Monte Carlo Simulation of the β-Sheet–Random Coil Transition of a Homopolypeptide. I. Equilibrium Study

Abstract

Monte Carlo simulation of the β-sheet – random coil conversion of a homopolypeptide chain was carried out on the basis of a model where successive two amino acid residues were assumed to change their states simultaneously and hence constituted a basic unit. Only three states were considered for each unit: extended, turn and coil. The conversion exhibited a transition between two states, random coil (C) and the β-sheet (B). In the transition region, two population maxima were always found, each corresponded to the local minimum of the free energy and there was an energy barrier between them. This behavior is characteristic of the all-or-none type transition. We have found that the nature of the first-order transition is retained in the case of a small system consisting of 100 units. The size of the cooperative unit was evaluated. According to the analytical theory of Kanô, a transition curve was obtained which was very close to the present one. This consistent result has suggested that equilibrium properties of the β-sheet-random coil transition are well evaluated with the mean field approximation. The matrix method of Mattice is also discussed.     

Vibrational circular dichroism spectra of three conformationally distinct states and an unordered state of poly(L-lysine) in deuterated aqueous solution

Fourier transform ir vibrational circular dichroism (VCD) spectra in the amide I′ region of poly(L-lysine) in D₂O solutions have confirmed the existence of three distinct conformational states and an unordered conformational state in this homopolypeptide. Characteristic VCD spectra are presented for the right-handed α-helix, the antiparallel β-sheet, an extended helix conformation previously referred to as the so-called “random coil,” and a completely unordered conformation characterized by the absence of any amide I′ VCD. VCD for the antiparallel β-sheet in solution and the unordered chain conformation are presented for the first time. Each of the four different VCD spectra is unique in appearance and lends weight to the view that VCD has the potential to become a sensitive new probe of the secondary structure of proteins in solution.     

Suppression of the statistical coil state during the α ↔ β transition in homopolypeptides

A matrix formulation of the conformational partition function has been used to examine helix ? sheet transitions in homopolyamino acids. α-Helices are weighted by Zimm-Bragg parameters σ and s. Antiparallel β-sheets with tight bends are weighted by the parameters t, δ, and τ, where t is the propagation parameter. In addition, each bend contributes a factor δ, and each residue in the sheet that does not have a partner in the preceding strand contributes a factor τ. The helix can be the dominant conformation in a long chain only if two conditions are satisfied simultaneously: (i) s > 1 , and (ii) either s > t, or σ, δ, and τ are assigned values that inflict a greater penalty on antiparallel sheets than on helices. The maximum amount of coil developed during the helix ? sheet transition is strongly influenced by the size of τ, but it is only weakly dependent on the size of δ. Previously reported optical rotatory dispersion, CD, laser Raman, and nmr studies of thermally induced α ? β transitions in homopolyamino acids, notably poly(L -lysine), demonstrate that little random coil is present. If the random coil content is to remain small during the helix ? sheet transition, τ must be significantly less than unity. A small value for τ means that there is a significant penalty assessed to lysyl residues in an antiparallel sheet that do not have a partner in a preceding strand.     

Time-resolved infrared spectroscopy of pH-induced aggregation of the Alzheimer Abeta(1-28) peptide

Aggregation of the Alzheimer's disease-related Aβ_1-28 peptide was induced by a rapid, sub-millisecond pH jump and monitored by time-resolved infrared spectroscopy on the millisecond to second time-scale. The release of protons was induced by the photolysis of a caged compound, 1-(2-nitrophenyl)ethyl sulfate (NPE-sulfate). The pH jump generated in our experimental setup is used to model the Aβ peptide structural conversions that may occur in the acidic endosomal/lysosomal cell compartment system. The aggregation of the Aβ_1-28 peptide induced by the pH jump from 8.5 to < 6 yields an antiparallel β-sheet structure. The kinetics of the structural transition is biphasic, showing an initial rapid phase with a transition from random coil to an oligomeric β-sheet form with a time constant of 3.6 s. This phase is followed by a second slower transition, which yields larger aggregates during 48.0 s.     

Flow-induced conformational changes and phase behavior of aqueous poly-L-lysine solutions

Poly-L -lysine exists as an α-helix at high pH and a random coil at neutral pH. When the α-helix is heated above 27°C, the macromolecule undergoes a conformational transition to a β-sheet. In this study, the stability of the secondary structure of poly-L -lysine in solutions subjected to shear flow, at temperatures below the α-helix to β-sheet transition temperature, were examined using Raman spectroscopy and CD. Solutions initially in the α-helical state showed time-dependent increases in viscosity with shearing, rising as much as an order of magnitude. Visual observation and turbidity measurements showed the formation of a gel-like phase under flow. Laser Raman measurements demonstrated the presence of small amounts of β-sheet structure evidenced by the amide I band at 1666 cm⁻¹. CD measurements indicated that solutions of predominantly α-helical conformation at 20°C transformed into 85% α-helix and 15% β-sheet after being sheared for 20 min. However, on continued shearing the content of β-sheet conformation decreased. The observed phenomena were explained in terms of a “zipping-up” molecular model based on flow enhanced hydrophobic interactions similar to that observed in gel-forming flexible polymers. © 1998 John Wiley & Sons, Inc. Biopoly 45: 239–246, 1998     

Simulation of the β- to α-sheet transition results in a twisted sheet for antiparallel and an α-nanotube for parallel strands: implications for amyloid formation

α-sheet has been proposed to be the main constituent of the toxic amyloid intermediate. Molecular dynamics simulations on proteins known to be involved in amyloid diseases have demonstrated that β-sheet can, under certain conditions, spontaneously convert to α-sheet via ββ→α(R)α(L) peptide-plane flipping. Using torsion-angle driving to simulate this flip the transition has been investigated for parallel and antiparallel sheets. Concerted and sequential flipping processes were simulated, the former allowing direct calculation of helical parameters. For antiparallel sheet, the strands tend to splay apart during the transition. This can be understood by consideration of the geometry of repeating dipeptide conformations. At the end of the transition antiparallel α-sheet is slightly twisted, comprising gently curving strands. In parallel sheet, the strands maintain identical conformations and stay hydrogen bonded during the transition as they curl up to suggest a hitherto unseen structure, the multi-helix α-nanotube. Intriguingly, the α-nanotube has some of the characteristics of the parallel β-helix, a single-helix structure also implicated in amyloid. Unlike the β-helix, α-nanotube formation could involve identical strands aligning with each other in register as in most amyloids.     

The interstrand amino acid pairs play a significant role in determining the parallel or antiparallel orientation of β-strands

It is widely considered that it is not appropriate to treat β-pairs in isolation, since other secondary structural models (such as helices, coils), protein topology and protein tertiary structures would limit β-strand pairing. However, to understand the underlying mechanisms of β-sheet formation, studies ought to be performed separately on more concrete aspects. In this study, we focus on the parallel or antiparallel orientation of β-strands. First, statistical analysis was performed on the relative frequencies of the interstrand amino acid pairs within parallel and antiparallel β-strands. Consequently, features were extracted by singular value decomposition from the statistical results. By using the support vector machine to distinguish the features extracted from the two types of β-strands, high accuracy was achieved (up to 99.4%). This suggests that the interstrand amino acid pairs play a significant role in determining the parallel or antiparallel orientation of β-strands. These results may provide useful information for developing other useful algorithms to examine to the β-strand folding pathways, and could eventually lead to protein structure predictions.     

Study of the aggregation mechanism of polyglutamine peptides using replica exchange molecular dynamics simulations

Polyglutamine (polyQ, a peptide) with an abnormal repeat length is the causative agent of polyQ diseases, such as Huntington’s disease. Although glutamine is a polar residue, polyQ peptides form insoluble aggregates in water, and the mechanism for this aggregation is still unclear. To elucidate the detailed mechanism for the nucleation and aggregation of polyQ peptides, replica exchange molecular dynamics simulations were performed for monomers and dimers of polyQ peptides with several chain lengths. Furthermore, to determine how the aggregation mechanism of polyQ differs from those of other peptides, we compared the results for polyQ with those of polyasparagine and polyleucine. The energy barrier between the monomeric and dimeric states of polyQ was found to be relatively low, and it was observed that polyQ dimers strongly favor the formation of antiparallel β-sheet structures. We also found a characteristic behavior of the monomeric polyQ peptide: a turn at the eighth residue is always present, even when the chain length is varied. We previously showed that a structure including more than two sets of β-turns is stable, so a long monomeric polyQ chain can act as an aggregation nucleus by forming several pairs of antiparallel β-sheet structures within a single chain. Since the aggregation of polyQ peptides has some features in common with an amyloid fibril, our results shed light on the mechanism for the aggregation of polyQ peptides as well as the mechanism for the formation of general amyloid fibrils, which cause the onset of amyloid diseases.     

Simulation Studies on the Stabilities of Aggregates Formed by Fibril-Forming Segments of α-Synuclein

Abstract

We performed molecular dynamics simulations for various oligomers with different β-sheet conformations consisting of α-Synuclein 71–82 residues using an all atom force field and explicit water model. Tetramers of antiparallel β-sheet are shown to be stable, whereas parallel sheets are highly unstable due to the repulsive interactions between bulky and polar side chains as well as the weaker backbone hydrogen bonds. We also investigated the stabilities of double antiparallel β-sheets stacked with asymmetric and symmetric geometries. Our results show that this 12 amino acid residue peptide can form stable β-sheet conformers at 320K and higher temperatures. The backbone hydrogen bonds in β-sheet and the steric packing between hydrophobic side chains between β-sheets are shown to give conformational stabilities.     

Stabilization of short helices by intramolecular cluster formation

The intramolecular formation of multiple clusters of interacting helices has been characterized in a homopolymer. The configuration partition function permits the formation of clusters in which the number of interacting helices may be as large as the greatest integer in n/2, where n denotes the number of amino acid residues in the chain. The theoretical formulation has its origin in a recent [Mattice, W. L. & Scheraga, H. A. (1984) Biopolymers 23 , 1701–1724], tractable matrix expression for the configuration partition function for intramolecular antiparallel β-sheet formation. Reassignment of the expression for one of the n(n+3)/2 elements in the sparse statistical weight matrix, along with a simple change in notation, converts that treatment into a matrix formulation of the configuration partition function for a chain containing multiple clusters of interacting antiparallel helices. The five statistical weights used are δ, f_l, w, and the Zimm-Bragg σ and s. Each tight bend that connects two interacting helices contributes a factor of δ, f_l is used in the weight for larger loops between interacting helices, and w arises from helix–helix interaction. The influence of the helix–helix interaction is well illustrated by two helix–coil transitions in a chain with n = 156 and σ = 0.001. In the absence of helix–helix interaction, the transition occurs by the nucleation and subsequent elongation of a small number of helices. When helix–helix interaction is attractive, the transition can occur by a different mechanism. Formation of a single pair of interacting helices is followed by addition of new helices to the initial cluster. In the latter process, individual helices experience relatively little growth after they are formed.     

Stoichiometry and Preferential Interaction: Two Components of the Principle for Protein Structure Organization

Abstract

The effect of pressure on the conformational structure of amyloid β (1–40) peptide (Aβ(1–40)), exacerbated with or without temperature, was determined by Fourier transform infrared (FT-IR) microspectroscopy. The result indicates the shift of the maximum peak of amide I band of intact solid Aβ(1–40) from 1655 cm^?1 (α-helix) to 1647–1643 cm^?1 (random coil) with the increase of the mechanical pressure. A new peak at 1634 cm^?1 assigned to β-antipar- allel sheet structure was also evident. Furthermore, the peak at 1540 cm^?1 also shifted to 1527 (1529) cm^?1 in amide II band. The former was assigned to the combination of α-helix and random coil structures, and the latter was due to β-sheet structure. Changes in the composition of each component in the deconvoluted and curve-fitted amide I band of the compressed Aβ(1–40) samples were obtained from 33% to 22% for α-helix/random coil structures and from 47% to 57% for β-sheet structure with the increase of pressure, respectively. This demonstrates that pressure might induce the conformational transition from α-helix to random coil and to β-sheet structure. The structural transformation of the compressed Aβ(1–40) samples was synergistically influenced by the combined effects of pressure and temperature. The thermal-induced formation of β-sheet structure was significantly dependent on the pressures applied. The smaller the pressure applied the faster the β-sheet structure transformed. The thermal-dependent transition temperatures of solid Aβ(1–40) prepared by different pressures were near 55–60 °C.     

Toxic prefibrillar α-synuclein amyloid oligomers adopt a distinctive antiparallel β-sheet structure

Parkinson's disease is an age-related movement disorder characterized by the presence in the mid-brain of amyloid deposits of the 140-amino-acid protein AS (α-synuclein). AS fibrillation follows a nucleation polymerization pathway involving diverse transient prefibrillar species varying in size and morphology. Similar to other neurodegenerative diseases, cytotoxicity is currently attributed to these prefibrillar species rather than to the insoluble aggregates. Nevertheless, the underlying molecular mechanisms responsible for cytotoxicity remain elusive and structural studies may contribute to the understanding of both the amyloid aggregation mechanism and oligomer-induced toxicity. It is already recognized that soluble oligomeric AS species adopt β-sheet structures that differ from those characterizing the fibrillar structure. In the present study we used ATR (attenuated total reflection)-FTIR (Fourier-transform infrared) spectroscopy, a technique especially sensitive to β-sheet structure, to get a deeper insight into the β-sheet organization within oligomers and fibrils. Careful spectral analysis revealed that AS oligomers adopt an antiparallel β-sheet structure, whereas fibrils adopt a parallel arrangement. The results are discussed in terms of regions of the protein involved in the early β-sheet interactions and the implications of such conformational arrangement for the pathogenicity associated with AS oligomers.     

Structural changes of IgG induced by heat treatment and by adsorption onto a hydrophobic Teflon surface studied by circular dichroism spectroscopy

Thermal denaturation of mouse monoclonal immunoglobulin G (isotype 1), as well as structural rearrangements resulting from adsorption on a hydrophobic Teflon surface, are studied by circular dichroism spectroscopy. Both heat-induced and adsorption-induced denaturation do not lead to complete unfolding into an extended polypeptide chain, but leave a significant part of the IgG molecule in a globular or corpuscular form. Heating dissolved IgG causes a decrease of the fractions of β-sheet and β-turn conformations, whereas those of random coil and, to a lesser extent, α-helix increase. Adsorption enhances the formation of α-helices and random coils, but the β-sheet content is strongly reduced. Heating adsorbed IgG results in a gradual break-down of the α-helix and β-turn contents, and a concomitant formation of β-sheet structures. Thus, the structural changes in IgG caused by heating and by adsorption, respectively, are very different. However, after heating, the structure of adsorbed IgG approaches the structure of thermally denatured IgG in solution.     

β-Barrel topology of Alzheimer's β-amyloid ion channels

Emerging evidence supports the ion channel mechanism for Alzheimer's disease pathophysiology wherein small β-amyloid (Aβ) oligomers insert into the cell membrane, forming toxic ion channels and destabilizing the cellular ionic homeostasis. Solid-state NMR-based data of amyloid oligomers in solution indicate that they consist of a double-layered β-sheets where each monomer folds into β-strand-turn-β-strand and the monomers are stacked atop each other. In the membrane, Aβ peptides are proposed to be β-type structures. Experimental structural data available from atomic force microscopy (AFM) imaging of Aβ oligomers in membranes reveal heterogeneous channel morphologies. Previously, we modeled the channels in a non-tilted organization, parallel with the cross-membrane normal. Here, we modeled a β-barrel-like organization. β-Barrels are common in transmembrane toxin pores, typically consisting of a monomeric chain forming a pore, organized in a single-layered β-sheet with antiparallel β-strands and a right-handed twist. Our explicit solvent molecular dynamics simulations of a range of channel sizes and polymorphic turns and comparisons of these with AFM image dimensions support a β-barrel channel organization. Different from the transmembrane β-barrels where the monomers are folded into a circular β-sheet with antiparallel β-strands stabilized by the connecting loops, these Aβ barrels consist of multimeric chains forming double β-sheets with parallel β-strands, where the strands of each monomer are connected by a turn. Although the Aβ barrels adopt the right-handed β-sheet twist, the barrels still break into heterogeneous, loosely attached subunits, in good agreement with AFM images and previous modeling. The subunits appear mobile, allowing unregulated, hence toxic, ion flux.     

N-Terminal domain of Bombyx mori fibroin mediates the assembly of silk in response to pH decrease

Fibroins serve as the major building blocks of silk fiber. As the major component of fibroin, the fibroin heavy chain is a considerably large protein comprising N-terminal and C-terminal hydrophilic domains and 12 highly repetitive Gly-Ala-rich regions flanked by internal hydrophilic blocks. Here, we show the crystal structure of the fibroin N-terminal domain (FibNT) at pH?4.7, revealing a remarkable double-layered anti-parallel β-sheet with each layer comprising two FibNT molecules entangled together. We also show that FibNT undergoes a pH-responsive conformational transition from random coil to β-sheets at around pH?6.0. Dynamic light scattering demonstrates that FibNT tends to oligomerize as pH decreases to 6.0, and electron microscopy reveals micelle-like oligomers. Our results are consistent with the micelle assembly model of silk fibroin and, more importantly, show that the N-terminal domain in itself has the capacity to form micelle-like structures in response to pH decrease. Structural and mutagenesis analyses further reveal the important role of conserved acidic residues clustered in FibNT, such as Glu56 and Asp100, in preventing premature β-sheet formation at neutral pH. Collectively, we suggest that FibNT functions as a pH-responsive self-assembly module that could prevent premature β-sheet formation at neutral pH yet could initiate fibroin assembly as pH decreases along the lumen of the posterior silk gland to the anterior silk gland.     

Conformational transitions of calmodulin as studied by vacuum-uv CD

CD measurements were made for calmodulin and its calcium (Ca²⁺) complexes at different ionic strengths and Ca²⁺ concentrations. Calmodulin at an ionic strength of 0.00M and in the absence of Ca²⁺ exists as an α-helical protein with a negligible amount of β-sheet. An increase in ionic strength, whether or not Ca²⁺ is present, increases α-helix at the expense of “other” (coil) structure. The changes in β-sheet and β-turns are insignificant. Binding of Ca²⁺ at low ionic strength occurs in stages with at least one folding intermediate before attaining the final stable state. Binding of Ca²⁺ at an ionic strength of 0.165M causes only a slight increase in α-helix, so that the secondary structure of the protein depends on ionic strength and is insensitive to the nature of the cation (i.e., Ca²⁺). Thus, the activation of calmodulin by Ca²⁺ must be due to a structural reorientation rather than to a major secondary structural alteration. The CD estimation of secondary structure with 4 mol Ca²⁺/calmodulin (61% α-helix, 2% antiparallel β-sheet, 2% parallel β-sheet, 21% β-turns, and 14% other) is in excellent agreement with the x-ray results.     

Studies on the rules of β-strand alignment in a protein β-sheet structure

To further disclose the underlying mechanisms of protein β-sheet formation, studies were made on the rules of β-strands alignment forming β-sheet structure using statistical and machine learning approaches. Firstly, statistical analysis was performed on the sum of β-strands between each β-strand pairs in protein sequences. The results showed a propensity of near-neighbor pairing (or called “first come first pair”) in the β-strand pairs. Secondly, based on the same dataset, the pairwise cross-combinations of real β-strand pairs and four pseudo-β-strand contained pairs were classified by support vector machine (SVM). A novel feature extracting approach was designed for classification using the average amino acid pairing encoding matrix (APEM). Analytical results of the classification indicated that a segment of β-strand had the ability to distinguish β-strands from segments of α-helix and coil. However, the result also showed that a β-strand was not strongly conserved to choose its real partner from all the alternative β-strand partners, which was corresponding with the ordination results of the statistical analysis each other. Thus, the rules of “first come first pair” propensity and the non-conservative ability to choose real partner, were possible important factors affecting the β-strands alignment forming β-sheet structures.     

肽键的统计分析和蛋白质的二级结构

 本文对蛋白质序列的肽键进行了统计分析,计算了二肽构象参数P_α、P_β、P_c和三肽构象参数Q_α、Q_β、Q_c。在此基础上提出了由氨基酸序列预测二级结构的规则。预测的正确率达90％,优于Chou-Fasman方法。这个结果表明二肽(三肽)关联在形成蛋白质二级结构中具有明显的重要性。