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.     

Unfolding free energy changes determined by the linear extrapolation method. 1. Unfolding of phenylmethanesulfonyl alpha-chymotrypsin using different denaturants

Characteristics and properties of the unfolding free energy change, delta G degrees N-U, as determined by the linear extrapolation method are assessed for the unfolding of phenylmethanesulfonyl chymotrypsin (PMS-Ct). Difference spectral measurements at 293 nm were used to define PMS-Ct unfolding brought about with guanidinium chloride, urea, and 1,3-dimethylurea. All three denaturants were shown to give identical extinction coefficient differences (delta epsilon N-U) between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of delta epsilon N-U on denaturant supports the linear extension of pre- and postdenaturational base lines into the transition zone, allowing evaluation of unfolding equilibrium constants based on the two-state assumption. An expression, based on the linear extrapolation method, was used to provide estimates of delta G degrees N-U for the three denaturants using nonlinear least-squares fitting of the primary data, delta epsilon versus [denaturant]. The three delta G degrees N-U values were identical, within error, suggesting that the free energy change is a property of the protein system and independent of denaturant. It is suggested that the error in delta G degrees N-U determined from use of the linear extrapolation method is significantly larger than commonly reported in the literature.     

Low-temperature unfolding of a mutant of phage T4 lysozyme. 1. Equilibrium studies

The mutant protein I3C-C97/C54T of phage T4 lysozyme is free of sulfhydryl groups and has a genetically engineered disulfide bridge between positions 3 and 97 (Perry & Wetzel, 1986). This protein has a maximum stability at 12 degrees C in 3 M guanidinium chloride and undergoes reversible high- and low-temperature melting at 28 and -3 degrees C, respectively, in this medium. The free energy of stabilization of the protein has been studied over a range of temperature that includes both melting transitions. The stability curve fits a constant delta Cp model over the entire range, permitting an unusually complete determination of the thermodynamic parameters of the protein and demonstrating that the low-temperature unfolded form of the protein may be interpreted as an extrapolation with constant delta Cp of the high-temperature unfolded form. The free energy of unfolding is a linear function of guanidinium concentration within experimental error which permits a rough estimate of the stability of the protein at low temperatures and of the differential interaction of the unfolded protein with guanidinium chloride. These equilibrium studies provide a basis for the interpretation of the kinetic studies reported in the following paper.     

Heat capacity change for ribonuclease A folding.

The change in heat capacity deltaCp for the folding of ribonuclease A was determined using differential scanning calorimetry and thermal denaturation curves. The methods gave equivalent results, deltaCp = 1.15+/-0.08 kcal mol(-1) K(-1). Estimates of the conformational stability of ribonuclease A based on these results from thermal unfolding are in good agreement with estimates from urea unfolding analyzed using the linear extrapolation method.     

Chemical modification of proteins: plotting of the remaining activity against the number of residues modified

In the study of chemical modification of proteins, it has been a common practice to plot the fractional remaining activity against the number of residues modified per protein molecule. Extrapolation of the initial, nearly linear portion of the curve to the axis giving numbers of residues has often been presumed to specify the actual number of critical groups modified, i.e., the stoichiometry of the modification and the inactivation reactions. However, this extrapolation method is not generally applicable (Horiike, K. & McCormick, D.B. (1979) J. Theor. Biol. 79, 403-414). This paper describes further examination of the underlying theoretical framework of the extrapolation method. The properties and features of the extrapolated values are considered and presented with numerical and graphical examples. And the theoretical conditions with which the extrapolated value gives the number of essential residues are derived.     

Conformational stability and thermodynamic characterization of homotetrameric Plasmodium falciparum beta-ketoacyl-ACP reductase

The conformational stability of the homotetrameric Plasmodium falciparum beta-ketoacyl-ACP reductase (FabG) was determined by guanidinium chloride-induced isothermal and thermal denaturation. The reversible unfolding transitions were monitored by intrinsic fluorescence, circular dichroism (CD) spectroscopy and by measuring the enzyme activity of FabG. The denaturation profiles were analyzed to obtain the thermodynamic parameters associated with unfolding of the protein. The data confirm the simple A(4) <--> 4A model of unfolding, based on the corroboration of CD data by fluorescence transition and similar Delta G estimation for denaturation curves obtained at four different concentration of the FabG. Denaturation is well described by the linear extrapolation model for denaturant-protein interactions. In addition, the conformational stability (Delta G(s)) as well as the Delta C(p) for the protein unfolding is quite high, 22.68 kcal/mole and 5.83 kcal/(mole K), respectively, which may be a reflection of the relatively large size of the tetrameric molecule (Mr 120, 000) and a large buried hydrophobic core in the folded protein. This study provides a prototype for determining conformational stability of other members of the short-chain alcohol dehydrogenase/reductase superfamily of proteins to which PfFabG belongs.     

Structural thermodynamics of a random coil protein in guanidine hydrochloride

An important problem in protein folding is to understand the relationship between the structure of a denatured ensemble and its thermodynamics. Using 0 – 6M GdnHCl at fixed pH, we evaluated dimensional changes of an extensively denatured ensemble along with a thermodynamic parameter (Δυ) that monitors the proton inventory of the ensemble. Reduced and carboxyamidated ribonuclease A (RCAM) is a member of a class of disulfide‐free RNase A molecules believed to be random coils (extensively denatured) in aqueous solution. Because GdnHCl interacts more favorably with the protein than water does, this denaturant is observed to increase the Stokes radius of the random coil, with the greatest Stokes radius change occurring in the 0 – 1.5M GdnHCl range. Measurement of the degree of protonation (proton inventory) of the ensemble as a function of GdnHCl at the fixed pH shows that the thermodynamic character of the ensemble also changes markedly in the 0 – 1.5M GdnHCl range, but with little or no change beyond 1.5M GdnHCl. To obtain denaturant‐independent ΔG°_N–D values, the linear extrapolation method (LEM) requires the thermodynamic character of the native and denatured ensembles to be invariant in the transition zone. The results reported here indicate that proteins with a transition midpoint in the 0 – 1.5M GdnHCl range will not give denaturant‐concentration independent ΔG°_N–D values. Such LEM‐derived ΔG°_N–D quantities are a property of the protein and the denaturant, a condition that considerably limits their value in understanding structural energetics. Proteins 2000;41:44–49. © 2000 Wiley‐Liss, Inc.     

Thermal versus guanidine-induced unfolding of ubiquitin. An analysis in terms of the contributions from charge-charge interactions to protein stability.

We have characterized the guanidine-induced unfolding of both yeast and bovine ubiquitin at 25 degrees C and in the acidic pH range on the basis of fluorescence and circular dichroism measurements. Unfolding Gibbs energy changes calculated by linear extrapolation from high guanidine unfolding data are found to depend very weakly on pH. A simple explanation for this result involves the two following assumptions: (1) charged atoms of ionizable groups are exposed to the solvent in native ubiquitin (as supported by accessible surface area calculations), and Gibbs energy contributions associated with charge desolvation upon folding (a source of pK shifts) are small; (2) charge-charge interactions (another source of pK shifts upon folding) are screened out in concentrated guanidinium chloride solutions. We have also characterized the thermal unfolding of both proteins using differential scanning calorimetry. Unfolding Gibbs energy changes calculated from the calorimetric data do depend strongly on pH, a result that we attribute to the pH dependence of charge-charge interactions (not eliminated in the absence of guanidine). In fact, we find good agreement between the difference between the two series of experimental unfolding Gibbs energy changes (determined from high guanidine unfolding data by linear extrapolation and from thermal denaturation data in the absence of guanidine) and the theoretical estimates of the contribution from charge-charge interactions to the Gibbs energy change for ubiquitin unfolding obtained by using the solvent-accessibility-corrected Tanford-Kirkwood model, together with the Bashford-Karplus (reduced-set-of-sites) approximation. This contribution is found to be stabilizing at neutral pH, because most charged groups on the native protein interact mainly with groups of the opposite charge, a fact that, together with the absence of large charge-desolvation contributions, may explain the high stability of ubiquitin at neutral pH. In general, our analysis suggests the possibility of enhancing protein thermal stability by adequately redesigning the distribution of solvent-exposed, charged residues on the native protein surface.     

Comparison of the stability of fish light meromyosins by guanidine hydrochloride denaturation

The guanidine hydrochloride denaturation of light meromyosins (LMMs) of fish (carp, sardine and greenling) and rabbit was investigated to determine their structural stability quantitatively. The circular dichroism (CD) and fluorescence spectroscopies were applied to monitor denaturation. The CD results indicate that the LMM α-helix undergoes a two-step unfolding. The free energy of denaturation was calculated based on the linear extrapolation method and the denaturant binding model. Total free energies of the two-step unfolding of the α-helix are related to the water temperatures in which the fish live and the body temperature of rabbit. The stability of α-helical structure of LMM was in the following descending order: rabbit>carp>sardine>greenling. The free energies of denaturation obtained by tryptophan fluorescence differ from the free energies of the unfolding α-helix. The data from the two spectroscopic measurements are discussed along with the conformational changes of LMMs.     

Uncertainty Distributions for Cancer Potency Factors: Laboratory Animal Carcinogenicity Bioassays and Interspecies Extrapolation

Current methodology uses a multistage dose-response formula to represent the dose-response curve of laboratory bioassays adequately at high doses, and to extrapolate to low doses. Standard likelihood methods are described to evaluate an uncertainty distribution for the linear term of the multistage formula, exactly analogous to the current method of obtaining a “95% confidence limit.” In the standard methodology, the number of terms in the dose-response formula and the assumed form for the distribution used to obtain the “95% confidence limit” are somewhat arbitrarily chosen. Modifications are described that allow consistent (although still arbitrary) treatment of all experiments, and potentially allow incorporation of mechanistic ideas about the correctness of the low-dose extrapolation. Also described are extensions that allow incorporation of results from multiple experiments into the uncertainty distribution. The result is a probability distribution for cancer potency factor in laboratory animals.

Empirical results describing the extrapolation between species of the linear term of multistage dose-response formulas are presented, and a method is given for analysis of any dose-response model. It is shown that the interspecies extrapolation as currently performed is well represented by a lognormal distribution with well-defined standard deviation but a median that depends on the species, and that is not representable by any simple allometric scaling law. The best available animal/human comparisons are analyzed in similar fashion to show consistency with the ideas presented, and obtain the best estimates for animal to human extrapolation.     

Detection of simple radially symmetric targets: further evidence for the matched filter processing scheme in human pattern detection

The detection of small radially symmetric targets was studied using a subthreshold summation paradigm. Small disc and disc-like patterns with diameters up to 0.6^∘ were used for superposition on Bessel functions of zero order, subthreshold contrast and various spatial frequencies. Contrast interrelation functions prove linear over the whole range of contrasts used for the Bessel functions while their slopes show systematic variation with spatial frequency. An extrapolation of sensitivity from the slopes reveals that sensitivity can be predicted by a simple model assuming detection to be mediated by a transfer function made up as a cascade of an even bandpass function and the disc pattern spectrum, as has been found previously using one dimensional luminance distributions. Problems concerning the formation of pattern-specific radial symmetric filters are discussed. Received: 31 January 2000 / Accepted in revised form: 16 June 2000     

Native state energetics of the Src SH2 domain: evidence for a partially structured state in the denatured ensemble

We have defined the free-energy profile of the Src SH2 domain using a variety of biophysical techniques. Equilibrium and kinetic experiments monitored by tryptophan fluorescence show that Src SH2 is quite stable and folds rapidly by a two-state mechanism, without populating any intermediates. Native state hydrogen-deuterium exchange confirms this two-state behavior; we detect no cooperative partially unfolded forms in equilibrium with the native conformation under any conditions. Interestingly, the apparent stability of the protein from hydrogen exchange is 2 kcal/mol greater than the stability determined by both equilibrium and kinetic studies followed by fluorescence. Native-state proteolysis demonstrates that this "super protection" does not result from a deviation from the linear extrapolation model used to fit the fluorescence data. Instead, it likely arises from a notable compaction in the unfolded state under native conditions, resulting in an ensemble of conformations with substantial solvent exposure of side chains and flexible regions sensitive to proteolysis, but backbone amides that exchange with solvent approximately 30-fold slower than would be expected for a random coil. The apparently simple behavior of Src SH2 in traditional unfolding studies masks the significant complexity present in the denatured-state ensemble.     

Stability of ribonuclease T2 from Aspergillus oryzae.

The stability of ribonuclease T2 (RNase T2) from Aspergillus oryzae against guanidine hydrochloride and heat was studied by using CD and fluorescence. RNase T2 unfolded and refolded reversibly concomitant with activity, but the unfolding and refolding rates were very slow (order of hours). The free energy change for unfolding of RNase T2 in water was estimated to be 5.3 kcal.mol-1 at 25 degrees C by linear extrapolation method. From the thermal unfolding experiment in 20 mM sodium phosphate buffer at pH 7.5, the Tm and the enthalpy change of RNase T2 were found to be 55.3 degrees C and 119.1 kcal.mol-1, respectively. From these equilibrium and kinetic studies, it was found that the stability of RNAse T2 in the native state is predominantly due to the slow rate of unfolding.     

A new method for the separation of the constant and the variable fluorescence of chlorophyll a in in vivo

The constant fluorescence of chlorophyll a in alga Dunaliella tertiolecta was estimated by a method of the least square regression applied to the linearized form of the equation y = axb. The value of the constant fluorescence obtained by this method was compared by the values estimated with simple linear extrapolation. Constant fluorescence, evaluated by the simple linear extrapolation of 10 ms of the initial variable fluorescence, was 50% higher than the value obtained by the method of the least square regression. We demonstrated that the estimation of constant fluorescence by the least square regression is a more correct method and provides a better comparison of results from different laboratories. This method offers a simple way to determine and separate constant fluorescence from variable fluorescence in the total yield of chlorophyll a fluorescence in "in vivo" conditions. Furthermore it facilitates the interpretation of the variable fluorescence phenomena in "in vivo".     

Conformational stability and thermodynamic characterization of the lipoic acid bearing domain of human mitochondrial branched chain alpha-ketoacid dehydrogenase

The lipoic acid bearing domain (hbLBD) of human mitochondrial branched chain alpha-ketoacid dehydrogenase (BCKD) plays important role of substrate channeling in oxidative decarboxylation of the branched chain alpha-ketoacids. Recently hbLBD has been found to follow two-step folding mechanism without detectable presence of stable or kinetic intermediates. The present study describes the conformational stability underlying the folding of this small beta-barrel domain. Thermal denaturation in presence of urea and isothermal urea denaturation titrations are used to evaluate various thermodynamic parameters defining the equilibrium unfolding. The linear extrapolation model successfully describes the two-step; native state <-->denatured state unfolding transition of hbLBD. The average temperature of maximum stability of hbLBD is estimated as 295.6 +/- 0.9 K. Cold denaturation of hbLBD is also predicted and discussed.     

Protein stability: functional dependence of denaturational Gibbs energy on urea concentration

Determination of protein stability (DeltaGD0) from the conformational transition curve induced by a chemical denaturant is problematic; for different values of DeltaGD0, the value of the Gibbs energy change on denaturation (DeltaGD) in the absence of the denaturant are obtained when different extrapolation methods are used to analyze the same set of (DeltaGD, denaturant concentration) data [Pace, C. N. (1986) Methods Enzymol. 131, 266-280]. We propose a practical solution to this problem and use it to test the dependence of DeltaGD of lysozyme, ribonuclease-A, and cytochrome-c on [urea], the molar urea concentration. This method employs (i) measurements of the urea-induced denaturation in the presence of different guanidine hydrochloride (GdnHCl) concentrations which by themselves disrupt the native state of the protein at the same temperature and pH at which denaturations by urea and GdnHCl have been measured; (ii) estimation of DeltaGDcor, the value of DeltaGD corrected for the effect of GdnHCl on the urea-induced denaturation using the relation (DeltaGDcor = DeltaGD + mg [GdnHCl] = DeltaGD0 - mu [urea], where mg and mu are the dependencies of DeltaGD on [GdnHCl] and [urea], respectively) whose parameters are all determined from experimental denaturation data; and (iii) mapping of DeltaGDcor onto the DeltaGD versus [urea] plot obtained in the absence of GdnHCl. Our results convincingly show that (i) [urea] dependence of DeltaGD of each protein is linear over the full concentration range; (ii) the effect of urea and GdnHCl on protein denaturation is additive; and (iii) KCl affects the urea-induced denaturation if the native protein contains charge-charge interaction and/or anion binding site, in a manner which is consistent with the crystal structure data.     

Three easy pieces

BackgroundDifferential scanning calorimetry is a powerful method that provides a complete thermodynamic characterization of the stability of a protein as a function of temperature. There are, however, circumstances that preclude a complete analysis of DSC data. The most common ones are irreversible denaturation transitions or transitions that take place at temperatures that are beyond the temperature limit of the instrument. Even for a protein that undergoes reversible thermal denaturation, the extrapolation of the thermodynamic data to lower temperatures, usually 25 °C, may become unreliable due to difficulties in the determination of ΔC_p.MethodsThe combination of differential scanning calorimetry and isothermal chemical denaturation allows reliable thermodynamic analysis of protein stability under less than ideal conditions.Results and conclusionsThis paper demonstrates how DSC can be used in combination with chemical denaturation to address three different scenarios: 1) estimation of an accurate ΔC_p value for a reversible denaturation using as a test system the envelope HIV-1 glycoprotein gp120; 2) determination of the Gibbs energy of stability in the region in which thermal denaturation is irreversible using HEW lysozyme at different pH values; and, 3) determination of Gibbs energy of stability for a thermostable protein, thermolysin. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Behaviour of DNA-RNase A complex in the presence of formaldehyde]

A formaldehyde-produced fixation of defects caused by a despiralizing action of a protein was studied in the case of DNA-RNAase A complex. The concentration of the defects fixed was measured by kinetic formaldehyde method (KF-method). It was shown that following processes take place in the complex in the presence of formaldehyde: (a) fixation of defects; (b) unwinding of DNA; (c) inactivation of the protein. The rates of all these processes depend on the concentration of formaldehyde, phi. At formaldehyde concentrations above some critical value phic the protein is inactivated before the defects are fixed. At phi less than phic the protein inactivation proceeds more slowly than the fixation of defects; at sufficiently low formaldehyde concentration no inactivation of protein occurs practically during the fixation time (20 min). The number of new defects formed during the time of fixation is linear with the formaldehyde concentration in the region where no inactivation of the protein occurs. Therefore the initial concentration of defects can be determined through an extrapolation to zero concentration of formaldehyde. On the basis of the data obtained a method is proposed for the evaluation of the number of defects in DNA caused by the despiralizing action of proteins. A model is proposed describing the behaviour of the complexes of DNA with despiralizing proteins in the presence of formaldehyde.     

Pharmacokinetic evaluation of medicinally important synthetic N,N′ diindolylmethane glucoside: Improved synthesis and metabolic stability

An improved route for the synthesis of N,N′-diindolyl methane (DIM) glycosides has been developed by using Fe/Al pillared clay catalyst. In-silico pharmacokinetics followed by in-vitro studies like aqueous solubility, lipophilicity, P-glycoprotein (P-gp) dependent ATPase activity, permeability, plasma protein binding, RBC partitioning, metabolic stability in different liver microsomes and its in-vitro-in-vivo extrapolation were conducted for the most potent derivative namely NGD16. The compound was found to have low solubility, optimum lipophilicity, no P-gp inhibitory activity, intermediate permeability, high plasma protein binding, low RBC partitioning, acceptable metabolic stability in rat liver microsomes (RLM) as well as human liver microsomes (HLM) with intermediate hepatic extraction ratio.