Thermodynamics of peptide binding to the transporter associated with antigen processing (TAP)

The ATP-binding cassette (ABC) transporter TAP plays an essential role in antigen processing and immune response to infected or malignant cells. TAP translocates proteasomal degradation products from the cytosol into the endoplasmic reticulum, where MHC class I molecules are loaded with these peptides. Kinetically stable peptide-MHC complexes are transported to the cell surface for inspection by cytotoxic T lymphocytes. The transport cycle of TAP is initiated by peptide binding, which is responsible for peptide selection and for stimulation of ATP-hydrolysis and subsequent translocation. Here we have analysed the driving forces for the formation of the peptide-TAP complex by kinetic and thermodynamic methods. First, the apparent peptide association and dissociation rates were determined at various temperatures. Strikingly, very high activation energies for apparent association (E(a)(ass)=106 kJmol(-1)) and dissociation (E(a)(diss)=80 kJmol(-1)) of the peptide-TAP complex were found. Next, the temperature-dependence of the peptide affinity constants was investigated by equilibrium-binding assays. Along with calculations of free enthalpy deltaG, enthalpy deltaH and entropy deltaS, a large positive change in heat capacity was resolved (deltaC degrees =23 kJmol(-1)K(-1)), indicating a fundamental structural reorganization of the TAP complex upon peptide binding. The inspection of the conformational entropy reveals that approximately one-fourth of all TAP residues is rearranged. These thermodynamic studies indicate that at physiological temperature, peptide binding is endothermic and driven by entropy.     

Effects of hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamics of the reconstitution of tuna cytochrome c from two peptide fragments

Two peptide fragments from tuna cytochrome c (cyt c), N-fragment (residues 1-44 containing the heme) and C-fragment (residues 45-103), combine to form a 1:1 fragment complex. This was clearly proved by ion-spray mass spectrometry. It was found from CD and NMR spectra that the structure of the fragment complex formed is similar to that of an intact cyt c, although each isolated fragment itself is unstructured. Binding constants and enthalpies upon the complex formation were directly observed by isothermal titration calorimetry. Thermodynamic parameters (deltaG(o)b, deltaHb, deltaS(o)b, and deltaC(b)p)) associated with the complex formation were determined at various pHs and temperatures. DeltaHb was found to be almost independent of pH values. The change in heat capacity accompanying the complex formation (deltaC(b)p) was directly determined from the temperature dependence of deltaHb. In addition, the change in heat capacity and enthalpy upon tuna cyt c unfolding were determined by differential scanning calorimetry. Thermodynamic parameters for the unfolding/dissociation process of the fragment complex were compared with those for cyt c unfolding at pH 3.9 and 303 K. In a comparison of two unfolding processes, the heat capacity change of each was very close to the other, while both the unfolding enthalpy and entropy of the fragment complex were larger than those of tuna cyt c. These thermodynamic data suggest that the internal interactions between polar groups (hydrogen bonding) and nonpolar groups (van der Waals interactions) are preserved in the fragment complex as well as in the native state of cyt c.     

Determination of thermodynamic parameters of proflavine interaction with ribodinucleoside monophosphates CpG and PpC in an aqueous solution from data of proton magnetic resonance

The temperature dependence of proton chemical shifts of proflavine in solution with isomeric ribodinucleoside monophosphates CpG and GpC has been studied. A scheme of calculation of thermodynamic parameters of dye aggregation and 1 : 1 and 1 : 2 complexes formation with dinucleotides has been proposed. The Gibbs' free energy, enthalpy and entropy of these reactions have been determined. It is concluded that hydrophobic interactions play an important part when 1 : 2 complex of proflavine with ribonucleosides is being formed.     

Studies on the heme environment of horse heart ferric cytochrome c. Azide and imidazole complexes of ferric cytochrome c.

Horse heart ferric cytochrome c was investigated by the following three methods: (I) Light absorption spectrophotometry at 23 degrees C and 77 degrees K; (II) Electron paramagnetic resonance (EPR) spectroscopy at 20 degrees K; (III) Precise equilibrium measurements of ferric cytochrome c with azide and imidazole between 14.43 and 30.90 degrees C. I and II have demonstrated that: (1) Ferric cytochrome c azide and imidazole complexes were in the purely low spin state between 20 degrees K and 23 degrees C; (2) The energy for the three t2g orbitals calculated in one hole formalism shows that azide or imidazole bind to the heme iron in a similar manner to met-hemoglobin azide or imidazole complexes, respectively. III has demonstrated that: (1) The change of standard enthalpy and that of standard entropy were -2.3 kcal/mol and -1.6 cal/mol per degree for the azide complex formation, and -1.4 kcal/mol and 2.9 cal/mol per degree for the imidazole complex formation. (2) A linear relationship between the change of entropy and that of enthalpy was observed for the above data for the cyanide complex formation. The complex formation of ferric cytochrome c was discussed based on the results of X-ray crystallographic studies compared with hemoglobin and myoglobin.     

Rigidification of a flexible protease inhibitor variant upon binding to trypsin

The Tyr35-->Gly replacement in bovine pancreatic trypsin inhibitor (BPTI) has previously been shown to dramatically enhance the flexibility of the trypsin-binding region of the free inhibitor and to destabilize the interaction with the protease by about 3 kcal/mol. The effects of this replacement on the enzyme-inhibitor interaction were further studied here by X-ray crystallography and isothermal titration calorimetry (ITC). The co-crystal structure of Y35G BPTI bound to trypsin was determined using 1.65 A resolution X-ray diffraction data collected from cryopreserved crystals, and a new structure of the complex with wild-type BPTI under the same conditions was determined using 1.62 A data. These structures reveal that, in contrast to the free protein, Y35G BPTI adopts a conformation nearly identical with that of the wild-type protein, with a water-filled cavity in place of the missing Tyr side-chain. The crystallographic temperature factors for the two complexes indicate that the mutant inhibitor is nearly as rigid as the wild-type protein when bound to trypsin. Calorimetric measurements show that the change in enthalpy upon dissociation of the complex is 2.5 kcal/mol less favorable for the complex containing Y35G BPTI than for the complex with the wild-type inhibitor. Thus, the destabilization of the complex resulting from the Y35G replacement is due to a more favorable change in entropy upon dissociation. The heat capacity changes for dissociation of the mutant and wild-type complexes were very similar, suggesting that the entropic effects probably do not arise from solvation effects, but are more likely due to an increase in protein conformational entropy upon dissociation of the mutant inhibitor. These results define the biophysical role of a highly conserved core residue located outside of a protein-binding interface, demonstrating that Tyr35 has little impact on the trypsin-bound BPTI structure and acts primarily to define the structure of the free protein so as to maximize binding affinity.     

Interactions in solution of cobalt(II) and nickel(II) with nicotinamide adenine dinucleotide: a potentiometric and calorimetric study

The equilibrium constants and the thermodynamic parameters enthalpy and entropy of the interaction between Ni(II) and Co(II) with NAD(+) in aqueous solution were determined by calorimetry and potentiometry methods (ionic strength adjusted to 0.1 with sodium nitrate at 25 degrees C). The macrochelation of the systems was also studied. All the data, including the protonation enthalpy data of NAD(+) (very similar to the protonation enthalpy of 5'-AMP) suggest a less restrictive model for the NAD(+) "folded" conformation without intramolecular stacking between the bases, in agreement both with recent theoretical calculations and with the X-ray structure of trimethylene-bisadeninium or the free acid form of NAD(+).     

Kinetic and thermodynamic characterization of HIV-1 protease inhibitors

Interaction kinetic and thermodynamic analyses provide information beyond that obtained in general inhibition studies, and may contribute to the design of improved inhibitors and increased understanding of molecular interactions. Thus, a biosensor-based method was used to characterize the interactions between HIV-1 protease and seven inhibitors, revealing distinguishing kinetic and thermodynamic characteristics for the inhibitors. Lopinavir had fast association and the highest affinity of the tested compounds, and the interaction kinetics were less temperature-dependent as compared with the other inhibitors. Amprenavir, indinavir and ritonavir showed non-linear temperature dependencies of the kinetics. The free energy, enthalpy and entropy (DeltaG, DeltaH, DeltaS) were determined, and the energetics of complex association (DeltaG(on), DeltaH(on), DeltaS(on)) and dissociation (DeltaG(off), DeltaH(off), DeltaS(off)) were resolved. In general, the energetics for the studied inhibitors was in the same range, with the negative free energy change (DeltaG < 0) due primarily to increased entropy (DeltaS > 0). Thus, the driving force of the interaction was increased degrees of freedom in the system (entropy) rather than the formation of bonds between the enzyme and inhibitor (enthalpy). Although the DeltaG(on) and DeltaG(off) were in the same range for all inhibitors, the enthalpy and entropy terms contributed differently to association and dissociation, distinguishing these phases energetically. Dissociation was accompanied by positive enthalpy (DeltaH(off) > 0) and negative entropy (DeltaS(off) < 0) changes, whereas association for all inhibitors except lopinavir had positive entropy changes (DeltaS(on) > 0), demonstrating unique energetic characteristics for lopinavir. This study indicates that this type of data will be useful for the characterization of target-ligand interactions and the development of new inhibitors of HIV-1 protease.     

Ion exchange of amino acids at a natural organic ion exchanger: Thermodynamics and energetics

The thermodynamics and energetics of the ion exchange of four amino acids at a cellulosic ion exchanger have been studied. Experimental work included determination of ion exchange isotherms and the use of high-sensitivity titration microcalorimetry. A rigorous thermodynamic analysis of the data was developed allowing calculation of the standard free energy, the standard enthalpy, and standard entropy of exchange, and also the differential free energy, incremental enthalpy, and incremental entropy of exchange. The results show that the relative contributions of the enthalpy and entropy to the overall free energy differ markedly for the chosen amino acids. The reasons for these differences are analyzed and discussed. A knowledge of these fundamental thermodynamic properties indicates the solution conditions likely to give enhanced affinity of the ion exchanger for selected amino acids. The experimental techniques and analysis procedures developed are generally applicable to ion exchange separations of biomolecules. (c) 1995 John Wiley & Sons, Inc.     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.     

ParDOCK: an all atom energy based Monte Carlo docking protocol for protein-ligand complexes

We report here an all-atom energy based Monte Carlo docking procedure tested on a dataset of 226 protein-ligand complexes. Average root mean square deviation (RMSD) from crystal conformation was observed to be approximately 0.53 A. The correlation coefficient (r(2)) for the predicted binding free energies calculated using the docked structures against experimental binding affinities was 0.72. The docking protocol is web-enabled as a free software at www.scfbio-iitd.res.in/dock.     

Structural prediction of peptides bound to MHC class I

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values < or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values < or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.     

Thermodynamics of the helix-coil transition: Binding of S15 and a hybrid sequence, disulfide stabilized peptide to the S-protein

Pancreatic ribonuclease A may be cleaved to produce two fragments: the S-peptide (residues 1-20) and the S-protein (residues 21-124). The S-peptide, or a truncated version designated as the S15 peptide (residues 1-15), combines with the S-protein to produce catalytically active complexes. The conformation of these peptides and many of their analogues is predominantly random coil at room temperature; however, they populate a significant fraction of helical form at low temperature under certain solution conditions. Moreover, they adopt a helical conformation when bound to the S-protein. A hybrid sequence, disulfide-stabilized peptide (ApaS-25), designed to stabilize the helical structure of the S-peptide in solution, also combines with the S-protein to yield a catalytically active complex. We have performed high-precision titration microcalorimetric measurements to determine the free energy, enthalpy, entropy, and heat capacity changes for the binding of ApaS-25 to S-protein within the temperature range 5-25 degrees C. The thermodynamic parameters for both the complex formation reactions and the helix-to-coil transition also were calculated, using a structure-based approach, by calculating changes in accessible surface area and using published empirical parameters. A simple thermodynamic model is presented in an attempt to account for the differences between the binding of ApaS-25 and the S-peptide. From this model, the thermodynamic parameters of the helix-to-coil transition of S15 can be calculated.     

Elusive affinities

The affinity of two molecules for each other and its temperature dependence are determined by the change in enthalpy, free enthalpy, entropy, and heat capacity upon dissociation. As we know the forces that stabilize-protein–protein or protein–DNA association and the three-dimensional structures of the complex, we can in principle derive values for each one of these parameters. The calculation is done first in gas phase by molecular mechanics, then in solution with the help of hydration parameters calibrated on small molecules. However, estimates of enthalpy and entropy changes in gas phase have excessively large error bars even under the approximation that the components of the complex associate as rigid bodies. No reliable result can be expected at the end. The fit to experimental values derived from binding and calorimetric measurements is poor, except for the dissociation heat capacity. This parameter can be attributed mostly to the hydration step and it correlates with the size of the interface. Many protein–protein complexes have interface areas in the range 1200–2000 Ų and only small conformation changes, so the rigid body approximation applies. It is less generally valid in protein–DNA complexes, which have interfaces covering 2200–3100 Ų, large dissociation heat capacities, and affect both the conformation and the dynamics of their components. © 1995 Wiley-Liss, Inc.     

Slow inhibition of almond beta-glucosidase by azasugars: determination of activation energies for slow binding

The thermodynamic and activation energies of the slow inhibition of almond beta-glucosidase with a series of azasugars were determined. The inhibitors studied were isofagomine ((3R,4R,5R)-3,4-dihydroxy-5-hydroxymethylpiperidine, 1), isogalactofagomine ((3R,4S,5R)-3,4-dihydroxy-5-hydroxymethylpiperidine, 2), (-)-1-azafagomine ((3R,4R,5R)-4,5-dihydroxy-3-hydroxymethylhexahydropyridazine, 3), 3-amino-3-deoxy-1-azafagomine (4) and 1-deoxynojirimycin (5). It was found that the binding of 1 to the enzyme has an activation enthalpy of 56.1 kJ/mol and an activation entropy of 25.8 J/molK. The dissociation of the enzyme-1 complex had an activation enthalpy of -2.5 kJ/mol and an activation entropy of -297 J/molK. It is suggested that the activation enthalpy of association is due to the breaking of bonds to water, while the large negative activation entropy of dissociation is due at least in part to the resolvation of the enzyme with water molecules. For the association of 1 DeltaH(0) is 58.6 kJ/mol and DeltaS(0) is 323.8 J/molK. Inhibitor 3 has an activation enthalpy of 39.3 kJ/mol and an activation entropy of -17.9 J/molK for binding to the enzyme, and an activation enthalpy of 40.8 kJ/mol and an activation entropy of -141.0 J/molK for dissociation of the enzyme-inhibitor complex. For the association of 3 DeltaH(0) is -1.5 kJ/mol and DeltaS(0) is 123.1 J/molK. Inhibitor 5 is not a slow inhibitor, but its DeltaH(0) and DeltaS(0) of association are -30 kJ/mol and -13.1 J/molK. The large difference in DeltaS(0) of association of the different inhibitors suggests that the anomeric nitrogen atom of inhibitors 1-4 is involved in an interaction that results in a large entropy increase.     

Protein docking using surface matching and supervised machine learning

Computational prediction of protein complex structures through docking offers a means to gain a mechanistic understanding of protein interactions that mediate biological processes. This is particularly important as the number of experimentally determined structures of isolated proteins exceeds the number of structures of complexes. A comprehensive docking procedure is described in which efficient sampling of conformations is achieved by matching surface normal vectors, fast filtering for shape complementarity, clustering by RMSD, and scoring the docked conformations using a supervised machine learning approach. Contacting residue pair frequencies, residue propensities, evolutionary conservation, and shape complementarity score for each docking conformation are used as input data to a Random Forest classifier. The performance of the Random Forest approach for selecting correctly docked conformations was assessed by cross-validation using a nonredundant benchmark set of X-ray structures for 93 heterodimer and 733 homodimer complexes. The single highest rank docking solution was the correct (near-native) structure for slightly more than one third of the complexes. Furthermore, the fraction of highly ranked correct structures was significantly higher than the overall fraction of correct structures, for almost all complexes. A detailed analysis of the difficult to predict complexes revealed that the majority of the homodimer cases were explained by incorrect oligomeric state annotation. Evolutionary conservation and shape complementarity score as well as both underrepresented and overrepresented residue types and residue pairs were found to make the largest contributions to the overall prediction accuracy. Finally, the method was also applied to docking unbound subunit structures from a previously published benchmark set.     

Equilibrium thermodynamics of a physiologically-relevant heme-protein complex

We used isothermal titration calorimetry to study the equilibrium thermodynamics for formation of the physiologically-relevant redox protein complex between yeast ferricytochrome c and yeast ferricytochrome c peroxidase. A 1:1 binding stoichiometry was observed, and the binding free energies agree with results from other techniques. The binding is either enthalpy- or entropy-driven depending on the conditions, and the heat capacity change upon binding is negative. Increasing the ionic strength destabilizes the complex, and both the binding enthalpy and entropy increase. Increasing the temperature stabilizes the complex, indicating a positive van't Hoff binding enthalpy, yet the calorimetric binding enthalpy is negative (-1.4 to -6.2 kcal mol(-)(1)). We suggest that this discrepancy is caused by solvent reorganization in an intermediate state. The measured enthalpy and heat capacity changes are in reasonable agreement with the values estimated from the surface area change upon complex formation. These results are compared to those for formation of the horse ferricytochrome c/yeast ferricytochrome c peroxidase complex. The results suggest that the crystal and solution structures for the yeast complex are the same, while the crystal and solution structures for horse cytochrome c/yeast cytochrome c peroxidase are different.     

Thermodynamic analysis of the interaction of prolactin with its receptor in the rabbit mammary-gland microsomes.

The interaction of prolactin (PRL) with its membrane receptor depends markedly on temperature. Thermodynamic parameters for this reaction have been evaluated from data for time-course kinetics and equilibrium binding at multiple temperatures between 19 and 31 degrees C. The free-energy change with temperature and the van't Hoff plot were found to be linear. These suggest that there are minimal structure changes at the PRL-receptor contact site over this temperature range. The positive signs of the entropy and enthalpy of reaction, and of the entropy of activation (delta S++) for association, indicate that the hydrophobic bonding is the most significant force involved in PRL-receptor formation. The delta S++ for dissociation was negative, and the enthalpy of activation for dissociation was about 20.3 kJ.mol-1 larger than that for association, indicating that the PRL-receptor complex is further stabilized by contributions of hydrogen bonds and van der Waals contacts after the initial interaction. The free energy of activation for dissociation, at 25 degrees C was about 2.5-fold larger than that for association. This would cause slow dissociation of PRL from its receptor.     

Thermodynamic characterization of the interaction of human cyclophilin 18 with cyclosporin A

Isothermal titration calorimetry (ITC) was used to investigate thermodynamic parameters of the cyclosporin A (CsA)-cyclophilin 18 (hCyp18) association reaction. We have calculated the thermodynamic parameters (enthalpy, entropy, heat capacity, and free energy of binding) of the CsA/hCyp18 complexation. All but two methods described in the literature underestimate the affinity to hCyp18 of CsA. We found that the association constant (1.1·10⁸ M⁻¹ at 10 °C) of CsA to hCyp18 is in close agreement with the reciprocal of the reported inhibitory constant of the peptidylprolyl cis/trans isomerase activity of hCyp18. Interpretation of the thermodynamic parameters in buffered solution of water, 30% glycerol and D₂O leads to the conclusion that the highly specific binding of CsA to hCyp18 is mainly mediated through hydrogen bonding and to a lesser degree through hydrophobic interaction. Furthermore, the pH dependence of the association constant was determined and analyzed according to a single proton linkage model, resulting in a pK_a value of 5.7 in free hCyp18 and below 4.5 in the CsA complexed form. Titration experiments using different single component buffers possessing different heats of ionization allowed us to estimate that statistically half a proton is transferred upon CsA binding from the binding interface of hCyp18 to the buffer at pH 5.5. No proton transfer was detected at pH 7.5. The thermodynamic results are discussed in relation to the published X-ray and NMR structure of the free and CsA complexed hCyp18.     

Removal of lead from aqueous solutions by agricultural waste maize bran

Maize bran is a low cost biosorbent that has been used for the removal of lead(II) from an aqueous solution. The effects of various parameters such as contact time, adsorbate concentration, pH of the medium and temperature were examined. Optimum removal at 20 degrees C was found to be 98.4% at pH 6.5, with an initial Pb(II) concentration of 100 mg l(-1). Dynamics of the sorption process and mass transfer of Pb(II) to maize bran were investigated and the values of rate constant of adsorption, rate constant of intraparticle diffusion and the mass transfer coefficients were calculated. Different thermodynamic parameters viz., changes in standard free energy, enthalpy and entropy were evaluated and it was found that the reaction was spontaneous and exothermic in nature. The adsorption data fitted the Langmuir isotherm. A generalized empirical model was proposed for the kinetics at different initial concentrations. The data were subjected to multiple regression analysis and a model was developed to predict the removal of Pb(II) from an aqueous solution.