SUPREX (Stability of Unpurified Proteins from Rates of H/D Exchange) analysis of the thermodynamics of synergistic anion binding by ferric-binding protein (FbpA), a bacterial transferrin

SUPREX (stability of unpurified proteins from rates of H/D exchange) is a H/D exchange- and matrix-assisted laser desorption/ionization (MALDI)-based technique for characterizing the equilibrium unfolding/refolding properties of proteins and protein-ligand complexes. Here, we describe the application of SUPREX to the thermodynamic analysis of synergistic anion binding to iron-loaded ferric-binding protein (Fe(3+)FbpA-X, X = synergistic anion). The in vivo function of FbpA is to transport unchelated Fe(3+) across the periplasmic space of certain Gram-negative bacteria, a process that requires simultaneous binding of a synergistic anion. Our results indicate that Fe(3+)FbpA-X is not a so-called "ideal" protein system for SUPREX analyses because it does not exhibit two-state folding properties and it does not exhibit EX2 H/D exchange behavior. However, despite these nonideal properties of the Fe(3+)FbpA-X protein-folding/unfolding reaction, we demonstrate that the SUPREX technique is still amenable to the quantitative thermodynamic analysis of synergistic anion binding to Fe(3+)FbpA. As part of this work, the SUPREX technique was used to evaluate the DeltaDeltaG(f) values of four synergistic anion-containing complexes of Fe(3+)FbpA (i.e., Fe(3+)FbpA-PO(4), Fe(3+)FbpA-citrate, Fe(3+)FbpA-AsO(4), and Fe(3+)FbpA-SO(4)). The DeltaDeltaG(f) value obtained for Fe(3+)FbpA-citrate relative to Fe(3+)FbpA-PO(4) (1.45 +/- 0.44 kcal/mol), is in good agreement with that reported previously (1.98 kcal/mol). The value obtained for Fe(3+)FbpA-AsO(4) (0.58 +/- 0.45 kcal/mol) was also consistent with that reported previously (0.68 kcal/mol), but the measurement error is very close to the magnitude of the value. This work (i) demonstrates the utility of the SUPREX method for studying anion binding by FbpA, (ii) provides the first evaluation of a DeltaDeltaG(f) value for Fe(3+)FbpA-SO(4), -1.43 +/- 0.17 kcal/mol, and (iii) helps substantiate our hypothesis that the synergistic anion plays a role in controlling the lability of iron bound to FbpA in the transport process.     

pH-dependent interactions and the stability and folding kinetics of the N-terminal domain of L9. Electrostatic interactions are only weakly formed in the transition state for folding

The role of electrostatic interactions in the stability and the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) was investigated by determining the effects of varying the pH conditions. Urea denaturations and thermal unfolding experiments were used to measure the free energy of folding, DeltaG degrees, at 18 different pH values, ranging from pH 1.1 to pH 10.5. Folding rates were measured at 19 pH values between pH 2.1 and pH 9.5, and unfolding rates were determined at 15 pH values in this range using stopped-flow fluorescence experiments. The protein is maximally stable between pH 5.5 and 7.5 with a value of DeltaG degrees =4.45 kcal mol(-1). The folding rate reaches a maximum at pH 5.5, however the change in folding rates with pH is relatively modest. Over the pH range of 2.1 to 5.5 there is a small increase in folding rates, ln (k(f)) changes from 5.1 to 6.8. However, the change in stability is more dramatic, with a difference of 2.6 kcal mol(-1) between pH 2.0 and pH 5.4. The change in stability is largely due to the smaller barrier for unfolding at low pH values. The natural log of the unfolding rates varies by approximately four units between pH 2.1 and pH 5.5. The stability of the protein decreases above pH 7.5 and again the change is largely due to changes in the unfolding rate. ln (k(f)) varies by less than one unit between pH 5.5 and pH 9.5 while DeltaG degrees decreases by 2.4 kcal mol(-1) over the range of pH 5. 4 to pH 10.0, which corresponds to a change in ln K(eq) of 4.0. These studies show that pH-dependent interactions contribute significantly to the overall stability of the protein but have only a small effect upon the folding kinetics, indicating that electrostatic interactions are weakly formed in the transition state for folding.     

pH-dependent stability and folding kinetics of a protein with an unusual alpha-beta topology: the C-terminal domain of the ribosomal protein L9

The folding kinetics and thermodynamics of the isolated C-terminal domain of the ribosomal protein L9 (CTL9) have been studied as a function of pH. CTL9 is an alpha-beta protein that contains a single beta-sheet with an unusual mixed parallel, anti-parallel topology. The folding is fully reversible and two-state over the entire pH range. Stopped-flow fluorescence and CD experiments yield the same folding rate, and the chevron plots have the characteristic V-shape expected for two-state folding. The values of DeltaG*(H2O) and the m value calculated from the kinetic experiments are in excellent agreement with the equilibrium measurements. The extrapolated initial amplitudes of both the stopped-flow fluorescence and CD measurements show that there is no detectable burst phase intermediate. The domain contains three histidine residues, two of which are largely buried in the native state. They do not participate in salt-bridges or take part in a hydrogen bonded network. NMR measurements reveal that the buried histidine residues have significantly perturbed pK(a) values in the native state. The equilibrium stability and the folding rate are found to be strongly dependent upon their ionization state. There is a linear relationship between the log of the folding rate and DeltaG* (H2O) . The protein is much more stable and folds noticeably faster at pH values above the native state pK(a) values. DeltaG*(H2O) of unfolding increases from 2.90 kcal mol(-1) at pH 5.0 to 6.40 kcal mol(-1) at pH 8.0 while the folding rate increases from 0.60 to 18.7 s(-1). Tanford linkage analysis revealed that the interactions involving the two histidine residues are largely developed in the transition state. The results are compared to other studies of the pH-dependence of folding.     

Stability and cooperativity of individual tertiary contacts in RNA revealed through chemical denaturation

For proteins, understanding tertiary interactions involved in local versus global unfolding has become increasingly important for understanding the nature of the native state ensemble, the mechanisms of unfolding, and the stability of both the native and intermediate states in folding. In this work we have addressed related questions with respect to RNA structure by combining chemical denaturation and hydroxyl radical footprinting methods. We have determined unfolding isotherms for each of 26 discrete sites of protection located throughout the Tetrahymena thermophila group I ribozyme. The cooperativity of folding, m-value, and the free energy, DeltaG degrees N-U, associated with formation of each tertiary contact was determined by analysis of the isotherms. The DeltaG degrees N-U values measured in this study vary from 1.7 +/- 0.2 to 7. 6 +/- 1.2 kcal mol-1. Thus, the stability of these discrete tertiary contacts vary by almost 104. In addition, an intradomain contact and three interdomain contacts show high cooperativity (m-values of 1.1 +/- 0.2 to 1.7 +/- 0.3 kcal mol-1 M-1) indicating that these contacts exhibit global cooperatively in their folding behavior. This new approach to examining RNA stability provides an exciting comparison to our understanding of protein structure and folding mechanisms.     

A mass spectrometry-based probe of equilibrium intermediates in protein-folding reactions

Described here is a mass spectrometry- and H/D exchange-based approach for the detection of equilibrium intermediate state(s) in protein-folding reactions. The approach utilizes the stability of unpurified proteins from rates of H/D exchange (SUPREX) technique to measure the m value (i.e., delta DeltaG/delta [denaturant] value) associated with the folding reaction of a protein. Such SUPREX m-value analyses can be made over a wide range of denaturant concentrations. Thus, the described approach is well-suited for the detection of high-energy intermediates that might be populated at low denaturant concentrations and hard to detect in conventional chemical denaturation experiments using spectroscopic probes. The approach is demonstrated on four known non-two-state folding proteins, including alpha-lactalbumin, cytochrome c, intestinal fatty acid binding protein (IFABP), and myoglobin. The non-two-state folding behavior of each model protein system was detected by the described method. The cytochrome c, myoglobin, and IFABP systems each had high-energy intermediate states that were undetected in conventional optical spectroscopy-based studies and previously required other more specialized biophysical approaches (e.g., nuclear magnetic resonance spectroscopy-based methods and protease protection assays) for their detection. The SUPREX-based approach outlined here offers an attractive alternative to these other approaches, because it has the advantage of speed and the ability to analyze both purified and unpurified protein samples in either concentrated or dilute solution.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Interleukin-1 beta folding between pH 5 and 7: experimental evidence for three-state folding behavior and robust transition state positions late in folding

The thermodynamic stability and folding kinetics of the all beta-sheet protein interleukin-1beta were measured between 0 and 4 M GdmCl concentrations and pH 5-7. Native interleukin-1beta undergoes a 3.5 kcal/mol decrease in thermodynamic stability, Delta, as pH is increased from 5 to 7. The native state parameter m(NU), measuring protein destabilization/[GdmCl], remains constant between pH 5 and 7, indicating that the solvent-exposed surface area difference between the native state and unfolded ensemble is unchanged across this pH range. Similarly, pH changes between 5 and 7 decrease only the thermodynamic stability, DeltaG(H)2(O), and not the m-values, of the kinetic intermediate and transition states. This finding is shown to be consistent with transition state configurations which continue to be the high-energy configurations of the transition state in the face of changing stability conditions. A three-state folding mechanism U right arrow over left arrow I right arrow over left arrow N is shown to be sufficient in characterizing IL-1beta folding under all conditions studied. The m-values of refolding transitions are much larger than the m-values of unfolding transitions, indicating that that the fast, T(2) (U right arrow over left arrow I), and slow, T(1) (I right arrow over left arrow N), transition states are highly similar to the intermediate I and native state N, respectively. Many of the folding properties of interleukin-1beta are shared among other members of the beta-trefoil protein family, although clear differences can exist.     

Thermodynamic stability measurements on multimeric proteins using a new H/D exchange- and matrix-assisted laser desorption/ionization (MALDI) mass spectrometry-based method

We recently reported on a new H/D exchange- and matrix-assisted laser desorption/ionization (MALDI) mass spectrometry-based technique, termed SUPREX, that removes several important limitations associated with measuring the thermodynamic stability of proteins. In contrast to conventional spectroscopy-based techniques for characterizing the equilibrium unfolding behavior of proteins, SUPREX is amenable to the thermodynamic analysis of both purified and unpurified proteins using mg to ng quantities of material. Here we report on the application of SUPREX to the analysis of multimeric protein systems. Included in this work are the SUPREX results we obtained in studies on six model multimeric proteins including the GCN4p1 dimer, the coil-V(a)L(d) trimer, the 4-oxalocrotonate tautomerase (4-OT) hexamer, the Trp repressor (TrpR) dimer, the Arc repressor (ArcR) dimer, and an ArcR mutant (the (DOA20)ArcR) dimer which contained two destabilizing mutations including an Asp to Ala mutation at position 20 and an amide to ester bond mutation between amino acid (aa) residues 19 and 20. As part of the work described here, we present a new method for the analysis of SUPREX data that is generally applicable to both monomeric and multimeric protein systems. Our results on the model proteins in this study indicate that this new method can be used to determine folding free energies for proteins with the accuracy and precision of conventional spectroscopy-based methods.     

The transition state for folding of a peripheral subunit-binding domain contains robust and ionic-strength dependent characteristics

The denaturant dependencies of the folding and unfolding kinetics were used to characterize the structure of the transition state for folding of E3BD, a peripheral subunit-binding domain. For the majority of E3BD mutants, the Phi-values calculated at 298 K from the analysis of chevron plots were in good agreement with those previously determined at 325 K using Arrhenius analysis. This agreement further demonstrates the general robustness of Phi-value analyses, since different experiments, methods of denaturation and thermodynamic assumptions were used to determine each set of Phi(F) values. The structure of the transition state for folding was grossly conserved at 298 K and 325 K, with residues in Helix I playing a lesser role in folding than those located in the 3(10) helix, disordered loop and Helix II. However, the energetic contributions of a cluster of basic residues close to the N-terminus and Helix I, which are an integral part of the ligand-binding site, were susceptible to ionic strength effects because of electrostatic strain in native and transition states of E3BD at low ionic strength. We found no evidence of the downhill folding previously proposed for E3BD, even though the conditions employed in this study significantly increased the energetic bias towards the native state.     

Simulation and experiment at high temperatures: ultrafast folding of a thermophilic protein by nucleation-condensation

We used Phi-value analysis to characterise the transition state for folding of a thermophilic protein at the relatively high temperature of 325 K. PhiF values for the folding of the three-helix bundle, peripheral subunit binding domain from Bacillus stearothermophilus (E3BD) were determined by temperature-jump experiments in the absence of chemical denaturants. E3BD folded in microseconds through a highly diffuse transition state. Excellent agreement was observed between experiment and the results from eight (independent) molecular dynamics simulations of unfolding at 373 K. We used a combination of heteronuclear NMR experiments and molecular dynamics simulations to characterise the denatured ensemble, and found that it contained very little persistent, residual structure. However, those regions that adopt helical structure in the native state were found by simulation to be poised for helix formation in the denatured state. These regions also had significant structure in the transition state for folding. The overall folding pathway appears to be nucleation-condensation.     

Folding of a de novo designed native-like four-helix bundle protein

The folding of a model native-like dimeric four-helix bundle protein, (alpha(2))(2), was investigated using guanidine hydrochloride, hydrostatic pressure, and low temperature. Unfolding by guanidine hydrochloride followed by circular dichroism and intrinsic fluorescence spectroscopy revealed a highly cooperative transition between the native-like and unfolded states, with free energy of unfolding determined from CD data, DeltaG(unf) = 14.3 +/- 0.8 kcal/mol. However, CD and intrinsic fluorescence data were not superimposable, indicating the presence of an intermediate state during the folding transition. To stabilize the folding intermediate, we used hydrostatic pressure and low temperature. In both cases, dissociation of the dimeric native-like (alpha(2))(2) into folded monomers (alpha(2)) was observed. van't Hoff analysis of the low temperature experiments, assuming a two-state dimer 171-monomer transition, yielded a free energy of dissociation of (alpha(2))(2) of DeltaG(diss) = 11.4 +/- 0.4 kcal/mol, in good agreement with the free energy determined from pressure dissociation experiments (DeltaG(diss) = 10.5 +/- 0.1 kcal/mol). Binding of the hydrophobic fluorescent probe 4,4'-dianilino-1,1'-binaphthyl-5,5'-disulfonic acid (bis-ANS) to the pressure- and cold-dissociated states of (alpha(2))(2) indicated the existence of molten-globule monomers. In conclusion, we demonstrate that the folding pathway of (alpha(2))(2) can be described by a three-state transition including a monomeric molten globule-like state.     

Linkage of monovalent and divalent ion binding in the folding of the P4-P6 domain of the Tetrahymena ribozyme

We have explored the linkage of monovalent and divalent ion binding in the folding of the P4-P6 domain of Tetrahymena thermophila ribozyme by examining the Mg2+-induced folding and the urea-induced denaturation of the folded state as a function of Na+ under equilibrium folding conditions using hydroxyl radical footprinting. These studies allowed a thermodynamic examination of eight discrete protection sites within P4-P6 that are involved in several tertiary structure contacts. Monovalent ions compete with Mg2+ ions in mediating P4-P6 folding. The urea denaturation isotherms demonstrated DeltaDeltaG values of >2 kcal x mol(-1) in experiments conducted in 10 versus 200 mM NaCl at a constant 10 mM MgCl2. However, the individual-site isotherms reported by footprinting revealed that larger than average changes in DeltaG values were localized to specific sites within the Mg2+-rich A-bulge. The competitive effects of monovalent ions were less when K+ rather than Na+ was the monovalent cation present. This result indicates the importance of the specific K+ binding sites that are associated with AA-platform structures to P4-P6 folding and stability. These site-specific footprinting data provide quantitative and site-specific measurements of the ion-linked stability for P4-P6 that are interpreted with respect to crystallographic data.     

Structural resiliency of an EGF-like subdomain bound to its target protein, thrombin.

The thrombin-bound structures of native peptide fragments from the fifth EGF-like domain of thrombomodulin were determined by use of NMR and transferred NOE spectroscopy. The bound peptides assume an EGF-like structure of an antiparallel beta-sheet, a novel structural motif observed for a bound peptide in protein-peptide complexes. There is a remarkable structural resiliency of this structure motif manifested in its ability to accommodate a different number of residues within the disulfide loop. Docking experiments revealed that the key contacts with thrombin are hydrophobic interactions between the side chains of residues Ile 414 and Ile 424 of thrombomodulin and a hydrophobic pocket on the thrombin surface. Residues Leu 415, Phe 419, and Ile 420, which would have been buried in intact EGF-like domains, are unfavorably exposed in the complex of thrombin with the EGF-like thrombomodulin fragment, thus providing a rationale for the enhancement of binding affinity upon the deletion of Ile 420. The unique beta-sheet structures of the bound peptides are specified by the presence of disulfide bridges in the peptides because a corresponding linear thrombomodulin fragment folds into a sheet structure with a different backbone topology. The different bound conformations for the linear and the cyclized peptides indicate that side-chain interactions within a specific environment may dictate the folding of bound peptides in protein-peptide complexes.     

Ionic-strength-dependent effects in protein folding: analysis of rate equilibrium free-energy relationships and their interpretation

The traditional approach to studying protein folding involves applying a perturbation, usually denaturant or mutation, and determining the effect upon the free energy of folding, DeltaG0, and the activation free energy, DeltaG(not equal). Data collected as a function of the perturbation can be used to construct rate equilibrium free-energy relationships, which report on the development of interactions in the transition state for folding. We examine the use of the ionic-strength-dependent rate equilibrium free-energy relationship in protein folding using the N-terminal domain of L9, a small alpha-beta protein, as a model system. Folding is two-state for the range of ionic strength examined, 0.045-1.52 M. The plot of DeltaG(not equal) versus DeltaG0 is linear (r2= 0.918), with a slope equal to 0.45. The relatively low value of the slope indicates that the ionic-strength-dependent interactions are modestly developed in the transition state. The slope is, however, greater than that of a plot of DeltaG(not equal) versus DeltaG0 constructed by varying pH, thus demonstrating directly that ionic-strength-dependent studies probe more than simple electrostatic interactions. Potential transition movement was probed by analysis of the denaturant, ionic strength cross-interaction parameters. The values are small but nonzero and positive, suggesting a small shift of the transition state toward the native state as the protein is destabilized, i.e., Hammond behavior. The complications that arise in the interpretation of ionic-strength-dependent rate equilibrium free-energy relationships are discussed, and it is concluded that the ionic-strength-dependent studies do not provide a reliable indicator of the role of electrostatic interactions. Complications include incomplete screening of electrostatic interactions, specific ion binding, Hofmeister effects, and the potential presence of electrostatic interactions in the denatured state ensemble.     

Energetics and cooperativity of tertiary hydrogen bonds in RNA structure.

Tertiary interactions that allow RNA to fold into intricate three-dimensional structures are being identified, but little is known about the thermodynamics of individual interactions. Here we quantify the tertiary structure contributions of individual hydrogen bonds in a "ribose zipper" motif of the recently crystallized Tetrahymena group I intron P4-P6 domain. The 2'-hydroxyls of P4-P6 nucleotides C109/A184 and A183/G110 participate in forming the "teeth" of the zipper. These four nucleotides were substituted in all combinations with their 2'-deoxy and (separately) 2'-methoxy analogues, and thermodynamic effects on the tertiary folding DeltaG degrees ' were assayed by the Mg2+ dependence of electrophoretic mobility in nondenaturing gels. The 2'-deoxy series showed a consistent trend with an average contribution to the tertiary folding DeltaG degrees' of -0.4 to -0.5 kcal/mol per hydrogen bond. Contributions were approximately additive, reflecting no cooperativity among the hydrogen bonds. Each "tooth" of the ribose zipper (comprising two hydrogen bonds) thus contributes about -1.0 kcal/mol to the tertiary folding DeltaG degrees'. Single 2'-methoxy substitutions destabilized folding by approximately 1 kcal/mol, but the trend reversed with multiple 2'-methoxy substitutions; the folding DeltaG degrees' for the quadruple 2'-methoxy derivative was approximately unchanged relative to wild-type. On the basis of these data and on temperature-gradient gel results, we conclude that entropically favorable hydrophobic interactions balance enthalpically unfavorable hydrogen bond deletions and steric clashes for multiple 2'-methoxy substitutions. Because many of the 2'-deoxy derivatives no longer have the characteristic hydrogen-bond patterns of the ribose zipper motif but simply have individual long-range ribose-base or ribose-ribose hydrogen bonds, we speculate that the energetic value of -0.4 to -0.5 kcal/mol per tertiary hydrogen bond may be more generally applicable to RNA folding.     

Influence of modulated structural dynamics on the kinetics of alpha-chymotrypsin catalysis. Insights through chemical glycosylation, molecular dynamics and domain motion analysis

Although the chemical nature of the catalytic mechanism of the serine protease alpha-chymotrypsin (alpha-CT) is largely understood, the influence of the enzyme's structural dynamics on its catalysis remains uncertain. Here we investigate whether alpha-CT's structural dynamics directly influence the kinetics of enzyme catalysis. Chemical glycosylation [Solá RJ & Griebenow K (2006) FEBS Lett 580, 1685-1690] was used to generate a series of glycosylated alpha-CT conjugates with reduced structural dynamics, as determined from amide hydrogen/deuterium exchange kinetics (k(HX)). Determination of their catalytic behavior (K(S), k(2), and k(3)) for the hydrolysis of N-succinyl-Ala-Ala-Pro-Phe p-nitroanilide (Suc-Ala-Ala-Pro-Phe-pNA) revealed decreased kinetics for the catalytic steps (k(2) and k(3)) without affecting substrate binding (K(S)) at increasing glycosylation levels. Statistical correlation analysis between the catalytic (DeltaG( not equal)k(i)) and structurally dynamic (DeltaG(HX)) parameters determined revealed that the enzyme acylation and deacylation steps are directly influenced by the changes in protein structural dynamics. Molecular modelling of the alpha-CT glycoconjugates coupled with molecular dynamics simulations and domain motion analysis employing the Gaussian network model revealed structural insights into the relation between the protein's surface glycosylation, the resulting structural dynamic changes, and the influence of these on the enzyme's collective dynamics and catalytic residues. The experimental and theoretical results presented here not only provide fundamental insights concerning the influence of glycosylation on the protein biophysical properties but also support the hypothesis that for alpha-CT the global structural dynamics directly influence the kinetics of enzyme catalysis via mechanochemical coupling between domain motions and active site chemical groups.     

Evaluation of gravimetric techniques to estimate the microvascular filtration coefficient

Microvascular permeability to water is characterized by the microvascular filtration coefficient (K(f)). Conventional gravimetric techniques to estimate K(f) rely on data obtained from either transient or steady-state increases in organ weight in response to increases in microvascular pressure. Both techniques result in considerably different estimates and neither account for interstitial fluid storage and lymphatic return. We therefore developed a theoretical framework to evaluate K(f) estimation techniques by 1) comparing conventional techniques to a novel technique that includes effects of interstitial fluid storage and lymphatic return, 2) evaluating the ability of conventional techniques to reproduce K(f) from simulated gravimetric data generated by a realistic interstitial fluid balance model, 3) analyzing new data collected from rat intestine, and 4) analyzing previously reported data. These approaches revealed that the steady-state gravimetric technique yields estimates that are not directly related to K(f) and are in some cases directly proportional to interstitial compliance. However, the transient gravimetric technique yields accurate estimates in some organs, because the typical experimental duration minimizes the effects of interstitial fluid storage and lymphatic return. Furthermore, our analytical framework reveals that the supposed requirement of tying off all draining lymphatic vessels for the transient technique is unnecessary. Finally, our numerical simulations indicate that our comprehensive technique accurately reproduces the value of K(f) in all organs, is not confounded by interstitial storage and lymphatic return, and provides corroboration of the estimate from the transient technique.     

Use of MM-PB/SA in estimating the free energies of proteins: application to native, intermediates, and unfolded villin headpiece

We investigated the stability of three different ensembles of the 36-mer villin headpiece subdomain, the native, a compact folding intermediate, and the random coil. Structures were taken from a 1-micros molecular dynamics folding simulation and a 100-ns control simulation on the native structure. Our approach for each conformation is to first determine the solute internal energy from the molecular mechanics potential and then to add the change resulting from solvation (DeltaG(solv)). Explicit water was used to run the simulation, and a continuum model was used to estimate DeltaG(solv) with the finite difference Poisson-Boltzmann model accounting for the polarization part and a linearly surface area-dependent term for the non-polar part. We leave out the solute vibrational entropy from these values but demonstrate that there is no statistical difference among the native, folding intermediate, and random coil ensembles. We find the native ensemble to be approximately 26 kcal/mol more stable than the folding intermediate and approximately 39 kcal/mol more stable than the random coil ensemble. With an experimental estimate for the free energy of denaturation equal to 3 kcal/mol, we approximate the non-native degeneracy to lie between 10(16) and 10.(25) We also present a possible scheme for the mechanism of folding, first-order exponential decay of a putative transition state, with an estimate for the t(1/2) of folding of approximately 1 micros.