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A newanalysis of the 20 μs equilibrium folding/unfoldingmolecular dynamics simulations of the three-stranded antiparallelβ-sheet miniprotein (beta3s) in implicit solvent is presented.The conformation space is reduced in dimensionality by introductionof linear combinations of hydrogen bond distances as the collectivevariables making use of a specially adapted principal component analysis(PCA); i.e., to make structured conformations more pronounced, onlythe formed bonds are included in determining the principal components.It is shown that a three-dimensional (3D) subspace gives a meaningfulrepresentation of the folding behavior. The first component, to whicheight native hydrogen bonds make the major contribution (four in eachbeta hairpin), is found to play the role of the reaction coordinatefor the overall folding process, while the second and third componentsdistinguish the structured conformations. The representative pointsof the trajectory in the 3D space are grouped into conformationalclusters that correspond to locally stable conformations of beta3sidentified in earlier work. A simplified kinetic network based onthe three components is constructed, and it is complemented by a hydrodynamicanalysis. The latter, making use of “passive tracers”in 3D space, indicates that the folding flow is much more complexthan suggested by the kinetic network. A 2D representation of streamlinesshows there are vortices which correspond to repeated local rearrangement,not only around minima of the free energy surface but also in flatregions between minima. The vortices revealed by the hydrodynamicanalysis are apparently not evident in folding pathways generatedby transition-path sampling. Making use of the fact that the valuesof the collective hydrogen bond variables are linearly related tothe Cartesian coordinate space, the RMSD between clusters is determined.Interestingly, the transition rates show an approximate exponentialcorrelation with distance in the hydrogen bond subspace. Comparisonwith the many published studies shows good agreement with the presentanalysis for the parts that can be compared, supporting the robustcharacter of our understanding of this “hydrogen atom”of protein folding. [ABSTRACT FROM AUTHOR]

Multiple independent molecular dynamics (MD) simulations are often carried out starting from a single protein structure or a set of conformations that do not correspond to a thermodynamic ensemble. Therefore, a significant statistical bias is usually present in the Markov state model generated by simply combining the whole MD sampling into a network whose nodes and links are clusters of snapshots and transitions between them, respectively. Here, we introduce a depth-first search algorithm to extract from the whole conformation space network the largest ergodic component, i.e., the subset of nodes of the network whose transition matrix corresponds to an ergodic Markov chain. For multiple short MD simulations of a globular protein (as in distributed computing), the steady state, i.e., stationary distribution determined using the largest ergodic component, yields more accurate free energy profiles and mean first passage times than the original network or the ergodic network obtained by imposing detailed balance by means of symmetrization of the transition counts. [ABSTRACT FROM AUTHOR]

It is difficult to investigate folding kinetics by conventional atomistic simulations of proteins. The replica exchange molecular dynamics (REMD) simulation technique enhances conformational sampling at the expenses of reduced kinetic information, which in REMD is directly available only for very short time scales. Here, we propose a procedure for obtaining kinetic data from REMD by making use of the equilibrium transitions network (ETN) sampled at the temperature of interest. This information is supplemented by mean folding times extracted from ETNs at higher REMD temperatures and scaled according to the Arrhenius equation. The procedure is applied to a three-stranded antiparallel β-sheet peptide which has a very heterogeneous denatured state with a broad entropic basin and several enthalpic traps. Despite the complexity of the system and the REMD exchange time of only 0.1 ns, the procedure is able to estimate folding times (ranging from about 0.1 μs at the melting temperature of 330 K to about 8 μs at 286 K) as well as transition times from individual non-native basins to the native state. [ABSTRACT FROM AUTHOR]

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 β-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. [ABSTRACT FROM AUTHOR]

The conformational space of a 20-residue three-stranded antiparallel β-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 µs. 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. [ABSTRACT FROM AUTHOR]

The flexibility and stability of both monomeric and dimeric HIV-1 PR were explored by 100 ns implicit solvent molecular dynamics simulation at 350 K with the aim to correlate the monomer stability with the dimerization mechanism. The principal component analysis (PCA) was applied to visualize the available regions in the conformational space of the two HIV-1 PR forms, to compare their structural diversity and to map the bottom of their underlying energy landscapes. It was found that whereas the flap tips (residues 45-55) are flexible and adopt close and open conformations in both monomeric and dimeric forms, the N- and C-termini (residues 1-4 and 96-99, respectively), which constitute the interface between the two subunits, are flexible only in the monomer. The different flexibility of the monomeric and dimeric HIV-1 PR is reflected in the different topography of their underlying energy landscape. Although the bottom of the monomer energy landscape is broad and rough, that of the dimer is narrower, deeper, and smoother, reflecting the enhanced flexibility of the monomer and the stabilizing interactions between the dimer subunits. Accordingly, blocking one or both terminals may prevent the formation of the active site. Despite the different flexibility of the termini in the monomeric and dimeric HIV-1 PR, their secondary structure contents are similar. The partial stability of the monomer together with the flexibility of its termini suggest that the HIV-1 PR is not a two-state dimer, as indicated by equilibrium denaturation experiments, but a three-state dimer with a marginally stable monomeric intermediate. This involves the swapping of the flexible termini across the two chains to form the dimer interface. [ABSTRACT FROM AUTHOR]

Aggregation of amyloid beta (Aβ) is the hallmarkof Alzheimer’sdisease (AD). Small molecules inhibiting Aβ can be valuabletherapeutics for AD. We have previously reported that 1,4-naphthoquinon-2-yl-l-tryptophan (NQTrp), reduces aggregation and oligomerizationof Aβ in vitro and in vivo. In silico analysis further showedthat certain functional groups of NQTrp, not in the aromatic rings,are also involved in binding and inhibiting Aβ. To better understandthe exact mode of action and identify the groups crucial for NQTrpinhibitory activity, we conducted structure–activity analysis.Four derivatives of NQTrp were studied in silico: a D-isomer, two single-methylated and one double-methylated derivative.In silico results showed that the NQTrp groups involved in hydrogenbonds are the anilinic NH (i.e., the NH linker between the quinoneand tryptophan moieties), the quinonic carbonyls, and the carboxylicacid. These predictions were supported by in vitro results. Our resultsshould aid in designing improved small-molecule inhibitors of Aβaggregation for treating AD. [ABSTRACT FROM AUTHOR]

Amyloid aggregates are highly ordered fibrillar assembliesof polypeptidesinvolved in a number of neurodegenerative diseases. Very little isknown on the pathways of self-assembly of peptides into the finalamyloid fibrils, which is due in part to the difficulty of triggeringthe aggregation process in a controlled manner. Here we present thedesign and validation of a cross-linked hexapeptide that reversiblyaggregates and dissociates under ultraviolet light irradiation control.First molecular dynamics simulations were carried out to identify,among hundreds of possible sequences, those with the highest propensityto form ordered (β-sheet) oligomers in the trans state of theazobenzene cross-linker, and at the same time with the highest solubilityin the cis state. In the simulations, the peptides were observed tospontaneously form ordered oligomers with cross-β contacts whenthe cross-linker was in the trans state, whereas in the cis statethey self-assemble into amorphous aggregates. For the most promisingsequence emerging from the simulations (Ac-Cys-His-Gly-Gln-Cys-Lys-NH2cross-linked at the two cysteine residues), the photoisomerizationof the azobenzene group was shown to induce reversible aggregationby time-resolved light scattering and fluorescence measurements. Theamyloid-like fibrillar topology was confirmed by electron microscopy.Potential applications of minimally designed peptides with photoswitchableamyloidogenic propensity are briefly discussed. [ABSTRACT FROM AUTHOR]

We propose a network-based method for determining basins and barriers of complex free energy surfaces (e.g., the protein folding landscape) from the time series of a single intramolecular distance. First, a network of transitions is constructed by clustering the points of the time series according to the short-time distribution of the signal. The transition network, which reflects the short-time kinetics, is then used for the iterative determination of individual basins by the minimum-cut-based free energy profile, a barrier-preserving one-dimensional projection of the free energy surface. The method is tested using the time series of a single Cβ−Cβdistance extracted from equilibrium molecular dynamics (MD) simulations of a structured peptide (20 residue three-stranded antiparallel β-sheet). Although the information of only one distance is employed to describe a system with 645 degrees of freedom, both the native state and the unfolding barrier of about 10 kJ/mol are determined with remarkable accuracy. Moreover, non-native conformers are identified by comparing long-time distributions of the same distance. To examine the applicability to single-molecule Förster resonance energy transfer (FRET) experiments, a time series of donor and acceptor photons is generated using the MD trajectory. The native state of the β-sheet peptide is determined accurately from the emulated FRET signal. Applied to real single-molecule FRET measurements on a monomeric variant of λ-repressor, the network-based method correctly identifies the folded and unfolded populations, which are clearly separated in the minimum-cut-based free energy profile. [ABSTRACT FROM AUTHOR]

A series of photoswitchable, α-helical peptides were studied using two-dimensional infrared spectroscopy (2D-IR). Single-isotope labeling with 13C18O at various positions in the sequence was employed to spectrally isolate particular backbone positions. We show that a single 13C18O label can give rise to two bands along the diagonal of the 2D-IR spectrum, one of which is from an amide group that is hydrogen-bonded internally, or to a solvent molecule, and the other from a non-hydrogen-bonded amide group. The photoswitch enabled examination of both the folded and unfolded state of the helix. For most sites, unfolding of the peptide caused a shift of intensity from the hydrogen-bonded peak to the non-hydrogen-bonded peak. The relative intensity of the two diagonal peaks gives an indication of the fraction of molecules hydrogen-bonded at a certain location along the sequence. As this fraction varies quite substantially along the helix, we conclude that the helix is not uniformly folded. Furthermore, the shift in hydrogen bonding is much smaller than the change of helicity measured by CD spectroscopy, indicating that non-native hydrogen-bonded or mis-folded loops are formed in the unfolded ensemble. [ABSTRACT FROM AUTHOR]

Multiple 4-μs molecular dynamics (MD) simulations are used to study the folding process of the cross-linked α-helical peptide Ac-EACAR5EAAAR10EAACR15Q-NH2(EAAAR peptide). The folding kinetics are single exponential at 330 K, while they are complex at 281 K with a clear deviation from single-exponential behavior, in agreement with time-resolved infrared (IR) spectroscopy measurements. Network analysis of the conformation space sampled by the MD simulations reveals four main folding channels which start from conformations with partially formed helical structure and non-native salt-bridges in a kinetically partitioned unfolded state. The independent folding pathways explain the comparable quality of models based on stretched exponential and multiexponential fitting of the kinetic traces at low temperature. The rearrangement of bulky side chains, and in particular their reorientation with respect to the cross-linker, makes the EAAAR peptide a slower folder at 281 K than a similar peptide devoid of the three glutamate side chains. On the basis of this simulation result, extracted from a total MD sampling of 1.0 ms, a mutant with additional bulky side chains (three methionines replacing alanines at positions 2, 7, and 12) is suggested to fold slower than the EAAAR peptide. This prediction is confirmed by time-resolved IR spectroscopy. [ABSTRACT FROM AUTHOR]