Statistical mechanical deconvolution of thermal transitions in macromolecules. III. Application to double-stranded to single-stranded transitions of nucleic acids

The statistical mechanical deconvolution theory for macromolecular conformational transitions is extended to the case of nucleic acids transitions involving strand separation. It is demonstrated that the partition function, Q, as well as all the relevant thermodynamic quantities of the system, can be calculated from experimental scanning calorimetric data. In particular, it is shown that important thermodynamic parameters such as the size of the average cooperative unit during strand separation, the mean helical segment length, and the mean coil-segment length can be calculated from the average excess enthalpy function 〈ΔH〉. The theory is applied to the double-stranded to single-stranded transition of the system poly(A)·poly(U) at different salt concentrations. It is shown that the mean helical segment length is a monotonically decreasing function of the temperature well before strand separation occurs. On the other hand, the mean coil segment length remains practically constant until temperatures very close to T_m. Both experimental findings clearly indicate that the unfolding of poly(A)·poly(U) proceeds through the formation of many short helical sequences. The cooperative unit for the strand separation is calculated to be about 120 base pairs and essentially independent of the salt concentration. The existence of a minimum helical segment length of 10 ± 2 base pairs within the double-stranded form is calculated.     

Thermodynamic functions of biopolymer hydration. II. Enthalpy–entropy compensation in hydrophilic hydration processes

The thermodynamic functions of biopolymer hydration were investigated by multitemperature vapor pressure studies. Desorption measurements were performed that allowed determination of reversible isotherms in the hydration range of 0.1 to 0.3–0.5 g H₂O/g dry polymer. These isotherms are accessible to thermodynamic interpretation and are relevant to the interaction of water with biopolymers in their solution conformation. The results obtained on a series of different biopolymers (lysozyme, α-chymotrypsin, apo-lactoferrin, and desoxyribonucleic acid), show the following common features of interest: (1) The differential excess enthalpies (ΔH^e ) and entropies (ΔS^e ) are negative, and exhibit pronounced anomalies in a well-defined low-humidity range (approx. 0.1 g H₂O/g dry polymer). These initial extrema are interpretable by structural changes, induced in the native biopolymer structures by water removal below a critical degree of hydration. (2) The ΔH^e and ΔS^e terms exhibit statistically significant linear enthalpy–entropy compensation effects in all biopolymer–water systems investigated. The compensation temperatures \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \beta = \overline {\Delta H} ^e /\overline {\Delta S} ^e $\end{document} are approximately identical for all biopolymers, ranging from 360 to 500 K. The compensation effects are attributable to phase transitions of water molecules between the bulk liquid and the inner-sphere hydration shell of native biopolymers. (3) The negative excess free energies (ΔG^e ) decrease monotonically with increasing water content and are close to zero at 0.3 to 0.5 g H₂O/g polymer. This result indicates that only transitions between the bulk liquid and the inner-sphere hydration shell are associated with significant net free energy effects. The outer-sphere hydration water is thermodynamically comparable to bulk water. The importance of the proportionality factor \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \beta $\end{document} in the control of the free energy term is discussed.     

Application of the nearest-neighbor Ising model to the helix-coil transition of polypeptides in mixed organic solvents.

Using the formalism of nearest-neighbor Ising model and assuming that the allowed states for a monomeric unity of a polypeptide chain in solutions containing strong acids are E (helix), C (coil), and CS (solvent-bonded coil), the partition function of the system was deduced analytically. Equations were obtained which permitted the prediction of the characteristic thermodynamic behavior of the helix–coil transition under these conditions. These equations were used to examine critically the possible correlations between experimental data obtained using different techniques. Particular attention was devoted to quantities called “transition enthalpies,” obtained from the slope of the transition curves at the point where the helix fraction is one-half (ΔH), or for measurements of the heat of solution of the polymer over the total range of solvent composition (ΔH), or from heat capacity measurements taken at various temperatures (ΔH). Literature data of ΔH(j = opt, sol, cal) for the system poly-γ-benzyl-L -glutamate in mixtures of dichloroacetic acid and 1,2-dichloroethane were carefully analyzed.     

Determination of thermodynamic functions from scanning calorimetry data. II. For the system that includes self-dissociation / association process

The basic relations between the molar fractions and the scanning calorimetry data for the system that includes self-dissociation/association process such as are presented, where m_i is the stoichiometric coefficient of the ith state A_i. The relations are described for each state j as where f_j(T) is the molar fraction function of state j and ΔH_j(T) is the difference enthalpy function of the system referred to the state j, which can be obtained by scanning calorimetry; R is the gas constant; and T is the absolute temperature. By these relations, scanning calorimetry data can be deconvoluted in order to determine the thermodynamic functions by means of single and double deconvolution. The concentration dependence of the data is analyzed by a method presented in this paper. The nonlinear least squares fitting method for the determination of the functions is discussed. For an example of the application of this method to the actual scanning calorimetry data, thermodynamic data of multistate thermal transition of Vibrio parahaemolyticus hemolysin are analyzed.     

Prodigiosin-25 C

The equilibrium constant of the isomerization reaction between d-glucose and d-fructose which is catalyzed by a. glucose isomerase from Streptomyces sp. was obtained by both methods of chemical analysis and of kinetic study over the temperature range of 25° to 70°C.

It was found that the formation of d-fructose from d-glucose was an endothermic reaction with the heat of the reaction, ΔH, of +2220 cal/mole. The standard free energy change, ΔG, and the standard entropy change, ΔS, associated with the isomeric change were found to be +180 cal/mole and + 6.8 cal/deg. mole at 25°C, respectively. The values of these thermodynamic quantities at other temperature are also summarized.     

Mean-square hydrophobic moment for partially helical polypeptides

A mean-square helical hydrophobic moment, 〈h²〉, is defined for polypeptides in analogy to the mean-square dipole moment, 〈μ²〉, for polymer chains. For a freely jointed polymer chain, 〈μ²〉 is given by Σm, where m_i denotes the dipole moment associated with bond i. In the absence of any correlations in the hydrophobic moments of individual amino acid residues in the helix, 〈h²〉 is specified by ΣH, where H_i denotes the hydrophobicity of residue i. The tendency for correlations in orientations of residue hydrophobic moments in helices therefore dictates the size of 〈h²〉/〈H²〉, where 〈H²〉 denotes the average value of ΣH for all helices. The value of 〈h²〉/〈H²〉 will be greater than one in amphiphilic helices. A necessary prerequisite for this diagnostic usage of 〈h²〉/〈H²〉 is that the residue hydrophobic moment be oriented prependicular to the principal axis of the helix. Matrix-generation schemes are formulated that permit rapid evaluation of 〈h²〉 and 〈H²〉. The behavior of 〈h²〉/〈H²〉 is illustrated by calculations performed for model sequential copolypeptides.     

Probing the Energetics of Antigen–Antibody Recognition by Titration Microcalorimetry

Our understanding of the energetics that govern antigen–antibody recognition lags behind the increasingly rapid accumulation of structural information on antigen–antibody complexes. Thanks to the development of highly sensitive microcalorimeters, the thermodynamic parameters of antigen–antibody interactions can now be measured with precision and using only nanomole quantities of protein. The method of choice is isothermal titration calorimetry, in which a solution of the antibody (or antigen) is titrated with small aliquots of the antigen (or antibody) and the heat change accompanying the formation of the antigen–antibody complex is measured with a sensitivity as high as 0.1 μcal s⁻¹. The free energy of binding (ΔG), the binding enthalpy (ΔH), and the binding entropy (ΔS) are usually obtained from a single experiment, and no spectroscopic or radioactive label must be introduced into the antigen or antibody. The often large and negative change in heat capacity (ΔC_p) accompanying the formation of an antigen–antibody complex is obtained from ΔHmeasured at different temperatures. The basic theory and the principle of the measurements are reviewed and illustrated by examples. The thermodynamic parameters relate to the dynamic physical forces that govern the association of the freely moving antigen and antibody into a well-structured and unique complex. This information complements the static picture of the antigen–antibody complex that results from X-ray diffraction analysis. Attempts to correlate dynamic and static aspects are discussed briefly.     

Kinetic and Equilibrium Studies on d-Mannose-d-Fructose Isomerization Catalyzed by Mannose Isomerase from Streptomyces aerocolorigenes

The equilibrium constant of the isomerization reaction between d-mannose and d-fructose which is catalyzed by a mannose isomerase from Streptomyces aerocolorigenes was obtained by using three methods over the temperature range from 1 to 40°C.

It was found that the equilibrium constant was scarcely dependent on temperature, ΔH, the heat of the formation of d-fructose from d-mannose, being approximately zero.

The standard free energy change, ΔG, and the standard entropy change, ΔS, of the reaction were calculated from the equilibrium constants at various temperatures and ΔH. The values of ΔG and ΔS at 25°C were ?650 cal/mole and + 2.2 cal/deg·mole, respectively.

By combining these thermodynamic data with those obtained for the isomerization reaction between d-glucose and d-fructose reported in the previous paper, ΔH, ΔG and ΔS for the isomerization between d-mannose and d-glucose were indirectly obtained to be +2220 cal/mole, +830 cal/mole and +4.6 cal/deg·mole at 25°C, respectively.     

Thermodynamics of gelation of sickle cell deoxyhemoglobin.

This paper describes the thermodynamic behavior of gels of deoxyhemoglobin S. The solubility of the protein with respect to assembled hemoglobin fibers has been measured using a sedimentation technique. The solubility in 0.15 m-potassium phosphate buffer (pH 7.15) is found to decrease with increasing temperature, attain a minimum value of 0.16 g cm^?3 at 37 °C, and then increase at higher temperatures. The amount of polymer present at various hemoglobin concentrations and temperatures is presented as part of a phase diagram that may be useful for the calibration of other measurement techniques. The effects of varying pH and urea concentration upon the solubility have also been studied.The heat absorption accompanying gelation has been measured by scanning calorimetry. Using sedimentation data on the amount of polymer formed, molar enthalpy changes are obtained. There is a large negative heat capacity change of ? 197 cal deg. mol^?1 and ΔH = 0 near 37 °C. Calorimetric molar enthalpy changes are found to agree with those calculated from the temperature dependence of the solubility by the van't Hoff equation.Our previous two-phase, two-component thermodynamic model of gelation is extended to include the effects of solution non-ideality. A large contribution to the activity of the hemoglobin in the solution phase results from the geometric effect of excluded volume. Incorporating solution phase non-ideality permits the calculation of standard state thermodynamic quantities for the gelation process at 37 °C: ΔG^O ? ?3 k cal mol^?1, ΔH^O ~ 0, ΔS^O ~ 10 cal deg.^?1 mol^?1. The excluded volume effect is also capable of explaining observations of the minimum gelling concentrations of hemoglobin mixtures containing deoxyhemoglobin S without requiring copolymerization of the non-S hemoglobin.     

Transition temperature and enthalpy change dependence on stabilizing and destabilizing ions in the helix–coil transition in native tendon collagen

The transition temperatures t_t and enthalpy changes ΔH in the helix–coil transition of solid tendon collagen soaked in a solution containing one of the following stabilizing or destabilizing agents, HCHO, NaF, NaCl, NaI, NaBr, NaOH, NH₂CONH₂, CaCl₂, MgCl₂, were measured as a function of molar concentration by a calorimetric method. The temperature and the enthalpy changes accompanying the transition behaved in a similar manner: when the t_t was depressed by the presence of ions, similar behaviour was observed in ΔH. Both parameters (t_t and ΔH) increased for HCHO, and decreased for NaF and NaCl at concentrations lower than 0.2 M. Above 0.2 M they increased for NaF and NaCl, and decreased in the presence of the other reagents listed above. The average t_t and the ΔH observed in collagen soaked in water were 63.5°C and 12.3 cal/g, respectively. In addition to the parameters mentioned above, the molar effectiveness of the various reagents was obtained for the cases where there was a linear relationship between the t_t and molar concentration of the reagent in the solution. Since both the t_t and the ΔH were observed to vary, the entropy change (ΔS) accompanying the transition was calculated using thermodynamic relations. In order to explain the ΔS observed as a function of ionic concentration, the thermodynamic relationships have been obtained from a partition function under suitable assumptions. Since the partition function is dependent on the number of hydrogen bonds responsible for collagen stability, the result obtained has been compared with the values predicted by the two most quoted models for collagen. The present study is in accordance with the Ramachandran model for collagen structure, which predicts more than one hydrogen bond per three residues.     

Characterization of group C meningococcal polysaccharide by light-scattering spectroscopy. III. Determination of molecular weight, radius of gyration, and translational diffusional coefficient.

Group-specific polysaccharides isolated by means of a cetavlon procedure are immunogenic in man and induce protective immunity against meningococcal meningitis. Minute quantities of the polymers in solution can act as vaccines. We now report the first characterization of a fractionated (C-1) group C polysaccharide in 0.4KM KCl and 0.05M sodium acetate by means of light-scattering spectroscopy. Independent measurements of refractive index increments, absolute scattered intensities, angular scattering intensities and line widths as a function of scattering angles and delay times at different concentrations using incident wavelengths of 632.8 nm from a He–Ne laser and of 488 nm from an argon–ion laser yield information on aggregation properties, molecular weight (M_r), radius of gyration 〈r⁰_g〉^1/2_z, translational diffusion coefficient 〈D〉⁰_z, and second virial coefficients A₂ and B₂ of C-1 polysaccharide. At relatively high ionic strength (0.04M KCl + 0.05M sodium acetate), we obtain for the C-1 polysaccharide in solution M_r = 5.15 × 10⁵, 〈r²_g〉^1/2_z = 345 Å, A₂ = 1.25 × 10^?4 ml/g, 〈D〉 = 1.16 × 10^?7 cm²/sec with a corresponding Stokes radius of 240 Å and B₂ = 4.4 ml/g. A₂ and B₂ are the second virial coefficients from intensity- and diffusion-coefficient measurements. The C-1 polysaccharide aggregates in solution and behaves hydrodynamically like random coils. Viscosity and sedimentation studies further confirm our conclusions that the fractioned C-1 polysaccharide aggregates in solution and EDTA can partially break up those aggregates. However, the system remains polydisperse even after adding an excess amount of EDTA. The weight-average molecular weight of the C-1 polysaccharide in solution depends upon ionic strength and exhibits a minimum at ～0.2M KCl. Finally, viscosity, light-scattering, and sedimentation results all show that the aggregated macromolecular system behaves like random-coiled polymers with no measurable shape factors.     

Thermodynamic stability of bovine α-crystallin in its interactions with other bovine crystallins

Light scattering measurements were performed on dilute solutions of α-crystallin mixed with different combinations of β_H, β_L and γ-fractions of bovine lens crystallins. Light scattering intensities were obtained as a function of scattering angle, concentration and temperature. The temperature dependence of the second virial coefficients was used to obtain partial molar enthalpy and end entropy of solutions. The difference between the thermodynamic parameters of the crystallin mixtures and those of the weighted averages of the individual components yielded the excess enthalpy and entropy functions of the solutions. Both the excess enthalpy and entropy functions indicated that thermodynamic stability of α-crystallin is progressively enhanced by its interactions with γ(β_H+γ)(β_H+β_L+γ) crystallins. The last two combinations showed negative values both for excess enthalpy as well for excess entropy of solutions. Other combinations demonstrated increasing positive values. This implies that the combination of all four crystallins in the vertebrate lens enables the best solvation property as well as the best packing as opposed to any other single or combinatorial arrangements of crystallins. Similar conclusions have been obtained in the past from water and other vapor sorption studies.     

Thermodynamic descriptors,profiles and driving forces in membrane receptor-ligand interactions

Extension of the (isothermal) Gibbs–Helmholtz equation for the heat capacity terms (ΔC_p) allows formulating a temperature function of the free (Gibbs) energy change (ΔG). An approximation of the virtually unknown ΔC_p temperature function enables then to determine and numerically solve temperature functions of thermodynamic parameters ΔH and ΔS (enthalpy and entropy change, respectively). Analytical solutions and respective numeric procedures for several such approximation formulas are suggested in the presented paper. Agreement between results obtained by this analysis with direct microcalorimetric measurements of ΔH (and ΔC_p derived from them) was approved on selected cases of biochemical interactions presented in the literature. Analysis of several ligand-membrane receptor systems indicates that temperature profiles of ΔH and ΔS are parallel, largely not monotonic, and frequently attain both positive and negative values within the current temperature range of biochemical reactions. Their course is determined by the reaction change of heat capacity: temperature extremes (maximum or minimum) of both ΔH and ΔS occur at ΔC_p?=?0, for most of these systems at roughly 285–305 K. Thus, the driving forces of these interactions may change from enthalpy-, entropy-, or enthalpy-entropy-driven in a narrow temperature interval. In contrast, thermodynamic parameters of ligand-macromolecule interactions in solutions (not bound to a membrane) mostly display a monotonic course. In the case of membrane receptors, thermodynamic discrimination between pharmacologically defined groups—agonists, partial agonists, antagonists—is in general not specified and can be achieved, in the best, solely within single receptor groups.     

Effect of inhibitor complex formation on the hydration properties of alpha-chymotrypsin. Changes induced in protein hydration by toxylation of the native enzyme

The effect of enzyme-inhibitor complex formation on the hydration properties of the macromolecular moiety was investigated on the model system of α-chymotrypsin and its Ser-195 tosyl derivative. The primary (A-shell) hydration of the native and modified enzyme was compared by sorption measurements. The secondary (B-shell) hydration water was investigated by differential scanning calorimetry. Tosylation is known to induce pronounced conformational changes in the chymotrypsin molecule. These structural modifications have the following effects on the hydration of the native enzyme. The water binding capacity of the protein surface is significantly increased, as shown by both the calorimetric and the sorption results. The amount of unfreezable water of primary hydration is increased by 50 mol H₂O/mol chymotrypsin. The heats (ΔH ) and entropies (ΔS ) of the interaction of water with chymotrypsin are strongly reduced in the modified enzyme. This effect is interpretable by a reduction of the H bonding potential of the protein surface. Parallel to this decrease in δH , the heats of fusion of the secondary hydration water (Q_fus) are significantly increased by tosylation (Q_fus = 256.2 ± 7.8 and 294.2 ± 4.8 J g^?1 H₂O for the native and the tosylated enzyme, respectively). This increase in Q_fus reflects an increase in the extent of H bonding in the B-shell hydration sphere. These changes in the hydration of the native enzyme, associated with the reaction: native chymotrypsin → tosylchymotrypsin, are interpreted by cooperative phase transitions of water molecules in the primary and secondary hydration water. One of these transitions was found to exhibit a significant, linear enthalpy–entropy compensation effect. The compensation temperature \documentclass{article}\pagestyle{empty}\begin{document}$ \hat{\beta} $\end{document} is 290.7 ± 2.8°K. This \documentclass{article}\pagestyle{empty}\begin{document}$ \hat{\beta} $\end{document} value agrees well with compensation temperatures reported in the literature for a series of biochemical reactions in aqueous solution (250–320° K). This agreement in \documentclass{article}\pagestyle{empty}\begin{document}$ \hat{\beta} $\end{document} may point to a common source of both compensation phenomena.     

The stability of Taq DNA polymerase results from a reduced entropic folding penalty; identification of other thermophilic proteins with similar folding thermodynamics

The thermal stability of Taq DNA polymerase is well known, and is the basis for its use in PCR. A comparative thermodynamic characterization of the large fragment domains of Taq (Klentaq) and E. coli (Klenow) DNA polymerases has been performed by obtaining full Gibbs‐Helmholtz stability curves of the free energy of folding (ΔG) versus temperature. This analysis provides the temperature dependencies of the folding enthalpy and entropy (ΔH and ΔS), and the heat capacity (ΔC_p) of folding. If increased or enhanced non‐covalent bonding in the native state is responsible for enhanced thermal stabilization of a protein, as is often proposed, then an enhanced favourable folding enthalpy should, in general, be observed for thermophilic proteins. However, for the Klenow–Klentaq homologous pair, the folding enthalpy (ΔH_fold) of Klentaq is considerably less favorable than that of Klenow at all temperatures. In contrast, it is found that Klentaq's extreme free energy of folding (ΔG_fold) originates from a significantly reduced entropic penalty of folding (ΔS_fold). Furthermore, the heat capacity changes upon folding are similar for Klenow and Klentaq. Along with this new data, comparable extended analysis of available thermodynamic data for 17 other mesophilic–thermophilic protein pairs (where enough applicable thermodynamic data exists) shows a similar pattern in seven of the 18 total systems. When analyzed with this approach, the more familiar “reduced ΔC_p mechanism” for protein thermal stabilization (observed in a different six of the 18 systems) frequently manifests as a temperature dependent shift from enthalpy driven stabilization to a reduced‐entropic‐penalty model. Proteins 2014; 82:785–793. © 2013 Wiley Periodicals, Inc.     

Theoretical Aspects of Differential Scanning Calorimetry as a Tool for the Studies of Equilibrium Thermodynamics in Pharmaceutical Solid Phase Transitions

Although differential scanning calorimetry (DSC) is a non-equilibrium technique, it has been used to gain energetic information that involves phase equilibria. DSC has been widely used to characterize the equilibrium melting parameters of small organic pharmaceutical compounds. An understanding of how DSC measures an equilibrium event could make for a better interpretation of the results. The aim of this mini-review was to provide a theoretical insight into the DSC measurement to obtain the equilibrium thermodynamics of a phase transition especially the melting process. It was demonstrated that the heat quantity obtained from the DSC thermogram (ΔH) was related to the thermodynamic enthalpy of the phase transition (ΔH ^P ) via: ΔH?=?ΔH ^P /(1?+?K ^??1) where K was the equilibrium constant. In melting, the solid and liquefied phases presumably coexist resulting in a null Gibbs free energy that produces an infinitely larger K. Thus, ΔH could be interpreted as ΔH ^P. Issues of DSC investigations on melting behavior of crystalline solids including polymorphism, degradation impurity due to heating in situ, and eutectic melting were discussed. In addition, DSC has been a tool for determination of the impurity based on an ideal solution of the melt that is one of the official methods used to establish the reference standard.     

A study of the growth of normal and iodinated collagen fibrils in vitro using electron microscope autoradiography

Electron microscopic autoradiographic observations on collagen fibrils grown in vitro allow growth rates in the N- and C-terminal directions to be measured on individual fibrils. Such observations, made on normal and iodinated collagen, show that normal fibrils grow at both ends (although rather more rapidly at the N-terminal end), whereas fully-iodinated collagen fibrils grow only at the N-terminal end. Measurements of growth rates at different temperatures provide estimates of the activation enthalpy (ΔH^≠) and entropy (ΔS^≠) of precipitation for the two types of collagen. Solubility measurements have also yielded values for the thermodynamic enthalpy (ΔH) and entropy (ΔS) of precipitation. Results show that the activated (rate-limiting) state is characterized by a large positive ΔH^≠ and ΔS^≠ similar in magnitude to the ΔH and ΔS of transition from solution to fibril. It is also concluded that the different rates of precipitation of normal and iodinated collagen cannot be explained in terms of fibril formation requiring ionization of the tyrosine residues.     

Thermodynamics of partitioning of substance P in isotropic bicelles

The temperature dependence of the partition of a neuropeptide, substance P (SP), in isotropic (q = 0.5) bicelles was investigated by using pulsed field gradient NMR diffusion technique. The partition coefficient decreases as the temperature is increased from 295 to 325 K, indicating a favorable (negative) enthalpy change upon partitioning of the peptide. Thermodynamic analysis of the data shows that the partitioning of SP at 300 K is driven by the enthalpic term (ΔH) with the value of ? 4.03 kcal mol^?1, while it is opposed by the entropic term (?TΔS) by approximately 1.28 kcal mol^?1 with a small negative change in heat capacity (ΔC_p). The enthalpy‐driven process for the partition of SP in bicelles is the same as in dodecylphosphocholine (DPC) micelles, however, the negative entropy change in bicelles of flat bilayer surface is in sharp contrast with the positive entropy change in DPC micelles of highly curved surface, indicating that the curvature of the membrane surface might play a significant role in the partitioning of peptides. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

Spectroscopic Investigation of the Interaction Between Copper (II) 2-oxo-propionic Acid Salicyloyl Hydrazone Complex and Bovine Serum Albumin

The interaction between copper (II) 2-oxo-propionic acid salicyloyl hydrazone (Cu^IIL) and bovine serum albumin (BSA) under physiological conditions was investigated by the methods of fluorescence spectroscopy, UV-Vis absorption, and circular dichroism spectroscopy. Fluorescence data showed that the fluorescence quenching of BSA by Cu^IIL was the result of the formation of the BSA–Cu^IIL complex. The apparent binding constants (K _a) between Cu^IIL and BSA at four different temperatures were obtained according to the modified Stern–Volmer equation. The thermodynamic parameters, enthalpy change (ΔH) and entropy change (ΔS), for the reaction were calculated to be ?80.79 kJ mol^?1 and ?175.48 J mol^?1 K^?1 according to van’t Hoff equation. The results indicated that van der Waals force and hydrogen bonds were the dominant intermolecular force in stabilizing the complex. The binding distance (r) between Cu^IIL and the tryptophan residue of BSA was obtained to be 4.1 nm according to Förster’s nonradioactive energy transfer theory. The conformational investigation showed that the application of Cu^IIL increased the hydrophobicity of amino acid residues and decreased the α-helical content of BSA (from 62.71% to 37.31%), which confirmed some microenvironmental and conformational changes of BSA molecules.