Kinetic studies of the helix–coil transition in aqueous solutions of poly(L-lysine)

The rate of conformational change of aqueous poly(α-L -lysine) solutions was measured using the electric field pulse relaxation method with conductivity detection. The relaxation time as a function of pH exhibits two maxima. One is assigned to a proton transfer reaction and the other to the helix–coil conformational transition. The helix nucleation parameter and the maximum relaxation time yield the rate constant of helix growth process (k_F) according to Schwarz's kinetic theory as k_F = 2 × 10⁷ sec^?1, which is comparable to that of the poly(glutamic acid) solution. The thermodynamic parameters of the helix growth process are compared with those of poly(glutamic acid).     

Calorimetric study of 2U:1A three-stranded complexes formed between poly(U) and adenine dinucleotides: ApA and diastereoisomers of nonionic adenine dideoxyribonucleoside methyl phosphonate

Melting parameters of 2U:1A complexes formed by polyuridylic acid [poly(U)] and three adenine dinucleotides, diribonucleoside monophosphonate ApA and diastereoisomers of dideoxyribonucleoside methyl phosphonate [(dApA)₁ and (dApA)₂], in 1M NaCl and at a number of dinucleotide concentrations were obtained from differential scanning microcalorimetric data and interpreted in terms of the theory of helix–coil equilibrium in oligonucleotide–polynucleotide systems. The apparent binding constant, 1/c_m, at 39°C and melting temperatures, T_m, at 1 × 10^?3 M dinucleotide concentration indicate the following order of thermodynamic stability of the complexes: 2 poly(U) · (dApA)₂ (2.27 × 10³M^?1, 44.2°C) > 2 poly(U) · (dApA)₁ (9.9 × 10²M¹, 39.2°C) > 2 poly(U) · (ApA) (5.9 × 10²M^?1, 35.8°C). Corresponding calorimetric enthalpies of melting, ΔH_m: 13.5, 12.7, and 12.8 kcal/mol (UUA base triplets) were found to be considerably lower than the van't Hoff enthalpies, ΔH_app: 29.4, 16.2, and 16.2 kcal/mol, respectively, evaluated from the dependence of the melting temperatures on dinucleotide concentration. Self-association of dinucleotides and their simultaneous binding as monomers, dimers, and higher-order associated species is suggested as the most probable cause of the differences between ΔH_m and ΔH_app values. The differences in thermodynamic properties of the complexes formed by (dApA)₁ and (dApA)₂ diastereoisomers are discussed in connection with their known conformational properties. The higher and essentially enthalpic stability of the 2 poly(U) · (dApA)₂ complex correlates with a lower degree of intramolecular stacking of the (dApA)₂ isomer. The hydrophobically enhanced strong self-association of the latter greatly influences the thermodynamics of its complex formation with poly(U) and results in ΔH_app/ΔH_m = 2.3.     

The Structure of Triple Helical Poly(U)·Poly(A)·Poly(U) Studied by Raman Spectroscopy

Abstract

Using Raman spectroscopy, we examined the ribose-phosphate backbone conformation, the hydrogen bonding interactions, and the stacking of the bases of the poly(U)·poly(A) ·poly(U) triple helix. We compared the Raman spectra of poly(U)·poly(A)·poly(U) in H₂O and D₂O with those obtained for single-stranded poly(A) and poly(U) and for double-stranded poly(A)·poly(U). The presence of a Raman band at 863 cm^?1 indicated that the backbone conformations of the two poly(U) chains are different in the triple helix. The sugar conformation of the poly(U) chain held to the poly(A) by Watson-Crick base pairing is C3′ endo; that of the second poly(U) chain may be C2′ endo. Raman hypochromism of the bands associated with base vibrations demonstrated that uracil residues stack to the same extent in double helical poly(A)·poly(U) and in the triple-stranded structure. An increase in the Raman hypochromism of the bands associated with adenine bases indicated that the stacking of adenine residues is greater in the triple helix than in the double helical form. Our data further suggest that the environment of the carbonyls of the uracil residues is different for the different strands.     

Local effects of partial adenine-N1-oxidation on poly A-poly U and poly A-2 poly U helix conformations

We prepared helices with noncomplementary bases by N1-oxidation of poly A, followed by reaction with poly U. Mixing curves indicate that doubly and triply helical structures form, with only the unmodified adenines involved in base pair formation. Circular dichroism spectra were examined particularly at the absorbance maximum of the adenine N1-oxide (A*). In the single strand poly (A,A*), there is a relatively strong pair of positive and negative CD bands from the A*. These are greatly reduced in the double helix, and abolished in the triple helix. We conclude that A* stacks in a conventional manner with A in the single strand, but is rotated out of the double and triple helix. In the double helix the A* probably maintains a preferred orientation with respect to the helix, but rotates randomly in the triple helix.     

Cooperative nonenzymic base recognition II. thermodynamics of the helix-coil transition of oligoadenylic + oligouridylic acids

The properties of oligonucleotide helices of adeuylic- and uridylic acid oligomers have been investigated by measurements of hypo-and hyperchromieity. High ionic strengths favor the formation of triple helices. Thus, the double helix-coil transition can be studied (without interference by triple helices) only at low ionic-strength. A “phase diagram” is given representing the T_m-values of the various transitions at different ionic strengths for the system A(pA)₁₇ + U(pU)₁₇. Oligonucleolides of chain lengths <8 always form both double and triple helices at the nucleotide concentrations required for base pairing. For this reason the double helix-coil transition without coupling of the triple helix equilibrium can only be measured for chain lengths higher than 7. Melting curves corresponding to this transition have been determined for chain lengths 8, 9, 10, 11, 14 and 18 at different concentrations. An increase in nucleotide concentration leads to an increase in melting temperature. The shorter the chain length the lower the T_m-value and the broader the helix-coil transition. The experimental transition curves have been analysed according to a staggering zipper model with consideration of the stacking of the adeuylic acid single strands and the electrostatic repulsion of tlip phosphate charges on opposite strands. The temperature dependence of the nucleation parameter has been accounted for by a slacking factor x. The stacking factor expresses the magnitude of the stacking enthalpy. By curve fitting xwas computed to be 0.7, corresponding to a stacking enthalpy of about S kcal/mole. The model described allows the reproduction of the experimental transition curves with relatively high accuracy. In an appendix the thermodynamic parameters of the stacking equilibrium of poly A and of the helix-coil equilibria of poly A + poly U at neutral pH are calculated (ΔH_A = ?7.9 kcal/mole for the poly A stacking and ΔH₁₂ = ?10.9 kcal/mole for the formation of the double helix from the randomly coiled single strands). A formula for the configurational entropy of polymers derived by Flory on the basis of a liquid lattice model is adapted to calculate the stacking entropies of adenylic oligomers.     

Triple helix–coil transition of covalently bridged collagenlike peptides

The thermal triple helix–coil transition of covalently bridged collagenlike peptides with repeating sequences of (Ala-Gly-Pro)_n, n = 5–15, was studied optically. The peptides were soluble in water/acetic acid (99:1) and were found to form triple-helical structures in this solvent system beginning with n = 8. The thermodynamic analysis of the transition equilibrium curves for n = 9–13 yielded the parameters ΔH°_s = ?7.0 kJ per tripeptide unit, ΔS°_s = ?23.1 J deg^?1 mol^?1 per tripeptide unit for the coil-to-helix transition, and the apparent nucleation parameter σ ? 5 × 10^?2. It was suggested through double-jump temperature experiments that the rate-limiting step during refolding is not only influenced by the difficulties of nucleation, but also by cis–trans isomerization of the Gly-Pro peptide bond.     

Dynamics of molecular organization in agarose sulphate

Nongelling solutions of structurally regular chain segments of agarose sulphate show disorder–order and order–disorder transitions (as monitored by the temperature dependence of optical rotation) that are closely similar to the conformational changes that accompany the sol–gel and gel–sol transitions of the unsegmented polymer. The transition midpoint temperature (T_m) for formation of the ordered structure on cooling is ～25 K lower than T_m for melting. Salt-induced conformational ordering, monitored by polarimetric stopped-flow, occurs on a millisecond time scale, and follows the dynamics expected for the process 2 coil ? helix. The equilibrium constant for helix growth (s) was calculated as a function of temperature from the calorimetric enthalpy change for helix formation (ΔH_cal = ?3.0 ± 0.3 kJ per mole of disaccharide pairs in the ordered state), measured by differential scanning calorimetry. The temperature dependence of the nucleation rate constant (k_nuc), calculated from the observed second-order rate constant (k_obs) by the relationship k_obs = k_nuc(1 ? 1/s) gave the following activation parameters for nucleation of the ordered structure of agarose sulphate (1 mg mL^?1; 0.5M Me₄NCl or KCl): ΔH* = 112 ± 5 kJ mol^?1; ΔS* = 262 ± 20 J mol^?1 K^?1; ΔG*₂₉₈ = 34 ± 6 kJ mol^?1; (k_nuc)₂₉₈ = (7.5 ± 0.5) × 10⁶ dm³ mol^?1 s^?1. The endpoint of the fast relaxation process corresponds to the metastable optical rotation values observed on cooling from the fully disordered form. Subsequent slow relaxation to the true equilibrium values (i.e., coincident with those observed on heating from the fully ordered state) was monitored by conventional optical rotation measurements over several weeks and follows second-order kinetics, with rate constants of (2.25 ± 0.07) × 10^?4 and (3.10 ± 0.10) × 10^?4 dm³ mol^?1 s^?1 at 293.7 and 296.2 K, respectively. This relaxation is attributed to the sequential aggregation processes helix + helix → dimer, helix + dimer → trimer, etc., with depletion of isolated helix driving the much faster coil–helix equilibrium to completion. Light-scattering measurements above and below the temperature range of the conformational transitions indicate an average aggregate size of 2–3 helices.     

On the possibility of true phase transition in heterogeneous DNA during thermal denaturation under conditions close to equal stability of A+T and G+C pairs

The DNA helix–coil transition has been studied in the presence of high concentrations of manganese ions (about 10^?3M), which corresponds to the conditions close to equal stability of the A+T and G+C pairs, at the ionic strengths of 10^?1, 10^?2, and 1.6 × 10^?3M Na⁺. With the Mn²⁺ ion effect, the transition range is significantly reduced to not more than 0.2°C at 1.2 × 10^?3M Mn²⁺ and 1.6 × 10^?3M Na⁺. The melting curves display a sharp kink at the end of the helix–coil transition, which is interpreted as an indication of the second-order phase transition. It is shown that the melting curves obtained can be approximated by a simple analytical expression 1 – θ = exp[–a(t_c - t)], where θ is the DNA helix fraction, t_c is the phase transition temperature, and a is an empirical parameter characterizing the breadth of the melting range and responsible for the magnitude of a jump of the helicity derivative with respect to the temperature at the phase transition point.     

Helix-coil dynamics of a Z-helix hairpin

The helix–coil transition of a Z-helix hairpin formed from d(C-G)₅T₄(C-G)₅ has been characterized by equilibrium melting and temperature jump experiments in 5M NaClO₄ and 10 mM Na₂HPO₄, pH 7.0. The melting curve can be represented by a simple all-or-none transition with a midpoint at 81.6 ± 0.4°C and an enthalpy change of 287 ± 15 kJ/mole. The temperature jump relaxation can be described by single exponentials at a reasonable accuracy. Amplitudes measured as a function of temperature provide equilibrium parameters consistent with those derived from equilibrium melting curves. The rate constants of Z-helix formation are found in the range from 1800 s^?1 at 70°C to 800 s^?1 at 90°C and are associated with an activation enthalpy of ?(50 ± 10) kJ/mole, whereas the rate constants of helix dissociation are found in the range from 200 s^?1 at 70°C to 4500 s^?1 at 90°C with an activation enthalpy +235 kJ/mole. These parameters are consistent with a requirement of 3–4 base pairs for helix nucleation. Apparently nucleation occurs in the Z-helix conformation, because a separate slow step corresponding to a B to Z transition has not been observed. In summary, the dynamics of the Z-helix–coil transition is very similar to that of previously investigated right-handed double helices.     

Phosphorus-31 nuclear magnetic resonance of double- and triple-helical nucleic acids. Phosphorus-31 chemical shifts as a probe of phosphorus-oxygen ester bond torsional angles

The temperature dependence to the 31P NMR spectra of poly[d(GC)] . poly [d(GC)],d(GC)4, phenylalanine tRNA (yeast) and mixtures of poly(A) + oligo(U) is presented. The 31P NMR spectra of mixtures of complementary RNA and of the poly d(GC) self-complementary DNA provide torsional information on the phosphate ester conformation in the double, triple, and "Z" helix. The increasing downfield shift with temperature of the single-strand nucleic acids provides a measure of the change in the phosphate ester conformation in the single helix to coil conversion. A separate upfield peak (20-60% of the total phosphates) is observed at lower temperatures in the oligo(U) . poly(A) mixtures which is assigned to the double helix/triple helix. Proton NMR and UV spectra confirm the presence of the multistrand forms. The 31P chemical shift for the double helix/triple helix is 0.2-0.5 ppm upfield from the chemical shift for the single helix which in turn is 1.0 ppm upfield from the chemical shift for the random coil conformation.     

Interaction of poly-L-lysine with nucleic acids. II. Poly(A+U), poly(A+2U), and rice dwarf virus RNA

The optical density–temperature profile of double-stranded poly(A + U), triple stranded poly(A + 2U), and double-stranded RNA from rice dwarf virus in solutions with and without poly-L -lysine has been examined. When poly-L -lysine is added, more than one melting temperature T_m is observed for poly(A + U) and poly(A + 2U). One of them is considered to correspond to the melting of the polynucleotide molecule free from poly-L -lysine, and another to the melting of a polynucleotide–poly-L -lysine complex. For rice dwarf virus RNA, the T_m assignable to the complex is not found to be lower than 99°C. In every case, however, the hyperchromicity observed at the T_m of the free poly-nucleotide molecule is lowered linearly as the amount of poly-L -lysine added to the solution increases. This fact is taken as indicating that there is a stoichiometric complex formed. The stoichiometric ratio lysine/nucleotide in each complex is determined by examining the relation between the amount of poly-L -lysine added to the solution and the percentage of hyperchromicity remaining at T_m of the free polynucleotide molecule. The ratio is found to be 2/3 for all of the three complexes. A discussion is given on the molecular conformations of four types of polynucleotide–polylysine complex hitherto found: (A) double-stranded DNA plus poly-L -lysine in which the lyslne/nucleotide ratio is 1, (B) three-stranded RNA [poly(A + 2U)] plus poly-L -lysine in which the ratio is 2/3, (C) double-stranded RNA [poly (A + U) or rice dwarf virus RNA] plus poly-L -lysine in which the ratio is 2/3, and (D) double-stranded RNA [poly(I + C)] plus poly-L -lysine in which the ratio is 1/2.     

The structure of triple helical poly(U).poly(A).poly(U) studied by Raman spectroscopy

Using Raman spectroscopy, we examined the ribose-phosphate backbone conformation, the hydrogen bonding interactions, and the stacking of the bases of the poly(U).poly(A).poly(U) triple helix. We compared the Raman spectra of poly(U).poly(A).poly(U) in H2O and D2O with those obtained for single-stranded poly(A) and poly(U) and for double-stranded poly(A).poly(U). The presence of a Raman band at 863 cm-1 indicated that the backbone conformations of the two poly(U) chains are different in the triple helix. The sugar conformation of the poly(U) chain held to the poly(A) by Watson-Crick base pairing is C3' endo; that of the second poly(U) chain may be C2' endo. Raman hypochromism of the bands associated with base vibrations demonstrated that uracil residues stack to the same extent in double helical poly(A).poly(U) and in the triple-stranded structure. An increase in the Raman hypochromism of the bands associated with adenine bases indicated that the stacking of adenine residues is greater in the triple helix than in the double helical form. Our data further suggest that the environment of the carbonyls of the uracil residues is different for the different strands.     

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.     

Raman studies of nucleic acids. VII. Poly A-poly U and poly G-poly C

Laser-excited Raman spectra of the double-helical complexes poly A·poly U and poly G·poly C are reported for ²H₂O and H₂O solutions. The spectra are discussed in relation to their use as quantitative reference spectra for determining the dependence of the Raman scattering of RNA on secondary structure. The Raman line at 815 cm^?1, due to the phosphodiester group, exhibits the same intrinsic intensity in spectra of poly A·poly U and poly G·poly C and is thus dependent only upon the amount of ordering of the helix and not on the kinds of nucleotides involved. The hypochromic Raman lines in spectra of poly A·poly U are identified and their intensity changes are determined quantitatively over the temperature range 32–85°C. Comparison of the spectra in the 1500–1750 cm^?1 region reveals that the Raman lines from carbonyl group vibrations of uracil are about sevenfold more intense than those of guanine and cytosine for both paired and unpaired states and will thus dominate the spectra of RNA. The Raman frequencies in this region are also compared with previously reported infrared frequencies and give evidence of being strongly perturbed by base-stacking interactions in the helices.     

Electro-optical studies of conformation and interaction of polynucleotides

Measurements by the technique of electric birefringence with pulsed sinusoidal electric fields on polyriboadenylic acid (poly-A) and polyribouridylic acid (poly-U) indicate that the kinetics of the double-stranded helix formation of poly (A + U) in the presence of Mg²⁺ is second order and consists of two steps: nucleation and propagation of base pairs from nuclei. The nucleation involves approximately 7 base pairs. It seems that the requirement of 7 base pairs to start the formation of a double-stranded helix is not peculiar to poly (A + U) but is associated with double-stranded helices of polynucleotides in general. This implies that it may be associated with spatial requirements of the phosphate-sugar backbone, rather than with the particular bases linked to the backbone. The decline in rate of poly (A + U) formation observed above a critical temperature is the consequence of changes in the poly-A conformation setting in at this critical temperature, rather than resulting from an increase in the reversibility of the base-pair propagation step of double-stranded helix formation. The dominant role of the conformation of poly-A in the double-stranded helix formation of poly (A + U) is further borne out by the pH dependence of the rate which completely parallels the conformation changes known to occur in poly-A as a function of pH. This indirectly suggests that at neutral pH poly-A is a single-stranded helix. The rotary diffusion coefficients attest to the flexibility of this helix, while the stacked nature of the base pairs at low temperatures is revealed by the identical increments in the specific Kerr constant on going from poly-A to poly (A + U) and from poly (A + U) to poly (A + 2U) helices. Results suggest that Mg²⁺ binds to the phosphate part of the backbone. Poly-U binds Mg²⁺ more strongly than poly-A; this difference in binding strength is attributed to differences in conformation (random coil versus helix). It is also borne out by the present results that the degree of order in the structure of poly-U, even at low temperatures and neutral pH, is at best an order of magnitude smaller than that of poly-A under similar conditions. Furthermore, the earlier proposed double-stranded structure of poly-U is called into question. A hairpinlike structure seems to agree with results of this investigation. Finally, the results support the contention that the ion atmosphere polarization is responsible for orientation of polyelectrolytes in the presence of alternating electric fields in the neighborhood of 25 kc./sec. frequency.     

Kinetic properties and the electric field effect of the helix-coil transition of poly(gamma-benzyl L-glutamate) determined from dielectric relaxation measurements

Dielectric relaxation of poly(γ-benzyl L -glutamate) in solution has been studied in the 5 kcps-10 Mcps range for various values of the helix content. The results give first experimental evidence for three effects of major significance. (1) The system exhibits dielectric relaxation due to a chemical rate process (namely helix formation). This confirms recent theoretical predictions. (2) The mean relaxation time τ* of the helix–coil transition could be evaluated as a function of the degree of transition. The results are in excellent agreement with a previously developed theory. At the midpoint of transition it is found τ*_max = 5 × 10^?7 sec. The elementary process of helical growth turns out to be practically diffusion-controlled (with a rate constant of hydrogen bond formation of 1.3 × 10¹⁰ sec^?1). (3) There is a considerable electric field effect of the helix–coil transition. This indicates that conformation changes in biological systems could be potentially caused by direct action of an electric field.     

The triple helix ⇌ coil conversion of collagen-like polytripeptides in aqueous and nonaqueous solvents. Comparison of the thermodynamic parameters and the binding of water to (L-Pro-L-Pro-Gly)n and (L-Pro-L-Hyp-Gly)n

The collagen-like peptides (L -Pro-L -Pro-Gly)_n and (L -Pro-L -Hyp-Gly)_n with n = 5 and 10, were examined in terms of their triple helix ? coil transitions in aqueous and nonaqueous solvents. The peptides were soluble in 1,2-propanediol containing 3% acetic acid and they were found to form triple-helical structures in this solvent system. The water content of the solvent system and the amount of water bound to the peptides were assayed by equilibrating the solvent with molecular sieves and carrying out Karl Fischer titrations on the solvent phase. After the solvent was dehydrated, much less than one molecule of water per tripeptide unit was bound to the peptides. Since the peptides remained in a triple-helical conformation, the results indicated that water was not an essential component of the triple-helical structure. Comparison of peptides with the same chain length demonstrated that the presence of hydroxyproline increased the thermal stability of the triple helix even under anhydrous conditions. The results, therefore, did not support recent hypotheses that hydroxyproline stabilizes the triple helix of collagen and collagen-like peptides by a specific interaction with water molecules. Analysis of the thermal transition curves in several solvent systems showed that although the peptides containing hydroxyproline had t_m values which were 18.6° to 32.7°C higher, the effect of hydroxyproline on ΔG was only 0.1 to 0.3 kcal per tripeptide unit at 25°C. The results suggested, therefore, that the influence of hydroxyproline on helical stability may be explained by intrinsic effects such as dipole–dipole interactions or by changes in the solvation of the peptides by alcohol, acetic acid, and water. A direct calorimetric measurement of the transition enthalpy for (L -Pro-L -Pro-Gly)_n in 3% or 10% acetic acid gave a value of ?1.84 kcal per tripeptide unit for the coil-to-helix transition. From the value for enthalpy and from data on the effects of different chain lengths on the thermal transition, it was calculated that the apparent free energy for nucleation was +5 kcal/mol at 25°C (apparent nucleation parameter = 2 × 10^?4 M^?2). The value was dependent on solvent and on chemical modification of end groups.     

Interaction of magnesium ions with poly A and poly U

The binding of Mg⁺⁺ to poly A and poly U has been measured quantitatively by using the metallochromic indicator calmagite. The method is described in detail. It is shown that there is electrostatic interaction between the binding sites, viz., the phosphate groups, and the intrinsic association constant, for the specific binding can be determined. After extrapolation to zero ionic strength we find that, for the binding of Mg⁺⁺ to poly A, k_int = 4 × 10⁴ and for that, to poly U, k_int = 3 × 10⁴. The intrinsic enthalpy of association is negative. The effect of Mg⁺⁺ on the secondary structure of poly A and poly U has been studied by measuring the ultraviolet absorbance, optical rotatory dispersion and viscosity as a function of the amount of added Mg⁺⁺ ions. It was found that Mg⁺⁺ promotes the formation of a more ordered secondary structure by neutralizing or screening the negative charges. It is concluded from the absorbance measurements that for poly A at pH ? 7 and for poly U at pH >xs 9 this ordering involves stacking of the bases. Likewise, in solutions of UDP with a pH around 10, base stacking occurs on addition of Mg⁺⁺.     

Polymer concentration effects on helix–coil transition widths

A theoretical study of effects of excluded volume intermolecular interactions on the sharpness of helix–coil transitions in solutions of polyamino acids or simple proteins indicates that the transition width may vary appreciably as a function of polymer concentration. The analysis is based on a second virial approximation for the excess free energy of mixing of a solution of polymers of varying degrees of helicity. The virial coefficients involved are roughly estimated on the basis of gross polymer geometry. For large N (degree of polymerization) the transition is found, typically to sharpen with increasing concentration, becoming second order and then first order at sufficiently high concentrations. The critical polymer concentration is found to be roughly of the order N^?1.2 ??₀^?1 for an “all or none” model and of order σ^1/2 N^?0.2 ??₀^?1 for a model with continuously variable degree of helicity (??₀ is the volume of a single helical molecule and σ^1/2 the normalized statistical weight of a helix–coil interface). In the second case for N ～ 10³ and σ ～ 10^?2–10^?4, the predicted critical concentration is in the range 10^?1–10^?3 g/cm.³ Comparison is made with experiments on solutions of poly(γ-benzyl-L glutamate).     

Cooperative nonenzymic base recognition. Thermodynamics of the helix--coil transition of a monomer--polymer double helix

The double-helical complex formed from m⁶m⁹A and poly U has been characterized by circular dichroism and u.v. spectrophotometry. The circular dichroism of the complex is similar to that of the double-helical poly A poly U complex both in shape and in magnitude and thus indicates a quite similar structure. The double Helix–coil transition has been studied at various nucleotide concentrations and at three different ionic strengths. As expected for the binding of a base to a polymer, the Helix–coil transition is shifted to higher temperatures by increasing nucleotide concentrations, but is not affected by changes of the ionic strength. The melting curves are analyzed according to a linear Ising model taking the stacking of the monomers into account. At 0°C the equilibrium constant for nucleation is found to be 2–5 M^?1 and that for chain growth is 500 M^?1. The enthalpy change associated with chain growth is ?11.2 ± 1 kcal M^?1.