Volume changes accompanying the complex formation of polyadenylic and polyuridylic acids

The complex formation of polyadenylic acid (poly A) and polyuridylic acid (poly U) in 0.1M NaCl solution containing 0.01M sodium cacodylate was followed by dilatometric measurements at various mixing ratios of poly A and poly U. The volume changes, ΔV, accompanying the formation of poly A. poly U and poly A.2poly U were + l.5 and + 2.5 ml per mole of the nucleotide residue, respectively. This increase in volume was probably due to the increased counterion binding when the single-stranded polynucleotides were converted into the double- and triple-stranded helices, since depletion of charged species from the solvent proper would lessen the effect of electrostriction, thus resulting in a positive ΔV. The conversion of a single-stranded poly A to a double-stranded helix in acidic solution led to a ΔV of + 3.8 ml per mole of the nucleotide residue. This increase in volume was attributed to the charge neutralization as a result of protonation of the adenine bases.     

Experimental thermodynamics of the helix--random coil transition. 3. Determination of the transition enthalpies of the helical complexes poly(I+C) and poly I in solution

The enthalpies of the helix-coil transitions of the ordered polynucleotide systems of poly(inosinic acid)–poly(cytidylic acid) [poly(I + C)], (helical duplex), and of poly (inosinic acid) [poly(I + I + I)], (proposed secondary structure: a triple-stranded helical complex), were determined by using an adiabatic twin-vessel differential calorimeter. Measuring the temperature course of the heat capacity of the aqueous polymer solutions, the enthalpy values for the dissociation of the helical duplex poly (I + C) and the three-stranded helical complex poly(I + 1 + 1), respectively, were obtained by evaluating the additional heat capacity involved in the conformational change of the polynucleotide system in the transition range. The ΔH values of the helix-coil transition of poly (I + C) resulting from the analysis of the calorimetric measurements vary between the limits 6.5 ± 0.4 kcal/mole (I + C) and 8.4 ± 0.4 kcal/mole (I + C). depending on the variation of the cation concentration ranging from 0.063 mole cations kg H₂O to 1.003 mole cations/kg H₂O. The calorimetric investigation of an aqueous poly I solution (cation concentration 1.0 mole/kg H₂O) yielded the enthalpy value ΔH = 1.9 ± 0.4 kcal/mole (I), a result which has been interpreted qualitatively following current models of inter- and intramolecular forces of biologically significant macromolecules. Additional information on the transition behavior of poly(I+ C)Was obtained by ultraviolet and infrared absorption measurements.     

Helix-coil transition of poly-gamma-N-carbobenzoxy-L-alpha, gamma-diaminobutyrate and poly-delta-N-carbobenzoxy-L-ornithine

The helix–coil transition of poly-γ-N-carbobenzoxy-L -α,γ-diaminobutyrate (PCLB) and poly-δ-N-carbobenzoxy-L -ornithine (PCLO) in chloroform–dichloroacetic acid mixtures was followed by optical rotatory dispersion. PCLB displays a “normal” temperature-induced transition, but PCLO an “inverse” one. The thermodynamic parameters for helix formation of the two polymers were determined using the Zimm-Bragg theory. The enthalpy for adding an amide residue to a helical region, ΔH, and the initiation factor σ were ΔH = ?180 cal/mole and σ = 9.2 × 10^?5 for PCLB and ΔH = +490 cal/mole and σ = 1.9 × 10^?5 for PCLO.     

Polypeptides. LVI. Effect of lithium bromide and of temperature on the conformation of a copolymer of glutamic acid and lysine

By using optical rotatory dispersion measurements, the helix content of poly Glu⁵⁰Lys⁵⁰ has been investigated and compared with that of poly Glu²⁰Lys²⁰Ala⁶⁰ in aqueous solutions. Measurements were made at pH 3 and at pH 8 in various concentrations of lithium bromide. Various factors affecting helix stabilization are considered and their perturbation by lithium bromide is related to the shape of the observed transition curves. A residual helix content of 12% in 8M LiBr, based upon a b₀ of +100 for a fully random conformation, was observed for poly Glu⁵⁰Lys⁵⁰ at pH 3 and 8. The loss of helix content of poly Glu⁵⁰Lys⁵⁰ as a function of temperature is also reported. ΔH is approximately ?6.9 kcal./mole for the overall transition, compared to ?6.5 kcal./mole for poly Glu²⁰Lys²⁰Ala⁶⁰. The midpoint of the broad transition is near 40°C. at pH 3, but much lower, at ?10 to 0°C., at pH 8. These results are discussed in terms of the stabilizing factors for the partial helix content of the polypeptides.     

Syntheses and conformational studies of poly(Nε-methyl-L-lysine), poly(Nδ-methyl-L-ornithine), poly(Nδ-ethyl-L-ornithine), and their carbobenzoxy derivatives

The helix–coil transitions of poly(N^ε-methyl, N^ε-carbobenzoxy-L -lysine), poly(N^δ-methyl, N^δ-carbobenzoxy-L -ornithine), and poly(N^δ-ethyl, N^δ-carbobenzoxy-L -ornithine) in chloroform–dichloroacetic acid and their corresponding decarbobenzoxylated polypeptides in alkaline solutions were followed by optical rotation measurements. The introduction of a methyl or an ethyl group to the side chains of the carbobenzoxy derivatives of poly(L -lysine) and poly(L -ornithine) appeared to weaken the helical conformation at 25°C. The thermodynamic quantities of the three water-soluble polypeptides were calculated from the data on potentiometric titrations at several temperatures. For uncharged coil-to-helix transition, ΔH = ?370 cal/mol and ΔS = ?1.1 eu/mol for poly(N^ε-methyl-L -lysine), and ΔH = ?540 cal/mol and ΔS = ?1.6 eu/mol for poly(N^δ-ethyl-L -ornithine) (all on molar residue basis). The absolute values of ΔH and ΔS dropped in the region of pH-induced transition and eventually both quantities became positive. The initiation factor σ was about 2 × 10^?3, which was essentially independent of temperature. For poly(N^δ-methyl-L -ornithine) the coil-to-helix transition was not complete even when the polymer was uncharged at high pH.     

Cis-Trans equilibrium and kinetic studies of acetyl-L-proline and glycyl-L-proline

By means of carbon-13 nmr (at 25 MHz) the trans/cis conformer ratio in glycyl-L -proline has been measured in aqueous (D₂O) solution over the temperature range 33–96°C. It is found that ΔH⁰ = ?4.2 kJ/mole and ΔS⁰ = ?9.7 J/mole/K. Measurements of the T₁ values for the proline ring carbons yielded values consistent with a fast puckering process involving both the β- and γ-carbons. Measurements of the rate of cis-trans conformational interconversion in glycyl-L -proline, using complete line-shape analysis for the glycyl α-carbon resonance, gave values for the trans → cis isomerization as follows: ΔH^≠ = 83.5 ± 0.2 kJ/mole; ΔS^≠ = 0.0 ± 10 J/mole/K. A more approximate determination from coalescence temperature observations gave a value of ΔG^≠ of 82.0 ± 0.4 kJ/mole for this process in acetyl-L -proline in aqueous solution. The presence of 12M NaSCN lowered this barrier by ca. 2.6 kJ/mole. Such measurements are relevant to present theoretical models of the denaturation-renaturation processes in proteins, in which proline residues may play a key role.     

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β-benzyl L-aspartate)

Simple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix-coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β-benzyl L -aspartate) (PBLA) with the result: σ = 1.6 × 10^?4 and ΔH = ?450 cal/mole for PBLA in m-cresol; σ = 0.6 × 10^?4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol-% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m-cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean-square radius of gyration, 〈S²〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S²〉.     

Pressure dependence of the helix–coil transition temperature of poly[d(G-C)]

The Pressure Dependence of the Helix-Coil Transition Temperature (T_m) of Poly[d(G-C)] was studied as a function of sodium ion concentration in phosphate buffer. The molar volume change of the transition (ΔV) was calculated using the Clapeyron equation and calorimetrically determined enthalpies. The ΔV of the transition increased from +4.80 (±0.56) to +6.03 (±0.76) mL mol^?1 as the sodium ion concentration changed from 0.052 to 1.0M. The van't Hoff enthalpy of the transition calculated from the half-width of the differentiated transition displayed negligible pressure dependence: however, the value of this parameter decreased with increasing sodium ion concentration, indicating a decrease in the size of the cooperative unit. The volume change of the transition exhibits the largest magnitude of any double-stranded DNA polymer measured using this technique. For poly[d(G-C)] the magnitude of the change in ΔV with sodium ion concentration (0.94 ± 0.05 mL mol^?1) is approximately one-half that observed for either poly[d(A-T)] or poly (dA)·poly(dT). The ΔV values are interpreted as arising from changes in the hydration of the polymer due to the release of counterions and changes in the stacking of the bases of the coil form. As a consequence of solvent electrostriction, the release of counterions makes a net negative contribution to the total ΔV, implying that disruption of the slacking interactions contributes a positive volume change to the total ΔV. The larger magnitude of the ΔV compared with that of other double-stranded polymers may be due in part to the high helix-coil transition temperature of poly[d(G-C)], which will attenuate the contribution of electrostriction to the total volume change. The data in addition show that in the absence of other cellular components, the covalent structure of DNA is stabile under conditions of temperature and pressure more extreme than those experienced by any known organism. © 1995 John Wiley & Sons, Inc.     

Thermodynamic parameters for the helix-coil thermal transition of ribonuclease-S-peptide and derivatives from 1H-NMR data

Values for the thermodynamic quantities, ΔH° = 11.8 ± 2.0 Kcal/mole and ΔS° = 43.6 ± 6.0 e.u., of the 3-13 helix–coil equilibrium of isolated S-peptide (19 residue N-terminal fragment of ribonuclease A) in aqueous solution (3 m M, 1M NaCl, pD 5.4) have been determined from a joint analysis of the Thr 3γ, Ala 6β, Phe 8meta, and Phe 8para ¹H chemical shift vs temperature curves (?7 to 80°C) in several aqueous–trifluorethanol mixtures. Chemical shifts in the coil and in the helix have been determined for up to 16 protons belonging to the 3-13 fragment. Thermodynamic parameters have also been determined for C-peptide (13 residue fragment) and a number of S-peptide derivatives. From the variation of the values of the thermodynamic parameters at pD 2.5, 5.4, and 8.0, a quantitation of the two helix-stabilizing side-chain interactions can be made: (1) Δ(ΔH°) ? 5 Kcal/mole and Δ(ΔS°) ? 18 e.u. for the salt bridge Glu 2^? … Arg 10⁺ and (2) Δ(ΔH°) ? 3 Kcal/mole and Δ(ΔS°) = 9 e.u. for the one in which the His 12⁺ imidazolium group is involved, presumably a partial stacking with the Phe 8 side chain.     

Thermal and charge-induced coil to -helix transition of poly-L-glutamic acid and random L-glutamic acid-L-alanine copolymers

Thermal and charge induced random coil to α-helix transitions of poly-L -glutamic acid (PGA) were measured by optical rotatory dispersion in various solvents. The data of PGA in 0.1M Nacl were analyzed by the Zimm-Rice theory. Enthalpy and entropy changes for the coil-to-helix transition in the unionized state were obtained: ΔH° = ?1020 ± 100 cal/residue mole; ΔH° = ?3.0 ± 0.4 e.u./residue mole. The initiation parameter, σ, of the Zimm-Rice theory was given by a value of 5 ± 1 × 10^-3. Random copolymers of L -glutamic acid and L -alanine containing 10, 30, and 40 molar percents of alanyl residue were synthesized. Stabilities of α-helix of the copolymers were compared to that of PGA. In water and water-ethanol solutions, stabilities of the polymers were almost equal after the simple correction about the ionized charge density of the polymers. In 0.1 M NaCl solution these copolymers showed some deviations from the transition curve of PGA, which would suggest the hydrophobic contribution of the alanyl residues.     

A calorimetric investigation of the heats of binding of Mg ++ to poly A, to poly U, and to their complexes

The heats of binding of Mg⁺⁺ ions to poly A, poly U, and to their complexes, in the presence of Na⁺ ions, have been measurd calorimetrically. In all cases the heat, ΔH(θ), exhibitis a distinct dependence on the extent of binding, θ, and in the cases of poly A and poly U also on the Na⁺ concentration. The values of ΔH(θ) range from +2 to +3 kcal/mole of Mg⁺⁺ bound at θ = 0 to 1.3 kcal/mole at θ = 0.5 except in poly A where at θ = 0 ΔH(θ) = ?2 to ?3 kcal/mole. This is interpreted as being due to a facilitation of base stacking by the binding of Mg⁺⁺. The extent of facilitation is consistent with current estimates of base stacking. A similar effect but of much smaller magnitude is believed to obtain in poly A poly U. An interpretation of the dependence of ΔH(θ) on θ in terms of simple electrostatic interactions, but neglecting solvent effects, was attempted and found to be inadequate.     

Thermodynamics of conformational transition and chain association of ι-carrageenan in aqueous solution: Calorimetric and chirooptical data

Isothermal microcalorimetry, differential scanning calorimetry (DSC), and chirooptical data obtained for ι-carrageenan in NaCl, LiCl, and NaI aqueous solutions are presented. The experiments have been performed as a function of concentration both for the polymer and for the simple salt as a cosolute. The experimental findings consistently show the occurrence of a salt-induced disorder-to-order transition. From microcalorimetric experiments the exothermic enthalpy of transition ΔH_tr is obtained as the difference between the theoretical, purely electrostatic ΔH_el enthalpy change and the actual mixing enthalpy ΔH_mix, measured when a ι-carrageenan salt-free solution at constant polymer concentration is mixed with a 1:1 electrolyte solution of variable concentration. In the case of added NaCl, the absolute values of enthalpy changes |ΔH_tr| are in good agreement with those obtained for the opposite process, at comparable polymer and salt concentrations, from DSC melting curves. The microcalorimetric results show that the negative maximum value of ΔH_tr corresponding to the interaction of Li⁺ counterion with ι-carrageenan polyion results to be significantly lower than the corresponding values obtained for Na⁺ counterion. At variance with the microcalorimetric data, chirooptical results show that the salt-induced disorder-to-order transition, occurring in the 0.02–0.2M salt concentration range, appears to be complete at a concentration of about 0.08–0.1M of the simple ion, irrespective of the polymer concentration and of the nature of added electrolyte. © 1998 John Wiley & Sons, Inc. Biopoly 45: 105–117, 1998     

Helix–coil transition of poly-N5-(3-hydroxypropyl)-L-glutamine: Thermodynamic and statistical analysis

The thermally induced conformational changes of poly-N⁵-(3-hydroxypropyl)-L -glutamine in water and in methanol–water (3:7 v/v) have been analyzed in terms of the Lifson-Roig theory. The transitions in both solvents can be described by using v = 0.017. The thermodynamic parameters for the random coil-to-helix transition of one amino acid residue at room temperature were found to be: in water, ΔH = ? 130 cal/mole and ΔS = ? 0.45 e.u.; in methanol–water (3:7 v/v), ΔH = ? 170 cal mole and ΔS = ? 0.45 e.u. The size distribution of helical segments is broad, and the results of numerical calculations are presented for three degrees of polymerization (DP = 100, 300, and 750).     

The binding of Mg++ ions to polyadenylate, polyuridylate, and their complexes

The binding of Mg ⁺⁺ to polyadenylate (poly A), Polyuridylate(poly U), and their complexes, poly (A + U) and poly (A + 2U), was studied by means of a technique in which the dye eriochrome black T is used to measure the concentration of free Mg^?. The apparent binding constant K_X = [MgN]/[Mg⁺⁺][N], N = site for Mg⁺⁺ binding (the phosphate group of the nucleotide), was found to decrease rapidly as the extent of binding increased and, at low extents of binding, as the concentration of Na^? increased in poly A, poly (A + U), and poly (A + 2U), and somewhat less so in poly U. K_x is generally in the range 10⁴ > K_X > 10². The cause of these dependences is apparently, primarily, the displacement of Na⁺ by Mg⁺⁺ in poly U and poly (A + U) on the basis of the similarity of extents of displacement measured in this work and those measured potentiometrically. was calculated and was found to approach zero as the concentration of Na⁺ increased. In poly U, poly (A + U), and poly (A + 2U) at low ΔH′ v.H. > 0, about + 2 kcal/“mole.” In poly A, also at low salt, ΔH′ v.H. ≈ ?4 kcal/“mol” for the initial binding of Mg⁺⁺, and increases to +2 kcal/“mol” at saturation. This enthalpic variation probably accounts for the anticooperativity in the binding of Mg⁺⁺ not ascribable to the displacement of Na⁺⁺.     

Volume changes correlate with entropies and enthalpies in the formation of nucleic acid homoduplexes: Differential hydration of A and B conformations

We have used a combination of densimetric, calorimetric, and uv absorption techniques to obtain a complete thermodynamic characterization for the formation of nucleic acid homoduplexes of known sequence and conformation. The volume change ΔV accompanying the formation of four duplexes was interpreted to reflect changes in hydration based on the electrostriction phenomenon. In 10 mM sodium phosphate buffer at pH 7, the magnitude of the measured ΔV's ranged from ?2.0 to +7.2 ml/mol base pair and followed the order of poly(rA) · poly(dT) ～ poly(dA) · poly(dT) < poly(rA) · poly(dU) ～ poly(rA) · poly(rU). Inclusion of 100 mM NaCl in the same buffer gave the range of ?17.4 to ?2.3 mL/mol base pair and the following order: poly(dA) · poly(dT) < poly(rA) · poly(dT) < poly(rA) · poly(rU) ～ poly(rA) ～ polyr(dU). Standard thermodynamic profiles of forming these duplexes from their corresponding complementary single strands indicated similar free energies that resulted from the compensation of favorable enthalpies with unfavorable entropies along with a similar counterion uptake at both ionic strengths. The differences in these compensating effects of entropy and enthalpy correlated very well with the volume change measurements in a manner suggesting that the homoduplexes in the B conformation are more hydrated than are those in the A conformation. Moreover, the increased thermal stability of these homoduplexes resulted from an increase in the salt concentration corresponding to larger hydration levels as reflected by the ΔV results. © 1993 John Wiley & Sons, Inc.     

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.     

Microcalorimetry of microorganism metabolism of monosaccharides and simple aromatic compounds

Heat conduction solution enable rapid determination of the heats of aerobic and anaerobic metabolism of substrate by microorganisms. Aliquots of 1.0 ml cell suspension, 5 × 10⁹ cell/ml, were mixed with a few dozen nmol substrate contained in 0.5 ml, under a controlled atmosphere of air, O₂, or N₂. At these substrate concentration, with adapted microorganisms, metabolism and its heat generation are usually complete within 300 to 600 sec. The raw data yield ΔH_app values. The ΔH_app were determined in the range 0.001 to 0.010% substrate, and extrapolated (limit substrate concentration →0), to yield Δ⁰H?, the limiting differential molar heat of metabolism. The Δ⁰H? values express the heat generated when there is rapid metabolism but little new growth, minimal contribution by H⁺ transfer from metabolites, and maintenance of aerobicity or anaerobicity as specified. Escherichiacoli B/5 was used for aerobic and anaerobic combustion of eight sugars. Pseudomonas multivorans, and an Acinetobacter, strain B-1, were used for aerobic metabolism of benzene, toluene, naphthalene, and a methylnaphthalene. The larger heats of combustion of the hydrocarbons enable the use of aqueous solutions of hydrocarbons well below their solubility limits. The quotient Δ⁰H?/n (n = atoms carbon/molecule substrate) varies from (-)36 to (-)67 kcal/mol carbon for the sugars. The most reduced sugar yields the largest exothermic heats. The quotient varies from (-)27 to (-)81 kcal/mol carbon for the aromatic hydrocarbons. Comparison of the calorimetric heats of metabolism of those from total aerobic combustion in aquo (where available) give measure of the efficiencies with which the heat contents of the aqueous substrate are used by the bacteria.     

Thermodynamics and kinetics of the helix-coil transition of oligomers containing GC base pairs

Absorbance-temperature profiles have been determined for the following self-complementary oligonucleotides or equimolar paris of complementary oligonucleotides containing GC base pairs: A₂GCU₂, A₃GCU₃, A₄GCU₄, A₆CG + CGU₆, A₈CG + CGU₈, A₄G₂ + C₂U₄, A₅G₂ + C₂U₅, A₄G₃ + C₃U₄, and A₅G₃ + C₃U₅. In all cases cooperative melting transitions indicate double-helix formation. As was found previously, the stability of GC containing oligomer helices is much higher than that of AU helices of corresponding length. Moreover, helices with the same length and base composition but different sequences also have quite different stabilites. The melting curves were andlyzed using a zipper model and the thermodynamic parameters for the AU pairs determined previously. The effect of single-strand stacking was considered separately. According to this model, the formation of a GC pair from unstacked single strands is associated with an ethalpy change of ?15 kcal/mole. Due to the high degree of single-strand stacking at room temperature the enthalpy change for the formation of GC pairs from unstacked single strands is only ?5 to ?6 kcal/mole. (The corresponding parameters for AU pairs are ?10.7 kcal/mole and ?5 to ?6 kcal/mole.) The sequence dependence of helix stability seems to be primarily entropic since no differences in ΔH were seen among the sequence isomers. The kinetics of helix formation was investigated for the same molecules using the temperature jump technique. Recombination of strands is second order with rate constants in the range of 10⁵ to 10⁷M^?1 sec^?1 depending on the chain length and the nucleotide sequence. Within a series of oligomers of a given type, the rates of recombination decrease with increasing chain length. Oligomers with the sequence A_nGCU_n recombine six to eight times slower than the other oligomers of corresponding chain length. The experimental enthalpies of activation of 6 to 9 kcal/mole suggest a nucleation length of one or two GC base pairs. The helix dissociation process has rate constants between 0.5 and 500 sec^?1 and enthalpies of activation of 25 to 50 kcal/mole. An increase of chain length within a given nucleotide series leads to decreased rates of dissociation and increased enthalpies of activation. An investigation of the effect of ionic strength on A_nGCU_n helix formation showed that the rates of recombination increase considerably with increased ionic strength.     

Thermodynamics of the slow–fast transition in bacteriophage T2L

We have measured the thermodynamic parameters of the slow-fast tail-fiber reorientation transition on T2L bateriophage. Proportions of the virus in each form were determined from peak-height measurements in sedimention-velocity runs and from average diffusion coefficients obtained by quasielastic laser light scattering. Computer simulation of sedimentation confirmed that there were no undetected intermediates in the transition, which was analyzed as a two-state process. Van't Hoff-type plots of the apparent equilibrium constant and of the pH midpoint of the transition as function of reciprocal temperature led to the following estimates of the thermodynamic parameters for the transition at pH 6.0 and 20°C: ΔH° = ?139 ± 18Kcal mol^?1, ΔS° = ?247 ± 46 cal K^?1 mol^?1, and ΔG° = ?66 ± 22 kcal mol^?1. Per mole of protons taken up in the transition, the analogous quantities were ?15.9 ± 1.7 kcal mol^?1, ?26.3 ± 2.2 cal K^?1 mol^?1, and ?8.22 ± 1.8 kcal mol^?1. The net number of protons taken up was about 8.5 ± 1.5. The large values of the thermodynamic functions are consistent with a highly cooperative reaction and with multiple interactions between the fibres and the remainder of the phage. The negative entropy of the transition is probably due to immobilization of the fibres.