Unfolded Polypeptide Chains Research Articles

Insight into the Structure of Amyloid Fibrils from the Analysis of Globular Proteins

The conversion from soluble states into cross-β fibrillar aggregates is a property shared by many different proteins and peptides and was hence conjectured to be a generic feature of polypeptide chains. Increasing evidence is now accumulating that such fibrillar assemblies are generally characterized by a parallel in-register alignment of β-strands contributed by distinct protein molecules. Here we assume a universal mechanism is responsible for β-structure formation and deduce sequence-specific interaction energies between pairs of protein fragments from a statistical analysis of the native folds of globular proteins. The derived fragment–fragment interaction was implemented within a novel algorithm, prediction of amyloid structure aggregation (PASTA), to investigate the role of sequence heterogeneity in driving specific aggregation into ordered self-propagating cross-β structures. The algorithm predicts that the parallel in-register arrangement of sequence portions that participate in the fibril cross-β core is favoured in most cases. However, the antiparallel arrangement is correctly discriminated when present in fibrils formed by short peptides. The predictions of the most aggregation-prone portions of initially unfolded polypeptide chains are also in excellent agreement with available experimental observations. These results corroborate the recent hypothesis that the amyloid structure is stabilised by the same physicochemical determinants as those operating in folded proteins. They also suggest that side chain–side chain interaction across neighbouring β-strands is a key determinant of amyloid fibril formation and of their self-propagating ability.

Protein polymer drag-tags for DNA separations by end-labeled free-solution electrophoresis

We demonstrate the feasibility of end-labeled free-solution electrophoresis (ELFSE) separation of DNA using genetically engineered protein polymers as drag-tags. Protein polymers are promising candidates for ELFSE drag-tags because their sequences and lengths are controllable not only to generate monodisperse polymers with high frictional drag, but also to meet other drag-tag requirements for high-resolution separations by microchannel electrophoresis. A series of repetitive polypeptides was designed, expressed in Escherichia coli, and purified. By performing an end-on conjugation of the protein polymers to a fluorescently labeled DNA oligomer (22 bases) and analyzing the electrophoretic mobilities of the conjugate molecules by free-solution capillary electrophoresis (CE), effects of the size and charge of the protein polymer drag-tags were investigated. In addition, the electrophoretic behavior of bioconjugates comprising relatively long DNA fragments (108 and 208 bases) and attached to uncharged drag-tags was observed, by conjugating fluorescently labeled polymerase chain reaction (PCR) products to charge-neutral protein polymers, and analyzing via CE. We calculated the amount of friction generated by the various drag-tags, and estimated the potential read-lengths that could be obtained if these drag-tags were used for DNA sequencing in our current system. The results of these studies indicate that larger and uncharged drag-tags will have the best DNA-resolving capability for ELFSE separations, and that theoretically, up to 233 DNA bases could be sequenced using one of the protein polymer drag-tags we produced, which is electrostatically neutral with a chain length of 337 amino acids. We also show that denatured (unfolded) polypeptide chains impose much greater frictional drag per unit molecular weight than folded proteins, such as streptavidin, which has been used as a drag-tag before.

Amyloid-like Properties of Bacterial Inclusion Bodies

Bacterial inclusion bodies are major bottlenecks in protein production, narrowing the spectrum of relevant polypeptides obtained by recombinant DNA. While regarded as amorphous deposits formed by passive and rather unspecific precipitation of unfolded chains, we prove here that they are instead organized aggregates sharing important structural and biological features with amyloids. By using an Escherichia coli beta-galactosidase variant, we show that aggregation does not necessarily require unfolded polypeptide chains but rather depends on specific interactions between solvent-exposed hydrophobic stretches in partially structured species. In addition, purified inclusion bodies are efficient and highly selective nucleation seeds, promoting deposition of soluble homologous but not heterologous polypeptides in a dose-dependent manner. Finally, inclusion bodies bind amyloid-diagnostic dyes, which, jointly with Fourier transform infra red spectroscopy data, indicates a high level of organized intermolecular beta-sheet structure. The evidences of amyloid-like structure of bacterial inclusion bodies, irrespective of potential applications in bioprocess engineering, prompts the use of bacterial models to explore the molecular determinants of protein aggregation by means of simple biological systems.

Models for Excluded Volume Interaction between an Unfolded Protein and Rigid Macromolecular Cosolutes: Macromolecular Crowding and Protein Stability Revisited

Statistical-thermodynamic models for the excluded volume interaction between an unfolded polypeptide chain and a hard sphere or hard rod cosolute are presented, permitting estimation of the free energy of transfer of a polypeptide chain with fixed radius of gyration from a dilute (ideal) solution to a solution containing volume fraction ϕ of either cosolute. Also presented is a general thermodynamic description of the equilibrium between a unique native state and a manifold of unfolded or partially unfolded states of a protein distinguished by their respective radii of gyration. Together with results of a Monte Carlo calculation of the distribution of radii of gyration of four different unfolded proteins published by Goldenberg in 2003, these models are used to estimate the effect of intermolecular excluded volume upon an experimentally measurable apparent two-state constant for equilibrium between native and nonnative conformations of each of the four proteins, and upon the experimentally measurable root mean-square radius of gyration of the unfolded protein. Model calculations predict that addition of inert cosolutes at volume fractions exceeding 0.1 stabilizes the native state relative to unfolded states by an amount that increases strongly with ϕ and with the size of the native protein relative to the size of inert cosolute, and results in significant compaction of the manifold of unfolded states. Predicted effects are in qualitative and/or semiquantitative accord with the results of several published experimental studies.

Molecular Basis for the Effect of Urea and Guanidinium Chloride on the Dynamics of Unfolded Polypeptide Chains

Chemical denaturants are frequently used to unfold proteins and to characterize mechanisms and transition states of protein folding reactions. The molecular basis of the effect of urea and guanidinium chloride (GdmCl) on polypeptide chains is still not well understood. Models for denaturant--protein interaction include both direct binding and indirect changes in solvent properties. Here we report studies on the effect of urea and GdmCl on the rate constants (k(c)) of end-to-end diffusion in unstructured poly(glycine-serine) chains of different length. Urea and GdmCl both lead to a linear decrease of lnk(c) with denaturant concentration, as observed for the rate constants for protein folding. This suggests that the effect of denaturants on chain dynamics significantly contributes to the denaturant-dependence of folding rate constants for small proteins. We show that this linear dependency is the result of two additive non-linear effects, namely increased solvent viscosity and denaturant binding. The contribution from denaturant binding can be quantitatively described by Schellman's weak binding model with binding constants (K) of 0.62(+/-0.01)M(-1) for GdmCl and 0.26(+/-0.01)M(-1) for urea. In our model peptides the number of binding sites and the effect of a bound denaturant molecule on chain dynamics is identical for urea and GdmCl. The results further identify the polypeptide backbone as the major denaturant binding site and give an upper limit of a few nanoseconds for residence times of denaturant molecules on the polypeptide chain.

Protein folding in the cell: on the mechanisms of its acceleration.

The mechanisms responsible for protein folding in the cell can be divided in two groups. The ones in the first group would be those preventing the aggregation of unfolded polypeptide chains or of incompletely folded proteins, as well as the mechanisms which provide for the energy-consuming unfolding of incorrectly folded structures, giving them a chance to begin a new folding cycle. Mechanisms of this type do not affect the rate of folding (it occurs spontaneously), yet considerably increase the efficiency of the entire process. By contrast, the mechanisms belonging to second group actually accelerate protein folding by exerting a direct influence on the rate-limiting steps of the overall reaction. Although not a conventional one, such a classification helps define the topic of this review. Its main purpose is to discuss the ability of chaperonins (and that of some chaperones) to interact directly with substrate proteins in the course of their folding and thus accelerate the rate-limiting steps of that process. (Mechanisms of protein folding acceleration produced by the action of enzymes, e.g., peptidyl-prolyl cis/trans isomerase and protein disulfide isomerase, are not considered in this review.) Specific cases demonstrating an accelerated folding of some proteins encapsulated in the bacterial chaperonin GroEL cavity are considered, and the conditions favoring such acceleration are examined. Experimental data supporting the notion that the structure and functional properties of GroEL are not optimal for an effective folding of many of its substrate proteins is discussed. The current status of research on the mechanism behind the active participation of different subunits of eucaryotic cytosol chaperonin (CCT) in the final steps of the folding of actin and tubulin is reviewed. Particular attention is devoted to steric chaperones, which dramatically accelerate the formation of the native structure of their substrate proteins by stabilizing certain folding intermediates. The structural foundations underlying the effect of the subtilisin pro-domain on the folding of the mature enzyme are considered. The prospects of future studies into the mechanisms responsible for accelerating protein folding in the cell are commented upon.

Intrachain diffusion in a protein loop fragment from carp parvalbumin

During protein folding a polypeptide chain has to form specific intrachain interactions starting from an ensemble of unfolded conformation. Thus, intrachain diffusion in unfolded polypeptide chains can be regarded as an elementary step in protein folding, which should determine the dynamics of the early stages in the folding process. We have previously applied exothermic triplet-triplet energy transfer from xanthone to naphthalene to determine rate constants for intrachain end-to-end contact formation in unstructured homo-polypeptide chains. Here we show that the method can be applied to determine absolute rate constants for intrachain diffusion in natural loop sequences, if they are free of methionine, tryptophan and tyrosine. We measured the rate of loop formation in an 18 amino acid polypeptide chain corresponding to a natural loop sequence from carp muscle β-parvalbumin (residues 85-102). Contact formation shows single exponential kinetics with a time constant (τ=1/k) of 53 ± 3 ns at 22.5°C in water. Comparison with the results on homo-polypeptide chains shows that this value agrees well with rates obtained earlier for a polyserine chain of the same length. © 2004 Elsevier B.V. All rights reserved.

Structural Characterization of Unfolded States of Apomyoglobin using Residual Dipolar Couplings

The conformational propensities of unfolded states of apomyoglobin have been investigated by measurement of residual dipolar couplings between 15N and 1H in backbone amide groups. Weak alignment of apomyoglobin in acid and urea-unfolded states was induced with both stretched and compressed polyacrylamide gels. In 8 M urea solution at pH 2.3, conditions under which apomyoglobin contains no detectable secondary or tertiary structure, significant residual dipolar couplings of uniform sign were observed for all residues. At pH 2.3 in the absence of urea, a change in the magnitude and/or sign of the residual dipolar couplings occurs in local regions of the polypeptide where there is a high propensity for helical secondary structure. These results are interpreted on the basis of the statistical properties of the unfolded polypeptide chain, viewed as a polymer of statistical segments. For a folded protein, the magnitude and sign of the residual dipolar couplings depend on the orientation of each bond vector relative to the alignment tensor of the entire molecule, which reorients as a single entity. For unfolded proteins, there is no global alignment tensor; instead, residual dipolar couplings are attributed to alignment of the statistical segments or of transient elements of secondary structure. For apomyoglobin in 8 M urea, the backbone is highly extended, with φ and ψ dihedral angles favoring the β or P II regions. Each statistical segment has a highly anisotropic shape, with the N–H bond vectors approximately perpendicular to the long axis, and becomes weakly aligned in the anisotropic environment of the strained acrylamide gels. Local regions of enhanced flexibility or chain compaction are characterized by a decrease in the magnitude of the residual dipolar couplings. The formation of a small population of helical structure in the acid-denatured state of apomyoglobin leads to a change in sign of the residual dipolar couplings in local regions of the polypeptide; the population of helix estimated from the residual dipolar couplings is in excellent agreement with that determined from chemical shifts. The alignment model described here for apomyoglobin can also explain the pattern of residual dipolar couplings reported previously for denatured states of staphylococcal nuclease and other proteins. In conjunction with other NMR experiments, residual dipolar couplings can provide valuable insights into the dynamic conformational propensities of unfolded and partly folded states of proteins and thereby help to chart the upper reaches of the folding landscape.

The Bacterial Protein–Translocation Complex: SecYEG Dimers Associate with One or Two SecA Molecules

In bacteria, the Sec-protein transport complex facilitates the passage of most secretory and membrane proteins across and into the plasma membrane. The core complex SecYEG forms the protein channel and engages either ribosomes or the ATPase SecA, which drive translocation of unfolded polypeptide chains through the complex and into the periplasmic space. Escherichia coli SecYEG forms dimers in membranes, but in detergent solution the population of these dimers is low. However, we find that stable dimers can be assembled by the addition of a monoclonal antibody. Normally, a stable SecYEG–SecA complex can only form on isolated membranes or on reconstituted proteo-liposomes. The antibody-stabilised SecYEG dimer binds one SecA molecule in detergent solution. In the presence of AMPPNP, a non-hydrolysable analogue of ATP, a complex forms containing one antibody and two each of SecYEG and SecA. SecYEG monomers or tetramers do not associate to a significant degree with SecA. The observed variability in the stoichiometry of SecYEG and SecA association and its nucleotide modulation may be important and necessary for the protein translocation reaction.

Dynamics of Unfolded Polypeptide Chains as Model for the Earliest Steps in Protein Folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet–triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/ k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.

Rationalization of the effects of mutations on peptide and protein aggregation rates.

In order for any biological system to function effectively, it is essential to avoid the inherent tendency of proteins to aggregate and form potentially harmful deposits. In each of the various pathological conditions associated with protein deposition, such as Alzheimer's and Parkinson's diseases, a specific peptide or protein that is normally soluble is deposited as insoluble aggregates generally referred to as amyloid. It is clear that the aggregation process is generally initiated from partially or completely unfolded forms of the peptides and proteins associated with each disease. Here we show that the intrinsic effects of specific mutations on the rates of aggregation of unfolded polypeptide chains can be correlated to a remarkable extent with changes in simple physicochemical properties such as hydrophobicity, secondary structure propensity and charge. This approach allows the pathogenic effects of mutations associated with known familial forms of protein deposition diseases to be rationalized, and more generally enables prediction of the effects of mutations on the aggregation propensity of any polypeptide chain.

Effects of charge–charge interactions on dimensions of unfolded proteins: A Monte Carlo study

Electrostatic interactions (EI) in denatured state of proteins are an important factor regulating folding/unfolding equilibria in these macromolecules. Therefore, a physically adequate model for description of EI in denatured proteins is highly desirable. For this purpose, unfolded polypeptide chains with excluded volume and charge–charge interactions taken into consideration were studied by means of Monte Carlo simulations. Charge–charge interactions were calculated using the Coulomb law both with constant, εs, and distance dependent, ε(r), dielectric permittivity. Average dimensions, in terms of radius of gyration, Rg, for chains of different lengths Nr, were obtained within a wide temperature range and for various distributions of positive and negative charges. The results suggest that unfolded proteins can adopt two distinct states, compact and expanded, depending on temperature and charge composition. The compact state is characterized by Rg close to that of native proteins, while the expanded state has Rg corresponding to a flexible homopolymer with excluded volume interactions only. A simple procedure for evaluation of Rg of unfolded proteins at different pH is proposed and the predicted Rg values are compared to the experimental data for fully unfolded states for several soluble denatured proteins.

The pentapeptide GGAGG has PII conformation.

Most of what we know about proteins reflects their native folded structure. Much less is understood about the structure of unfolded proteins, which tends to be referred to as "random coil", lacking extended alpha-helix or beta-strand structure. Recent work suggests that unfolded proteins might adopt significant population of PII structure, an extended left-handed helix found in collagen and proline-rich peptides. A series of short peptides AcGGXGGNH2 has been adopted as a model for studying unfolded protein structure because of the minimal steric effect imposed by flanking glycines. Peptide AcGGAGGNH2 makes possible a host-guest conformation analysis of the middle residue alanine. NMR experiments reveal that the Phi and Psi dihedral angles of the central alanine are -73 degrees and 125 degrees , respectively, placing the alanine in the PII region of the Ramachandran plot. Circular dichroism shows a typical PII spectrum with a strong negative absorbance at 190 nm. Temperature experiments show the alanine structure shifts to increasing beta-strand at high temperature. Because the alanine side chain most closely represents unsubstituted peptide backbone, these results have significant implications for the conformational entropy of unfolded polypeptide chains.

A systematic study of bovine serum albumin (BSA) and sodium dodecyl sulfate (SDS) interactions by surface tension and small angle X-ray scattering

Classical parameters obtained from surface tension technique coupled to small angle X-ray scattering (SAXS) measurements gave support to investigate conformational changes in the bovine serum albumin (BSA)–sodium dodecyl sulfate (SDS) complexes, as well as the size of the micelle-like clusters distributed along the polypeptide chain. The studied systems were composed of 1 wt% of BSA in the absence and presence of increasing SDS molar concentration up to 80 mM, under experimental conditions of low ionic strength and pH 5.40. At SDS concentrations below the critical aggregation concentration ( cac) of 2.2 mM, SAXS results indicate that the detergent does not modify the native protein conformation. However, the beginning of protein unfolding, evidenced by SAXS through an increase in the values of radius of gyration R g and protein maximum dimension D max, is coincident with the onset of SDS cooperative binding to BSA identified by the first breakpoint in the surface tension–SDS profile. Further SDS addition leads to the formation of micelle-like aggregates randomly distributed along the unfolded polypeptide chain, consistent to a necklace and bead model. The SAXS data also demonstrate that the SDS micelles grow in size up to 50 mM detergent. At 50 mM surfactant, the micelles stop growing. This concentration is near the BSA saturation binding by SDS measured by dialyzes and indicated by the second breakpoint in surface tension–SDS profile. The SAXS and surface tension data are also consistent with the formation of free micelles in equilibrium with BSA–SDS complexes for surfactant amount above the saturation.

Hammond Behavior versus Ground State Effects in Protein Folding: Evidence for Narrow Free Energy Barriers and Residual Structure in Unfolded States

Apparent transition state movement upon mutation or changes in solvent conditions is frequently observed in protein folding and is often interpreted in terms of Hammond behavior. This led to the conclusion that barrier regions in protein folding are broad maxima on the free energy landscape. Here, we use the concept of self-interaction and cross-interaction parameters to test experimental data of 21 well-characterized proteins for Hammond behavior. This allows us to characterize the origin of transition state movements along different reaction coordinates. Only one of the 21 proteins shows a small but coherent transition state movement in agreement with the Hammond postulate. In most proteins the structure of the transition state is insensitive to changes in protein stability. The apparent change in the position of the transition state upon mutation, which is frequently observed in φ-value analysis, is in most cases due to ground-state effects caused by structural changes in the unfolded state. This argues for significant residual structure in unfolded polypeptide chains of many proteins. Disruption of these residual interactions by mutation often leads to decreased folding rates, which implies that these interactions are still present in the transition state. The failure to detect Hammond behavior shows that the free energy barriers encountered by a folding polypeptide chain are generally rather narrow and robust maxima for all experimentally explorable reaction coordinates.

Distance and exposure dependent effective dielectric function.

In an effort to develop a dielectric screening function for molecular dynamics simulations of biomolecules in implicit solvent, effective dielectric constants (D(eff)) for a large number of atom pairs in a typical globular protein are calculated by continuum electrostatics. Plots of D(eff) versus the intercharge distance are in general sigmoidal with the characteristics of the curve depending on the distance of the two charges from the dielectric boundary and, secondarily, on the extent to which the area surrounding each charge is occupied by solvent (the "exposure"). The D(eff) values were fitted to an empirical, analytical function of these parameters that reproduces the data reasonably well, although considerable scatter exists in the range of D(eff) from 30 to 80. In the system used for parameterization, the mean square deviation of electrostatic interaction energies with this function is 0.48 kcal/mol, compared to 1.45 for an analytical Generalized Born model and 1.52 for the linear distance-dependent dielectric model. When tested in other proteins of varying size and compactness, the present function is superior to both of the above models, except for a fully unfolded polypeptide chain, where the Generalized Born model is superior.

On the interpretation of force extension curves of single protein molecules

The atomic force microscope can be used to forcibly unfold and extend single polypeptide chains. The resulting force versus distance curves have been widely interpreted to arise from the loss of entropy that the unfolded polypeptide chain experiences as it is extended. Here, we have used Monte Carlo simulations of unfolded polypeptide chains to examine the average distance between the ends of a polypeptide chain as a function of the force that pulls these ends apart. We examine two types of experiments: (a) A rigid force-sensor (bead-type) experiment: The chain is subjected to a constant stretching force f and the resulting chain extension is measured. (b) A flexible force-sensor (cantilever-type) experiment: The force is measured by the deflection of a cantilever that is attached to one end of the chain. The total length of the chain plus the displacement of the cantilever is fixed. In case (b), in the limit of a large cantilever force constant, the entropic force f is related to the free energy of the chain F(r) constrained to have the end-to-end distance r by the usual thermodynamic relationship: f=dF/dr. However in case (a) this relationship is invalid. The reason of its failure is that large fluctuations in the end-to-end distance r cannot be neglected at the single molecule level and so macroscopic thermodynamics relationships cannot be used. Thus the two types of experiments measure different force extension curves f(r). We compute the force extension curves for a model of a polypeptide chain in each case and find that they are significantly different. We further discuss implications of our findings with regard to the results of cantilever-type unfolding experiments.

Evaluation of similarities in the cis/trans isomerase function of trigger factor and DnaK.

Two functionally redundant enzymes, trigger factor and the hsp70 chaperone DnaK, have been found to assist de novo protein folding in E coli. Trigger factor is a peripheral peptidyl prolyl cis/trans isomerase (PPIase) of the large subunit of the ribosome. In contrast, DnaK displays two catalytic features: the secondary amide peptide bond cis/trans isomerase (APIase) function supplemented by the ATPase site. APIases accelerate the cis/trans isomerization of nonprolyl peptide bonds. Both enzymes have affinity for an unfolded polypeptide chain. The diminished low temperature cell viability in the presence of trigger factor variants with impaired PPlase activity indicates that the enhancement of folding rates plays a crucial role in protein folding in vivo. For the DnaK-mediated increase in the folding yield in vitro, the minimal model for APlase catalysis involves the catalyzed partitioning of a rapidly formed folding intermediate as could be inferred from the DnaK/DnaJ/GrpE/ATP-assisted refolding of GdmCl-denatured luciferase. Using three different peptide bond cis/trans isomerization assays in vitro, we could show that there is no overlapping substrate specificity of trigger factor and DnaK. We propose that only if trigger factor recruits supplementing molecules is it capable of exhibiting functional complementarity with DnaK in protein folding.

What does it mean to be natively unfolded?

Natively unfolded or intrinsically unstructured proteins constitute a unique group of the protein kingdom. The evolutionary persistence of such proteins represents strong evidence in the favor of their importance and raises intriguing questions about the role of protein disorders in biological processes. Additionally, natively unfolded proteins, with their lack of ordered structure, represent attractive targets for the biophysical studies of the unfolded polypeptide chain under physiological conditions in vitro. The goal of this study was to summarize the structural information on natively unfolded proteins in order to evaluate their major conformational characteristics. It appeared that natively unfolded proteins are characterized by low overall hydrophobicity and large net charge. They possess hydrodynamic properties typical of random coils in poor solvent, or premolten globule conformation. These proteins show a low level of ordered secondary structure and no tightly packed core. They are very flexible, but may adopt relatively rigid conformations in the presence of natural ligands. Finally, in comparison with the globular proteins, natively unfolded polypeptides possess 'turn out' responses to changes in the environment, as their structural complexities increase at high temperature or at extreme pH.

Model for calculation of electrostatic interactions in unfolded proteins.

An approach for the calculation of electrostatic interactions and titration properties of unfolded polypeptide chains (denatured proteins) is proposed. It is based on a simple representation of the denatured proteins as a state with titratable sites distributed on the surface of a sphere, radius of which is assumed to be equal to the radius of gyration, R(g), of an unfolded molecule. Distances between the charges, d, obey constraints arising from the protein sequence. Criteria for evaluation of the parameters R(g) and d were obtained from computer simulations on a polypeptide consisting of 20 identical amino acids (polylysine). The model was applied for calculation of titration curves of denatured barnase and staphylococcal nuclease. It was demonstrated that the approach proposed gives considerably better agreement with the experimental data than the commonly used null approximation. It was also found that titration properties of denatured proteins are slightly, but distinguishably influenced by the amino-acid sequence of the protein.