% to 77%, using single-molecule magnetic tweezer measurements in which the length of a single DNA molecule is measured as a function of applied stretching force and supercoiling density. At low force (<0.5pN), supercoiling results into twisting of the dsDNA backbone and loop formation (plectonemes), without inducing any DNA melting. This process was not influenced by the DNA sequence. When negative supercoiling is introduced at increasing force, local melting of DNA is introduced. We measured for the different DNA molecules a characteristic force F _char, at which negative supercoiling induces local melting of the dsDNA. Surprisingly, GC-rich sequences melt at lower forces than AT-rich sequences: F _char = 0.56pN for 77% GC but 0.73pN for 38% GC. An explanation for this counterintuitive effect is provided by the realization that supercoiling densities of a few percent only induce melting of a few percent of the base pairs. As a consequence, denaturation bubbles occur in local AT-rich regions and the sequence-dependent effect arises from an increased DNA bending/torsional energy associated with the plectonemes. This new insight indicates that an increased GC-content adjacent to AT-rich DNA regions will enhance local opening of the double-stranded DNA helix.     

Long-range structural effects in supercoiled DNA: statistical thermodynamics reveals a correlation between calculated cooperative melting and contextual influence on cruciform extrusion

We have previously described [K. M. Sullivan and D. M. J. Lilley (1986) Cell 47, 817-827] a set of sequences, called C-type inducing sequences, which cause cruciform extrusion by adjacent inverted repeats to occur by an abnormal kinetic pathway involving a large denatured region of DNA. In this paper we apply statistical thermodynamic DNA helix melting theory to these sequences. We find a marked correlation between the ability of sequences to confer C-type cruciform character experimentally and their calculated propensity to undergo cooperative melting, and no exceptions have been found. The correlations are both qualitative and quantitative. Thus the ColE1 flanking sequences behave as single melting units, while the DNA of the S-type plasmid pIRbke8 exhibits no propensity to melt in the region of the bke cruciform. The results of the calculations are also fully consistent with the following experimental observations: 1. the ability of the isolated colL and colR fragments of the ColE1 flanking sequences, as well as the short sequence col30, to confer C-type character; 2. C-type induction by an A + T rich Drosophila sequence; 3. low-temperature cruciform extrusion by an (AT)34 sequence; 4. the effect of changing sequences at a site 90 base pairs (bp) removed from the inverted repeat; 5. the effects of systematic deletion of the colL sequence; and 6. the effects of insertion of various sequences in between the colL sequence and the xke inverted repeat. These studies show that telestability effects on thermal denaturation as predicted from equilibrium helix melting theory of linear DNA molecules may explain all the features that are revealed by studying the extrusion of cruciforms in circular DNA molecules subjected to superhelical stress.     

Melting of Cross-Linked DNA: I. Model and Theoretical Methods

Abstract

Covalent and strong coordination binding to DNA of a large number of antitumour drugs and other compounds leads to interstrand cross-link formation. To investigate cross-link influence on double helix stability, two methods are developed for the calculation of melting curves. The first method is based on Poland's approach. It requires computer time proportional to u-N, where u is the average distance (in base pairs) between neighboring crosslinks, and N is the number of base pairs in the DNA chain. The method is more suitable when u is not large, and small loops formed by interstrand cross-links in melted regions strongly affect DNA melting. The computer time for the second method, based on the Fixman-Freire approach, does not depend on the number of cross-links and is proportional to I N (I is the number of exponential functions used for a decomposition of the loop entropy factor). It is more appropriate when N and u are large, and therefore particular values of the entropy factors of small loops do not influence DNA melting behavior.     

High resolution thermal denaturation analyses of small sequenced DNA restriction fragments containing Escherichia coli lactose genetic control loci.

Differential melting curves are reported for four DNA restriction fragments (789, 301, 203, and 95 base pairs in length) spanning the lactose control region. All but the smallest melt with two or more subtransitions. Maps are proposed which identify the positions of regions of different thermal stability in the sequences. The sizes of regions comprising subtransitions range from 60 to 200 base pairs. An analysis is made of the cooperativity exhibited between regions in the sequence. The effect on the shape of the differential melting curves of Na+ between 10 mM and 0.5 M as well as that of Mg2+ and glycerol has been determined. An 81-bp-long sequence of unusual thermal stability occurs at the lactose promoter. Its TM change, resulting from the above change in salt concentration, is out of step by 1.5 degree C with the neighboring DNA sequence. The potential biological significance of this behavior is discussed.     

Distortions induced in double-stranded oligonucleotides by the binding of cis- or trans-diammine-dichloroplatinum(II) to the d(GTG) sequence.

Conformational changes induced in double-stranded oligonucleotides by the binding of trans- or cis-diamminedichloro platinum(II) to the d(GTG) sequence have been characterized by means of melting temperatures, electrophoretic migrations in non-denaturing polyacrylamide gels, reactivities with the artificial nuclease Phenanthroline-copper and with chemical probes. The cis-platinum adduct behaves more as a centre of directed bend than as a hinge joint, the induced bend angle being of the order of 25-30 degrees. The double helix is locally denatured over 2 base pairs (corresponding to the platinated 5'G residue and the central T residue) and is distorted over 4-5 base pairs. The trans-platinum adduct behaves also more as a centre of directed bend than as a hinge joint, the induced bend angle being of the order of 60 degrees. The double helix is locally denatured over 4 base pairs (corresponding to the immediately 5'T residue adjacent to the adduct and to the three base residues of the adduct). Both the cis- and trans-platinum adducts decrease the thermal stability of the double helix.