Studies on the lack of cooperativity in the melting of lipid bilayers

The gel-to-fluid first-order melting transition of lipid bilayers is simulated by the use of a microscopic interaction model which includes a variable number of lipid-chain conformational states. The results suggest that the experimental observation of ‘continuous melting’ in pure wet lipid bilayers, rather than being ascribed to the presence of impurities, may be explained as a result of kinetically caused metastability of intermediate lipid-chain conformations.     

Stacking and hydrogen bonding: DNA cooperativity at melting

By taking into account base-base stacking interactions we improve the Generalized Model of Polypeptide Chain (GMPC). Based on a one-dimensional Potts-like model with many-particle interactions, the GMPC describes the helix-coil transition in both polypeptides and polynucleotides. In the framework of the GMPC we show that correctly introduced nearest-neighbor stacking interactions against the background of hydrogen bonding lead to increased stability (melting temperature) and, unexpectedly, to decreased cooperativity (maximal correlation length). The increase in stability is explained as due to an additional stabilizing interaction (stacking) and the surprising decrease in cooperativity is seen as a result of mixing of contributions of hydrogen bonding and stacking.     

Analysis of thermal melting curves

T(m) is defined as Temperature of melting or, more accurately, as temperature of midtransition. This term is often used for nucleic acids (DNA and RNA, oligonucleotides and polynucleotides). A thermal denaturation experiment determines the stability of the secondary structure of a DNA or RNA and aids in the choice of the sequences for antisense oligomers or PCR primers. Beyond a simple numerical value (the T(m)), a thermal denaturation experiment, in which the folded fraction of a structure is plotted vs. temperature, yields important thermodynamic information. We present the classic problems encountered during these experiments and try to demonstrate that a number of useful pieces of information can be extracted from these experimental curves.     

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%).     

Effects of heterogeneity and cooperativity on the forms of binding curves for multivalent ligands

An exploratory investigation is made of the binding behavior that is likely to be encountered with multivalent ligands under circumstances where a single intrinsic binding constant does not suffice to describe all acceptor-ligand interactions. Numerical simulations of theoretical binding behavior have established that current criteria for recognizing heterogeneity and cooperativity of acceptor sites on the basis of the deviation of the binding curve from rectangular hyperbolic form for univalent ligands also apply to the interpretation of the corresponding binding curves for multivalent ligands. However, for systems in which the source of the departure from equivalence and independence of binding sites resides in the ligand, these criteria are reversed. On the basis of these observations a case is then made for attributing results of an experimental binding study of the interaction between pyruvate kinase and muscle myofibrils to positive cooperativity of enzyme sites rather than to heterogeneity or negative cooperativity of the myofibrillar sites.     

Characterization of the structure and melting of DNAs containing backbone nicks and gaps

A DNA molecule containing a gap (a missing phosphate) has been examined and compared to two other molecules of the same sequence, one containing a nick (a phosphorylated gap) and the other a normal duplex containing no break in the backbone. A second gapped sequence was also compared to a normal duplex of the same sequence. The molecules containing nicks or gaps were generated as dumbbell molecules, short helices closed by a loop at each end. The dumbbells were formed by the association of two hairpins with self-complementary dangling 5'-ends. Nuclear magnetic resonance was used to monitor the melting transition and to probe structural differences between molecules. Under the conditions used here no change in stability was observed upon phosphorylation of the gap. Structural changes upon phosphorylation of a gap or closure of a nick were minimal and were localized to the region immediately around the gap or nick. Two transitions can be observed as a gapped or nicked molecule melts, although the resolution of the two transitions varies with the salt concentration. At moderate to high salt (greater than or equal to 30 mM) the molecule melts essentially all at once. At low salt the two transitions occur at temperatures that differ by as much as 15 degrees C. In addition, comparison with other NMR melting studies indicates that the duplex formed by the overlap of the dangling ends of the hairpins is stabilized relative to a free duplex of the same sequence, probably by stacking onto the hairpin stem.     

The ionic strength dependence of the cooperativity factor for DNA melting

The melting temperature for the d(AT)24.d(AT)24 stretch, located inside the DNA helix and terminally, have been determined in a wide range of ionic strength values (0.01 - 1 M Na+). The cooperativity factor was calculated from the shifts in the melting temperature of the stretch due to its different boundary conditions. With the sodium concentration decreasing from 1 M to 0.01 M the cooperativity factor dropped by three orders of magnitude, its change being less marked at high than at low ionic strength.     

Inverted repeat sequences can influence the melting transitions of linear DNAs

The influence of inverted repeat sequences on the melting transitions of linear DNAs has been examined. Derivative melting curves (DMC) of a 514 base pair (bp) DNA, seven subfragments of this DNA, and four other DNAs have been compared to predictions of DNA melting theory. The 514-bp DNA contains three inverted repeat sequences that can form cruciform structures in supercoiled DNA. We refer to these sequences as c-inverted repeats. Previous work showed that the DMC of this DNA, unlike a number of other DNAs, is not accurately predicted by DNA melting theory. Since the theoretical model does not include hairpin-like structures, it was suggested that hairpin or cruciform formation in these inverted repeats may be responsible for this discrepancy. Our results support this hypothesis. Predicted DMCs are in good agreement with DNAs with no inverted repeats, or inverted repeats not evident in supercoiled DNA. Differences between the theoretical and experimental Tm's are less than or equal to 0.3 degrees C. DNA molecules that contain one or more of the three c-inverted repeats are not as accurately predicted. Experimental Tm values are lower than predicted values by 0.7-3.8 degrees C. It is concluded that some inverted repeat sequences can form hairpin-like structures during the melting of linear DNAs. These structures appear to lower overall DNA stability.     

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).     

Calculation of melting curves for DNA

A method is reported for calculating the melting curve of a DNA molecule of random base sequence, including in the formalism the dependence of the free energy of base pair formation on the size of a denatured section. Some explicit results are shown for a “typical” base sequence, in particular the probability of helix formation at individual base pairs in several different regions of the molecule and the amount of melting from the end of the chain. Particular attention is drawn to the variation of local melting behavior from one region of the molecule to another. It is found that sections rich in AT melt at relatively low temperatures with a fairly broad transition curve, whereas regions rich in GC pairs melt at higher temperatures (as expected) with a very abrupt, local transition curve. To account qualitatively for the results one may divide melting into two kinds of processes: (a) the nucleation and growth of denatured regions, and (b) the merging together of two denatured sections at the expense of the intervening helix. The first of these processes dominates in the first stages of melting, and leads to rather broad local melting curves, whereas the second process predominates in the later stages, and occurs, in a particular part of the molecule, over a very narrow temperature range. It is estimated that the average length of a helix plus adjacent coil section at the midpoint of the transition is approximately 600 base pairs. Since transition curves which measure the local melting behavior reflect local compositions fluctuations, these curves contain information about the broad outlines of base sequence in the molecule. Some suggestions are made concerning experiments by which this potential information source could be exploited. In particular, it is pointed out that one might hope to map AT or GC rich regions at particular genetic loci in a biologically active DNA molecule. Values of the relevant parameters found earlier for the transition of homopolymers produce melting curves for a DNA of random base sequence which are in good agreement with the experimental transition curve for T2 phage DNA. Hence the present theoretical picture of the melting of polynucleotides is at least internally self-consistent.     

Direct observation of the temperature-induced melting process of the Salmonella fourU RNA thermometer at base-pair resolution

In prokaryotes, RNA thermometers regulate a number of heat shock and virulence genes. These temperature sensitive RNA elements are usually located in the 5′-untranslated regions of the regulated genes. They repress translation initiation by base pairing to the Shine–Dalgarno sequence at low temperatures. We investigated the thermodynamic stability of the temperature labile hairpin 2 of the Salmonella fourU RNA thermometer over a broad temperature range and determined free energy, enthalpy and entropy values for the base-pair opening of individual nucleobases by measuring the temperature dependence of the imino proton exchange rates via NMR spectroscopy. Exchange rates were analyzed for the wild-type (wt) RNA and the A8C mutant. The wt RNA was found to be stabilized by the extraordinarily stable G14–C25 base pair. The mismatch base pair in the wt RNA thermometer (A8–G31) is responsible for the smaller cooperativity of the unfolding transition in the wt RNA. Enthalpy and entropy values for the base-pair opening events exhibit linear correlation for both RNAs. The slopes of these correlations coincide with the melting points of the RNAs determined by CD spectroscopy. RNA unfolding occurs at a temperature where all nucleobases have equal thermodynamic stabilities. Our results are in agreement with a consecutive zipper-type unfolding mechanism in which the stacking interaction is responsible for the observed cooperativity. Furthermore, remote effects of the A8C mutation affecting the stability of nucleobase G14 could be identified. According to our analysis we deduce that this effect is most probably transduced via the hydration shell of the RNA.     

Change in conformation of various DNAs on melting as followed by circular dichroism

The intensities of the CD bands at about 275 and 190 nm were monitored for DNAs with different G + C contents as a function of temperature. The 190-nm bands showed a nearly complete and cooperative collapse on melting of the DNA, demonstrating that the CD arises from base–base interactions. The small cooperative change on melting shown by the 275-nm bands indicates that base–base interactions do not contribute much CD intensity here. No significant difference in melting temperature was found between the two wavelengths, but the lack of premelting in the 190-nm bands contrasted with the significant premelting in the 275 nm bands. Since the 190-nm bands are particularly sensitive to base–base interactions, the relative positions of the bases must not change much during premelting. Still, changes in such interactions would be noticeable on top of the low intensity of the 275-nm bands. Premelting is discussed in the light of recent studies on DNA conformation.     

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.     

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.     

Singular value decomposition of 3-D DNA melting curves reveals complexity in the melting process

The thermal denaturation of synthetic deoxypolynucleotides of defined sequence was studied by a three dimensional melting technique in which complete UV absorbance spectra were recorded as a function of temperature. The results of such an experiment defined a surface bounded by absorbance, wavelength, and temperature. A matrix of the experimental data was built, and analyzed by the method of singular value decomposition (SVD). SVD provides a rigorous, model-free analytical tool for evaluating the number of significant spectral species required to account for the changes in UV absorbance accompany-ing the duplex – to – single strand transition. For all of the polynucleotides studied (Poly dA – Poly dT; [Poly (dAdT)]₂; Poly dG – Poly dC; [Poly(dGdC)]₂), SVD indicated the existence of at least 4 – 5 significant spectral species. The DNA melting transition for even these simple repeating sequences cannot, therefore, be a simple two-state process. The basis spectra obtained by SVD analysis were found to be unique for each polynucleotide studied. Differential scanning calorimetry was used to obtain model free estimates for the enthalpy of melting for the polynucleotides studied, with results in good agreement with previously published values. Received: 16 April 1997 / Accepted: 9 July 1997     

Negative cooperativity may explain flat concentration-response curves of ATP-sensitive potassium channels

Blockage of ATP-sensitive K⁺ channels by various drugs has been reported to exhibit a weak concentration dependence with Hill coefficients below unity. This phenomenon is interpreted by a negative cooperativity between K⁺ channels whereby drug binding to one channel lowers the drug affinities of neighbouring channels. Results are presented for a dimeric and a tetrameric channel model and compared with published experimental data. Correspondence to: S. Hehl