De novo design of a monomeric three-stranded antiparallel beta-sheet

Rational design of antibody-like peptides for targeting the human complement fragment protein C5a

Human complement fragment 5a (C5a) is one of the most potent glycoproteins generated downstream of C3a and C4a during late-stage activation of the complement signaling cascade. C5a recruits receptors like C5aR1 and C5aR2 and is established to play a critical role in complement-mediated inflammation. Thus, excessive C5a in the plasma due to aberrant activation of the complement contributes to the pathophysiology of several chronic inflammatory diseases. Therefore, restricting the excessive interaction of C5a with its receptors by neutralizing C5a has been one of the most effective therapeutic strategies for the management of inflammatory diseases. Indeed, antibodies targeting C5 (Eculizumab), the precursor of C5a, and C5a (Vilobelimab) have already been approved by the FDA. Still, small designer peptides that work like antibodies and can target and stop C5a from interacting with its receptors seem to be a possible therapeutic alternative to antibodies because they are smaller, cheaper to make, more specific to their target, and can get through membrane barriers. As a proof-of-principle, the current study describes the computational design and evaluation of a pair of peptides that are able to form stable high-affinity complexes with the epitope regions of C5a that are important for the recruitment of C5aR1 and C5aR2. The computational data further supports the potential of designer peptides for mimicking the function of antibodies targeting C5a. However, further experimental studies will be required to establish the structure-function relationship of the designer peptides and also to establish the hypothesis of antibody-like peptides targeting C5a.

NMR Analysis of Protein Folding Interaction Networks

Theory and experimental evidence unequivocally indicate that protein folding is far more complex than the two-state (all-or-none) model that is usually assumed in the analysis of folding experiments. Proteins tend to fold hierarchically by forming secondary structure elements, followed by supersecondary arrangements, and other intermediate states that ultimately adopt the native tertiary fold as a result of a delicate balance between interatomic interactions and entropic contributions. However, small proteins with simple folds typically follow downhill folding, characterized by very small energetic barriers (<3 RT) that allow multiple protein conformations to be populated along the folding path down the free energy landscape, reaching the native fold at the lowest energy level.Here we describe the use of solution-state nuclear magnetic resonance (NMR) for the analysis of protein folding interaction networks at atomic resolution. The assignment of NMR spectra acquired at different unfolding conditions provides hundreds of atomic unfolding curves that are analyzed to infer the network of folding interactions. The method is particularly useful to study small proteins that fold autonomously in the sub-millisecond timescale. The information obtained from the application of this method can potentially unveil the basic relationships between protein structure and folding.

Tau Inclusions in Alzheimer's, Chronic Traumatic Encephalopathy and Pick's Disease. A Speculation on How Differences in Backbone Polarization Underlie Divergent Pathways of Tau Aggregation

Tau-related dementias appear to involve specific to each disease aggregation pathways and morphologies of filamentous tau assemblies. To understand etiology of these differences, here we elucidate molecular mechanism of formation of tau PHFs based on the PMO theory of misfolding and aggregation of pleiomorphic proteins associated with neurodegenerative diseases. In this model, fibrillization of tau is initiated by the coupled binding and folding of the MTB domains that yields antiparallel homodimers, in analogy to folding of split inteins. The free energy of binding is minimized when the antiparallel alignment brings about backbone-backbone H-bonding between the MTBD segments of similar “strand” propensities. To assess these propensities, a function of the NMR shielding tensors of the C^α atoms is introduced as the folding potential function FP_i; the C^α tensors are obtained by the quantum mechanical modeling of protein secondary structure (GIAO//B3LYP/D95^**). The calculated FP_i plots show that the “strand” propensities of the MBTD segments, and hence the homodimer's register, can be affected by the relatively small changes in the environment's pH, as a result of protonation of MBTD's conserved histidines. The assembly of the antiparallel tau dimers into granular aggregates and their subsequent conversion into the parallel cross-β structure of paired helical filaments is expected to follow the same path as the previously described fibrillization of Aβ. Consequently, the core structure of the nascent tau fibril is determined by the register of the tau homodimer. This model accounts for the reported differences in (i) fibril-core structure of in vivo and in vitro filaments, (ii) cross-seeding of isoforms, (iii) effects of reducing/non-reducing conditions, (iv) effects of PHF6 mutations, and (v) homologs' aggregation properties. The proposed model also suggests that in contrast to Alzheimer's and chronic traumatic encephalopathy disease, the assembly of tau prions in Pick's disease would be facilitated by a moderate drop in pH that accompanies e.g., transit in the endosomal system, inflammation response or an ischemic injury.

Peptide and Protein Structure Prediction with a Simplified Continuum Solvent Model

A continuum solvent model based on screened Coulomb potentials has been simplified and parametrized to sample native-like structures in replica-exchange simulations of each of six different peptides and miniproteins. Low-energy, native, and non-native structures were used to iteratively refine 11 parameter values. The centroid of the largest cluster of structures sampled in simulations initiated from an extended conformation represents the predicted structure. The main-chain rms deviation of this prediction from the experimental structure was 0.47 Å for the 12-residue Trp-zip2, 0.86 Å for the 14-residue MBH12, 2.53 Å for the 17-residue U(1-17)T9D, 2.03 Å for the 20-residue BS1, 1.08 Å for the 20-residue Trp-cage, and 3.64 Å for the 35-residue villin headpiece subdomain HP35. The centroid of the sixth largest cluster sampled for HP35 deviated by 0.91 Å. The CHARMM22/CMAP force field was used, with an additional ψ torsion term for residues other than glycine and proline. Six parameters govern the dielectric response of the continuum solvent, and four values of surface tension approximate nonpolar effects. An atom's self-energy and interaction energies are screened independently, each depending on whether the atom is part of a charged group, a neutral hydrogen-bonding main-chain group, or any other neutral group. The parameters inferred result in strong main-chain hydrogen bonds, consistent with the view that protein folding is dominated by the formation of these bonds. (1,2) Conformations of MBH12 and BS1 were excluded from the energy-function refinement, suggesting the parameters, referred to as SCP18, are transferable. An efficient estimate of solvent-accessible surface area is also described.

Aromatic interactions in β-hairpin scaffold stability: A historical perspective

Non-covalent interactions between naturally occurring aromatic residues have been widely exploited as scaffold stabilizing agents in de novo designed peptides and in Nature - inspired structures. Our understanding of the factors driving aromatic interactions and their observed interaction geometries have advanced remarkably with improvements in conventional structural studies, availability of novel molecular methods and in silico studies, which have together provided atomistic information on aromatic interactions and interaction strengths. This review attempts to recapitulate the early advances in our understanding of aromatic interactions as stabilizing agents of peptide β-hairpins.

Protein folding, misfolding and aggregation: The importance of two-electron stabilizing interactions

Proteins associated with neurodegenerative diseases are highly pleiomorphic and may adopt an all-α-helical fold in one environment, assemble into all-β-sheet or collapse into a coil in another, and rapidly polymerize in yet another one via divergent aggregation pathways that yield broad diversity of aggregates’ morphology. A thorough understanding of this behaviour may be necessary to develop a treatment for Alzheimer’s and related disorders. Unfortunately, our present comprehension of folding and misfolding is limited for want of a physicochemical theory of protein secondary and tertiary structure. Here we demonstrate that electronic configuration and hyperconjugation of the peptide amide bonds ought to be taken into account to advance such a theory. To capture the effect of polarization of peptide linkages on conformational and H-bonding propensity of the polypeptide backbone, we introduce a function of shielding tensors of the C^α atoms. Carrying no information about side chain-side chain interactions, this function nonetheless identifies basic features of the secondary and tertiary structure, establishes sequence correlates of the metamorphic and pH-driven equilibria, relates binding affinities and folding rate constants to secondary structure preferences, and manifests common patterns of backbone density distribution in amyloidogenic regions of Alzheimer’s amyloid β and tau, Parkinson’s α-synuclein and prions. Based on those findings, a split-intein like mechanism of molecular recognition is proposed to underlie dimerization of Aβ, tau, αS and PrP^C, and divergent pathways for subsequent association of dimers are outlined; a related mechanism is proposed to underlie formation of PrP^Sc fibrils. The model does account for: (i) structural features of paranuclei, off-pathway oligomers, non-fibrillar aggregates and fibrils; (ii) effects of incubation conditions, point mutations, isoform lengths, small-molecule assembly modulators and chirality of solid-liquid interface on the rate and morphology of aggregation; (iii) fibril-surface catalysis of secondary nucleation; and (iv) self-propagation of infectious strains of mammalian prions.

Automated protein design: Landmarks and operational principles

Protein design has an eventful history spanning over three decades, with handful of success stories reported, and numerous failures not reported. Design practices have benefited tremendously from improvements in computer hardware and advances in scientific algorithms. Though protein folding problem still remains unsolved, the possibility of having multiple sequence solutions for a single fold makes protein design a more tractable problem than protein folding. One of the most significant advancement in this area is the implementation of automated design algorithms on pre-defined templates or completely new folds, optimized through deterministic and heuristic search algorithms. This progress report provides a succinct presentation of important landmarks in automated design attempts, followed by brief account of operational principles in automated design methods.

Foldameric probes for membrane interactions by induced β-sheet folding

Design strategies were devised for α/β-peptide foldameric analogues of the antiangiogenic anginex with the goal of mimicking the diverse structural features from the unordered conformation to a folded β-sheet in response to membrane interactions. Structure-activity relationships were investigated in the light of different β-sheet folding levels.

Equilibration of Protein States: A Time Dependent Free-Energy Disconnectivity Graph

The process of equilibration of protein states in a three-stranded antiparallel β-sheet miniprotein is studied using a time-dependent free energy disconnectivity graph. To determine the rates of transitions, the molecular dynamics simulation results of a recent work (Kalgin, I. V.; J. Phys. Chem. B 2013, 117, 6092) are employed. The vertices of the graph are the free energies of characteristic states of the protein, and the edges are the transition state free energies. To determine the latter, the "complete" partition function (Eyring, 1935) is used, which includes the translational partition function corresponding to the ballistic motion of the system along the reaction coordinate. The distance along the reaction coordinate that enters the translational partition function is taken to be proportional to the observation time and thus measures the number of representative points that cross the transition state surface during given time. As the time increases, the free energy barriers between the clusters of characteristic conformations (native-like, helical, and β-sheet conformations of different degree of organization) decrease and (local) equilibrium between the clusters is established. With time, these clusters are grouped into larger clusters, extending the equilibrium to a larger portion of protein states.

Induced folding of protein-sized foldameric β-sandwich models with core β-amino acid residues

The mimicry of protein-sized β-sheet structures with unnatural peptidic sequences (foldamers) is a considerable challenge. In this work, the de novo designed betabellin-14 β-sheet has been used as a template, and α→β residue mutations were carried out in the hydrophobic core (positions 12 and 19). β-Residues with diverse structural properties were utilized: Homologous β(3) -amino acids, (1R,2S)-2-aminocyclopentanecarboxylic acid (ACPC), (1R,2S)-2-aminocyclohexanecarboxylic acid (ACHC), (1R,2S)-2-aminocyclohex-3-enecarboxylic acid (ACEC), and (1S,2S,3R,5S)-2-amino-6,6-dimethylbicyclo[3.1.1]heptane-3-carboxylic acid (ABHC). Six α/β-peptidic chains were constructed in both monomeric and disulfide-linked dimeric forms. Structural studies based on circular dichroism spectroscopy, the analysis of NMR chemical shifts, and molecular dynamics simulations revealed that dimerization induced β-sheet formation in the 64-residue foldameric systems. Core replacement with (1R,2S)-ACHC was found to be unique among the β-amino acid building blocks studied because it was simultaneously able to maintain the interstrand hydrogen-bonding network and to fit sterically into the hydrophobic interior of the β-sandwich. The novel β-sandwich model containing 25 % unnatural building blocks afforded protein-like thermal denaturation behavior.

Folding of a β-sheet miniprotein: probability fluxes, streamlines, and the potential for the driving force

In this work we continue the study of the first-passage folding of an antiparallel β-sheet miniprotein (beta3s) that was initiated in the previous work [Kalgin et al. J. Phys. Chem. B, 2014, 118, 4287]. We consider a larger ensemble of folding trajectories, which allows us to gain a closer insight into the folding dynamics. In particular, we calculate the potential for the driving force of folding in a reduced space of collective variables. The potential has two components. One component (Φ) is responsible for the source and sink of the folding flow, which are formed, respectively, in the regions of the unfolded and native states of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the sides of the reaction channel and provides the canalization of the folding flow between the source and sink. We show that both components obey Poisson's equations with the corresponding source/sink terms. The resulting components have a very simple form: the Φ-surface consists of two well-defined peaks of different signs, which correspond, respectively, to the source and sink of the folding flow, and the Ψ-surface consists of two ridges of different signs that connect the source and sink of the flow.

Role of Backbone Dipole Interactions in the Formation of Secondary and Supersecondary Structures of Proteins

We present a generic solvated coarse-grained protein model that can be used to characterize the driving forces behind protein folding. Each amino acid is coarse-grained with two beads, a backbone, and a side chain. Although the backbone beads are modeled as polar entities, side chains are hydrophobic, polar, or charged, thus allowing the exploration of how sequence patterning determines a protein fold. The change in orientation of the atoms of the coarse-grained unit is captured by the addition of two oppositely charged dummy particles inside the backbone coarse-grained bead. These two dummy charges represent a dipole that can fluctuate, thus introducing structural polarization into the coarse-grained model. Realistic α/β content is achieved de novo without any biases in the force field toward a particular secondary structure. The dipoles created by the dummy particles interact with each other and drive the protein models to fold into unique structures depending on the amino acid patterning and presence of capping residues. We have also characterized the role of dipole–dipole and dipole–charge interactions in shaping the secondary and supersecondary structure of proteins. Formation of helix bundles and β-strands are also discussed.

First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach?

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.

Design of monomeric water-soluble β-hairpin and β-sheet peptides

Since the first report in 1993 (JACS 115, 5887-5888) of a peptide able to form a monomeric β-hairpin structure in aqueous solution, the design of peptides forming either β-hairpins (two-stranded antiparallel β-sheets) or three-stranded antiparallel β-sheets has become a field of growing interest and activity. These studies have yielded great insights into the principles governing the stability and folding of β-hairpins and antiparallel β-sheets. This chapter provides an overview of the reported β-hairpin/β-sheet peptides focussed on the applied design criteria, reviews briefly the factors contributing to β-hairpin/β-sheet stability, and describes a protocol for the de novo design of β-sheet-forming peptides based on them. Guidelines to select appropriate turn and strand residues and to avoid self-association are provided. The methods employed to check the success of new designed peptides are also summarized. Since NMR is the best technique to that end, NOEs and chemical shifts characteristic of β-hairpins and three-stranded antiparallel β-sheets are given.

Foldameric α/β-peptide analogs of the β-sheet-forming antiangiogenic anginex: structure and bioactivity

The principles of β-sheet folding and design for α-peptidic sequences are well established, while those for sheet mimetics containing homologated amino acid building blocks are still under investigation. To reveal the structure-function relations of β-amino-acid-containing foldamers, we followed a top-down approach to study a series of α/β-peptidic analogs of anginex, a β-sheet-forming antiangiogenic peptide. Eight anginex analogs were developed by systematic α → β(3) substitutions and analyzed by using NMR and CD spectroscopy. The foldamers retained the β-sheet tendency, though with a decreased folding propensity. β-Sheet formation could be induced by a micellar environment, similarly to that of the parent peptide. The destructuring effect was higher when the α → β(3) exchange was located in the β-sheet core. Analysis of the β-sheet stability versus substitution pattern and the local conformational bias of the bulky β(3)V and β(3)I residues revealed that a mismatch between the H-bonding preferences of the α- and β-residues played a minor role in the structure-breaking effect. Temperature-dependent CD and NMR measurements showed that the hydrophobic stabilization was scaled-down for the α/β-peptides. Analysis of the biological activity of the foldamer peptides showed that four anginex derivatives dose-dependently inhibited the proliferation of a mouse endothelial cell line. The α → β(3) substitution strategy applied in this work can be a useful approach to the construction of bioactive β-sheet mimetics with a reduced aggregation tendency and improved pharmacokinetic properties.

Two-Dimensional Infrared (2DIR) Spectroscopy of the Peptide Beta3s Folding

Probing underlying free energy landscape, pathways, and mechanism is the key for understanding protein folding in theory and experiment. Recently time-resolved two-dimensional infrared (2DIR) with femtosecond laser pulses, has emerged as a promising tool for investigating the protein folding dynamics on faster timescales than possible by NMR. We have employed molecular dynamics simulations to compute 2DIR spectra of the folding process of a peptide, Beta3s. Simulated non-chiral and chiral 2DIR signals illustrate the variation of the spectra as the peptide conformation evolves along the free energy landscape. Chiral spectra show stronger changes than the non-chiral signals because cross peaks caused by the formation of the β-sheet are clearly resolved. Chirality-induced 2DIR may be used to detect the folding of β-sheet proteins with high spectral and temporal resolution.

New insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: application to a hydrodynamic analysis of the folding flow

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present analysis for the parts that can be compared, supporting the robust character of our understanding of this "hydrogen atom" of protein folding.

PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Mutational effects on the folding dynamics of a minimized hairpin

The fold stabilities and folding dynamics of a series of mutants of a model hairpin, KTW-NPATGK-WTE (HP7), are reported. The parent system and the corresponding DPATGK loop species display submicrosecond folding time constants. The mutational studies revealed that ultrafast folding requires both some prestructuring of the loop and a favorable interaction between the chain termini in the transition state. In the case of YY-DPETGT-WY, another submicrosecond folding species [Davis, C. M., Xiao, S., Raleigh, D. P., and Dyer, R. B. (2012) J. Am. Chem. Soc. 134, 14476-14482], a hydrophobic cluster provides the latter. In the case of HP7, the Coulombic interaction between the terminal NH3(+) and CO2(-) units provides this; a C-terminal Glu to amidated Ala mutation results in a 5-fold retardation of the folding rate. The effects of mutations within the reversing loop indicate the balance between loop flexibility (favoring fast conformational searching) and turn formation in the unfolded state is a major factor in determining the folding dynamics. The -NAAAKX- loops examined display no detectable turn formation propensity in other hairpin constructs but do result in stable analogues of HP7. Peptide KTW-NAAAKK-WTE displays the same fold stability as HP7, but both the folding and unfolding time constants are greater by a factor of 20.

Distribution of Reciprocal of Interatomic Distances: A Fast Structural Metric

We present a structural metric based on the Distribution of Reciprocal of Interatomic Distances (DRID) for evaluating geometrical similarity between two conformations of a molecule. A molecular conformation is described by a vector of 3N orientation-independent DRID descriptors where N is the number of molecular centroids, for example, the non-hydrogen atoms in all nonsymmetric groups of a peptide. For two real-world applications (pairwise comparison of snapshots from an explicit solvent simulation of a protease/peptide substrate complex and implicit solvent simulations of reversible folding of a 20-residue β-sheet peptide), the DRID-based metric is shown to be about 5 and 15 times faster than coordinate root-mean-square deviation (cRMSD) and distance root-mean-square deviation (dRMSD), respectively. A single core of a mainstream processor can perform about 10(8) DRID comparisons in one-half a minute. Importantly, the DRID metric has closer similarity to kinetic distance than does either cRMSD or dRMSD. Therefore, DRID is suitable for clustering molecular dynamics trajectories for kinetic analysis, for example, by Markov state models. Moreover, conformational space networks and free energy profiles derived by DRID-based clustering preserve the kinetic information.

Free Energy Guided Sampling

A free energy-guided sampling (FEGS) method is proposed for accelerating exploration of conformational space in unbiased molecular dynamics. Using the cut-based free energy profile and Markov state models, FEGS speeds up sampling of the canonical ensemble by iteratively restarting multiple short simulations in parallel from regions of the free energy surface visited rarely. This exploration stage is followed by a refinement stage in which multiple independent runs are initiated from Boltzmann distributed conformations. Notably, FEGS does not require either collective variables or reaction coordinates and can control the kinetic distance from the starting conformation. We applied FEGS to the alanine dipeptide, which has a human-comprehensible two-dimensional free energy landscape, and a three-stranded antiparallel β-sheet peptide of 20 residues whose folding/unfolding process is governed by a delicate interplay of enthalpy and entropy. For these two systems, FEGS speeds up the exploration of conformational space by 1 to 2 orders of magnitude with respect to conventional sampling and preserves the basins and barriers on the free energy profile.

The mechanism of antiparallel β-sheet formation based on conditioned self-avoiding walk

By introducing an additional hydrogen bond to hydrogen bond interaction in the force field of the CSAW (Conditioned Self-Avoiding Walk) model, we investigate into the mechanism of antiparallel β-sheet formation based on the folding of a short polyalanine in gas phase. Through our numerical simulation, we detect the possible presence of a transient helix during β-sheet formation, whose presence is shown to have slowed the formation of β-sheets by an order of magnitude. While we observe the mechanisms of nucleation, zipping and induction that drives the formation of a β-sheet, we uncover a new mechanism that involves transient β-turns and short β-sheets during the formation of long β-sheets. Our results have enabled us to provide an overview on the mechanisms of β-sheet formation via two main folding pathways: slow folding through the intermediate state of transient helix, and fast folding from the nucleation of β-turn.

Extracting physically intuitive reaction coordinates from transition networks of a beta-sheet miniprotein

Simulations are important for understanding complex reactions, but their interpretation is challenging owing to the large number of degrees of freedom typically involved. To address this issue, various means for relating the dynamics of a stochastic system to its structural and energetic features have been introduced. Here, we show how two leading approaches can be combined to advantage. We use the network of transitions observed in a reversible folding/unfolding simulation of a 20-residue three-stranded antiparallel beta-sheet peptide (beta3s) to estimate the probabilities of committing to stable states (the native state and major nonnative states), and these then serve as the basis for an efficient statistical procedure for identifying physical variables that describe the dynamics. We find that a single coordinate that jointly characterizes the formation of the two native turns of beta3s can adequately describe the overall folding process, despite its complex nature. Additional features associated with major pathways leading from individual nonnative states are resolved; indeed, a key result is an improved understanding of the unfolded state. Connections to other methods for analyzing complex reactions are discussed.

beta-Strand interactions at the domain interface critical for the stability of human lens gammaD-crystallin

Human age-onset cataracts are believed to be caused by the aggregation of partially unfolded or covalently damaged lens crystallin proteins; however, the exact molecular mechanism remains largely unknown. We have used microseconds of molecular dynamics simulations with explicit solvent to investigate the unfolding process of human lens gammaD-crystallin protein and its isolated domains. A partially unfolded folding intermediate of gammaD-crystallin is detected in simulations with its C-terminal domain (C-td) folded and N-terminal domain (N-td) unstructured, in excellent agreement with biochemical experiments. Our simulations strongly indicate that the stability and the folding mechanism of the N-td are regulated by the interdomain interactions, consistent with experimental observations. A hydrophobic folding core was identified within the C-td that is comprised of a and b strands from the Greek key motif 4, the one near the domain interface. Detailed analyses reveal a surprising non-native surface salt-bridge between Glu135 and Arg142 located at the end of the ab folded hairpin turn playing a critical role in stabilizing the folding core. On the other hand, an in silico single E135A substitution that disrupts this non-native Glu135-Arg142 salt-bridge causes significant destabilization to the folding core of the isolated C-td, which, in turn, induces unfolding of the N-td interface. These findings indicate that certain highly conserved charged residues, that is, Glu135 and Arg142, of gammaD-crystallin are crucial for stabilizing its hydrophobic domain interface in native conformation, and disruption of charges on the gammaD-crystallin surface might lead to unfolding and subsequent aggregation.

Probing the folding of mini-protein Beta3s by two-dimensional infrared spectroscopy; simulation study

We propose to use infrared coherent two-dimensional correlation spectroscopy (2DCS) to characterize the folding mechanism of the mini-protein Beta3s. In this study Beta3s was folded by molecular dynamics (MD) simulation and intermediate conformational ensembles were identified. The one and two-dimensional correlation spectrum was calculated for the intermediate and native states of the mini-protein. A direct structure-spectra relationship was determined by analysis of conformational properties and specific residue contributions. We identified the structural origin of diagonal and off-diagonal peaks in the 2DCS spectra for the native and intermediate conformational ensembles in the folding mechanism. This work supports the implementation of computational techniques in conjunction with experimental 2DCS to study the folding mechanism of proteins. In addition to exploring the folding mechanism the work presented here can be applied in combination with experiment to refine and validate current molecular dynamics force fields.

PACS Codes: 87.15.Cc, 87.15.hm, 87.15.hp

Folding, self-assembly, and bulk material properties of a de novo designed three-stranded beta-sheet hydrogel

A de novo designed three-stranded beta-sheet (TSS1) has been prepared that undergoes temperature-induced folding and self-assembly to afford a network of beta-sheet rich fibrils that constitutes a mechanically rigid hydrogel. Circular dichroism and infrared spectroscopies show that TSS1 folds and self-assembles into a beta-sheet secondary structure in response to temperature. Rheological measurements show that the resulting hydrogels are mechanically rigid [at pH 9, G' = 1750-9000 Pa, and at pH 7.4, G' = 8500 Pa] and that the storage modulus can be modulated by temperature and peptide concentration. Nanoscale structure analysis by transmission electron microscopy and small angle neutron scattering indicate that the hydrogel network is comprised of fibrils that are about 3 nm in width, consistent with the width of TSS1 in the folded state. A unique property of the TSS1 hydrogel is its ability to shear-thin into a low viscosity gel upon application of shear stress and immediately recover its mechanical rigidity upon termination of stress. This attribute allows the hydrogel to be delivered via syringe to a target site with spatial and temporal resolution. Finally, experiments employing C3H10t1/2 mesenchymal stem cells seeded onto the hydrogel and incubated for 24 h indicate that the TSS1 hydrogel surface is noncytotoxic, supports cell adhesion, and allows cell migration.

ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions

A new implicit solvation model for use in Monte Carlo simulations of polypeptides is introduced. The model is termed ABSINTH for self-Assembly of Biomolecules Studied by an Implicit, Novel, and Tunable Hamiltonian. It is designed primarily for simulating conformational equilibria and oligomerization reactions of intrinsically disordered proteins in aqueous solutions. The paradigm for ABSINTH is conceptually similar to the EEF1 model of Lazaridis and Karplus (Proteins 1999, 35, 133). In ABSINTH, the transfer of a polypeptide solute from the gas phase into a continuum solvent is the sum of a direct mean field interaction (DMFI), and a term to model the screening of polar interactions. Polypeptide solutes are decomposed into a set of distinct solvation groups. The DMFI is a sum of contributions from each of the solvation groups, which are analogs of model compounds. Continuum-mediated screening of electrostatic interactions is achieved using a framework similar to the one used for the DMFI. Promising results are shown for a set of test cases. These include the calculation of NMR coupling constants for short peptides, the assessment of the thermal stability of two small proteins, reversible folding of both an alpha-helix and a beta-hairpin forming peptide, and the polymeric properties of intrinsically disordered polyglutamine peptides of varying lengths. The tests reveal that the computational expense for simulations with the ABSINTH implicit solvation model increase by a factor that is in the range of 2.5-5.0 with respect to gas-phase calculations.

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed α/β protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49–67-residue systems with high statistical accuracy, using only modest computational resources by today's standards.

PACS Codes: 87.14.E-, 87.15.A-, 87.15.Cc

One-dimensional barrier-preserving free-energy projections of a beta-sheet miniprotein: new insights into the folding process

The conformational space of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 micros. The resulting one-dimensional free-energy profiles (FEPs) provide a detailed description of the free-energy basins and barriers for the folding reaction. The similarity of the FEPs obtained using the probability of folding before unfolding (pfold) or the mean first passage time supports the robustness of the procedure. The folded state and the most populated free-energy basins in the denatured state are described by the one-dimensional FEPs, which avoid the overlap of states present in the usual one- or two-dimensional projections. Within the denatured state, a basin with fluctuating helical conformations and a heterogeneous entropic state are populated near the melting temperature at about 11% and 33%, respectively. Folding pathways from the helical basin or enthalpic traps (with only one of the two hairpins formed) reach the native state through the entropic state, which is on-pathway and is separated by a low barrier from the folded state. A simplified equilibrium kinetic network based on the FEPs shows the complexity of the folding reaction and indicates, as augmented by additional analyses, that the basins in the denatured state are connected primarily by the native state. The overall folding kinetics shows single-exponential behavior because barriers between the non-native basins and the folded state have similar heights.

Folding pathways and rates for the three-stranded beta-sheet peptide Beta3s using discrete path sampling

The discrete path sampling method was used to investigate the folding of a three-stranded antiparallel beta-sheet peptide, Beta3s, described by an empirical potential and implicit solvent model. After application of a coarse-graining scheme that groups together sets of minima in local equilibrium, the calculated folding time was in reasonable agreement with other simulations and consistent with the experimental upper bound. The folding mechanism exhibited by the most significant discrete paths involves early formation of the C-terminal hairpin followed by docking of the N-terminal strand.

FACTS: Fast analytical continuum treatment of solvation

An efficient method for calculating the free energy of solvation of a (macro)molecule embedded in a continuum solvent is presented. It is based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The two measures of solvent displacement are combined in empirical equations to approximate the atomic (or self) electrostatic solvation energy and the solvent accessible surface area. The former directly yields the effective Born radius, which is used in the generalized Born (GB) formula to calculate the solvent-screened electrostatic interaction energy. A comparison with finite-difference Poisson data shows that atomic solvation energies, pair interaction energies, and their sums are evaluated with a precision comparable to the most accurate GB implementations. Furthermore, solvation energies of a large set of protein conformations have an error of only 1.5%. The solvent accessible surface area is used to approximate the nonpolar contribution to solvation. The empirical approach, called FACTS (Fast Analytical Continuum Treatment of Solvation), is only four times slower than using the vacuum energy in molecular dynamics simulations of proteins. Notably, the folded state of structured peptides and proteins is stable at room temperature in 100-ns molecular dynamics simulations using FACTS and the CHARMM force field.

Design of a soluble mini-protein through tandem duplication of the minimally engineered beta hairpin 'tongue' motif of alpha-hemolysin

In an attempt to fashion a globular protein out of two conjoined beta hairpin structural motif(s), we created a gene encoding, in tandem, two copies of the 40 residues-long transmembrane beta hairpin tongue (BHT) motif of the pore-forming toxin, alpha-hemolysin, of Staphylococcus aureus. Seven selected hydrophobic residues on each copy of the BHT motif's lipid-facing surface were mutated to hydrophilic residues, to prevent or reduce any non-specific aggregation based on hydrophobic interactions. Tandem BHT turned out to be expressed as a soluble polypeptide which could be raised to concentrations of approximately 2mg/ml. It displayed several characteristics of a folded mini-protein, although not the characteristics of a typical well-folded globular protein. These characteristics include (i) far-UV CD and FTIR spectra indicative of the presence of sheet structure mixed with polyproline type II secondary structure, (ii) a near-UV CD spectrum, indicating some formation of tertiary structure, (iii) evidence of unfolding and dissociation transitions in the presence of denaturants, accompanied by increase in random coil content, and (iv) the ability to transform from sheet to helical structure through a biphasic structural transition in the presence of the cosolvent, trifluorethanol. Importantly, however, tandem BHT displayed no cooperativity during unfolding; taken together with the poor structural content revealed in the far-UV CD spectrum and some non-canonical gel filtration behavior seen in the presence of denaturants, this suggests a partially unsuccessful instance of protein design.

Understanding protein folding: small proteins in silico

Recent improvements in methodology and increased computer power now allow atomistic computer simulations of protein folding. We briefly review several advanced Monte Carlo algorithms that have contributed to this development. Details of folding simulations of three designed mini proteins are shown. Adding global translations and rotations has allowed us to handle multiple chains and to simulate the aggregation of six beta-amyloid fragments. In a different line of research we have developed several algorithms to predict local features from sequence. In an outlook we sketch how such biasing could extend the application spectrum of Monte Carlo simulations to structure prediction of larger proteins.

Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single-point mutation of a β-sheet miniprotein

The effects of a single-point mutation on folding thermodynamics and kinetics are usually interpreted by focusing on the native structure and the transition state. Here, the entire conformational spaces of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) and of its single-point mutant W10V are sampled close to the melting temperature by equilibrium folding-unfolding molecular dynamics simulations for a total of 40 micros. The folded state as well as the most populated free energy basins in the denatured state are isolated by grouping conformations according to fast relaxation at equilibrium. Such kinetic analysis provides more detailed and useful information than a simple projection of the free energy. The W10V mutant has the same native structure as the wild type peptide, and similar folding rate and stability. In the denatured state, the N-terminal hairpin is about 20% more structured in W10V than the wild type mainly because of van der Waals interactions. Notably, the W10V mutation influences also the van der Waals energy at the transition state ensemble causing a shift in the ratio of fluxes between two different transition state regions on parallel folding pathways corresponding to nucleation at either of the two beta-hairpins. Previous experimental studies have focused on the effects of denaturant-dependent or temperature-dependent changes in the structure of the denatured state. The atomistic simulations show that a single-point mutation in the central strand of a beta-sheet peptide results in remarkable changes in the topography of the denatured state ensemble. These changes modulate the relative accessibility of parallel folding pathways because of kinetic partitioning of the denatured state. Therefore, the observed dependence of the folding process on the starting ensemble raises questions on the biological significance of in vitro folding studies under strongly denaturing conditions.

Minimization and optimization of designed beta-hairpin folds

Minimized beta hairpins have provided additional data on the geometric preferences of Trp interactions in TW-loop-WT motifs. This motif imparts significant fold stability to peptides as short as 8 residues. High-resolution NMR structures of a 16- (KKWTWNPATGKWTWQE, DeltaG(U)(298) >or= +7 kJ/mol) and 12-residue (KTWNPATGKWTE, DeltaG(U)(298) = +5.05 kJ/mol) hairpin reveal a common turn geometry and edge-to-face (EtF) packing motif and a cation-pi interaction between Lys(1) and the Trp residue nearest the C-terminus. The magnitude of a CD exciton couplet (due to the two Trp residues) and the chemical shifts of a Trp Hepsilon3 site (shifted upfield by 2.4 ppm due to the EtF stacking geometry) provided near-identical measures of folding. CD melts of representative peptides with the -TW-loop-WT- motif provided the thermodynamic parameters for folding, which reflect enthalpically driven folding at laboratory temperatures with a small DeltaC(p) for unfolding (+420 J K(-)(1)/mol). In the case of Asx-Pro-Xaa-Thr-Gly-Xaa loops, mutations established that the two most important residues in this class of direction-reversing loops are Asx and Gly: mutation to alanine is destabilizing by about 6 and 2 kJ/mol, respectively. All indicators of structuring are retained in a minimized 8-residue construct (Ac-WNPATGKW-NH(2)) with the fold stability reduced to DeltaG(U)(278) = -0.7 kJ/mol. NMR and CD comparisons indicate that -TWXNGKWT- (X = S, I) sequences also form the same hairpin-stabilizing W/W interaction.

Improving an all-atom force field

Experimentally well-characterized proteins that are small enough to be computationally tractable provide useful information for refining existing all-atom force fields. This is used by us for reparametrizing a recently developed all-atom force field. Relying on high statistics parallel tempering simulations of a designed 20 residue beta-sheet peptide, we propose incremental changes that improve the force field's range of applicability.

Macrocyclic beta-sheet peptides that mimic protein quaternary structure through intermolecular beta-sheet interactions

This paper reports the design, synthesis, and characterization of a family of cyclic peptides that mimic protein quaternary structure through beta-sheet interactions. These peptides are 54-membered-ring macrocycles comprising an extended heptapeptide beta-strand, two Hao beta-strand mimics [JACS 2000, 122, 7654] joined by one additional alpha-amino acid, and two delta-linked ornithine beta-turn mimics [JACS 2003, 125, 876]. Peptide 3a, as the representative of these cyclic peptides, contains a heptapeptide sequence (TSFTYTS) adapted from the dimerization interface of protein NuG2 [PDB ID: 1mio]. 1H NMR studies of aqueous solutions of peptide 3a show a partially folded monomer in slow exchange with a strongly folded oligomer. NOE studies clearly show that the peptide self-associates through edge-to-edge beta-sheet dimerization. Pulsed-field gradient (PFG) NMR diffusion coefficient measurements and analytical ultracentrifugation (AUC) studies establish that the oligomer is a tetramer. Collectively, these experiments suggest a model in which cyclic peptide 3a oligomerizes to form a dimer of beta-sheet dimers. In this tetrameric beta-sheet sandwich, the macrocyclic peptide 3a is folded to form a beta-sheet, the beta-sheet is dimerized through edge-to-edge interactions, and this dimer is further dimerized through hydrophobic face-to-face interactions involving the Phe and Tyr groups. Further studies of peptides 3b-3n, which are homologues of peptide 3a with 1-6 variations in the heptapeptide sequence, elucidate the importance of the heptapeptide sequence in the folding and oligomerization of this family of cyclic peptides. Studies of peptides 3b-3g show that aromatic residues across from Hao improve folding of the peptide, while studies of peptides 3h-3n indicate that hydrophobic residues at positions R3 and R5 of the heptapeptide sequence are important in oligomerization.

Measuring cooperativity in the formation of a three-stranded beta sheet (double hairpin)

Recently validated chemical shift measures of hairpin structuring have been applied to a series of turn mutants of the Schenck-Gellman three-strand beta-sheet model with the aim of measuring the entropic advantage associated with aligning an additional strand onto an existing hairpin versus aligning the same two strands in an initial hairpin formation. In a four-state analysis (unfolded, 2 single hairpins, and the double hairpin fold in equilibrium) a cooperativity index can be defined as the factor by which the equilibrium constant for hairpin formation is improved when one strand is prestructured. This cooperativity index is 2.7 +/- 0.7 for hairpin formation about a stable D-Pro-Gly turn locus and increases to 7.6 +/- 1.2 for an Asn-Gly turn locus. The latter corresponds to a cooperativity induced DeltaDeltaG increment of 4.9 kJ/mol for the folding of a hairpin. Although larger than previous experimental measures of folding cooperativity in three-stranded sheets, the magnitude of this effect (which is considerably less than the TDeltaDeltaS expectation for prestructuring three or more beta-strand residue sites) likely reflects the intrinsic preference of these designed sequences for extended conformations. If similar or larger effects apply to protein beta-sheet folding, it is not surprising that particularly favorable hairpin alignments serve as nucleation sites in protein folding pathways.

Design and NMR conformational study of a beta-sheet peptide based on Betanova and WW domains

A good approach to test our current knowledge on formation of protein beta-sheets is de novo protein design. To obtain a three-stranded beta-sheet mini-protein, we have built a series of chimeric peptides by taking as a template a previously designed beta-sheet peptide, Betanova-LLM, and incorporating N- and/or C-terminal extensions taken from WW domains, the smallest natural beta-sheet domain that is stable in absence of disulfide bridges. Some Betanova-LLM strand residues were also substituted by those of a prototype WW domain. The designed peptides were cloned and expressed in Escherichia coli. The ability of the purified peptides to adopt beta-sheet structures was examined by circular dichroism (CD). Then, the peptide showing the highest beta-sheet population according to the CD spectra, named 3SBWW-2, was further investigated by 1H and 13C NMR. Based on NOE and chemical shift data, peptide 3SBWW-2 adopts a well defined three-stranded antiparallel beta-sheet structure with a disordered C-terminal tail. To discern between the contributions to beta-sheet stability of strand residues and the C-terminal extension, the structural behavior of a control peptide with the same strand residues as 3SBWW-2 but lacking the C-terminal extension, named Betanova-LYYL, was also investigated. beta-Sheet stability in these two peptides, in the parent Betanova-LLM and in WW-P, a prototype WW domain, decreased in the order WW-P > 3SBWW-2 > Betanova-LYYL > Betanova-LLM. Conclusions about the contributions to beta-sheet stability were drawn by comparing structural properties of these four peptides.

Folding of proteins with diverse folds

Using parallel tempering simulations with high statistics, we investigate the folding and thermodynamic properties of three small proteins with distinct native folds: the all-helical 1RIJ, the all-sheet beta3s, and BBA5, which has a mixed helix-sheet fold. In all three cases, simulations with our energy function find the native structures as global minima in free energy at experimentally relevant temperatures. However, the folding process strongly differs for the three molecules, indicating that the folding mechanism is correlated with the form of the native structure.

Reversible thermal denaturation of a 60-kDa genetically engineered beta-sheet polypeptide

A de novo 687-amino-acid residue polypeptide with a regular 32-amino-acid repeat sequence, (GA)(3)GY(GA)(3)GE(GA)(3)GH(GA)(3)GK, forms large beta-sheet assemblages that exhibit remarkable folding properties and, as well, form fibrillar structures. This construct is an excellent tool to explore the details of beta-sheet formation yielding intimate folding information that is otherwise difficult to obtain and may inform folding studies of naturally occurring materials. The polypeptide assumes a fully folded antiparallel beta-sheet/turn structure at room temperature, and yet is completely and reversibly denatured at 125 degrees C, adopting a predominant polyproline II conformation. Deep ultraviolet Raman spectroscopy indicated that melting/refolding occurred without any spectroscopically distinct intermediates, yet the relaxation kinetics depend on the initial polypeptide state, as would be indicative of a non-two-state process. Thermal denaturation and refolding on cooling appeared to be monoexponential with characteristic times of approximately 1 and approximately 60 min, respectively, indicating no detectable formation of hairpin-type nuclei in the millisecond timescale that could be attributed to nonlocal "nonnative" interactions. The polypeptide folding dynamics agree with a general property of beta-sheet proteins, i.e., initial collapse precedes secondary structure formation. The observed folding is much faster than expected for a protein of this size and could be attributed to a less frustrated free-energy landscape funnel for folding. The polypeptide sequence suggests an important balance between the absence of strong nonnative contacts (salt bridges or hydrophobic collapse) and limited repulsion of charged side chains.