A ternary nucleation model for the nucleation pathway of protein folding

Recently [Y. S. Djikaev and E. Ruckenstein, J. Phys. Chem. B 111, 886 (2007)], the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads and the composition of the growing cluster of protein residues was assumed to be constant and equal to the overall protein composition. Here, they further develop the model by considering a protein as a three-component heteropolymer and by allowing the composition of the growing cluster of protein residues to vary independently of the overall one. All the bonds in the heteropolymer (now consisting of hydrophobic, hydrophilic, and neutral beads) have the same constant length, and all the bond angles are equal and fixed. As a crucial idea of the model, an overall potential around the cluster wherein a residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials assigned to the bead. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine its emission and absorption rates by using a first passage time analysis. Knowing these rates as functions of three independent variables of a ternary cluster, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein using a ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time. As an illustration, the model is applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids whereof 40 are hydrophobic, 81 hydrophilic, and 3 neutral. With a reasonable choice of diffusion coefficients of the residues in the native state and potential parameters, the model predicts folding times in the range of 1-100 s.     

Model for the nucleation mechanism of protein folding

A nucleation-like pathway of protein folding involves the formation of a cluster containing native residues that grows by including residues from the unfolded part of the protein. This pathway is examined by using a heteropolymer as a protein model. The model heteropolymer consists of hydrophobic and hydrophilic beads with fixed bond lengths and bond angles. The total energy of the heteropolymer is determined by the pairwise repulsive/attractive interactions between nonlinked beads and by the contribution from the dihedral angles involved. The parameters of these interactions can be rigorously defined, unlike the ill-defined surface tension of a cluster of protein residues that constitutes the basis of a previous nucleation model. The main idea underlying the new model consists of averaging the dihedral potential of a selected residue over all possible configurations of all neighboring residues along the protein chain. The resulting average dihedral potential depends on the distance between the selected residue and the cluster center. Its combination with the average pairwise potential of the selected residue and with a confining potential caused by the bonds between the residues leads to an overall potential around the cluster that has a double-well shape. Residues in the inner (closer to the cluster) well are considered as belonging to the folded cluster, whereas those in the outer well are treated as belonging to the unfolded part of the protein. Transitions of residues from the inner well into the outer one and vice versa are considered as elementary emission and absorption events, respectively. The double-well character of the potential well around the cluster allows one to determine the rates of both emission and absorption of residues by the cluster using a first passage time analysis. Once these rates are found as functions of the cluster size, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein. The model allows one to evaluate the size of the nucleus and the protein folding time. The latter is evaluated as the sum of the times necessary for the first nucleation event to occur and for the nucleus to grow to the maximum size (of the folded protein). Depending on the diffusion coefficients of the native residues in the range from 10(-6) to 10(-8) cm2/s, numerical calculations for a protein of 2500 residues suggest that the folding time ranges from several seconds to several hundreds of seconds.     

Temperature effects on the nucleation mechanism of protein folding and on the barrierless thermal denaturation of a native protein

Recently, the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was treated as a heteropolymer with all the bonds and bond angles equal and constant. As a crucial idea of the model, an overall potential around a cluster of native residues in which a protein residue performs a chaotic motion is considered to be a combination of three potentials: effective pairwise, average dihedral, and confining. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine the rates with which the cluster emits and absorbs residues by using a first passage time analysis. One can then develop a kinetic theory for the nucleation mechanism of protein folding and evaluate the protein folding time. In the present paper we evaluate the optimal temperature at which the protein folding time is the shortest. A method is also proposed to determine the temperature dependence of the folding time without carrying out the time consuming calculations for a series of temperatures. Using Taylor series expansions in the formalism of the first passage time analysis, one can calculate the temperature dependence of the cluster emission and absorption rates in the vicinity of some temperature T(0) if they are known at T(0). Thus one can evaluate the protein folding time t(f) at any other temperature T in the vicinity of T(0) at which the folding time t(f) is known. We also present a model for the thermal denaturation of a protein occurring via the decay of the native structure of the protein. Due to a sufficiently large temperature increase or decrease, the rate with which a cluster of native residues within a protein emits residues becomes larger than the absorption rate in the whole range of cluster sizes up to the size of the whole protein. This leads to the unfolding of the protein in a barrierless way, i.e., as spinodal decomposition. Knowing the cluster emission and absorption rates as functions of temperature and cluster size, one can find the threshold temperatures of cold and hot barrierless denaturation as well as the corresponding unfolding times. Both proposed methods are illustrated by numerical calculations for two model proteins, one consisting of 124 amino acids, the other consisting of 2500 residues. The first one roughly mimicks a bovine pancreatic ribonuclease while the second one is a representative of the largest proteins which are extremely difficult to study by straightforward Monte Carlo or molecular dynamics simulations.     

Morphology and phase separation of hydrophobic clusters of soy globular protein polymers

Protein hydrophobic interaction has been considered the most important factor dominating protein folding, aggregation, gelling, self-assembly, adhesion, and cohesion properties. In this paper, morphology and phase separation of hydrophobic clusters, networks, and aggregates of soy globular protein polymers, induced by using a reducing agent (NaHSO3), are studied using microscopic instruments. The morphology and phase separation of these hydrophobic clusters are sensitive to protein structure and composition, pH, and ionic-strength (I(m)). Most of the clusters are in spherical-shape architecture and mainly consist of hydrophobic polypeptides. Rod-shape clusters were also observed at higher ionic strength, and mainly consist of hydrophilic polypeptides. The ratio of hydrophobic/hydrophilic (HB/HL) polypeptides is important to facilitate the formation of clusters in an environment with a certain pH value and ionic strength. At HB/HL 0.8, uniform spherical clusters were observed and diameters ranged from 30 to 70 nm. At HB/HL <0.8, large spherical clusters were formed with diameters ranging from 100 to 1,000 nm, and at HB/HL >or=1.8, large hydrophobic aggregates formed, and size of aggregates can be up to 2 500 nm. When solid content increased from 3% to 38%, at I(m) or= 0.115 mol x L(-1), HB/HL ratio >or=1.8, the large aggregates became very cohesive and viscoelastic. Clear phase separation was observed during curing between hydrophobic and hydrophilic protein polymers. Phase-separation degree increased as HB/HL ratio increased.     

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.     

pH响应木质素基胶体球的制备和表征

以造纸制浆废液中的松木碱木质素（AL）为原料,通过季铵化改性,制备了季铵化碱木质素（QAL）.QAL与十二烷基苯磺酸钠（SDBS）通过静电作用形成QAL/SDBS复配物,将QAL/SDBS复配物在乙醇/水混合溶剂中进行自组装得到具有pH响应性的胶体球.采用X射线光电子能谱（XPS）、扫描电子显微镜（SEM）、透射电子显微镜（TEM）、元素分析和静态接触角研究了胶体球的形成过程和结构.研究结果表明,QAL/SDBS复配物通过疏水聚集作用形成具有较疏水的“核”和较亲水的“壳”结构的规整胶体球.在pH=3.0时,由于QAL与SDBS间的静电作用和疏水作用使胶体球能够稳定存在.当pH>7.5时,季铵化碱木质素上的羧基电离,由于静电斥力的作用使胶体球开始解聚,当pH=10.5时,季铵化碱木质素上的酚羟基的电离使得QAL与SDBS间的静电斥力增大,胶体球完全解聚.这种在酸性条件下稳定,中性条件下解聚的胶体球在药物缓释方面具有潜在的应用.     

Thermodynamical properties of reaction intermediates during apoplastocyanin folding in time domain

Two intermediates observed for the folding process of apoplastocyanin (apoPC) were investigated by using a photoinduced triggering system combined with the transient grating and transient lens methods. The thermodynamic quantities, enthalpy, heat capacity, partial volume, and thermal expansion volume changes during the protein folding reaction were measured in time domain for the first time. An interesting observation is the positive enthalpy changes during the folding process. This positive enthalpy change must be compensated by positive entropy changes, which could be originated from the dehydration effect of hydrophobic residues and/or the translational entropy gain of bulk water molecules. Observed negative heat capacity change was explained by the dehydration effect of hydrophilic residues and/or motional confinement of amino acid side chains and water molecules in apoPC. The signs of the volume change and thermal expansion volume were different for two processes and these changes were interpreted in terms of the different relative contributions of the hydration and the dehydration of the hydrophilic residues. These results indicated two-step hydrophobic collapses in the early stage of the apoPC folding, but the nature of the dynamics was different.     

二维紧密蛋白质链折叠序列的特性研究

采用完全计数法,研究了二维紧密蛋白质链在不同HP序列时的构象性质,特别是具有唯一基态能量的折叠序列的性质.对于具有N个单体的紧密蛋白质链,发现有一定比例的序列为折叠序列.在这些折叠序列中,疏水基团(H)的数目比亲水基团(P)多20%,并同200种真实蛋白质分子的疏水基团和亲水基团的结果进行了比较.对于不同的折叠序列,根据序列中其疏水基团的数目,把具有相同疏水基团数目的序列归在同一类,发现这样的序列在总的序列中的相对含量满足高斯分布.同时还对序列中H(或者P)团族大小及其分别进行了研究,发现折叠序列与无规随机序列不同.还研究了不同折叠序列在不同链长时的比热情况,发现其相转变温度TC主要与链长有关,与折叠序列无关.     

Selective adsorption of protein molecules on phase-separated sapphire surfaces

Site-selective adsorption of protein molecules was found on sapphire surfaces that exhibit a phase separation into two domains: weakly charged hydrophobic domain and negatively charged hydrophilic one. Ferritin and bovine serum albumin molecules, which are negatively charged in a buffer solution, are adsorbed to the hydrophobic domains. Avidin molecules, which are positively charged, are adsorbed to the other domain. Fibrinogen molecules, which consist of both negative and positive modules, are adsorbed to the whole sapphire surface. Hemoglobin molecules, whose net charge is almost zero, are also adsorbed to the whole surfaces. These results indicate that electrostatic double layer interaction is the primary origin of the observed selectivity. Dependence of protein adsorption or desorption behaviors on the pH value can also be interpreted by the proposed model.     

Thermodynamic stability and kinetic foldability of a lattice protein model

By using serial mutations, i.e., a residue replaced by 19 kinds of naturally occurring residues, the stability of native conformation and folding behavior of mutated sequences are studied. The 3 x 3 x 3 lattice protein model with two kinds of interaction potentials between the residues, namely the original Miyazawa and Jernigan (MJ) potentials and the modified MJ potentials (MMJ), is used. Effects of various sites in the mutated sequences on the stability and foldability are characterized through the Z-score and the folding time. It is found that the sites can be divided into three types, namely the hydrophobic-type (H-type), the hydrophilic-type (P-type) and the neutral-type (N-type). These three types of sites relate to the hydrophobic core, the hydrophilic surface and the parts between them. The stability of the native conformation for the serial mutated sequences increases (or decreases) as the increasing in the hydrophobicity of the mutated residues for the H-type sites (or the P-type sites), while varies randomly for the N-type sites. However, the foldability of the mutated sequences is not always consistent with the thermodynamic stability, and their relationship depends on the site types. Since the hydrophobic tendency of the MJ potentials is strong, the ratio between the number of the H-type sites and the number of the P-type sites is found to be 1:2. Differently, for the MJJ potentials it is found that such a ratio is about 1:1 which is relevant to that of real proteins. This suggests that the modification of the MJ potentials is rational in the aspect of thermodynamic stability. The folding of model proteins with the MMJ potentials is fast. However, the relationship between the foldability and the thermodynamic stability of the mutated sequences is complex.     

蛋白质分子的HNP格点模型

从 6 0种球形蛋白质的结构出发 ,采用Miyazawa Jernigan相互作用矩阵 ,计算了蛋白质分子中氨基酸之间的相互作用能 .发现构成蛋白质分子的 2 0种氨基酸可分成疏水 (Hydrophobic ,H)、中性 (Neutral,N)、亲水(Hydrophilic ,P)基团 .在计算它们之间相互作用能的基础上 ,建立了蛋白质分子的HNP格点模型 .用这个模型计算了二维蛋白质分子在自然态 (Nativestate)时的构象性质 .同时研究了氨基酸序列为HHNHNPNHPP HPNPPHPHPPHHPHNH的折叠过程 ,得到其基态能量为 - 6 4 89RT .这能为研究球形蛋白质的构象性质及折叠过程提供一种更合理的格点模型     

Modification of the thermal unfolding pathways of myoglobin upon drug interaction in different aqueous media

In this work, we have analyzed the influence of two structurally related phenothiazine drugs, promazine and triflupromazine hydrochlorides, when bound to myoglobin, a model protein, and how the drug concentration and solution conditions may affect the denaturation process of this protein. In this manner, we derive the thermodynamic quantities of the unfolding process by using a spectroscopic technique such as UV-vis spectroscopy at different drugs concentrations and at pH 2.5, 5.5, and 9.0. To do this, a thermodynamic model was used which included experimental data corresponding to the pre- and post-transition into the observable transition. It has been found that both drugs play a destabilizing role for the protein, at least at low concentrations. In addition, at acidic pH and higher drug concentrations, a stabilizing effect can be observed, which may be related to the formation of some type of protein refolding, subsequent aggregation, or both. The reason for this behavior has been suggested to be the different protein conformations at acidic pH, the increase of solvent-exposed hydrophobic and hydrophilic residues after denaturation and/or binding, and the different strength of drug-protein interactions when changing the solution conditions. For this reason, thermodynamic quantities such as Gibbs energies, DeltaG, and entropies of unfolding, DeltaS(m), increase as the solution pH increases provided that additional solvent-exposed hydrophobic residues are present, which were previously buried at room temperature. Moreover, the larger binding affinity at pH 9.0 due to enhanced electrostatic interactions between protein and drug molecules (drug and protein differ in their net electrical charge) additionally collaborates to this residue exposition to solvent as a consequence of the alteration of protein conformation as due to drug binding. Comparison of thermodynamic data between promazine and triflupromazine hydrochlorides also shows that drug-protein affinity and hydrophobicity also affect the thermodynamic denaturation parameters.     

Oscillatory molecular driving force for protein folding at high concentration: a molecular simulation

This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained beta-barrel protein at high concentration follows the "collapse-rearrangement" mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the "nucleus" of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (epsilon*(p)) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (epsilon*(p)) to promote the dissociation of aggregates in the low epsilon*(p) regime while promoting folding at a high epsilon*(p). The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.     

Adsorption of monoclonal IgG on polystyrene microspheres

In this paper the adsorption of a monoclonal antibody IgG-1 isotype against HBsAg onto positively and negatively charged polystyrene beads has been studied. To determine the role played by electrostatic forces in the adsorption process different pH values were used. It was confirmed that the affinity of adsorption isotherms depends on the electrostatic interaction between protein and polymer surface. The maximum adsorption amount is located around the i.e.p. of the dissolved protein, and decreases markedly as pH moves away. Thus, the major driving force for adsorption of monoclonal antibodies on polystyrene beads comes from the hydrophobic interaction between the antibody molecules and the adsorbent surface. Desorption of preadsorbed IgG molecules by increasing ionic strength has shown that the positively charged polystyrene is also more hydrophobic in character than the negatively charged one. Finally, electrokinetic experiments have determined that the electric double layer (e.d.l.) of monoclonal antibody changes as the consequence of adsorbing on charged polymer surfaces.     

Polymer thermodynamics of adsorbed protein layers

Since proteins are polymers, their adsorption at interfaces should share some common features with polymers whose adsorption behavior is being rather well understood using current theoretical approaches. Some theoretical developments are highlighted and recent experimental data obtained mostly with β-casein are compared to them. The general conclusions are that the alternating hydrophilic/hydrophobic block theory gives a general frame for the adsorption of proteins. However, the detailed behavior of proteins at interface seems also influenced by non-covalent, say, electrostatic and hydrogen bonds, whose extent and effects are specified by the local conditions (nature of the fluid phases, temperature, pH, ionic strength, etc.).     

Identification of characteristic protein folding channels in a coarse-grained hydrophobic-polar peptide model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.     

Critical residue that promotes protein dimerization: a story of partially exposed Phe25 in 14-3-3σ

Many proteins exist and function as oligomers. While hydrophobic interactions have been recognized as the major driving force for oligomerization, detailed molecular mechanisms for the assembly are unknown. Here, we used 14-3-3σ as a model protein and investigated the role of hydrophobic residues at the dimeric interface using MD simulations and coimmunoprecipitations. We found that a half-exposed and half-buried residue in the interface, Phe(25), plays a more important role in promoting homodimerization than the hydrophobic core residues by organizing both favorable hydrophobic and hydrophilic interactions. Phe(25) is critical in packing and stabilizing hydrophobic core residues. We conclude that the structural stability of hydrophobic cores is critical for a stable homodimer complex and this stable property can be bestowed by residues outside of hydrophobic core. The important organizing activity of Phe(25) for homodimerization of 14-3-3σ originates from its unique physical location, rigidity, size, and hydrophobicity. Thus, hydrophobic residues that are not deeply buried at the oligomeric interface may play important but different roles from the buried core residues and they may promote oligomerization by organizing co-operativity of core and other residues for favorable hydrophobic and electrostatic interactions.     

Redox entropy of plastocyanin: developing a microscopic view of mesoscopic polar solvation

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.     

Structure and dynamics of the solvation of bovine pancreatic trypsin inhibitor in explicit water: a comparative study of the effects of solvent and protein polarizability

To isolate the effects of the inclusion of polarizability in the force field model on the structure and dynamics of the solvating water in differing electrostatic environments of proteins, we present the results of molecular dynamics simulations of the bovine pancreatic trypsin inhibitor (BPTI) in water with force fields that explicitly include polarization for both the protein and the water. We use three model potentials for water and two model potentials for the protein. Two of the water models and one of the protein models are polarizable. A total of six systems were simulated representing all combinations of these polarizable and nonpolarizable protein and water force fields. We find that all six systems behave in a similar manner in regions of the protein that are weakly electrostatic (either hydrophobic or weakly hydrophilic). However, in the vicinity of regions of the protein with relatively strong electrostatic fields (near positively or negatively charged residues), we observe that the water structure and dynamics are dependent on both the model of the protein and the model of the water. We find that a large part of the dynamical dependence can be described by small changes in the local environments of each region that limit the local density of non-hydrogen-bonded waters, precisely the water molecules that facilitate the dynamical relaxation of the water-water hydrogen bonds. We introduce a simple method for rescaling for this effect. When this is done, we are able to effectively isolate the influence of polarizability on the dynamics. We find that the solvating water's relaxation is most affected when both the protein and the water models are polarizable. However, when only one model (or neither) is polarizable, the relaxation is similar regardless of the models used.