An in situ Infrared Spectroscopic Study of Glutamic Acid and of Aspartic Acid Adsorbed on TiO(2): Implications for the Biocompatibility of Titanium

In situ ATR-IR spectroscopy has been applied to the study of glutamic (Glu) and aspartic (Asp) acid adsorbed on amorphous TiO(2) particle films. Unlike Asp, which gives evidence of one major adsorbed species, Glu yields several spectroscopically distinct structures upon adsorption to TiO(2). The pH dependence of Glu and Asp adsorption is also different, with Glu adsorbing markedly to TiO(2) at pH where electrostatic interactions between the surface and adsorbate are unfavorable. Application of the Langmuir model to adsorption isotherms yields a single binding constant for Asp and two binding constants for Glu, further supporting the evidence for different adsorbed Glu species. This is the first investigation of the molecular structure of Glu and Asp species adsorbed on amorphous TiO(2) using in situ ATR-IR spectroscopy. Copyright 2000 Academic Press.     

Vibrational spectroscopic studies on fibrinogen adsorption at polystyrene/protein solution interfaces: hydrophobic side chain and secondary structure changes

Structural changes of fibrinogen after adsorption to polystyrene (PS) were examined at the PS/protein solution interface in situ using sum frequency generation (SFG) vibrational spectroscopy and attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR). Different behaviors of hydrophobic side chains and secondary structures of adsorbed fibrinogen molecules have been observed. Our results indicate that upon adsorption, the hydrophobic PS surface induces fast structural changes of fibrinogen molecules by aligning some hydrophobic side chains in fibrinogen so that they face to the surface. Such structural changes of fibrinogen hydrophobic side chains are local changes and do not immediately induce significant changes of the protein secondary structures. Our research also shows that the interactions between adsorbed fibrinogen and the PS surface can induce significant changes of protein secondary structures or global conformations which occur on a much longer time scale.     

Amino acid adsorption on mesoporous materials: influence of types of amino acids, modification of mesoporous materials, and solution conditions

In order to disclose the dominant interfacial interaction between amino acids and ordered mesoporous materials, the adsorption behaviors of five amino acids on four mesoporous materials were investigated in aqueous solutions with adjustable amino acid concentration, ion strength, and pH. The selected amino acids were acidic amino acid glutamic acid (Glu), basic amino acid arginine (Arg), and neutral amino acids phenylalanine (Phe), leucine (Leu), and alanine (Ala), and the selected mesoporous materials were SBA-15, Al-SBA-15, CH3(10%)-SBA-15, and CH3(20%)-SBA-15. The adsorption capacities of Glu and Arg were strongly dependent on pH and surface charge of the mesoporous adsorbent. The adsorption of Phe showed pH insensitivity but depended on the surface organic functionalization of mesoporous adsorbent. On the basis of the theoretical analysis about the interaction between amino acid and adsorbent, such a remarkable difference was attributed to the different nature of the interaction between amino acid and adsorbent. Arg could be readily adsorbed on the surface of SBA-15, especially Al-SBA-15, under appropriate pH in which the electrostatic interaction was predominant. The driving force of Phe adsorption on mesoporous adsorbent mainly came from the hydrophobic interaction. Therefore, the adsorption capability of Arg decreased with increasing ion strength of solution, while the adsorption capability of Phe increased with the increasing degree of CH3 functionalization on SBA-15. For neutral amino acid Phe, Ala, and Leu, the adsorption capability increased with the increase of the length of their side chains, which was another evidence of hydrophobic effect. Thus, all the adsorption of amino acids on mesoporous silica materials can be decided by the combined influence of two fundamental interactions: electrostatic attraction and hydrophobic effect.     

Exploring the inter-molecular interactions in amyloid-β protofibril with molecular dynamics simulations and molecular mechanics Poisson-Boltzmann surface area free energy calculations

Aggregation of amyloid-β (Aβ) peptides correlates with the pathology of Alzheimer's disease. However, the inter-molecular interactions between Aβ protofibril remain elusive. Herein, molecular mechanics Poisson-Boltzmann surface area analysis based on all-atom molecular dynamics simulations was performed to study the inter-molecular interactions in Aβ(17-42) protofibril. It is found that the nonpolar interactions are the important forces to stabilize the Aβ(17-42) protofibril, while electrostatic interactions play a minor role. Through free energy decomposition, 18 residues of the Aβ(17-42) are identified to provide interaction energy lower than -2.5 kcal/mol. The nonpolar interactions are mainly provided by the main chain of the peptide and the side chains of nine hydrophobic residues (Leu17, Phe19, Phe20, Leu32, Leu34, Met35, Val36, Val40, and Ile41). However, the electrostatic interactions are mainly supplied by the main chains of six hydrophobic residues (Phe19, Phe20, Val24, Met35, Val36, and Val40) and the side chains of the charged residues (Glu22, Asp23, and Lys28). In the electrostatic interactions, the overwhelming majority of hydrogen bonds involve the main chains of Aβ as well as the guanidinium group of the charged side chain of Lys28. The work has thus elucidated the molecular mechanism of the inter-molecular interactions between Aβ monomers in Aβ(17-42) protofibril, and the findings are considered critical for exploring effective agents for the inhibition of Aβ aggregation.     

Study of cetyltrimethylammonium and cetylpyridinium adsorption on montmorillonite

Adsorption of cetyltrimethylammonium (CTA) and cetylpyridinium (CP) onto Na-rich montmorillonite (MMT) was studied. For this purpose, the adsorption isotherms of CTA and CP, along with desorption curves of metal cations (Na+, K+, Ca2+, Mg2+), were obtained by means of capillary isotachophoresis and atomic absorption spectrometry. Infrared, X-ray diffraction pattern, specific surface area, porosity, and moisture adsorption measurements of montmorillonite revealed that CTA and CP were adsorbed in monolayer arrangements. CTA is assumed to be attached to the negatively charged MMT surface mainly by electrostatic forces. On the other hand, CP, adsorbed in higher amounts, can be additionally bound via other interactions of pyridinium rings, such as induced and pi-pi interactions. By the surfactant adsorption, the montmorillonite surface became hydrophobic and its micro- and mesopores were significantly diminished. Using scanning electron microscopy, aggregation of such organically modified MMT particles was observed.     

Adsorption of different amphiphilic molecules onto polystyrene latices

In order to know the influence of the surface characteristics and the chain properties on the adsorption of amphiphilic molecules onto polystyrene latex, a set of experiments to study the adsorption of ionic surfactants, nonionic surfactants and an amphiphilic synthetic peptide on different latex dispersions was performed. The adsorbed amount versus the equilibrium surfactant concentration was determined. The main adsorption mechanism was the hydrophobic attraction between the nonpolar tail of the molecule and the hydrophobic regions of the latex surface. This attraction overcame the electrostatic repulsion between chains and latex surface with identical charge sign. However, the electrostatic interactions chain-surface and chain-chain also played a role. General patterns for the adsorption of ionic chains on charged latex surfaces could be established. Regarding the shape, the isotherms presented different plateaus corresponding to electrostatic effects and conformational changes. The surfactant size also affects the adsorption results: the higher the hydrophilic moiety in the surfactant molecule the lower the adsorbed amount.     

Conformational relaxation and water penetration coupled to ionization of internal groups in proteins

Molecular dynamics simulations were used to examine the effects of ionization of internal groups on the structures of eighteen variants of staphylococcal nuclease (SNase) with internal Lys, Asp, or Glu. In most cases the RMSD values of internal ionizable side chains were larger when the ionizable moieties were charged than when they were neutral. Calculations of solvent-accessible surface area showed that the internal ionizable side chains were buried in the protein interior when they were neutral and moved toward crevices and toward the protein-water interface when they were charged. The only exceptions are Lys-36, Lys-62, and Lys-103, which remained buried even after charging. With the exception of Lys-38, the number of internal water molecules surrounding the ionizable group increased upon charging: the average number of water oxygen atoms within the first hydration shell increased by 1.7 for Lys residues, by 5.2 for Asp residues, and by 3.2 for Glu residues. The polarity of the microenvironment of the ionizable group also increased when the groups were charged: the average number of polar atoms of any kind within the first hydration shell increased by 2.7 for Lys residues, by 4.8 for Asp residues, and by 4.0 for Glu residues. An unexpected correlation was observed between the absolute value of the shifts in pK(a) values measured experimentally, and several parameters of structural relaxation: the net difference in the polarity of the microenvironment of the charged and neutral forms of the ionizable groups, the net difference in hydration of the charged and neutral forms of the ionizable groups, and the difference in RMSD values of the charged and neutral forms of the ionizable groups. The effects of ionization of internal groups on the conformation of the backbone were noticeable but mostly small and localized to the area immediately next to the internal ionizable moiety. Some variants did exhibit local unfolding.     

Selective Desorption of Intercalated Bovine Serum Albumin and Lysozyme by Organically Modified Montmorillonite

The organically modified montmorillonite (M‐Mt) was applied as an adsorbent for the purification of bovine serum albumin (BSA). In order to differentiate the selectivity and perform the purification of BSA, two kinds of proteins, BSA and lysozyme (LYZ) were mixed together and prepared at different pH, which could change the electrical charges on the surfaces of the proteins. BSA and LYZ can be adsorbed at the lower pH into the organically modified montmorillonite, which could be confirmed by powder X‐ray diffraction (XRD) in the d‐value increased after the adsorption of proteins. However, there is only BSA desorption was observed, approved by the method of Sodium dodecyl sulfate (SDS)‐polyacrylamide gel electrophoresis (PAGE), from this adsorbed protein mixture when the pH of the solution was adjusted and optimized. These results indicate that there is electrostatic interaction between a suitably modified montmorillonite and proteins BSA and LYZ to perform the selective desorption from BSA in the mixture of these proteins.     

Interactions between hydrophobic and ionic solutes in aqueous guanidinium chloride and urea solutions: lessons for protein denaturation mechanism

In order to clarify the mechanism of denaturant-induced unfolding of proteins we have calculated the interactions between hydrophobic and ionic species in aqueous guanidinium chloride and urea solutions using molecular dynamics simulations. Hydrophobic association is not significantly changed in urea or guanidinium chloride solutions. The strength of interaction between ion pairs is greatly diminished by the guanidinium ion. Although the changes in electrostatic interactions in urea are small, examination of structures, using appropriate pair functions, of urea and water around the solutes show strong hydrogen bonding between urea's carbonyl oxygen and the positively charged solute. Our results strongly suggest protein denaturation occurs by the direct interaction model according to which the most commonly used denaturants unfold proteins by altering electrostatic interactions either by solvating the charged residues or by engaging in hydrogen bonds with the protein backbone. To further validate the direct interaction model we show that, in urea and guanidinium chloride solutions, unfolding of an unusually stable helix (H1) from mouse PrPC (residues 144-153) occurs by hydrogen bonding of denaturants to charged side chains and backbone carbonyl groups.     

Adsorption of Bovine Serum Albumin and Lysozyme on Hydrophobic Calcium Hydroxyapatites

The adsorption of bovine serum albumin (BSA) and lysozyme (LSZ) to oleyl phosphate(OP)-grafted calcium hydroxyapatite (OP-CaHAP) with different degrees of hydrophobicity, ranging the number of surface oleyl group per unit nm2 (nO) from 0 to 2.60, was investigated. The pronounced effects of the hydrophobic moiety of adsorbent on protein adsorption were observed. The saturated amount of adsorbed BSA (ns) was increased up to nO = 0.6 by an enlargement of hydrophobic interaction between hydrophobic CaHAP particle and proteins. However, ns decreased at nO >/= 1.3 by increasing the electrostatic repulsive force between negatively charged BSA and OP-CaHAP particles. On the other hand, the ns value of LSZ was continuously increased up to nO = 2.0 and saturated by increasing either the hydrophobic interaction or the electrostatic attraction of positively charged LSZ and negatively charged OP-grafted CaHAPs. The BSA adsorption experiment revealed that the effect of positively charged adsorption sites on the exposed ac or bc crystal faces (C-sites) of the CaHAPs is screened by the OP-groups grafted on their particle surfaces. Copyright 1999 Academic Press.     

Study of hydrophobic interaction adsorption of bovine serum albumin under overloaded conditions using flow microcalorimetry

The adsorption behavior of bovine serum albumin (BSA) on a Sepharose based hydrophobic interaction support has been studied. Flow microcalorimetry has been used to determine the heat of adsorption under overloaded chromatographic conditions. These data have been complemented with capacity factor and isotherm measurements to provide insight on the mechanisms of adsorption. The heat of adsorption data have confirmed that the hydrophobic interaction adsorption of BSA under linear isotherm conditions is driven by entropy changes. Under overloaded (non-linear) conditions, however, it has been shown that the changes in enthalpy can drive adsorption; this behavior is not evident from analyses of capacity factor data. It is postulated that for BSA adsorption on the Sepharose derivative of interest, attractive force interactions between adsorbed protein molecules drive the adsorption process under overloaded conditions in a high (NH4)2SO4 environment. It is further postulated that these interactions are due to a change in confirmation of the adsorbed protein under these conditions.     

Adsorption of BSA on the amphiphilic PEG graft copolymer-coated particles

The amphiphilic copolymers comprising several monomethoxy poly(ethylene glycol) (mPEG) and lauryl side chains were prepared and coated on the polystyrene (PS) particles to study the interactions between these particles and bovine serum albumin (BSA). The surface mPEG density and mPEG chain length were the primary parameters of interest. A significant fraction of the graft copolymer was washed away from the particle surface during five cycles of centrifugation-dispersion treatment, especially for the one with the smallest number of lauryl side chains. At pH 5, the BSA adsorption data did not follow the Langmuir isotherm model for the graft copolymer-modified particles. This was attributed to the presence of a surface mPEG layer that severely retarded the approach of BSA to the particle. The amount of the adsorbed BSA decreased with increasing the surface mPEG density. A mechanistic model was proposed to qualitatively describe the adsorption of BSA on the mPEG-containing particles and the native particles as well.     

Amphiphilic derivatives of dextran: adsorption at air/water and oil/water interfaces

Ionic amphiphilic dextran derivatives were synthesized by the attachment of sodium sulfopropyl and phenoxy groups on the native polysaccharide. A family of dextran derivatives was thus obtained with varying hydrophobic content and charge density in the polymer chains. The surface-active properties of polymers were studied at the air-water and dodecane-water interfaces using dynamic surface/interfacial tension measurements. The adsorption was shown to begin in a diffusion-limited regime at low polymer concentrations, that is to say, with the diffusion of macromolecules in the bulk solution. In contrast, at long times the interfacial adsorption is limited by interfacial phenomena: adsorption kinetics or transfer into the adsorbed layer. A semiempirical equation developed by Filippov was shown to correctly fit the experimental curves over the whole time range. The presence of ionic groups in the chains strongly lowers the adsorption kinetics. This effect can be interpreted by electrostatic interactions between the free molecules and the already adsorbed ones. The adsorption kinetics at air-water and oil-water interfaces are compared.     

VEGFR-2 与抑制剂Sunitinib 的分子对接及分子动力学研究

用分子对接方法研究了VEGFR-2 和抑制剂Sunitinib 的相互作用模式, 并对其复合物进行了10 ns 的分子动力学(Molecular Dynamics, MD)模拟. 结果表明, 抑制剂Sunitinib 能与VEGFR-2 中位于活性空腔的Glu885, Ile888, His1026,Asp1028, Asp1046 五个氨基酸残基形成疏水作用; 另外, VEGFR-2 中His1026, Cys1024, Asp1046 三个氨基酸残基能与Sunitinib 形成三个作用强度不同的氢键. 这些基团之间的相互作用是Sunitinib 抑制VEGFR-2 活性的关键因素. 研究结果可为VEGFR-2 抑制剂的结构改良、分子设计、合成提供理论参考, 并有助于寻找活性更高、效果更好的抗肿瘤药物.     

Adsorption behavior of Pb(II) on montmorillonite

The present work investigated the adsorption and desorption behaviors of Pb(II) on montmorillonite. The adsorption experiments were carried out using batch process. The results show that the adsorption is dependent on the pH value of the medium, and the uptake of Pb(II) increases with the pH increasing in the pH range of 2.0–10.0. The adsorption kinetics is in better agreement with pseudo-second order kinetics, and the adsorption data is a good fit with Langmuir isotherm. The presence of EDTA may result in a decrease of the amount of Pb(II) adsorbed. The presence of electrolyte and EDTA may enhance the desorption of Pb(II) ions adsorbed. The adsorption mechanism of Pb(II) on montmorillonite may be explained in two aspects: the chemical binding between Pb(II) ions and surface hydroxyl groups; and the electrostatic binding between Pb(II) ions and the permanent negatively charged sites of montmorillonite.     

Effect of electrostatic interaction on the adsorption of globular proteins on octacalcium phosphate crystal film

The electrostatic effect on the adsorption of globular proteins, such as bovine serum albumin (BSA), hen egg white lysozyme (LZM), and beta-lactoglobulin (beta-Lg), on octacalcium phosphate (OCP)-like crystal thin films was investigated. A poorly crystalline thin film was synthesized on a tissue culture polystyrene (TCP) surface and used as a model surface in this study. The solution pH clearly affected the electrostatic properties of both proteins and surface. The adsorbed amounts obtained at quasi-steady state were readily related to the solution pH for each protein. The adsorption rate is fast during the initial period and levels off gradually. The maximum adsorbed mass occurred at pH 7 for BSA and at pH 9 for LZM. beta-Lg adsorbed similar amounts at pHs lower than 9, but the adsorbed mass decreased at pHs higher than 9 where electrostatic repulsion exists. The pH values where the maximum adsorbed mass occurred may be considered as the conditions where electrostatic attraction is most favorable. The adsorbed mass of beta-Lg was the greatest among the proteins of interest while BSA adsorbed the least despite its greater molecular mass. LZM falls into the intermediate region. According to these observations, BSA has undergone conformational changes that prevent further adsorption to a greater extent than the others. A simple relationship between the adsorption rate and the electrostatic properties was not established. However, the order of magnitude of the adsorption rate at the initial period tends to be the same as that of maximum adsorbed mass for each protein.     

Conformational changes of α-lactalbumin adsorbed at oil-water interfaces: interplay between protein structure and emulsion stability

The conformation and structural dimensions of α-lactalbumin (α-La) both in solution and adsorbed at oil-water interfaces of emulsions were investigated using synchrotron radiation circular dichroism (SRCD) spectroscopy, front-face tryptophan fluorescence (FFTF) spectroscopy, and dual polarization interferometry (DPI). The near-UV SRCD and the FFTF results demonstrated that the hydrophobic environment of the aromatic residues located in the hydrophobic core of native α-La was significantly altered upon adsorption, indicating the unfolding of the hydrophobic core of α-La upon adsorption. The far-UV SRCD results showed that adsorption of α-La at oil-water interfaces created a new non-native secondary structure that was more stable to thermally induced conformational changes. Specifically, the α-helical conformation increased from 29.9% in solution to 45.8% at the tricaprylin-water interface and to 58.5% at the hexadecane-water interface. However, the β-sheet structure decreased from 18.0% in solution to less than 10% at both oil-water interfaces. The DPI study showed that adsorption of α-La to a hydrophobic C18-water surface caused a change in the dimensions of α-La from the native globule-like shape (2.5-3.7 nm) to a compact/dense layer approximately 1.1 nm thick. Analysis of the colloidal stability of α-La stabilized emulsions showed that these emulsions were physically stable against droplet flocculation at elevated temperatures both in the absence and in the presence of 120 mM NaCl. In the absence of salt, the thermal stability of emulsions was due to the strong electrostatic repulsion provided by the adsorbed α-La layer, which was formed after the adsorption and structural rearrangement. In the presence of salt, although the electrostatic repulsion was reduced via electrostatic screening, heating did not induce strong and permanent droplet flocculation. The thermal stability of α-La stabilized emulsions in the presence of salt is a combined effect of the electrostatic repulsion and the lack of covalent disulfide interchange reactions. This study reports new information on the secondary and tertiary structural changes of α-La upon adsorption to oil-water interfaces. It also presents new results on the physical stability of α-La stabilized emulsions during heating and at moderate ionic strength (120 mM NaCl). The results broaden our understanding of the factors controlling protein structural change at emulsion interfaces and how this affects emulsion stability.     

Surface-induced unfolding of human lactoferrin

We have determined the structural conformations of human lactoferrin adsorbed at the air/water interface by neutron reflectivity (NR) and its solution structure by small angle neutron scattering (SANS). The neutron reflectivity measurements revealed a strong structural unfolding of the molecule when adsorbed at the interface from a pH 7 phosphate buffer solution (PBS with a total ionic strength at 4.5 mM) over a wide concentration range. Two distinct regions, a top dense layer of 15-20 angstroms on the air side and a bottom diffuse layer of some 50 angstroms into the aqueous subphase, characterized the unfolded interfacial layer. At a concentration around 1 g dm(-3), close to the physiological concentration of lactoferrin in biological fluids, the adsorbed amount was 5.5 x 10(-8) mol m(-2) in the absence of NaCl, but the addition of 0.3 M NaCl reduced protein adsorption to 3.5 x 10(-8) mol m(-2). Although the polypeptide distributions at the interface remained similar, quantitative analysis showed that the addition of NaCl reduced the layer thickness. Parallel measurements of lactoferrin adsorption in D2O instead of null reflecting water confirmed the unfolded structure at the interface. Furthermore, the D2O data indicated that the polypeptide in the top layer was predominantly protruded out of water, consistent with it being hydrophobic. In contrast, the scattering intensity profiles from SANS were well described by a cylindrical model with a diameter of 47 angstroms and a length of 105 angstroms in the presence of 0.3 M NaCl, indicating a retention of the globular framework in the bulk solution. In the absence of NaCl but with the same amount of phosphate buffer, the length of the cylinder increased to some 190 angstroms and the diameter remained constant. The length increase is indicative of changes in distance and orientation between the bilobal monomers due to the change in charge interactions. The results thus demonstrate that the surface structural unfolding was caused by the exposure of the protein molecule to the unsymmetrical energetic balance following surface adsorption.     

Quantification of binary diffusion in protein crystals

The use of confocal laser scanning microscopy for visualization and quantification of binary diffusion within anisotropic porous material is described here for the first time. The dynamics of adsorption profiles of dianionic fluorescein, zwitterionic rhodamine B, and their mixture in the cationic native orthorhombic lysozyme crystal were subsequently analyzed. All data could be described by a classical pore diffusion model. There was no change in the adsorption characteristics, but diffusion decreased with the introduction of a second solute in the solution. It was found that diffusion is determined by the combination of steric and electrostatic interactions,while adsorption is dependent on electrostatic and hydrophobic interactions. Thus, it was established that the outcome of binary transport depends on the solute, protein, and crystal characteristics.     

Effects of pH on protein association: modification of the proton-linkage model and experimental verification of the modified model in the case of cytochrome c and plastocyanin.

Effects of pH on protein association are not well understood. To understand them better, we combine kinetic experiments, calculations of electrostatic properties, and a new theoretical treatment of pH effects. The familiar proton-linkage model, when used to analyze the dependence of the association constant K on pH, reveals little about the individual proteins. We modified this model to allow determination not only of the numbers of the H+ ions involved in the association but also of the pK(a) values, in both the separate and the associated proteins, of the side chains that are responsible for the dependence of K on pH. Some of these side chains have very similar pK(a) values, and we treat them as a group having a composite pK(a) value. Use of these composite pK(a) values greatly reduces the number of parameters and allows meaningful interpretation of the experimental results. We experimentally determined the variation of K in the interval 5.4 < or = pH < or = 9.0 for four diprotein complexes, those that the wild-type cytochrome c forms with the wild-type plastocyanin and its mutants Asp42Asn, Glu59Gln, and Glu60Gln. The excellent fittings of the experimental results to the modified model verified this model and revealed some unexpected and important properties of these prototypical redox metalloproteins. Protein association causes a decrease in the pK(a) values of the acidic side chains and an increase in the pK(a) values of the basic side chains. Upon association, three carboxylic side chains in wild-type plastocyanin each release a H+ ion. These side chains in free plastocyanin have an anomalously high composite pK(a) value, approximately 6.3. Upon association, five or six side chains in cytochrome c, likely those of lysine, each take up a H+ ion. Some of these side chains have anomalously low pK(a) values, less than 7.0. The unusual pK(a) values of the residues in the recognition patches of plastocyanin and cytochrome c may be significant for the biological functions of these proteins. Although each mutation in plastocyanin markedly, and differently, changed the dependence of K on pH, the model consistently gave excellent fittings. They showed decreased numbers of H+ ions released or taken up upon protein association and altered composite pK(a) values of the relevant side chains. Comparisons of the fitted composite pK(a) values with the theoretically calculated pK(a) values for plastocyanin indicated that Glu59 and Asp61 in the wild-type plastocyanin each release a H+ ion upon association with cytochrome c. Information of this kind cannot readily be obtained by spectroscopic methods. Our modification of the proton-linkage model is a general one, applicable also to ligands other than H+ ion and to processes other than association.