Model for calculation of electrostatic interactions in unfolded proteins

An efficient method to predict protein thermostability in alanine mutation

The relationship between protein sequence and its thermodynamic stability is a critical aspect of computational protein design. In this work, we present a new theoretical method to calculate the free energy change (ΔΔG) resulting from a single-point amino acid mutation to alanine in a protein sequence. The method is derived based on physical interactions and is very efficient in estimating the free energy changes caused by a series of alanine mutations from just a single molecular dynamics (MD) trajectory. Numerical calculations are carried out on a total of 547 alanine mutations in 19 diverse proteins whose experimental results are available. The comparison between the experimental ΔΔG_exp and the calculated values shows a generally good correlation with a correlation coefficient of 0.67. Both the advantages and limitations of this method are discussed. This method provides an efficient and valuable tool for protein design and engineering.

Sealing hyaluronic acid microgels with oppositely-charged polypeptides: A simple strategy for packaging hydrophilic drugs with on-demand release

A simple route to deliver on demand hydrosoluble molecules such as peptides, packaged in biocompatible and biodegradable microgels, is presented. Hyaluronic acid hydrogel particles with a controlled structure are prepared using a microfluidic approach. Their porosity and their rigidity can be tuned by changing the crosslinking density. These negatively-charged polyelectrolytes interact strongly with positively-charged linear peptides such as poly-l-lysine (PLL). Their interactions induce microgel deswelling and inhibit microgel enzymatic degradability by hyaluronidase. While small PLL penetrate the whole volume of the microgel, PLL larger than the mesh size of the network remain confined at its periphery. They make a complexed layer with reduced pore size, which insulates the microgel inner core from the outer medium. Consequently, enzymatic degradation of the matrix is fully inhibited and non-affinity hydrophilic species can be trapped in the core. Indeed, negatively-charged or small neutral peptides, without interactions with the network, usually diffuse freely across the network. By simple addition of large PLL, they are packaged in the core and can be released on demand, upon introduction of an enzyme that degrades selectively the capping agent. Single polyelectrolyte layer appears as a simple generic method to coat hydrogel-based materials of various scales for encapsulation and controlled delivery of hydrosoluble molecules.

Ionic Strength, Surface Charge, and Packing Density Effects on the Properties of Peptide Self-Assembled Monolayers

The various environmental parameters of packing density, ionic strength, and solution charge were examined for their effects on the properties of the immobilized peptide mimotope CH19 (CGSGSGSQLGPYELWELSH) that binds with the therapeutic antibody Trastuzumab (Herceptin) on a gold substrate. The immobilization of CH19 onto gold was examined with a quartz crystal microbalance (QCM). The QCM data showed the presence of intermolecular interactions resulting in the increase of viscoelastic properties of the peptide self-assembled monolayer (SAM). The CH19 SAM was diluted with CS7 (CGSGSGS) to decrease the packing density as CH19/CS7. The packing density and ionic strength parameters were evaluated by atomic force microscopy (AFM), ellipsometry, and QCM. AFM and ellipsometry showed a distinct conformational difference between CH19 and CH19/CS7, indicating a relationship between packing density and conformational state of the immobilized peptide. The CH19 SAM thickness was 40 Å with a rough topology, while the CH19/CS7 SAM thickness was 20 Å with a smooth topology. The affinity studies showed that the affinity of CH19 and CH19/CS7 to Trastuzumab were both on the order of 10⁷ M^-1 in undiluted PBS buffer, while the dilution of the buffer by 1000× increased both SAMs affinities to Trastuzumab to the order of 10¹⁵ M^-2 and changed the binding behavior from noncooperative to cooperative binding. This indicated that ionic strength had a more pronounced effect on binding properties of the CH19 SAM than packing density. Electrochemical impedance spectroscopy (EIS) was conducted on the CH19/CS7 SAM, which showed an increase in impedance after each EIS measurement cycle. Cyclic voltammetry on the CH19/CS7 SAM decreased impedance to near initial values. The impact of the packing density, buffer ionic strength, and local charge perturbation of the peptide SAM properties was interpreted based on the titratable sites in CH19 that could participate in the proton transfer and water equilibrium.

Predicting folding free energy changes upon single point mutations

MOTIVATION

The folding free energy is an important characteristic of proteins stability and is directly related to protein's wild-type function. The changes of protein's stability due to naturally occurring mutations, missense mutations, are typically causing diseases. Single point mutations made in vitro are frequently used to assess the contribution of given amino acid to the stability of the protein. In both cases, it is desirable to predict the change of the folding free energy upon single point mutations in order to either provide insights of the molecular mechanism of the change or to design new experimental studies.

RESULTS

We report an approach that predicts the free energy change upon single point mutation by utilizing the 3D structure of the wild-type protein. It is based on variation of the molecular mechanics Generalized Born (MMGB) method, scaled with optimized parameters (sMMGB) and utilizing specific model of unfolded state. The corresponding mutations are built in silico and the predictions are tested against large dataset of 1109 mutations with experimentally measured changes of the folding free energy. Benchmarking resulted in root mean square deviation = 1.78 kcal/mol and slope of the linear regression fit between the experimental data and the calculations was 1.04. The sMMGB is compared with other leading methods of predicting folding free energy changes upon single mutations and results discussed with respect to various parameters.

AVAILABILITY

All the pdb files we used in this article can be downloaded from http://compbio.clemson.edu/downloadDir/mentaldisorders/sMMGB_pdb.rar.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Electrostatic contribution to the thermodynamic and kinetic stability of the homotrimeric coiled coil Lpp-56: A computational study

The protein moiety of the Braun's E. coli outer membrane lipoprotein (Lpp-56) is an attractive object of biophysical investigation in several aspects. It is a homotrimeric, parallel coiled coil, a class of coiled coils whose stability and folding have been studied only occasionally. Lpp-56 possesses unique structural properties and exhibits extremely low rates of folding and unfolding. It is natural to ask how the specificity of the structure determines the extraordinary physical chemical properties of this protein. Recently, a seemingly controversial data on the stability and unfolding rate of Lpp-56 have been published (Dragan et al., Biochemistry 2004;43: 14891-14900; Bjelic et al., Biochemistry 2006;45:8931-8939). The unfolding rate constant measured using GdmCl as the denaturing agent, though extremely low, was substantially higher than that obtained on the basis of thermal unfolding. If this large difference arises from the effect of screening of electrostatic interactions induced by GdmCl, electrostatic interactions would appear to be an important factor determining the unusual properties of Lpp-56. We present here a computational analysis of the electrostatic properties of Lpp-56 combining molecular dynamics simulations and continuum pK calculations. The pH-dependence of the unfolding free energy is predicted in good agreement with the experimental data: the change in DeltaG between pH 3 and pH 7 is approximately 60 kJ mol(-1). The results suggest that the difference in the stability of the protein observed using different experimental methods is mainly because of the effect of the reduction of electrostatic interactions when the salt (GdmCl) concentration increases. We also find that the occupancy of the interhelical salt bridges is unusually high. We hypothesize that electrostatic interactions, and the interhelical salt bridges in particular, are an important factor determining the low unfolding rate of Lpp-56.

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.

Interaction between lysozyme and poly(acrylic acid) microgels

The interaction between lysozyme and oppositely charged poly(acrylic acid) microgels was investigated by micromanipulator-assisted light microscopy, confocal microscopy and circular dichroism. Lysozyme uptake and distribution within the microgel particles, and its effect on microgel deswelling, was studied regarding effects of pH, ionic strength and lysozyme concentration. For a range of conditions, lysozyme distributes nonuniformly within the microgels, forming a lysozyme/microgel shell in the outer parts of the microgel. This shell formation is associated both with increased lysozyme loading to the microgels and with increased lysozyme-induced microgel deswelling. At high microgel charge density, the shell formation displays nonmonotonic ionic strength dependence. The shells formed are characterized by a net positive charge, and by relatively fast exchange of lysozyme between shell and solution, although the exchange kinetics decreases strongly with decreasing ionic strength. At conditions of slower exchange kinetics, the shells are characterized by an effective pore size of less than about 4 nm.

Electrostatically tuned rate of peptide self-assembly resolved by multiple particle tracking

Hydrogels formed from the self-assembly of oligopeptides are being extensively studied for biomedical applications. The kinetics of their gelation, as well as a quantitative description of the forces controlling the rate of assembly has not yet been addressed. We report here the use of multiple particle tracking to measure the self-assembly kinetics of the model peptide FKFEFKFE (KFE8). KFE8 forms well-defined β-sheet intermediates and is often used as a model peptide system that forms a fibrous network in aqueous solvent. We find that increasing the pH of this system from 3.5 to 4.0 decreases the time of KFE8 gelation by almost hundredfold, from hours to minutes. A remarkable self-similarity between measurements performed at different pH suggests that, although accelerated by the pH increase, gelation follows an invariable mechanism. We propose a semi-quantitative interpretation for the order of magnitudes of gelation time using a simple model for the interaction driving the self-assembly in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Such understanding is important for the development of current and future therapeutic applications ( drug delivery).

Visualizing the interaction between poly-L-lysine and poly(acrylic acid) microgels using microscopy techniques: effect of electrostatics and peptide size

The interaction between lightly cross-linked poly(acrylic acid) (pAA) microgels (50-150 microm in diameter) and poly-L-lysine (pLys) was studied as a function of pH, ionic strength, peptide size, and concentration. The swelling response and distribution of polypeptides within microgel particles was monitored by micromanipulator-assisted light microscopy and confocal laser scanning microscopy, while binding isotherms of pLys in the microgels were determined spectrophotometrically. Conformational changes of pLys were investigated by circular dichroism. The molecular weight of pLys was found to influence the degree of peptide-induced microgel deswelling, largely due to limitation of peptides larger than the effective network mesh size to penetrate the entire gel. Large peptides were concentrated within a surface layer of the gel particles, and at low ionic strength this dense surface layer was shown to act as a largely steric barrier for further penetration of compounds into the gel core. Small peptides, however, distributed evenly throughout the microgel particles and were able to create large microgel volume reductions. The deswelling of microgels increased with decreasing pH, while the uptake of pLys was significantly reduced at low pH. The effect of ionic strength on the interactions of pLys and oppositely charged pAA microgels was moderate and only pronounced for deswelling of gels at high pH. A significant increase in the alpha-helix content of pLys interacting with the oppositely charged microgels was observed for high molecular weight peptides, and the extent of alpha-helix formation was as expected more pronounced at high pH, i.e., at high charge density of the microgels but reduced charge density of the peptides.

Statistical Studies of Flexible Nonhomogeneous Polypeptide Chains

Unfolded proteins attract increasing attention nowadays because of the accumulation of experimental evidence that they play an important role in different biological processes. Therefore, studies of various statistical properties of flexible protein-like polypeptide chains are becoming increasingly important as well. This paper presents distributions (histograms) of distances between atoms of titratable residues for flexible polypeptide chains with various residue compositions and with the hard-spheres potential taken into consideration. The factors influencing the parameters of the obtained histograms have been identified and analyzed. It was found that the sensitivity of the distributions with respect to the internal structure of intermediate residues increases with the number of residues between the considered charged residues. It was shown that branching at C(beta) atoms of the side chains of the intermediate residues is among the most considerable factors influencing the shape of the distance distribution and the average distance between atoms in flexible chains. Despite the model simplicity, the results of the calculations can be applied for systems with other types of interactions presented, and this was demonstrated for the charge-charge interactions. In particular, it was shown that those interactions have a significant effect on distances between the unlike charges, while such an effect for the like charges is much less pronounced. The comparison of predictions made on the basis of the presented calculations to some experimental data is also given, and possible applications of the theoretical concept described in the paper are discussed.

Nonspherical assemblies generated from polystyrene-b-poly(L-lysine) polyelectrolyte block copolymers

This report describes the aqueous solution self-assembly of a series of polystyrene(m)-b-poly(L-lysine)n block copolymers (m = 8-10; n = 10-70). The polymers are prepared by ring-opening polymerization of epsilon-benzyloxycarbonyl-L-lysine N-carboxyanhydride using amine terminated polystyrene macroinitiators, followed by removal of the benzyloxycarbonyl side chain protecting groups. The critical micelle concentration of the block copolymers determined using the pyrene probe technique shows a parabolic dependence on peptide block length exhibiting a maximum at n = approximately 20 (m = 8) or n = approximately 60 (m = 10). The shape and size of the aggregates has been studied by dynamic and static light scattering, small-angle neutron scattering (SANS), and analytical ultracentrifugation (AUC). Surprisingly, Holtzer and Kratky analysis of the static light scattering results indicates the presence of nonspherical, presumably cylindrical objects independent of the poly(L-lysine)n block length. This is supported by SANS data, which can be fitted well by assuming cylindrical scattering objects. AUC analysis allows the molecular weight of the aggregates to be estimated as several million g/mol, corresponding to aggregation numbers of several 10s to 100s. These aggregation numbers agree with those that can be estimated from the length and diameter of the cylinders obtained from the scattering results.

A coarse-grained molecular model for glycosaminoglycans: application to chondroitin, chondroitin sulfate, and hyaluronic acid

A coarse-grained molecular model is presented for the study of the equilibrium conformation and titration behavior of chondroitin (CH), chondroitin sulfate (CS), and hyaluronic acid (HA)-glycosaminoglycans (GAGs) that play a central role in determining the structure and biomechanical properties of the extracellular matrix of articular cartilage. Systematic coarse-graining from an all-atom description of the disaccharide building blocks retains the polyelectrolytes' specific chemical properties while enabling the simulation of high molecular weight chains that are inaccessible to all-atom representations. Results are presented for the characteristic ratio, the ionic strength-dependent persistence length, the pH-dependent expansion factor for the end-to-end distance, and the titration behavior of the GAGs. Although 4-sulfation of the N-acetyl-D-galactosamine residue is found to increase significantly the intrinsic stiffness of CH with respect to 6-sulfation, only small differences in the titration behavior of the two sulfated forms of CH are found. Persistence length expressions are presented for each type of GAG using a macroscopic (wormlike chain-based) and a microscopic (bond vector correlation-based) definition. Model predictions agree quantitatively with experimental conformation and titration measurements, which support use of the model in the investigation of equilibrium solution properties of GAGs.

Site-specific contributions to the pH dependence of protein stability

Understanding protein stability is a significant challenge requiring characterization of interactions within both folded and unfolded states. Of these, electrostatic interactions influence ionization equilibria of acidic and basic groups and diversify their pK(a) values. The pH dependence of the thermodynamic stability (Delta G(FU)) of a protein arises as a consequence of differential pK(a) values between folded and unfolded states. Previous attempts to calculate pH-dependent contributions to stability have been limited by the lack of experimental unfolded state pK(a) values. Using recently developed NMR spectroscopic methods, we have determined residue-specific pK(a) values for a thermodynamically unstable Src homology 3 domain in both states, enabling the calculation of the pH dependence of stability based on simple analytical expressions. The calculated pH stability profile obtained agrees very well with experiment, unlike profiles derived from two current models of electrostatic interactions within unfolded states. Most importantly, per-residue contributions to the pH dependence of Delta G(FU) derived from the data provide insights into specific electrostatic interactions in both the folded and unfolded states and their roles in protein stability. These interactions include a hydrogen bond between the Asp-8 side-chain and the Lys-21 backbone amide group in the folded state, which represents a highly conserved interaction in Src homology 3 domains.

Residual charge interactions in unfolded staphylococcal nuclease can be explained by the Gaussian-chain model

The discrepancy of the pH dependence of the unfolding free energy for staphylococcal nuclease from what is expected from an idealized model for the unfolded state is accounted for by the recently developed Gaussian-chain model. Residual electrostatic effects in the unfolded state are attributed to nonspecific interactions dominated by charges close along the sequence. The dominance of nonspecific local interactions appears to be supported by some experimental evidence.

Modeling of denatured state for calculation of the electrostatic contribution to protein stability

Existing models of the denatured state of proteins consider only one possible spatial distribution of protein charges and therefore are applicable to a limited number of cases. In this article, a more general framework for the modeling of the denatured state is proposed. It is based on the assumption that the titratable groups of an unfolded protein can adopt a quasi-random distribution restricted by the protein sequence. The model was applied for the calculations of electrostatic interactions in two proteins, barnase and N-terminal domain of the ribosomal protein L9. The calculated free energy of denaturation, DeltaG(pH), reproduces the experimental data better than the commonly used null approximation (NA). It was shown that the seemingly good agreement with experimental data obtained by NA originates from the compensatory effect between the pairwise electrostatic interactions and the desolvation energy of the individual sites. It was also found that the ionization properties of denatured proteins are influenced by the protein sequence.

Residual electrostatic effects in the unfolded state of the N-terminal domain of L9 can be attributed to nonspecific nonlocal charge-charge interactions

Residual electrostatic interactions in the unfolded state of the N-terminal domain of L9 (NTL9) were found by Kuhlman et al. [(1999) Biochemistry 38, 4896-4903]. These residual interactions are analyzed here by the Gaussian-chain model [Zhou, H.-X. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 3569-3574]. The original model is made more realistic by replacing "standard" model-compound pK(a) values for ionizable groups by those measured by Kuhlman et al. in peptide fragments of NTL9. The predicted pH dependence of the unfolding free energy is in agreement with experiment over the pH range of 1-7 at ionic strengths of 100 and 750 mM. This indicates that the residual electrostatic effects in the unfolded state of NTL9 can be attributed to nonspecific nonlocal charge-charge interactions.