Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

Study of the photocycle and charge motions of the bacteriorhodopsin mutant D96N.

Absorption kinetic and electric measurements were performed on oriented purple membranes of D96N bacteriorhodopsin mutant embedded in polyacrylamide gel and the kinetic parameters of the photointermediates determined. The rate constants, obtained from fits to time-dependent concentrations, were used to calculate the relative electrogenicity of the intermediates. The signals were analyzed on the basis of different photocycle models. The preferred model is the sequential one with reversible reaction. To improve the quality of the fits the necessity of introducing a second L intermediate arose. We also attempted to interpret our data in the view of reversible reactions containing two parallel photocycles, but the pH dependencies of the rate constants and electrogenicities favored the model containing sequential reversible transitions. A fast equilibrium for the L2<==>M1 transition and a strong pH dependence of the M2 electrogenicity was found, indicating that the M1 to M2 transition involves complex charge motions, as is expected in a conformational change of the protein.     

Electric signals during the bacteriorhodopsin photocycle, determined over a wide pH range.

From the electric signals measured after photoexcitation, the electrogenicity of the photocycle intermediates of bacteriorhodopsin were determined in a pH range of 4.5-9. Current measurements and absorption kinetic signals at five wavelengths were recorded in the time interval from 300 ns to 0.5 s. To fit the data, the model containing sequential intermediates connected by reversible first-order reactions was used. The electrogenicities were calculated from the integral of the current signal, by using the time-dependent concentrations of the intermediates, obtained from the fits. Almost all of the calculated electrogenicities were pH independent, suggesting that the charge motions occur inside the protein. Only the N intermediate exhibited pH-dependent electrogenicity, implying that the protonation of Asp96, from the intracellular part of the protein, is not from a well-determined proton donor. The calculated electrogenicities gave good approximations of all of the details of the measured electric signals.     

Activation parameters for the halorhodopsin photocycle: a phase lifetime spectroscopic study of the 520- and 640-nanometer intermediates

Phase lifetime spectroscopy is used to investigate the kinetics of the 520- and 640-nm intermediates in the halorhodopsin photocycle. These intermediates decay on the millisecond time scale and are strongly implicated in the chloride transport steps. The temperature dependence of the 520 and 640 relaxations was measured for chloride and nitrate buffers at pH 6, 7, and 8 and for iodide buffer at pH 6. The 640 relaxations have small activation energies but large entropy barriers. The two relaxation times observed for the 640 intermediate were interpreted by using a mechanism in which two 640 species exist in equilibrium. The second 640 species is not along the main decay path for the photocycle. A quantitative analysis of the data allowed rate constants and activation parameters to be calculated for the elementary steps of this isomerization process. These parameters are similar for both chloride and nitrate buffers but differ somewhat in iodide. The derived calculated rate constants were consistent with the relaxation times observed for the 520 intermediate. These results indicate that the 520 and two 640 intermediates have very similar free energies as well as similar free energies of activation for the various interconversion processes.     

Thermodynamic parameters for salt‐induced reversible protein precipitation from automated microscale experiments

Reversible precipitation can be used as an efficient purification tool for proteins. In addition, identifying conditions under which precipitation or aggregation occurs is of key importance in the bioprocessing and pharmaceutical industry, as this can aid in better formulations and hinder aggregation in chromatography. We have evaluated the precipitation of proteins as determined by light scattering in microplates as a tool for the high‐throughput determination of thermodynamic parameters for protein precipitation, with the potential for screening of formulation additives and relevant bioprocess conditions such as pH. This provides a useful complementary technique to existing microplate‐based protein thermostability measurements. Using hen egg‐white lysozyme and alcohol dehydrogenase as model proteins we have determined the extent of reversible precipitation as a function of ammonium sulfate and sodium chloride concentrations, and also demonstrated global fitting of the data to generate a model where the fraction precipitated can be predicted for any given condition. The global fit provided thermodynamic parameters, including the free energy for protein precipitation, and also allowed an approximate determination of the average size of the structural nucleus that contributes to the free energy of precipitation for each protein. The rapid collection of thermodynamic parameters for protein precipitation, in parallel with protein thermostability measurements, will provide a powerful platform for protein formulation, and also lead to datasets useful for testing theoretical predictions of reversible precipitation based on the molecular modeling of specific protein structure interactions. Biotechnol. Bioeng. 2011;108: 322–332. © 2010 Wiley Periodicals, Inc.     

Adsorption Optimization of Lead (II) Using Saccharum Bengalense as a Non-Conventional Low Cost Biosorbent: Isotherm and Thermodynamics Modeling

In the present study a novel biomass, derived from the pulp of Saccharum bengalense, was used as an adsorbent material for the removal of Pb (II) ions from aqueous solution. After 50 minutes contact time, almost 92% lead removal was possible at pH 6.0 under batch test conditions. The experimental data was analyzed using Langmuir, Freundlich, Timken and Dubinin-Radushkevich two parameters isotherm model, three parameters Redlich—Peterson, Sip and Toth models and four parameters Fritz Schlunder isotherm models. Langmuir, Redlich—Peterson and Fritz-Schlunder models were found to be the best fit models. Kinetic studies revealed that the sorption process was well explained with pseudo second-order kinetic model. Thermodynamic parameters including free energy change (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°) have been calculated and reveal the spontaneous, endothermic and feasible nature of the adsorption process. The thermodynamic parameters of activation (ΔG ^#, ΔH ^#and ΔS ^#) were calculated from the pseudo-second order rate constant by using the Eyring equation. Results showed that Pb (II) adsorption onto SB is an associated mechanism and the reorientation step is entropy controlled.     

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.     

Binding of reduced and oxidized nicotinamide adenine dinucleotide to pig heart supernatant malate dehydrogenase.

The association reactions of NADH and NAD+ with dimeric pig heart supernatant malate dehydrogenase (s-MDH) have been measured at pH 6 and 8 by calorimetric and fluorescence methods, and the thermodynamic parameters describing these reactions have been evaluated. Coenzyme binding is associated with the uptake of 0.55 mol of H+/mol of NADH at pH 8 and 0.19 mol of H+ at pH 6. No significant effect of NAD+ binding on proton binding was observed. Increase in ionic strength strongly affects the free energies of binding of NAD+ and NADH. No cooperativity was observed in the enthalpy or free energy changes for binding of NAD+ or NADH. The differences in free energy of binding of NAD+ and NADH and the effect of pH on binding of NADH are entropy based. These effects are interpreted as reflecting a small number of interactions within the active site that are predominantly ionic.     

Photoacoustic spectroscopy of bacteriorhodopsin photocycle

Photoacoustic spectroscopy was applied to study the energetics and the kinetics of the slow intermediates of the bacteriorhodopsin photocycle. An analysis of the modulation frequency dependence of the photoacoustic signal allowed us to estimate the enthalpy changes and the kinetic parameters associated with those intermediates. The effects of pH, salt concentration, and protein aggregation were studied. Three photoacoustic transitions were found. The two low frequency transitions were attributed to O660 and M412, respectively. The third transition was interpreted as resulting from a protein conformational change undetected spectrophotometrically. The frequency spectra were simulated between 5 and 180 Hz at pH's 5.1, 7.0, and 8.9 assuming a branching in the bacteriorhodopsin photocycle at the M412 level. The enthalpy changes associated with M412 and O660 were computed and compared with the experimental values.     

Linkage of proton binding to the thermal dissociation of triple helix complex

The effects of cytosine protonation on the thermodynamic properties of parallel pyrimidine motif DNA triplex were investigated and characterized by different techniques, such as circular dichroism (CD), ultraviolet spectroscopy (UV) and differential scanning calorimetry (DSC). A thermodynamic model was developed which, by linking the cytosine ionization equilibrium to the dissociation process of the triplex, is able to rationalize the experimental data and to reproduce the pH dependence of the free energy, enthalpy and entropy changes associated with the triplex formation. The results are useful to systematically introduce the effect of pH in a more general model able to predict the stability of DNA triplexes on the basis of the sequence alone.     

Thermodynamics and energy coupling in the bacteriorhodopsin photocycle

Time-resolved absorption changes of photoexcited bacteriorhodopsin were measured with a gated multichannel analyzer between 100 ns and 100 ms at six temperatures between 5 and 30 degrees C. The energetics of the chromophore reaction cycle were analyzed on the basis of a model containing a single cycle and reversible reactions. The calculated thermodynamic parameters provide insights to general principles of the active transport. They indicate that in this light-driven proton pump the free energy is retained after absorption of the photon as the enthalpy of the pKa shift in the chromophore which allows deprotonation of the Schiff base. Part of the excess free energy is dissipated at the "switch" step where the reaction and transport cycles are coupled, and the rest at the chromophore recovery step. All other reactions take place near equilibrium. The "switch" step is the M1----M2 transition in the reaction cycle [Váró, G., & Lanyi, J. K. (1991) Biochemistry (preceeding paper in this issue)]. It provides for return of the chromophore pKa to its initial value so the Schiff base will become a proton acceptor, for reordering access of the Schiff base from one side of the membrane to the other, and for unidirectionality of the proton transfer. Conformational energy of the protein, acquired during the "switch" step, drives the completion of the photocycle.     

Folding and stability of trp aporepressor from Escherichia coli

Equilibrium and kinetic studies of the urea-induced unfolding of trp aporepressor from Escherichia coli were performed to probe the folding mechanism of this intertwined, dimeric protein. The equilibrium unfolding transitions at pH 7.6 and 25 degrees C monitored by difference absorbance, fluorescence, and circular dichroism spectroscopy are coincident within experimental error. All three transitions are well described by a two-state model involving the native dimer and the unfolded monomer; the free energy of folding in the absence of denaturant and under standard-state conditions is estimated to be 23.3 +/- 0.9 kcal/mol of dimer. The midpoint of the equilibrium unfolding transition increases with increasing protein concentration in the manner expected from the law of mass action for the two-state model. We find no evidence for stable folding intermediates. Kinetic studies reveal that unfolding is governed by a single first-order reaction whose relaxation time decreases exponentially with increasing urea concentration and also decreases with increasing protein concentration in the transition zone. Refolding involves at least three phases that depend on both the protein concentration and the final urea concentration in a complex manner. The relaxation time of the slowest of these refolding phases is identical with that for the single phase in unfolding in the transition zone, consistent with the results expected for a reaction that is kinetically reversible. The two faster refolding phases are presumed to arise from slow isomerization reactions in the unfolded form and reflect parallel folding channels.     

Combined optical and photoelectric study of the photocycle of 13-cis bacteriorhodopsin.

The photocycle of the 13-cis retinal containing bacteriorhodopsin was studied by three different techniques. The optical multichannel analyzer monitored the spectral changes during the photocycle and gave information about the number and the spectrum of the intermediates. The absorption kinetic measurements provided the possibility of following the absorbance changes at several characteristic wavelengths. The electric signal provided information about the charge motions during the photocycle. The results reveal the existence of two intermediates in the 13-cis photocycle, one with a short lifetime having an average of 1.7 microseconds and an absorption maximum at 620 nm. The other, a long-living intermediate, has a lifetime of about 50 ms and an absorption maximum around 585 nm. The data analysis suggests that these intermediates are in two parallel branches of the photocycle, and branching from the intermediate with the shorter lifetime might be responsible for the light-adaptation process.     

Unfolding free energy changes determined by the linear extrapolation method. 2. Incorporation of delta G degrees N-U values in a thermodynamic cycle

The linear extrapolation method was used to evaluate the unfolding free energy changes (delta G degrees N-U) for phenylmethanesulfonyl chymotrypsin (PMS-Ct) at pH 6.0. The nonlinear least-squares fits of difference spectral data using urea and guanidinium chloride as denaturants gave identical values for delta G degrees N-U and delta epsilon degrees U, the latter being extinction coefficient differences between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of these parameters from the nature of solvent suggests strongly that they are characteristic properties of the protein alone. The delta G degrees N-U data at pH 6.0 and 4.0, which differ by more than 100-fold in stability of the protein, were incorporated into a thermodynamic cycle involving free energy changes for titration of native and unfolded PMS-Ct from pH 4.0 to 6.0. The purpose of the cycle was to test whether delta G degrees N-U obtained by use of the linear extrapolation method exhibits the characteristics required of a thermodynamic function of state. Within error, the thermodynamic cycle was found to accommodate the delta G degrees N-U quantities obtained at pH 4.0 and 6.0 for PMS-Ct.     

Compensational phenomena in reactivation of dimethyl- and diethylphosphoryl butyrylcholinesterases.

The thermodynamic and kinetic parameters for spontaneous and oxime reactivation of dimethyl- and diethylphosphoryl butyrylcholinesterases (acylcholine acyl-hydrolase, EC 3.1.1.8) are reported. The enthalpy and entropy changes in both the binding (deltaH0 and deltaS0) and the dephosphorylation steps (deltaH* and deltaS*) were found to be coupled, resulting in a minor variation in free energy changes (deltaG0 and deltaG*). While neither enthalpies nor entropies alone bore any relationship with the kinetic parameters KD and kR, the changes of free energies (deltaG0 and deltaG*) correlated linearly with the logarithmic values of the dissociation constants (KD) and bimolecular rate constants (kR/KD), respectively. Compensation plots of entropies versus enthalpies gave straight lines with compensation temperatures of 275 K for the binding 260 K for the dephosphorylation. Spontaneous reactivation of dimethyl phosphoryl butyrylcholinesterase was investigated at various pH values and three temperatures. It implicated two catalytic sites with values of pKi of 9.4 and 7.5, and heats of ionisation of 5.3 and 9.6 kcal - mol-1, respectively. Possible conformational alteration of the inhibited enzyme arising from the binding of oximes is discussed.     

Porcine beta-lactoglobulin chemical unfolding: identification of a non-native alpha-helical intermediate

The chemical unfolding behavior of porcine beta-lactoglobulin (PLG) has been followed at pH 2 and 6 in the presence of guanidinium hydrochloride. The PLG unfolding transition, monitored by tryptophan fluorescence, far and near UV circular dichroism and 1D-NMR, can be described by a three-state transition suggesting the presence of at least one intermediate state that appears to display an excess of non-native alpha-helical structures. The thermodynamic parameters, as determined through a global analysis fitting procedure, give estimates of the free energy differences of the transitions connecting the native, the intermediate and the unfolded state: DeltaG(NI) (0) = 2.8 +/- 0.7 kcal mol(-1) (pH 2) and 4.2 +/- 0.5 kcal mol(-1) (pH 6) and DeltaG(NU) (0) = 7.2 +/- 0.6 kcal mol(-1) (pH 2) and 6.9 +/- 0.6 kcal mol(-1) (pH 6). CD unfolding data of the bovine species (BLG) have been collected here under the same experimental conditions of PLG to allow a careful comparison of the two beta-lactoglobulins. Intermediates with different characteristics have been identified for BLG and PLG, and their nature has been discussed on a structural analysis basis. The thermodynamic data reported here for PLG and BLG and the comparative analysis with data reported for equine beta lactoglobulin, show that homologous beta-barrel proteins, belonging to the same family and displaying high sequence identity (52-64%) populate unfolding intermediates to different extents, even though a common tendency to the formation of non-native alpha-helical intermediates, can be envisaged. The present results provide a prerequisite foundation of knowledge for the design and interpretation of future folding kinetic studies.     

Enhanced thermodynamic stability of beta-lactoglobulin at low pH. A possible mechanism.

The thermodynamic stability of beta-lactoglobulin (beta-Lg) was studied at acidic and near-neutral pH values using equilibrium thermal-unfolding measurements. Transition temperature increased with a decrease in pH from 7.5 to 6.5 and 3.0 to 1.5, suggesting an increase in the net protein stability. Determination of the change in free energy of unfolding and extrapolation into the nontransition region revealed that beta-Lg increases its stability by increasing the magnitude of the change in free energy of unfolding at the temperature of maximum stability, as well as by increasing the temperature of maximum stability. The relative difference in the change in free energy of unfolding at 70 degrees C (with a reference pH of 7.5) was positive and its magnitude increased with a decrease in pH from 7.0 to 1.5 van't Hoff plots of thermal unfolding of beta-Lg at all pH values studied were non-linear and the measured changes in the enthalpy and entropy of unfolding for beta-Lg were high and positive. The relative magnitude of change of both enthalpy and entropy at 70 degrees C (compared with pH 7.5) increased with a decrease in pH up to 1.5. A possible mechanism for the increased stability of beta-Lg at low pH is discussed.     

Photoreactions of bacteriorhodopsin at acid pH.

It has been known that bacteriorhodopsin, the retinal protein in purple membrane which functions as a light-driven proton pump, undergoes reversible spectroscopic changes at acid pH. The absorption spectra of various bacteriorhodopsin species were estimated from measured spectra of the mixtures that form at low pH, in the presence of sulfate and chloride. The dependency of these on pH and the concentration of Cl- fit a model in which progressive protonation of purple membrane produces "blue membrane", which will bind, with increasing affinity as the pH is lowered, chloride ions to produce "acid purple membrane." Transient spectroscopy with a multichannel analyzer identified the intermediates of the photocycles of these altered pigments, and described their kinetics. Blue membrane produced red-shifted KL-like and L-like products, but no other photointermediates, consistent with earlier suggestions. Unlike others, however, we found that acid purple membrane exhibited a very different photocycle: its first detected intermediate was not like KL in that it was much more red-shifted, and the only other intermediate detectable resembled the O species of the bacteriorhodopsin photocycle. An M-like intermediate, with a deprotonated Schiff base, was not found in either of these photocycles. There are remarkable similarities between the photoreactions of the acid forms of bacteriorhodopsin and the chloride transport system halorhodopsin, where the Schiff base deprotonation seems to be prevented by lack of suitable aspartate residues, rather than by low pH.     

Thermodynamic data on the binding of six M2(+)-ions to bovine, goat, and human alpha-lactalbumin.

By batch microcalorimetry we titrated the apo-forms of bovine, goat, and human alpha-lactalbumin with Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, and Cd2+ ions at pH 7.5 and 25 degrees C. The titration curves enabled us to calculate the apparent enthalpy changes and binding constants and thus, also the free energy and the entropy changes of the binding. CD-spectra showed that all cations induce the same conformational change to the native form of the protein. The calorimetric and spectroscopic results, as well as sequence comparisons confirm the hypothesis that all these ions occupy the very same site on the molecule. The thermodynamic parameters, plotted vs the ionic radii, run parallel for the three proteins, which illustrates the earlier proposed "rigid site" model.