Einstein Model of a Graph to Characterize Protein Folded/Unfolded States.

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates.

Exploring Structural Flexibility and Stability of α-Synuclein by the Landau-Ginzburg-Wilson Approach.

α-Synuclein (αS) is the principal protein component of the Lewy body and Lewy neurite deposits that are found in the brains of the victims of one of the most prevalent neurodegenerative disorders, Parkinson's disease. αS can be qualified as a chameleon protein because of the large number of different conformations that it is able to adopt: it is disordered under physiological conditions in solution, in equilibrium with a minor α-helical tetrameric form in the cytoplasm, and is α-helical when bound to a cell membrane. Also, , αS forms polymorphic amyloid fibrils with unique arrangements of cross-β-sheet motifs.

Wild-Type -Synuclein and Variants Occur in Different Disordered Dimers and Pre-Fibrillar Conformations in Early Stage of Aggregation.

-Synuclein is a 140 amino-acid intrinsically disordered protein mainly found in the brain. Toxic -synuclein aggregates are the molecular hallmarks of Parkinson's disease. studies showed that -synuclein aggregates in oligomeric structures of several 10th of monomers and into cylindrical structures (fibrils), comprising hundred to thousands of proteins, with polymorphic cross--sheet conformations.

Mechanistic Kinetic Model Reveals How Amyloidogenic Hydrophobic Patches Facilitate the Amyloid-β Fibril Elongation.

Abnormal aggregation of amyloid β (Aβ) peptides into fibrils plays a critical role in the development of Alzheimer's disease. A two-stage "dock-lock" model has been proposed for the Aβ fibril elongation process. However, the mechanisms of the Aβ monomer-fibril binding process have not been elucidated with the necessary molecular-level precision, so it remains unclear how the lock phase dynamics leads to the overall in-register binding of the Aβ monomer onto the fibril.

Probing Protein Aggregation Using the Coarse-Grained UNRES Force Field.

Protein aggregation is the cause of many, often lethal, diseases, including the Alzheimer's, Parkinson's, and Huntington's diseases, and familial amyloidosis. Theoretical investigation of the mechanism of this process, including the structures of the oligomeric intermediates which are the most toxic, is difficult because of long time scale of aggregation. Coarse-grained models, which enable us to extend the simulation time scale by three or more orders of magnitude, are, therefore, of great advantage in such studies.

Missense Mutations Modify the Conformational Ensemble of the -Synuclein Monomer Which Exhibits a Two-Phase Characteristic.

-Synuclein is an intrinsically disordered protein occurring in different conformations and prone to aggregate in -sheet structures, which are the hallmark of the Parkinson disease. Missense mutations are associated with familial forms of this neuropathy. How these single amino-acid substitutions modify the conformations of wild-type -synuclein is unclear.

Investigation of Phosphorylation-Induced Folding of an Intrinsically Disordered Protein by Coarse-Grained Molecular Dynamics.

Apart from being the most common mechanism of regulating protein function and transmitting signals throughout the cell, phosphorylation has an ability to induce disorder-to-order transition in an intrinsically disordered protein. In particular, it was shown that folding of the intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can be induced by multisite phosphorylation. Here, the principles that govern the folding of phosphorylated 4E-BP2 (pT37pT46 4E-BP2) are investigated by analyzing canonical and replica exchange molecular dynamics trajectories, generated with the coarse-grained united-residue force field, in terms of local and global motions and the time dependence of formation of contacts between Cs of selected pairs of residues.

How Useful can the Voigt Profile be in Protein Folding Processes?

The analytical expression for the Voigt profile, along with its simplified forms for the Gaussian and Lorentzian dominance, is presented. The applicability of the Voigt profile in the description of anomalous diffusion phenomena, ubiquitous in different fields of science including protein folding, is discussed. It is shown that the Voigt profile is a good descriptor of the processes occurring in protein folding and in the native state.

Curvature and Torsion of Protein Main Chain as Local Order Parameters of Protein Unfolding.

Thermal protein unfolding resembles a global (two-state) phase transition. At the local scale, protein unfolding is, however, heterogeneous and probe dependent. Here, we consider local order parameters defined by the local curvature and torsion of the protein main chain.

New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain.

Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain.

Dependence of the Formation of Tau and Aβ Peptide Mixed Aggregates on the Secondary Structure of the N-Terminal Region of Aβ.

One of the hallmarks of Alzheimer's disease is the formation of aggregates of the tau protein, a process that can be facilitated by the presence of fibrils formed by the amyloid β peptide (Aβ). However, the mechanism that triggers tau aggregation is still a matter of debate. The effect of Aβ fibrils on the aggregation of the repeat domain of tau (TauRD) is investigated here by employing coarse-grained molecular dynamics simulations.

From a Highly Disordered to a Metastable State: Uncovering Insights of α-Synuclein.

α-Synuclein (αS) is a major constituent of Lewy bodies, the insoluble aggregates that are the hallmark of one of the most prevalent neurodegenerative disorders, Parkinson's disease (PD). The vast majority of experiments in vitro and in vivo provide extensive evidence that a disordered monomeric form is the predominant state of αS in water solution, and it undergoes a large-scale disorder-to-helix transition upon binding to vesicles of different types. Recently, another form, tetrameric, of αS with a stable helical structure was identified experimentally.

Statistical Model To Decipher Protein Folding/Unfolding at a Local Scale.

Protein folding/unfolding can be analyzed experimentally at a local scale by monitoring the physical properties of local probes as a function of the temperature, for example, the distance between fluorophores or the values of chemical shifts of backbone atoms. Here, the analytical Lifson-Roig model for the helix-coil transition is modified to analyze local thermal unfolding of the fast-folder W protein of bacteriophage lambda (gpW) simulated by all-atom molecular dynamics (MD) simulations in explicit solvent at 15 different temperatures. The protein structure is described by the coarse-grained dihedral angles (γ) and bond angles (θ) built between successive C-C virtual bonds.

Lysosomal enzyme tripeptidyl peptidase 1 destabilizes fibrillar Aβ by multiple endoproteolytic cleavages within the β-sheet domain.

Accumulation of amyloid-beta (Aβ), which is associated with Alzheimer's disease, can be caused by excess production or insufficient clearance. Because of its β-sheet structure, fibrillar Aβ is resistant to proteolysis, which would contribute to slow degradation of Aβ plaques in vivo. Fibrillar Aβ can be internalized by microglia, which are the scavenger cells of the brain, but the fibrils are degraded only slowly in microglial lysosomes.

Sequence-, structure-, and dynamics-based comparisons of structurally homologous CheY-like proteins.

We recently introduced a physically based approach to sequence comparison, the property factor method (PFM). In the present work, we apply the PFM approach to the study of a challenging set of sequences-the bacterial chemotaxis protein CheY, the N-terminal receiver domain of the nitrogen regulation protein NT-NtrC, and the sporulation response regulator Spo0F. These are all response regulators involved in signal transduction.

Elucidating Important Sites and the Mechanism for Amyloid Fibril Formation by Coarse-Grained Molecular Dynamics.

Fibrils formed by the β-amyloid (Aβ) peptide play a central role in the development of Alzheimer's disease. In this study, the principles governing their growth and stability are investigated by analyzing canonical and replica-exchange molecular dynamics trajectories of Aβ fibrils. In particular, an unstructured monomer was allowed to interact freely with an Aβ fibril template.

Eliminating a Protein Folding Intermediate by Tuning a Local Hydrophobic Contact.

Intermediate states in protein folding may slow folding, and sometimes can provide a starting point for aggregation. Recently, the FBP28 WW domain of the formin-binding protein was used as a model for a computational study of the origin and prevention of intermediate-state formation, and local hydrophobic interactions of Leu26 were implicated. Here, we combine new simulations over a broad temperature range with experimental temperature-jump data to study this site in more detail.

Preventing fibril formation of a protein by selective mutation.

The origins of formation of an intermediate state involved in amyloid formation and ways to prevent it are illustrated with the example of the Formin binding protein 28 (FBP28) WW domain, which folds with biphasic kinetics. Molecular dynamics of protein folding trajectories are used to examine local and global motions and the time dependence of formation of contacts between C(α)s and C(β)s of selected pairs of residues. Focus is placed on the WT FBP28 WW domain and its six mutants (L26D, L26E, L26W, E27Y, T29D, and T29Y), which have structures that are determined by high-resolution NMR spectroscopy.

New Insights into Protein (Un)Folding Dynamics.

A fundamental open problem in biophysics is how the folded structure of the main chain (MC) of a protein is determined by the physics of the interactions between the side chains (SCs). All-atom molecular dynamics simulations of a model protein (Trp-cage) revealed that strong correlations between the motions of the SCs and the MC occur transiently at 380 K in unfolded segments of the protein and during the simulations of the whole amino-acid sequence at 450 K. The high correlation between the SC and MC fluctuations is a fundamental property of the unfolded state and is also relevant to unstructured proteins as intrinsically disordered proteins (IDPs), for which new reaction coordinates are introduced.

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements.

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecond-timescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed.

Accounting for a mirror-image conformation as a subtle effect in protein folding.

By using local (free-energy profiles along the amino acid sequence and (13)C(α) chemical shifts) and global (principal component) analyses to examine the molecular dynamics of protein-folding trajectories, generated with the coarse-grained united-residue force field, for the B domain of staphylococcal protein A, we are able to (i) provide the main reason for formation of the mirror-image conformation of this protein, namely, a slow formation of the second loop and part of the third helix (Asp29-Asn35), caused by the presence of multiple local conformational states in this portion of the protein; (ii) show that formation of the mirror-image topology is a subtle effect resulting from local interactions; (iii) provide a mechanism for how protein A overcomes the barrier between the metastable mirror-image state and the native state; and (iv) offer a plausible reason to explain why protein A does not remain in the metastable mirror-image state even though the mirror-image and native conformations are at least energetically compatible.

Kinks, loops, and protein folding, with protein A as an example.

The dynamics and energetics of formation of loops in the 46-residue N-terminal fragment of the B-domain of staphylococcal protein A has been studied. Numerical simulations have been performed using coarse-grained molecular dynamics with the united-residue (UNRES) force field. The results have been analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger (DNLS) equation.

Local vs global motions in protein folding.

It is of interest to know whether local fluctuations in a polypeptide chain play any role in the mechanism by which the chain folds to the native structure of a protein. This question is addressed by analyzing folding and non-folding trajectories of a protein; as an example, the analysis is applied to the 37-residue triple β-strand WW domain from the Formin binding protein 28 (FBP28) (PDB ID: 1E0L). Molecular dynamics (MD) trajectories were generated with the coarse-grained united-residue force field, and one- and two-dimensional free-energy landscapes (FELs) along the backbone virtual-bond angle θ and backbone virtual-bond-dihedral angle γ of each residue, and principal components, respectively, were analyzed.