Determination of Gibbs free energy of transfer for some univalent ions from water to methanol,acetonitrile, dimethylsulfoxide,pyridine, tetrahydrothiophene and liquid ammonia; standard electrode potentials of some couples in these solvents

The free energy of transfer, ΔG°_tr, for 21 univalent ions are determined from water to methanol, acetonitrile, dimethylsulfoxide (DMSO), pyridine, tetrahydrothiophene and liquid ammonia. These solvents show a wide range of donor properties, whereby water and methanol are regarded as hard donors, dimethylsulfoxide and acetonitrile are on the borderline between hard and soft, and the remaining solvents are regarded as typical soft donors. The ΔG°_tr values of ionic compounds are calculated from solubility product measurements of 1:1 salts. The extrathermodynamic tetraphenylarsonium tetraphenylborate (TATB) assumption has been applied in order to calculate the contributions from the single ions. The TATB assumption implies that the two large ions Ph₄As⁺ and BPh₄⁻ are equally solvated, thus ΔG°_tr(AsPh₄⁺)=ΔG°_tr(BPh₄⁻), for all solvent pairs. Standard electrode potentials in non-aqueous solvents can be calculated from the standard electrode potentials in water and the ΔG°_tr values. The standard electrode potentials calculated from the solubility product measurements, and the potentiometrically determined ones were found to be in excellent agreement. The extrathermodynamic assumption has thereby been experimentally shown to be close to the truth.     

RosettaDDGPrediction for high-throughput mutational scans: From stability to binding

Reliable prediction of free energy changes upon amino acid substitutions (ΔΔGs) is crucial to investigate their impact on protein stability and protein–protein interaction. Advances in experimental mutational scans allow high-throughput studies thanks to multiplex techniques. On the other hand, genomics initiatives provide a large amount of data on disease-related variants that can benefit from analyses with structure-based methods. Therefore, the computational field should keep the same pace and provide new tools for fast and accurate high-throughput ΔΔG calculations. In this context, the Rosetta modeling suite implements effective approaches to predict folding/unfolding ΔΔGs in a protein monomer upon amino acid substitutions and calculate the changes in binding free energy in protein complexes. However, their application can be challenging to users without extensive experience with Rosetta. Furthermore, Rosetta protocols for ΔΔG prediction are designed considering one variant at a time, making the setup of high-throughput screenings cumbersome. For these reasons, we devised RosettaDDGPrediction, a customizable Python wrapper designed to run free energy calculations on a set of amino acid substitutions using Rosetta protocols with little intervention from the user. Moreover, RosettaDDGPrediction assists with checking completed runs and aggregates raw data for multiple variants, as well as generates publication-ready graphics. We showed the potential of the tool in four case studies, including variants of uncertain significance in childhood cancer, proteins with known experimental unfolding ΔΔGs values, interactions between target proteins and disordered motifs, and phosphomimetics. RosettaDDGPrediction is available, free of charge and under GNU General Public License v3.0, at https://github.com/ELELAB/RosettaDDGPrediction .     

A new method for predicting binding free energy between receptor and ligand

A practical method to estimate binding free energy, ΔG_bind, of a given ligand structure to the target receptor has been developed. The method assumes that ΔG_bind is given by the summation of intermolecular interaction energy, ΔG_inter, and partial desolvation energy, ΔG_desolv. ΔG_desolv is calculated from the buried surface area in the complex between the ligand and receptor, based on solvation energy, ΔG_solv, formulated by an equation which can be calibrated with observed values. Then, the method was applied to arabinose-binding protein (ABP) and dihydrofolate reductase (DHFR), after recalibrating the weights for ΔG_inter and each term of ΔG_desolv using observed ΔG_bind data for 29 known ligands to avidin (AV). The usefulness of our method was confirmed by the fact that correlation coefficients between the calculated and observed ΔG_bind's in AV, ABP and DHFR were 0.92, 0.77, and 0.88, whereas the corresponding values obtained by simple force field calculation were 0.79, 0.30, and 0.79, respectively. Further investigations to improve the method and validate the parameters are in progress. Proteins 33:62–73, 1998. © 1998 Wiley-Liss, Inc.     

Calorimetric measurement of enthalpy change in the isothermal helix-coil transition of poly(L-ornithine) in aqueous solution.

The enthalpy change associated with the isothermal pH-induced uncharged coil-to-helix transition ΔH_h° in poly(L -ornithine) in 0.1 N KCl has been determnined calorimetrically to be ?1530 ± 210 and ?1270 ± 530 cal/mol at 10° and 25°C, respectively. Titration data provided information about the state of charge of the polymer in the calorimetric experiments, and optical rotatory dispersion data about its conformation. In order to compute ΔH_h°, the observed calorimetric heat was corrected for the heat of breaking the sample cell, the heat of dilution of HCl, the heat of neutralization of the OH^? ion, and the heat of ionization of the δ-amino group in the random coil. The latter was obtained from similar calorimetric measurements on poly(D ,L -ornithine). Since it was discovered that poly(L -ornithine) undergoes chain cleavage at high pH, the calorimetric measurements were carried out under conditions where no degradation occurred. From the thermally induced uncharged helix–coil transition curve for poly(L -ornithine) at pH 11.68 in 0.1 N KCl in the 0°–40°C region, the transition temperature T_tr and the quantity (?θ_h/?T)_Ttr have been obtained. From these values, together with the measured values of ΔH_h°, the changes in the standard free energy ΔG_h° and entropy ΔG_h°, associated with the uncharged coil-to-helix transition at 10°C have been calculated to be ?33 cal/mol and ?5.3 cal/mol deg, respectively. The value of the Zimm–Bragg helix–coil stability constant σ has been calculated to be 1.4 × 10^?2 and the value of s calculated to be 1.06 at 10°C, and between 0.60 and 0.92 at 25°C.     

Osmolyte effects on protein stability and solubility: a balancing act between backbone and side-chains

In adaptation biology the discovery of intracellular osmolyte molecules that in some cases reach molar levels, raises questions of how they influence protein thermodynamics. We've addressed such questions using the premise that from atomic coordinates, the transfer free energy of a native protein (ΔG_tr, N) can be predicted by summing measured water-to-osmolyte transfer free energies of the protein's solvent exposed side chain and backbone component parts. ΔG_tr, D is predicted using a self avoiding random coil model for the protein, and ΔG_tr, D − ΔG_tr, N, predicts the m-value, a quantity that measures the osmolyte effect on the N ? D transition. Using literature and newly measured m-values we show 1:1 correspondence between predicted and measured m-values covering a range of 12 kcal/mol/M in protein stability for 46 proteins and 9 different osmolytes. Osmolytes present a range of side chain and backbone effects on N and D solubility and protein stability key to their biological roles.     

Kinetic and thermodynamic properties of purified alkaline protease from Bacillus pumilus Y7 and non‐covalent immobilization to poly(vinylimidazole)/clay hydrogel

The characterization of the hydrogel was performed using Fourier‐transform infrared spectroscopy, X‐ray diffraction, and scanning electron microscopy. Purified Bacillus pumilus Y7‐derived alkaline protease was immobilized in Poly (vinylimidazole)/clay (PVI/SEP) hydrogel with 95% yield of immobilization. Immobilization decreased the pH optimum from 9 to 6 for free and immobilized enzyme, respectively. Temperature optimum 3°C decreased for immobilized enzyme. The K_m, V_m, and k_cat of immobilized enzyme were 4.4, 1.7, and 7.5‐fold increased over its free counterpart. Immobilized protease retained about 65% residual activity for 16^th reuse. The immobilized protease endured its 35% residual activity in the material after six cycle's batch applications. The results of thermodynamic analysis for casein hydrolysis showed that the ΔG^≠ (activation free energy) and ΔG^≠_E‐T (activation free energy of transition state formation) obtained for the immobilized enzyme decreased in comparison to those obtained for the free enzyme. On the other hand, the value of ΔG^≠_ES (free energy of substrate binding) was observed to have increased. These results indicate an increase in the spontaneity of the biochemical reaction post immobilization. Enthalpy value of immobilized enzyme that was 2.2‐fold increased over the free enzyme indicated lower energy for the formation of the transition state, and increased ΔS^≠ value implied that the immobilized form of the enzyme was more ordered than its free form.     

Fitting protein-folding free energy landscape for a certain conformation to an NK fitness landscape

The NK fitness landscape is a mathematical landscape model with a parameter k that governs the degree of ruggedness of the landscape. We presented a procedure to fit a given landscape to the NK fitness landscape by introducing the “apparent k-value” k_app. In this paper, we defined the protein free energy (ΔG) landscape in amino acid sequence space, where ΔG is the folding free energy from a random coil to a “certain conformation”. Applying this landscape to our fitting procedure, we examined the statistical properties of the landscape. For calculation of a conformation energy, amino acid residues are represented by points, and interaction energies among amino acid residues are given as (1+K)-body interactions, that is, an unit of interacting (1+K) residues cooperatively contribute a single energy value to the conformational energy. Our results suggest that the apparent k-value of the free energy landscape is k_app≈K, and that the number of possible interactions among residues is unrelated to the k_app value. This leads to the inference that k_app takes values about 1-3 in real landscapes, if nature adopts two-body ∼four-body interaction energies.     

Insight into the binding modes and inhibition mechanisms of adamantyl-based 1,3-disubstituted urea inhibitors in the active site of the human soluble epoxide hydrolase

Soluble epoxide hydrolase (sEH) is a promising new target for treating hypertension and inflammation. Considerable efforts have been devoted to develop novel inhibitors. In this study, the binding modes and interaction mechanisms of a series of adamantyl-based 1,3-disubstituted urea inhibitors were investigated by molecular docking, molecular dynamics simulations, binding free energy calculations, and binding energy decomposition analysis. Based on binding affinity, the most favorable binding mode was determined for each inhibitor. The calculation results indicate that the total binding free energy (ΔG_TOT, the sum of enthalpy ΔG_MM-GB/SA, and entropy ?TΔS) presents a good correlation with the experimental inhibitory activity (IC₅₀, r²?=?.99). The van der Waals energy contributes most to the total binding free energy (ΔG_TOT). A detailed discussion on the interactions between inhibitors and those residues located in the active pocket is made based on hydrogen bond and binding modes analysis. According to binding energy decomposition, the residues Asp333 and Trp334 contribute the most to binding free energy in all systems. Furthermore, Hip523 plays a major role in determining this class of inhibitor-binding orientations. Combined with the results of hydrogen bond analysis and binding free energy, we believe that the conserved hydrogen bonds play a role only in anchoring the inhibitors to the exact site for binding and the number of hydrogen bonds may not directly relate to the binding free energy. The results we obtained will provide valuable information for the design of high potency sEH inhibitors.     

Thermodynamic parameters of stabilization of the Yersinia pestis Caf113-149 subunit in compact form

Several experimental methods (circular dichroism, viscosity, intrinsic fluorescence, and fluorescence labeling) were used to study the conformational folding/unfolding transitions in a compact monomeric form of the Caf1_13-149 subunit under the action of guanidine hydrochloride in the temperature range 5–45°C. It has been shown that transitions always occur between two major states (unfolded and compact). This has made it possible to determine all the main thermodynamic functions that characterize the compact state of the Caf1_13-149 subunit: stability temperature T _m, free energy of stabilization ΔG _st, enthalpy ΔH _tr, and heat capacity jump ΔC in collapse of the structure. These data have been confirmed by an independent experiment on melting of fluorescently labeled protein.     

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 × 10⁻¹⁹ dyne cm², and persistence length, P = 500 Å. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (Δ1) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever Δ1 lies in the transition region. The free energies of the two minima are equal when Δ1_c = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be ΔG_bar = (0.20) k_BT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for Δ1 values in the transition region, and the two minimum mean potential energies are equal when Δ1 = 1.50. At the midpoint writhe, Δ1_c = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) k_BT, and the difference in their entropies is 1.3 k_B. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of Δ1 values from 0.85 to 1.85. The twist energy parameter (E_T), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition. © 1996 John Wiley & Sons, Inc.     

Zinc finger protein binding to DNA: an energy perspective using molecular dynamics simulation and free energy calculations on mutants of both zinc finger domains and their specific DNA bases

Energy calculations based on MM-GBSA were employed to study various zinc finger protein (ZF) motifs binding to DNA. Mutants of both the DNA bound to their specific amino acids were studied. Calculated energies gave evidence for a relationship between binding energy and affinity of ZF motifs to their sites on DNA. ΔG values were ?15.82(12), ?3.66(12), and ?12.14(11.6) kcal/mol for finger one, finger two, and finger three, respectively. The mutations in the DNA bases reduced the value of the negative energies of binding (maximum value for ΔΔG = 42Kcal/mol for F1 when GCG mutated to GGG, and ΔΔG = 22 kcal/mol for F2, the loss in total energy of binding originated in the loss in electrostatic energies upon mutation (r = .98). The mutations in key amino acids in the ZF motif in positions-1, 2, 3, and 6 showed reduced binding energies to DNA with correlation coefficients between total free energy and electrostatic was .99 and with Van der Waal was .93. Results agree with experimentally found selectivity which showed that Arginine in position-1 is specific to G, while Aspartic acid (D) in position 2 plays a complicated role in binding. There is a correlation between the MD calculated free energies of binding and those obtained experimentally for prepared ZF motifs bound to triplet bases in other reports (), our results may help in the design of ZF motifs based on the established recognition codes based on energies and contributing energies to the total energy.     

Determination of stability of the DNA double helix in an aqueous medium

The possibility of determining the free energy of stabilization ΔG₀ of native DNA structure with the help of calorimetric data on heats ΔH of transition from the native to denaturated state is considered. Results of microcalorimetric measurements of heats of denaturation of T₂ phage DNA at, different values of pH and ionic strength of solution are given. Values of free energy of stabilization of the DNA native structure ΔG₀ under various conditions have been obtained. It is shown that under conditions close to physiological ΔG₀ approaches 1200 cal/mole per base pair.     

On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions

This paper describes a methodology to calculate the binding free energy (ΔG) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the binding free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as purely nonpolar entities, and the final complex is then recharged. The total electrostatic free energies of the protein, the ligand, and the complex in water are calculated with the finite difference Poisson-Boltzmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a single alkane/water surface tension coefficient (γ_aw). The loss in backbone and side-chain configurational entropy upon binding is estimated and added to the electrostatic and the nonpolar components of ΔG. The methodology is applied to the binding of the murine MHC class I protein H-2K^b with three distinct peptides, and to the human MHC class I protein HLA-A2 in complex with five different peptides. Despite significant differences in the amino acid sequences of the different peptides, the experimental binding free energy differences (ΔΔG_exp) are quite small (<0.3 and <2.7 kcal/mol for the H-2K^b and HLA-A2 complexes, respectively). For each protein, the calculations are successful in reproducing a fairly small range of values for ΔΔG_calc (<4.4 and <5.2 kcal/mol, respectively) although the relative peptide binding affinities of H-2K^b and HLA-A2 are not reproduced. For all protein-peptide complexes that were treated, it was found that electrostatic interactions oppose binding whereas nonpolar interactions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are generally opposed by increased electrostatic contributions favoring dissociation. The factors that drive the binding of peptides to MHC proteins are discussed in light of our results.     

Conformational transitions of a dipeptide in water: Effects of imposed pathways using umbrella sampling techniques

The free energy difference between two states of a molecular system separated by an energy barrier can generally be computed using the technique of umbrella sampling along a chosen reaction coordinate or pathway. The effect of a particular choice of pathway upon the obtained free energy difference is investigated by molecular dynamics simulation of a model system consisting of a glycine dipeptide in aqueous solution. Two different reaction coordinates connecting the so-called C₅ and C₇ conformations, one involving intramolecular hydrogen bonds and the other involving the peptide ?, ψ angles, are considered. The Gibbs free energy differences ΔG(C₅ – C₇) are small in both cases, 1.5 ± 1 kJ mol^?1 and 2.2 ± 1 kJ mol ^?1, respectively. The two different reaction coordinates yield free energy differences that are identical to within their statistical error. It is found that the exchange of solute–solute, solute–water, and water–water hydrogen bonds involves free energy changes of less than k_BT, which points at the existence of a multitutde of low free energy pathways connecting the C₅ and C₇ dipeptide conformations. © 1994 John Wiley & Sons, Inc.     

Transfer free energies of peptide backbone unit from water to aqueous electrolyte solutions at 298.15 K

Transfer free energies (ΔG_tr) of amino acids from water to aqueous electrolyte solutions have been determined from the solubility measurements, as a function of salt concentration at 298.15 K under atmospheric pressure. The investigated aqueous systems contain amino acids of zwitterionic glycine peptides: glycine (Gly), diglycine (Gly₂), triglycine (Gly₃), and tetraglycine (Gly₄) and cyclic glycylglycine (c(GG)) with an electrolyte compound of potassium chloride (KCl), potassium bromide (KBr) or potassium acetate (KAc). The solubilities of glycine and diglycine in aqueous solution decrease with increasing the concentration of salts (salting-out effect), whereas those of triglycine and tetraglycine increase with increasing the concentration of salts (salting-in effect). Furthermore, salting-in effect was found in aqueous c(GG)/KBr system, while salting-out effect was observed in aqueous c(GG)/KCl or c(GG)/KAc system. The experimental results were used to estimate the transfer free energies (Δg_tr) of the peptide backbone unit (–CH₂CONH–) from water to the aqueous electrolyte solutions. We developed a new trail to determine the activity coefficients (γ) for aqueous and aqueous electrolyte solutions using an activity coefficient model, with which the total contribution of transfer free energy between solute and the solvent was calculated. We compared the difference between neglecting and using the activity coefficients term in predicting ΔG_tr. Since the transfer free energy contribution is negative, interactions between the ionic salts and the peptide backbone unit of zwitterionic glycine peptides are favorable and thus the ionic salts destabilize these amino acids. It was also found that KBr stabilizes c(GG), whereas KCl and KAc destabilize c(GG). These results provide evidence for the existence of interactions between the amide unit and ionic salts, in aqueous solution, which may be of importance in maintaining protein structure as well as in protein–solute and protein–solvent interactions.     

Thermodynamic interaction between urea and the peptide group in aqueous solutions at 25°C

Isopiestic vapor pressure measurements of the ternary systems water + triglycine + urea and water + glycine-L-alanine + urea were made and used to calculate the Gibbs free energy of these systems. Together with recently published analogous results on systems, in which the first solute was glycine or alanine or diglycine, and measurements of the excess enthalpy of all these solutions, it is possible to calculate the Gibbs free energy of transfer and the enthalpy of transfer of the peptide group from water to aqueous urea solutions. The transfer can be described as a binding of urea to the peptide group with ΔG = ?1.85 kJ mol^?1 and ΔH = ?18.7 kJ mol^?1 at 298.1 K.     

Kinetics and thermodynamics of catalysis and thermal inactivation of a novel α-amylase (Tp-AmyS) from Thermotoga petrophila

Abstract

This research is focussed on kinetic, thermodynamic and thermal inactivation of a novel thermostable recombinant α-amylase (Tp-AmyS) from Thermotoga petrophila. The amylase gene was cloned in pHIS-parallel1 expression vector and overexpressed in Escherichia coli. The steady-state kinetic parameters (V_max, K_m, k_cat and k_cat/K_m) for the hydrolysis of amylose (1.39?mg/min, 0.57?mg, 148.6?s^?1, 260.7), amylopectin (2.3?mg/min, 1.09?mg, 247.1?s^?1, 226.7), soluble starch (2.67?mg/min, 2.98?mg, 284.2?s^?1, 95.4) and raw starch (2.1?mg/min, 3.6?mg, 224.7?s^?1, 61.9) were determined. The activation energy (E_a), free energy (ΔG), enthalpy (ΔH) and entropy of activation (ΔS) at 98?°C were 42.9?kJ mol^?1, 74?kJ mol^?1, 39.9?kJ mol^?1 and ?92.3 J mol^?1 K^?1, respectively, for soluble starch hydrolysis. While ΔG of substrate binding (ΔG_E-S) and ΔG of transition state binding (ΔG_E-T) were 3.38 and ?14.1?kJ mol^?1, respectively. Whereas, EaD, Gibbs free energy (ΔG*), increase in the enthalpy (ΔH*) and activation entropy (ΔS*) for activation of the unfolding of transition state were 108, 107, 105?kJ mol^?1 and ?4.1 J mol^?1 K^?1. The thermodynamics of irreversible thermal inactivation of Tp-AmyS revealed that at high temperature the process involves the aggregation of the protein.     

Quantitative estimates of steric effects: Intramolecular strain energy effects on the activation energy for aquation of some trans-dichlorotetraaminecobalt(III) complexes

In an effort to quantitatively estimate steric contributions to the aquation rates of a series of structurally related cobalt(III) tetraamine complexes, strain energy minimization calculations have been performed on the reactant and some plausible transition state structures. Free energies of activation ΔG*_obs, are factored as: ΔG*_obs, = ΔG*_bb + ΔG*_strain + Δ_G*_CF + ΔG*_solvation + … where ΔG*_bb is the free energy change associated with bond breaking, ΔG*_solvation is the solvation free energy difference between the reactant and a proposed transition stare, ΔG*_CF is the difference in crystal field stabilization between the reactant and a proposed transition state, and ΔG*_strain is the strain energy difference between the reactant complex and a proposed transition state. The activation energy for the aquation of a hypothetical ‘strain free’ complex is defined as ΔG*_int and reflects the energy required for the bond breaking step with all other terms. For the cations trans-(RR,SS)-dichloro-1,8- diamino-3,6-diazaoctanecobalt(III)(trans [Co(2,2,2- tet)Cl₂]⁺), trans-(RR,SS)- or trans-(RS)-dichloro-1.9- diamino-3,7-diazanonanecobalt(III)(trans [Co(2,3,2- tet)Cl₂]⁺ and trans-(RS)-dichloro-1,10-diamino-4,7- diazadecanecobalt(III)(trans[Co(3,2,3-tet)Cl₂]⁺) ΔG*_int is found to be a constant 123 kJ/mol. For the trans-dichlorocobalt(III) complexes with the ligands 1,4,7,10-tetraazacyclotridecane([13]-ane-N₄), 1,4,8, 11-tetraazacyclotetradecane([14]-ane-N₄), 1,4,8,12- tetraazacyclopentadecane([15]-ane-N₄) and 1,5,9,13- tetraazacyclohexadecane([16]-ane-N₄), ΔG*_int lies in the range 133–139 kJ/mol.     

Conformational studies on copolymers of L-lysine and L-leucine: circular dichroism and potentiometric titration studies

Conformational aspects of a series of copolymers of L -Leucine and L -leucine [poly-(Lys^xLeu^y)] containing 0 to 0.41 mole fraction L -leucine have been studied by circular dichroism (CD) and potentiometric titration in 0.05M KF solution. CD studies on the α-helical conformation showed a dependence of the magnitude of the CD ellipticity band at 222 nm on copolymer composition; the [θ]₂₂₂ decreasing with higher leucine contents. This was interpreted as the result of an increase of the hydrophobicity of the environment of the amide group due to the presence of the leucyl residues. Values of the Zimm-Rice parameter, σ, for the copolymers were obtained from the potentiometric titrations and used to fit theoretical curves to the experimental data. Using the variation of σ with polymer composition, a value of σ for the leucyl residue was estimated to be 6.3 × 10^?2, assuming independence of σ on the amino acid sequence in the copolymer. The free energy change for the conversion of one mole residue from uncharged helix to uncharged coil, ΔG_hc°, was also obtained from the titration data for each copolymer up to a leucine mole fraction of 0.16; a value of 385 cal mole^?1 was estimated for ΔG_hc° for a leucyl residue. These values for σ and ΔG_hc° are compared with other values in the literature for various amino acid residues obtained from titration and melting curve data.