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.     

A test of the linear extrapolation of unfolding free energy changes over an extended denaturant concentration range.

Guanidine hydrochloride (GdnHCl) and thermally induced unfolding measurements on the oxidized form of Escherichia coli thioredoxin at pH 7 were combined for the purpose of assessing the functional dependence of unfolding free energy changes on denaturant concentration over an extended GdnHCl concentration range. Conventional analysis of GdnHCl unfolding exhibits a linear plot of unfolding delta G vs [GdnHCl] in the transition zone. In order to extend unfolding delta G measurements outside of that narrow concentration range, thermal unfolding measurements were performed using differential scanning calorimetry (DSC) in the presence of low to moderate concentrations of GdnHCl. The unfolding delta G values from the DSC measurements were corrected to 25 degrees C using the Gibbs-Helmholtz equation and mapped onto the delta G vs [GdnHCl] plot. The dependence of unfolding delta G on [GdnHCl] was found to be linear over the full denaturant concentration range, provided that the chloride ion concentration was kept at a threshold of greater than or equal to 1.5 M. In the DSC experiments performed in the presence of GdnHCl, chloride concentrations were maintained at 1.5 M by addition of appropriate amounts of NaCl. The linear extrapolation method (LEM) gives an unfolding free energy change in the absence of denaturant (delta G degrees N-U) in excellent agreement with the delta G determined by DSC measurement in 1.5 M NaCl. The various methods give a consensus unfolding delta G value of 8.0 kcal/mol at 25 degrees C in the absence of denaturant.(ABSTRACT TRUNCATED AT 250 WORDS)     

Stability of polypeptide conformational states as determined by computer simulation of the free energy

A method is developed to extract the entropy of polypeptides and proteins from samples of conformations. It is based on techniques suggested previously by Meirovitch, and has the advantage that it can be applied not only to states in which the molecule undergoes harmonic or quasiharmonic conformational fluctuations, but also to the random coil, as well as to mixtures of these extreme states. In order to confine the search to a region of conformational space corresponding to a stable state, the transition probabilities are determined not by “looking to the future,” as in the previous method [H. Meirovitch and H. A. Scheraga (1986) J. Chem. Phys. 84 , 6369–6375], but by analyzing the previous steps in the generation of the chain. The method is applied to a model of decaglycine with rigid geometry, using the potential energy function ECEPP (Empirical Conformational Energy Program for Peptides). The model is simulated with the Metropolis Monte Carlo method to generate samples of conformations in the α-helical and hairpin regions, respectively, at T = 100 K. For the α-helix, the four dihedral angles of the N- and C-terminal residues are found to undergo full rotational variation. The results show that the α-helix is a more stable structure than the hairpin. Both its Helmholtz free energy F and energy E are lower than those of the hairpin by ΔF ～ 0.4 and ΔE ～ 0.3 kcal/mole/residue, respectively. It should be noted that the contribution of the entropy ΔS to ΔF is significant (TΔS ～ 0.1 kcal/mole/residue). Also, the entropy of the α-helix is found to be larger than that of the hairpin. This is a result of the extra entropy arising from the rotational freedom about the four terminal single bonds of the α-helix.     

Free energy changes in denaturation of ribonuclease A by mixed denaturants. Effects of combinations of guanidine hydrochloride and one of the denaturants lithium bromide, lithium chloride, and sodium bromide

The denaturation of ribonuclease A by guanidine hydrochloride, lithium bromide, and lithium chloride and by mixed denaturants consisting of guanidine hydrochloride and one of the denaturants lithium chloride, lithium bromide, and sodium bromide was followed by difference spectral measurements at pH 4.8 and 25 degrees C. Both components of mixed denaturant systems enhance each other's effect in unfolding the protein. The effect of lithium bromide on the midpoint of guanidine hydrochloride denaturation transition is approximately the sum of the effects of the constituent ions. For all the mixed denaturants tested, the dependence of the free energy change on denaturation is linear. The conformational free energy associated with the guanidine hydrochloride denaturation transition in water is 7.5 +/- 0.1 kcal mol-1, and it is unchanged in the presence of low concentrations of lithium bromide, lithium chloride, and sodium bromide which by themselves are not concentrated enough to unfold the protein. The conformational free energy associated with the lithium bromide denaturation transition in water is 11.7 +/- 0.3 kcal mol-1, and it is not affected by the presence of low concentrations of guanidine hydrochloride which by themselves do not disrupt the structure of native ribonuclease A.     

The interpretation of site-directed mutagenesis experiments by linear free energy relations

Fersht and co-workers have applied a linear free energy relation (Br?nsted equation) to analyze site-directed mutagenesis experiments involving the enzyme tyrosyl-tRNA synthetase and have suggested that the Br?nsted exponent is linearly correlated with the value of the reaction coordinate at the transition state. We point out that when the mutants differ solely through the formation or deletion of a hydrogen bond away from the reaction center, a linear free energy relation is expected only in limiting cases for which the Br?nsted relation exponent is 0, 1 or infinity. The results may be correlated with a conformational coordinate but not with the development of the reaction coordinate per se.     

The linear interaction energy method for the prediction of protein stability changes upon mutation

The coupling of protein energetics and sequence changes is a critical aspect of computational protein design, as well as for the understanding of protein evolution, human disease, and drug resistance. To study the molecular basis for this coupling, computational tools must be sufficiently accurate and computationally inexpensive enough to handle large amounts of sequence data. We have developed a computational approach based on the linear interaction energy (LIE) approximation to predict the changes in the free-energy of the native state induced by a single mutation. This approach was applied to a set of 822 mutations in 10 proteins which resulted in an average unsigned error of 0.82 kcal/mol and a correlation coefficient of 0.72 between the calculated and experimental ΔΔG values. The method is able to accurately identify destabilizing hot spot mutations; however, it has difficulty in distinguishing between stabilizing and destabilizing mutations because of the distribution of stability changes for the set of mutations used to parameterize the model. In addition, the model also performs quite well in initial tests on a small set of double mutations. On the basis of these promising results, we can begin to examine the relationship between protein stability and fitness, correlated mutations, and drug resistance.     

Stabilities of leucine zipper dimers estimated by an empirical free energy method.

The leucine zipper motif is a characteristic amino acid sequence found in dimeric DNA-binding proteins. Computer-generated models for leucine zippers were constructed as alpha-helical coiled dimers with leucine repeated every seventh residue. An empirical Gibbs free energy, delta G, function which incorporates hydrophobic force, electrostatic interactions, and conformational entropy loss as the major intermolecular interactions was used to estimate the delta G of dimer formation in fos, jun, and GCN4 zipper sequences. The calculations showed that complexes known to form stable homo- or heterodimers have favorable (negative) delta G, while other less stable complexes have unfavorable (positive) delta G. Leucines in position d of the coiled coil contribute large hydrophobic stabilization energies while residues in the a position contribute less to dimer stability. Hydrophobic contributions show little sequence specificity, however, and do not contribute significantly to homo/heterodimer preference. Charged residues in the e and g positions, on the other hand, determine homo/heterodimer specificity. In GCN4 homodimers, residues GLU el, Glu b2, Lys g2, and Lys e4 greatly contribute to dimer stability. The preferential stability of fos-jun heterodimer over the jun-jun and fos-fos homodimers is primarily due to the side chains Asp b1, Glu g1, Asp b2, Glu e2, Glu g2, Glu g3, and Lys a5 of the fos helix, and Arg c1, Lys g1, Lys b2, Lys e2, Arg e4, and Glu g4 of the jun helix.     

The molecular code for hemoglobin allostery revealed by linking the thermodynamics and kinetics of quaternary structural change. 1. Microstate linear free energy relations

A novel model linking the thermodynamics and kinetics of hemoglobin's allosteric (R --> T) and ligand binding reactions is applied to photolysis data for human HbCO. To describe hemoglobin's kinetics at the microscopic level of structural transitions and ligand-binding events for individual [ij]-ligation microstates ((ij)R --> (ij)T, (ij)R + CO --> ((i)(+1))(k)R, and (ij)T + CO --> ((i)(+1))(k)T), the model calculates activation energies, (ij)DeltaG(++), from previously measured cooperative free energies of the equilibrium microstates (Huang, Y., and Ackers, G. K. (1996) Biochemistry 35, 704-718) by using linear free energy relations ((ij)DeltaG(++) - (01)DeltaG(++) = alpha[(ij)DeltaG - (01)DeltaG], where the parameter alpha, describing the variation of activation energy with reaction energy perturbation, can depend on the natures of both the reaction and the perturbation). The alpha value measured here for the allosteric dynamics, 0.21 +/- 0.03, corresponds closely to values observed previously, strongly suggesting that the thermodynamic microstate energies directly underlie the allosteric kinetics (as opposed to the alpha((ij)DeltaG(RT)) serving merely as arbitrary fitting parameters). Besides systematizing the study of hemoglobin kinetics, the utility of the microstate linear free energy model lies in the ability to test microscopic aspects of allosteric dynamics such as the "symmetry rule" for quaternary change deduced previously from thermodynamic evidence (Ackers, G. K., et al. (1992) Science 255, 54-63). Reflecting a remarkably detailed correspondence between thermodynamics and kinetics, we find that a kinetic model that includes the large free energy splitting between doubly ligated T microstates implied by the symmetry rule fits the data significantly better than one that does not.     

Resolvability of free energy changes for oxygen binding and subunit association by human hemoglobin.

Probability distributions of the free energy changes for oxygen binding, subunit association, and quaternary enhancement by human hemoglobin were obtained from Monte Carlo simulations performed on two independent sets of variable protein concentration equilibrium oxygen-binding data. Uncertainties in unliganded and fully liganded dimer to tetramer association free energy changes (0 delta G'2 and 4 delta G'2) were accounted for in the simulations. Distributions of the dimer to tetramer association free energy changes for forming singly and triply liganded tetramers (1 delta G'2 and 3 delta G'2) are well defined and quite symmetric, whereas that for forming doubly liganded tetramers (2 delta G'2) is poorly defined and highly asymmetric. The distribution of the dimer stepwise oxygen-binding free-energy change (delta g'2i) is well defined and quite symmetric as are those of the tetramer stepwise oxygen-binding free-energy changes for binding the first and last oxygens to tetramers (delta g'41 and delta g'44). Distributions of the intermediate tetramer stepwise oxygen-binding free-energy changes (delta g'42 and delta g'43) are poorly defined and highly asymmetric, but are compensatory in that their sum (delta g'4[2 + 3]) is again well defined and nearly symmetric. Distributions of the free energy changes corresponding to the tetramer product Adair oxygen binding constants (delta G'4i) are well defined and quite symmetric for i = 1, 3, 4 but not for i = 2. The distribution of delta g'44 - delta g'2i (the quaternary enhancement free energy change) is relatively narrow, nearly symmetric, and confined to the negative free-energy domain. This suggests that the quaternary enhancement free energy change (a) may be resolved with good confidence from this data and (b) is finite and negative under the conditions of these experiments. Our results also suggest two different four-state combinatorial switch models that provide accurate characterization of hemoglobin's functional behavior.     

Structure-activity relationships in engineered proteins: analysis of use of binding energy by linear free energy relationships

The activity of mutant enzymes can be analyzed quantitatively by structure-activity relationships in a manner analogous to Br?nsted or Hammett plots for simple organic reactions. The slopes of such plots, the beta values, indicate for the enzymatic reactions the fraction of the overall binding energy used in stabilizing particular complexes. In particular, information can be derived about the interactions between the enzyme and the transition state. The activities of many mutant tyrosyl-tRNA synthetases fit well simple linear free energy relationships. The formation of enzyme-bound tyrosyl adenylate (E.Tyr-AMP) from enzyme-bound tyrosine and ATP (E.Tyr-ATP) results in an increase in binding energy between the enzyme and the side chain of tyrosine and the ribose ring of ATP. Linear free energy plots of enzymes mutated in these positions give the fraction of the binding energy change that occurs on formation of the transition state for the chemical reaction and the various complexes. It is shown that groups that specifically stabilize the transition state of the reaction are characterized by beta values much greater than 1. This is found for residues that bind the gamma-phosphate of ATP (Thr-40 and His-45) and have previously been postulated to be involved in transition-state stabilization.(ABSTRACT TRUNCATED AT 250 WORDS)     

Activity and conformational changes of alpha-chymotrypsin in reverse micelles studied by spin labeling.

alpha-Chymotrypsin (CT), spin-labeled at the active site by using an acylating label which constitutes a substrate for this protein, has been investigated in reverse micelles formed by AOT in isooctane. The electron spin resonance spectra provided information on conformation, dynamics and deacylation activity. The dynamics of the label bound to CT appears to be more hindered in reverse micelles than in aqueous solution, probably owing to the effect of the micellar environment on protein conformation. The deacylation rate in reverse micelles does not show the characteristic bell-shaped dependence on water content which is generally found for CT enzymatic activity.     

Prediction of protein complexes using empirical free energy functions.

A long sought goal in the physical chemistry of macromolecular structure, and one directly relevant to understanding the molecular basis of biological recognition, is predicting the geometry of bimolecular complexes from the geometries of their free monomers. Even when the monomers remain relatively unchanged by complex formation, prediction has been difficult because the free energies of alternative conformations of the complex have been difficult to evaluate quickly and accurately. This has forced the use of incomplete target functions, which typically do no better than to provide tens of possible complexes with no way of choosing between them. Here we present a general framework for empirical free energy evaluation and report calculations, based on a relatively complete and easily executable free energy function, that indicate that the structures of complexes can be predicted accurately from the structures of monomers, including close sequence homologues. The calculations also suggest that the binding free energies themselves may be predicted with reasonable accuracy. The method is compared to an alternative formulation that has also been applied recently to the same data set. Both approaches promise to open new opportunities in macromolecular design and specificity modification.     

Effect of bolus fluid intake on energy expenditure values as determined by the doubly labeled water method.

The doubly labeled water (DLW, 2H(2)18O) method is a highly accurate method for measuring energy expenditure (EE). A possible source of error is bolus fluid intake before body water sampling. If there is bolus fluid intake immediately before body water sampling, the saliva may reflect the ingested water disproportionately, because the ingested water may not have had time to mix fully with the body water pool. To ascertain the magnitude of this problem, EE was measured over a 5-day period by the DLW method. Six subjects were dosed with 2H2(18)O. After the reference salivas for the two-point determination were obtained, subjects drank water (700-1,000 ml), and serial saliva samples were collected for the next 3 h. Expressing the postbolus saliva enrichments as a percentage of the prebolus value, we found 1) a minimum in the saliva isotopic enrichments were reached at approximately 30 min with the minimum for 2H (95.48 +/- 0.43%) being significantly lower than the minimum for 18O (97.55 +/- 0.44, P less than 0.05) and 2) EE values calculated using the postbolus isotopic enrichments are appreciably higher (19.9 +/- 7.5%) than the prebolus reference values. In conclusion, it is not advisable to collect saliva samples for DLW measurements within approximately 1 h of bolus fluid intake.     

A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison.

This article describes the latest version of an RNA folding algorithm that predicts both optimal and suboptimal solutions based on free energy minimization. A number of RNA's with known structures deduced from comparative sequence analysis are folded to test program performance. The group of solutions obtained for each molecule is analysed to determine how many of the known helixes occur in the optimal solution and in the best suboptimal solution. In most cases, a structure about 80% correct is found with a free energy within 2% of the predicted lowest free energy structure.     

Effect of denaturants on the structural properties of soybean lipoxygenase-1.

The effect of chemical (urea) and physical (temperature and high pressure) denaturation on the structural properties of soybean lipoxygenase-1 (LOX1) was analyzed through dynamic fluorescence spectroscopy and circular dichroism. We show that the fluorescence decay of the native protein could be fitted by two lorentzian distributions of lifetimes, centered at 1 and 4 ns. The analysis of the urea-denatured protein suggested that the shorter distribution is mostly due to the tryptophan residues located in the N-terminal domain of LOX1. We also show that a pressure of 2400 bar and a temperature of 55 degrees C brought LOX-1 to a state similar to a recently described stable intermediate "I." Analysis of circular dichroism spectra indicated a substantial decrease of alpha-helix compared with beta-structure under denaturing conditions, suggesting a higher stability of the N-terminal compared with the C-terminal domain in the denaturation process.