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The self-assembling propensity of amyloid peptides such as diphenylalanine (FF) allows them to form ordered, nanoscale structures, with biocompatible properties important for biomedical applications. Moreover, piezoelectric properties allow FF molecules and their aggregates (e.g., FF nanotubes) to be aligned in a controlled way by the application of external electric fields. However, while the behavior of FF nanostructures emerges from the biophysical properties of the monomers, the detailed responses of individual peptides to both temperature and electric fields are not fully understood. Here, we study the temperature-dependent conformational dynamics of FF peptides solvated in explicit water molecules, an environment relevant to biomedical applications, by using an enhanced sampling method, replica exchange molecular dynamics (REMD), in conjunction with applied electric fields. Our simulations highlight and overcome possible artifacts that may occur during the setup of REMD simulations of explicitly solvated peptides in the presence of external electric fields, a problem particularly important in the case of short peptides such as FF. The presence of the external fields could overstabilize certain conformational states in one or more REMD replicas, leading to distortions of the underlying potential energy distributions observed at each temperature. This can be overcome by correcting the REMD initial conditions to include the lower-energy conformations induced by the external field. We show that the converged REMD data can be analyzed using a Markovian description of conformational states and show that a rather complex, 3-state, temperature-dependent conformational dynamics in the absence of electric fields collapses to only one of these states in the presence of the electric fields. These details on the temperature- and electric-field-dependent thermodynamic and kinetic properties of small FF amyloid peptides can be useful in understanding and devising new methods to control their aggregation-prone biophysical properties and, possibly, the structural and biophysical properties of FF molecular nanostructures.

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.

Human islet amyloid polypeptide (hIAPP), also known as amylin, is a 37-amino-acid peptide, co-secreted with insulin, and widely found in fibril form in type-2 diabetes patients. By using all-atom molecular dynamics simulations, we study hIAPP fibril segments (i.e., fibrillar oligomers) formed with sequences of naturally occurring variants from cat, rat, and pig, presenting different aggregation propensities. We characterize the effect of mutations on the structural dynamics of solution-formed hIAPP fibril models built from solid-state NMR data. Results from this study are in agreement with experimental observations regarding their respective relative aggregation propensities. We analyze in detail the specific structural characteristics and infer mechanisms that modulate the conformational stability of amylin fibrils. Results provide a platform for further studies and the design of new drugs that could interfere with amylin aggregation and its cytotoxicity. One particular mutation, N31K, has fibril-destabilizing properties, and could potentially improve the solubility of therapeutic amylin analogs.

Nanocomposites of diphenylalanine (FF) and carbon based materials provide an opportunity to overcome drawbacks associated with using FF micro- and nanostructures in nanobiotechnology applications, in particular, their poor structural stability in liquid solutions. In this study, FF/graphene oxide (GO) composites were found to self-assemble into layered micro- and nanostructures, which exhibited improved thermal and aqueous stability. Dependent on the FF/GO ratio, the solubility of these structures was reduced to 35.65% after 30 min as compared to 92.4% for pure FF samples. Such functional nanocomposites may extend the use of FF structures to, e.g., biosensing, electrochemical, electromechanical or electronic applications. European Commission - European Regional Development Fund European Commission - Seventh Framework Programme (FP7) Science Foundation Ireland Programme for Research in Third Level Institutions (PRTLI) Cycle 5 Russian Foundation for Fundamental Research CICECO-Aveiro Institute of Materials FCT/MEC PT2020 Partnership Agreement

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.

Peptide cyclization can improve stability, conformational constraint, and compactness. However, apart from beta-turn structures, which are well incorporated into cyclic peptides (CPs), many primary peptide structures and functions are markedly altered by cyclization. Accordingly, to mimic linear peptide interfaces with cyclic peptides, it can be beneficial to screen combinatorial cyclic peptide libraries. Computational methods have been developed to screen CPs, but face a number of challenges. Here, we review methods to develop in silico computational libraries, and the potential for screening naturally occurring libraries of CPs. The simplest and most rapid computational pharmacophore methods that estimate peptide three-dimensional structures to be screened versus targets are relatively easy to implement, and while the constraint on structure imposed by cyclization makes them more effective than the same approaches with linear peptides, there are a large number of limiting assumptions. In contrast, full molecular dynamics simulations of cyclic peptide structures not only are costly to implement, but also require careful attention to interpretation, so that not only is the computation time rate limiting, but the interpretation time is also rate limiting due to the analysis of the typically complex underlying conformational space of CPs. A challenge for the field of computational cyclic peptide screening is to bridge this gap effectively. Natural compound libraries of short cyclic peptides, and short cyclized regions of proteins, encoded in the genomes of many organisms present a potential treasure trove of novel functionality which may be screened via combined computational and experimental screening approaches.

Peptide cyclization can improve stability, conformational constraint, and compactness. However, apart from beta-turn structures, which are well incorporated into cyclic peptides (CPs), many primary peptide structures and functions are markedly altered by cyclization. Accordingly, to mimic linear peptide interfaces with cyclic peptides, it can be beneficial to screen combinatorial cyclic peptide libraries. Computational methods have been developed to screen CPs, but face a number of challenges. Here, we review methods to develop in silico computational libraries, and the potential for screening naturally occurring libraries of CPs. The simplest and most rapid computational pharmacophore methods that estimate peptide three-dimensional structures to be screened versus targets are relatively easy to implement, and while the constraint on structure imposed by cyclization makes them more effective than the same approaches with linear peptides, there are a large number of limiting assumptions. In contrast, full molecular dynamics simulations of cyclic peptide structures not only are costly to implement, but also require careful attention to interpretation, so that not only is the computation time rate limiting, but the interpretation time is also rate limiting due to the analysis of the typically complex underlying conformational space of CPs. A challenge for the field of computational cyclic peptide screening is to bridge this gap effectively. Natural compound libraries of short cyclic peptides, and short cyclized regions of proteins, encoded in the genomes of many organisms present a potential treasure trove of novel functionality which may be screened via combined computational and experimental screening approaches.

Background Kinases are a family of enzymes that catalyze the transfer of the ɤ-phosphate group from ATP to a protein's residue. Malfunctioning kinases are involved in many health problems such as cardiovascular diseases, diabetes, and cancer. Kinases transitions between multiple conformations of inactive to active forms attracted considerable interest. Method A reaction coordinate is computed for the transition between the active to inactive conformation in Abl kinase with a focus on the DFG-in to DFG-out flip. The method of Rock Climbing is used to construct a path locally, which is subsequently optimized using a functional of the entire path. The discrete coordinate sets along the reaction path are used in a Milestoning calculation of the free energy landscape and the rate of the transition. Results The estimated transition times are between a few milliseconds and seconds, consistent with simulations of the kinetics and with indirect experimental data. The activation requires the transient dissociation of the salt bridge between Lys271 and Glu286. The salt bridge reforms once the DFG motif is stabilized by a locked conformation of Phe382. About ten residues are identified that contribute significantly to the process and are included as part of the reaction space. Conclusions The transition from DFG-in to DFG-out in Abl kinase was simulated using atomic resolution of a fully solvated protein yielding detailed description of the kinetics and the mechanism of the DFG flip. The results are consistent with other computational methods that simulate the kinetics and with some indirect experimental measurements. General significance The activation of kinases includes a conformational transition of the DFG motif that is important for enzyme activity but is not accessible to conventional Molecular Dynamics. We propose a detailed mechanism for the transition, at a timescale longer than conventional MD, using a combination of reaction path and Milestoning algorithms. The mechanism includes local structural adjustments near the binding site as well as collective interactions with more remote residues.

Nanoscale fibrils formed by amyloid peptides have a polymorphic character, adopting several types of molecular structures in similar growth conditions. As shown by experimental (e.g., solid-state NMR) and computational studies, amyloid fibril polymorphism hinders both the structural characterization of Alzheimer's Aβ amyloid protofilaments and fibrils at a molecular level, as well as the possible applications (e.g., development of drugs or biomarkers) that rely on similar, controlled molecular arrangements of the Aβ peptides in amyloid fibril structures. We have explored the use of several contact potentials for the efficient identification of minimal sequence mutations that could enhance the stability of specific fibril structures while simultaneously destabilizing competing topologies, controlling thus the amount of structural polymorphism in a rational way. We found that different types of contact potentials, while having only partial accuracy on their own, lead to similar results regarding ranking the compatibility of wild-type (WT) and mutated amyloid sequences with different fibril morphologies. This approach allows exhaustive screening and assessment of possible mutations and the identification of minimal consensus mutations that could stabilize fibrils with the desired topology at the expense of other topology types, a prediction that is further validated using atomistic molecular dynamics with explicit water molecules. We apply this two-step multiscale (i.e., residue and atomistic-level) approach to predict and validate mutations that could bias either parallel or antiparallel packing in the core Alzheimer's Aβ9-40 amyloid fibril models based on solid-state NMR experiments. Besides shedding new light on the molecular origins of structural polymorphism in WT Aβ fibrils, our study could also lead to efficient tools for assisting future experimental approaches for amyloid fibril determination, and for the development of biomarkers or drugs aimed at interfering with the stability of amyloid fibrils, as well as for the future design of amyloid fibrils with a controlled (e.g., reduced) level of structural polymorphism.

RAF kinases are key players in the MAPK signaling pathway and are important targets for personalized cancer therapy. RAF dimerization is part of the physiological activation mechanism, together with phosphorylation, and is known to convey resistance to RAF inhibitors. Herein, molecular dynamics simulations are used to show that phosphorylation of a key N-terminal acidic (NtA) motif facilitates RAF dimerization by introducing several interprotomer salt bridges between the αC-helix and charged residues upstream of the NtA motif. Additionally, we show that the R-spine of RAF interacts with a conserved Trp residue in the vicinity of the NtA motif, connecting the active sites of two protomers and thereby modulating the cooperative interactions in the RAF dimer. Our findings provide a first structure-based mechanism for the auto-transactivation of RAF and could be generally applicable to other kinases, opening new pathways for overcoming dimerization-related drug resistance. Back to back: Biochemical kinase assays and structural evidence from MD simulations reveal a key electrostatic role for the phosphorylated NtA motif in RAF kinase transactivation. Interprotomer salt bridges and a conserved tryptophan residue located at the N-terminal end of the kinase domain play crucial roles by connecting the R-spines of the two protomers, and phosphorylation leads to important structural changes in the highly conserved HRD motif.

The molecular pathogenesis of Alzheimer's disease (AD) is complex and sparsely understood. The relationship between AD's amyloid β (Aβ) peptides and neuronal membranes is central to Aβ's cytotoxicity and is directly modulated by the composition of the lipid headgroups. Molecular studies of the insertion of model Aβ40 protofilaments in lipid bilayers revealed strong interactions that affect the structural integrity of both the membranes and the ordered amyloid aggregates. In particular, electrostatics plays a crucial role in the interaction between Aβ protofilaments and palmytoil-oleoyl-phosphatidylethanolamine (POPE) lipids, a common component of neuronal plasma membranes. Here, we use all-atom molecular dynamics and steered molecular dynamics simulations to systematically compare the effects that POPE and palmytoil-oleoyl-phosphatidylcholine (POPC) headgroups have on the Aβ-lipid interactions. We find that Aβ protofilaments exhibit weaker electrostatic interactions with POPC headgroups and establish significantly shorter-lived contacts with the POPC bilayer. This illustrates the crucial yet complex role of electrostatic and hydrogen bonding interactions in modulating the anchoring and insertion of Aβ peptides into lipid bilayers. Our study reveals the atomistic details behind the barrier created by the lipid headgroup region in impeding solution-aggregated fibrillar oligomers to spontaneously insert into POPC bilayers, in contrast to the POPE case. While the biological reality is notoriously more complex (e.g., including other factors such as cholesterol), our results evidence a simple experimentally and computationally testable case for probing the factors that control the insertion of Aβ oligomeric aggregates in neuronal cell membranes--a process central to their neurotoxicity.

Due to their homophilic and heterophilic binding properties, cell adhesion molecules (CAMs) such as integrin, cadherin and the immunoglobulin superfamily CAMs are of primary importance in cell-cell and cell-substrate interactions, signalling pathways and other crucial biological processes. We study the molecular structures and conformational dynamics of the two fibronectin type III (Fn-III) extracellular domains of the Aplysia californica CAM (apCAM) protein, by constructing and probing an atomically-detailed structural model based on apCAM's homology with other CAMs. The stability and dynamic properties of the Fn-III domains, individually and in tandem, are probed and analysed using all-atom explicit-solvent molecular dynamics (MD) simulations and normal mode analysis of their corresponding elastic network models. The refined structural model of the Fn-III tandem of apCAM reveals a specific pattern of amino acid interactions that controls the stability of the β-sheet rich structure and could affect apCAM's response to physical or chemical changes of its environment. It also exposes the important role of several specific charged residues in modulating the structural properties of the linker segment connecting the two Fn-III domains, as well as of the inter-domain interface.

Aromatic peptides such as diphenylalanine (FF) have the characteristic capacity to self-assemble into ordered nanostructures such as peptide nanotubes, which are biocompatible, thermally and chemically stable, and have strong piezoelectric activity and high mechanical strength. The physical properties of FF aggregates open up a variety of potential biomedical applications. Electric fields are commonly applied to align FF nanotubes, yet little is known about the effect of the electric field on the assembly process. Using all-atom molecular dynamics with explicit water molecules, we probe the conformational dynamics of individual, solvated FF molecules with both charged and neutral ends, to account for different possible pH conditions. With charged ends, the FF molecules show more complex dynamics, experiencing three main conformational states (cis, trans and extended). We first examine the structural response of FF monomers to the application of a constant external electric field over a range of intensities. We also probe the aggregation mechanism of FF peptides, both with and without an externally applied electric field, and find that the presence of even relatively weak fields can accelerate the formation of ordered FF aggregates, primarily by facilitating the alignment of individual molecular dipole moments. The correlation between the strength of the external electric field and the local dipolar interactions is modulated both by the conformational response of individual FF peptides (e.g. backbone stretching, hydrogen bonds and relative alignment of aromatic sidechains) and by the response of neighboring FF and water molecules. These field-dependent observations may facilitate future studies on the controlled formation of nano-structured aggregates of piezoelectric peptides and the understanding of their specific electromechanical properties.

We show how accurate rates of formation and dissociation of peptide dimers can be calculated using direct transition counting (DTC) from replica-exchange molecular dynamics (REMD) simulations. First, continuous trajectories corresponding to system replicas evolving at different temperatures are used to assign conformational states. Second, we analyze the entire REMD data to calculate the corresponding rates at each temperature directly from the number of transition counts. Finally, we compare the kinetics extracted directly, using the DTC method, with indirect estimations based on trajectory likelihood maximization using short-time propagators and on decay rates of state autocorrelation functions. For systems with relatively low-dimensional intrinsic conformational dynamics, the DTC method is simple to implement and leads to accurate temperature-dependent rates. We apply the DTC rate-extraction method to all-atom REMD simulations of dimerization of amyloid-forming NNQQ tetrapetides in explicit water. In an assessment of the REMD sampling efficiency with respect to standard MD, we find a gain of more than a factor of two at the lowest temperature.

We characterize the kinetics of dimer formation of the short amyloid microcrystal-forming tetrapeptides NNQQ by constructing coarse master equations for the conformational dynamics of the system, using temperature replica-exchange molecular dynamics (REMD) simulations. We minimize the effects of Kramers-type recrossings by assigning conformational states based on their sequential time evolution. Transition rates are further estimated from short-time state propagators, by maximizing the likelihood that the extracted rates agree with the observed atomistic trajectories without any a priori assumptions about their temperature dependence. Here, we evaluate the rates for both continuous replica trajectories that visit different temperatures, and for discontinuous data corresponding to each REMD temperature. While the binding-unbinding kinetic process is clearly Markovian, the conformational dynamics of the bound NNQQ dimer has a complex character. Our kinetic analysis allows us a quantitative discrimination between short-lived encounter pairs and strongly bound conformational states. The conformational dynamics of NNQQ dimers supports a kinetically driven aggregation mechanism, in agreement with the polymorphic character reported for amyloid aggregates such as microcrystals and fibrils. Irish Research Council The Engineering and Physical Sciences Research Council (EPSRC)

Fibrillar aggregates of misfolded amyloid proteins are involved in a variety of diseases such as Alzheimer disease (AD), type 2 diabetes, Parkinson, Huntington and prion-related diseases. In the case of AD amyloid β (Aβ) peptides, the toxicity of amyloid oligomers and larger fibrillar aggregates is related to perturbing the biological function of the adjacent cellular membrane. We used atomistic molecular dynamics (MD) simulations of Aβ9–40 fibrillar oligomers modeled as protofilament segments, including lipid bilayers and explicit water molecules, to probe the first steps in the mechanism of Aβ-membrane interactions. Our study identified the electrostatic interaction between charged peptide residues and the lipid headgroups as the principal driving force that can modulate the further penetration of the C-termini of amyloid fibrils or fibrillar oligomers into the hydrophobic region of lipid membranes. These findings advance our understanding of the detailed molecular mechanisms and the effects related to Aβ-membrane interactions, and suggest a polymorphic structural character of amyloid ion channels embedded in lipid bilayers. While inter-peptide hydrogen bonds leading to the formation of β-strands may still play a stabilizing role in amyloid channel structures, these may also present a significant helical content in peptide regions (e.g., termini) that are subject to direct interactions with lipids rather than with neighboring Aβ peptides.

We study the conformational dynamics of the human Islet Amyloid Polypeptide (hIAPP) molecule - a 37 residue-long peptide associated to type 2 diabetes - using molecular dynamics (MD) simulations. We identify partially structured conformational states of the hIAPP monomer, categorized by both end-to-end distance and secondary structure, as suggested by previous experimental and computational studies. The MD trajectories of hIAPP are analyzed using data-driven methods, in particular principal component analysis, in order to identify preferred conformational states of the amylin monomer and to discuss their relative stability as compared to corresponding states in the amylin dimer. These potential hIAPP conformational states could be further tested and described experimentally, or in conjunction with modern computational analysis tools such as Markov state-based methods for extracting kinetics and thermodynamics from atomistic MD trajectories.

The folding kinetics of proteins is frequently single-exponential, as basins of folded and unfolded conformations are well separated by a high barrier. However, for relatively short peptides, a two-state character of folding is rather the exception than the rule. In this work, we use a Zwanzig-type model of protein conformational dynamics to study the dependence of folding kinetics on the protein chain length, M. The analysis is focused on the gap in the eigenvalue spectrum of the rate matrix that describes the protein's conformational dynamics. When there is a large gap between the two smallest in magnitude nonzero eigenvalues, the corresponding relaxation times have qualitatively different physical interpretations. The longest of these two times characterizes the interbasin equilibration (i.e., folding), whereas the second time characterizes the intrabasin relaxation. We derive approximate analytical solutions for the two eigenvalues that show how they depend on M. From these solutions, we infer that there is a large gap between the two, and thus, the kinetics is essentially single-exponential when M is large enough such that 2(M+1) is much larger than M(2).

Recent molecular modeling methods using Markovian descriptions of conformational states of biomolecular systems have led to powerful analysis frameworks that can accurately describe their complex dynamical behavior. In conjunction with enhanced sampling methods, such as replica exchange molecular dynamics (REMD), these frameworks allow the systematic and accurate extraction of transition probabilities between the corresponding states, in the case of Markov state models, and of statistically-optimized transition rates, in the case of the corresponding coarse master equations. However, applying automatically such methods to large molecular dynamics (MD) simulations, with explicit water molecules, remains limited both by the initial ability to identify good candidates for the underlying Markovian states and by the necessity to do so using good collective variables as reaction coordinates that allow the correct counting of inter-state transitions at various lag times. Here, we show that, in cases when representative molecular conformations can be identified for the corresponding Markovian states, and thus their corresponding collective evolution of atomic positions can be calculated along MD trajectories, one can use them to build a new type of simple collective variable, which can be particularly useful in both the correct state assignment and in the subsequent accurate counting of inter-state transition probabilities. In the case of the ubiquitously used root-mean-square deviation (RMSD) of atomic positions, we introduce the relative RMSD (RelRMSD) measure as a good reaction coordinate candidate. We apply this method to the analysis of REMD trajectories of amyloid-forming diphenylalanine (FF) peptides—a system with important nanotechnology and biomedical applications due to its self-assembling and piezoelectric properties—illustrating the use of RelRMSD in extracting its temperature-dependent intrinsic kinetics, without a priori assumptions on the functional form (e.g., Arrhenius or not) of the underlying conformational transition rates. The RelRMSD analysis enables as well a more objective assessment of the convergence of the REMD simulations. This type of collective variable may be generalized to other observables that could accurately capture conformational differences between the underlying Markov states (e.g., distance RMSD, the fraction of native contacts, etc.).

We construct coarse master equations for peptide folding dynamics from atomistic molecular dynamics simulations. A maximum-likelihood propagator-based method allows us to extract accurate rates for the transitions between the different conformational states of the small helix-forming peptide Ala5. Assigning the conformational states by using transition paths instead of instantaneous molecular coordinates suppresses the effects of fast non-Markovian dynamics. The resulting master equations are validated by comparing their analytical correlation functions with those obtained directly from the molecular dynamics simulations. We find that the master equations properly capture the character and relaxation times of the entire spectrum of conformational relaxation processes. By using the eigenvectors of the transition rate matrix, we are able to systematically coarse-grain the system. We find that a two-state description, with a folded and an unfolded state, roughly captures the slow conformational dynamics. A four-state model, with two folded and two unfolded states, accurately recovers the three slowest relaxation process with time scales between 1.5 and 7 ns. The master equation models not only give access to the slow conformational dynamics but also shed light on the molecular mechanisms of the helix-coil transition.

O-Glycan biosynthesis is initiated by the transfer of N-acetylgalactosamine (GalNAc) from a nucleotide sugar donor (UDP-GalNAc) to Ser/Thr residues of an acceptor substrate. The detailed transfer mechanism, catalyzed by the UDP-GalNAc polypeptide:N-acetyl-alpha-galactosaminyltransferases (ppGalNAcTs), remains unclear despite structural information available for several isoforms in complex with substrates at various stages along the catalytic pathway. We used all-atom molecular dynamics simulations with explicit solvent and counterions to study the conformational dynamics of ppGalNAcT-2 in several enzymatic states along the catalytic pathway. ppGalNAcT-2 is simulated both in the presence and in the absence of substrates and reaction products to examine the role of conformational changes in ligand binding. In multiple 40-ns-long simulations of more than 600 ns total run time, we studied systems ranging from 45,000 to 95,000 atoms. Our simulations accurately identified dynamically active regions of the protein, as previously revealed by the X-ray structures, and permitted a detailed, atomistic description of the conformational changes of loops near the active site and the characterization of the ensemble of structures adopted by the transferase complex on the transition pathway between the ligand-bound and ligand-free states. In particular, the conformational transition of a functional loop adjacent to the active site from closed (active) to open (inactive) is correlated with the rotameric state of the conserved residue W331. Analysis of water dynamics in the active site revealed that internal water molecules have an important role in enhancing the enzyme flexibility. We also found evidence that charged side chains in the active site rearrange during site opening to facilitate ligand binding. Our results are consistent with the single-displacement transfer mechanism previously proposed for ppGalNAcTs based on X-ray structures and mutagenesis data and provide new evidence for possible functional roles of certain amino acids conserved across several isoforms.

Knowledge-based contact potentials are routinely used in fold recognition, binding of peptides to proteins, structure prediction, and coarse-grained models to probe protein folding kinetics. The dominant physical forces embodied in the contact potentials are revealed by eigenvalue analysis of the matrices, whose elements describe the strengths of interaction between amino acid side chains. We propose a general method to rank quantitatively the importance of various inter-residue interactions represented in the currently popular pair contact potentials. Eigenvalue analysis and correlation diagrams are used to rank the inter-residue pair interactions with respect to the magnitude of their relative contributions to the contact potentials. The amino acid ranking is shown to be consistent with a mean field approximation that is used to reconstruct the original contact potentials from the most relevant amino acids for several contact potentials. By providing a general, relative ranking score for amino acids, this method permits a detailed, quantitative comparison of various contact interaction schemes. For most contact potentials, between 7 and 9 amino acids of varying chemical character are needed to accurately reconstruct the full matrix. By correlating the identified important amino acid residues in contact potentials and analysis of about 7800 structural domains in the CATH database we predict that it is important to model accurately interactions between small hydrophobic residues. In addition, only potentials that take interactions involving the protein backbone into account can predict dense packing in protein structures. Proteins 2008. © 2007 Wiley-Liss, Inc.

The detailed, atomistic-level understanding of molecular signaling along the tumor-suppressive Hippo signaling pathway that controls tissue homeostasis by balancing cell proliferation and death through apoptosis is a promising avenue for the discovery of novel anticancer drug targets. The activation of kinases such as Mammalian STE20-Like Protein Kinases 1 and 2 (MST1 and MST2)-modulated through both homo- and heterodimerization (e.g. interactions with Ras association domain family, RASSF, enzymes)-is a key upstream event in this pathway and remains poorly understood. On the other hand, RASSFs (such as RASSF1A or RASSF5) act as important apoptosis activators and tumor suppressors, although their exact regulatory roles are also unclear. We present recent molecular studies of signaling along the Ras-RASSF-MST pathway, which controls growth and apoptosis in eukaryotic cells, including a variety of modern molecular modeling and simulation techniques. Using recently available structural information, we discuss the complex regulatory scenario according to which RASSFs perform dual signaling functions, either preventing or promoting MST2 activation, and thus control cell apoptosis. Here, we focus on recent studies highlighting the special role being played by the specific interactions between the helical Salvador/RASSF/Hippo (SARAH) domains of MST2 and RASSF1a or RASSF5 enzymes. These studies are crucial for integrating atomistic-level mechanistic information about the structures and conformational dynamics of interacting proteins, with information available on their system-level functions in cellular signaling.

Cadmium (Cd) has several industrial applications, and is found in tobacco products, a notable source of human exposure. Vascular endothelial cells are key targets of Cd toxicity. Here, we aim to quantify the alteration to vascular branching pattern following Cd exposure in the chick extra-embryonic membrane (EEM) using fractal analysis, and explore molecular cues to angiogenesis such as VEGF-A and VEGF-R2 expression following Cd treatment. Chicken embryos were incubated for 60 h to Hamburger-Hamilton developmental stage 16-17, then explanted and treated with 50 μL of 50 μmol cadmium acetate (CdAc) or an equivalent volume of equimolar sodium acetate (NaAc). Images of embryos and their area vasculosa (AV) were captured and analyzed at 4 different time points (4, 8, 24 and 48 h) following treatment. Vascular branching in the AV was quantified using its fractal dimension (Df), estimated using a box counting method. Gallinaceous VEGF ELISA was used to measure the VEGF-A concentration in the EEM following treatment, with determination of the relative expression of VEGF-A and VEGF-R2 using quantitative real-time RT-PCR. Vascular branching increased monotonically in the control group at all time points. The anti-angiogenic effect of Cd exposure on the AV was reflected by a significant reduction in Df when compared with controls. Df was more markedly reduced in cultures with abnormal embryos. The expression of VEGF-A protein, and VEGF-A and VEGF-R2 mRNA were reduced in Cd-exposed EEMs. Both molecules contribute to growth, vessel sprouting and branching processes, which supports our findings using fractal analysis.

We develop coarse-grained, distance- and orientation-dependent statistical potentials from the growing protein structural databases. For protein structural classes (alpha, beta, and alpha/beta), a substantial number of backbone-backbone and backbone-side-chain contacts stabilize the native folds. By taking into account the importance of backbone interactions with a virtual backbone interaction center as the 21st anisotropic site, we construct a 21 x 21 interaction scheme. The new potentials are studied using spherical harmonics analysis (SHA) and a smooth, continuous version is constructed using spherical harmonic synthesis (SHS). Our approach has the following advantages: (1) The smooth, continuous form of the resulting potentials is more realistic and presents significant advantages for computational simulations, and (2) with SHS, the potential values can be computed efficiently for arbitrary coordinates, requiring only the knowledge of a few spherical harmonic coefficients. The performance of the new orientation-dependent potentials was tested using a standard database of decoy structures. The results show that the ability of the new orientation-dependent potentials to recognize native protein folds from a set of decoy structures is strongly enhanced by the inclusion of anisotropic backbone interaction centers. The anisotropic potentials can be used to develop realistic coarse-grained simulations of proteins, with direct applications to protein design, folding, and aggregation.

We present results obtained for anisotropic potentials for protein simulations extracted from the continually growing databases of protein structures. This work is based on the assumption that the detailed information on molecular conformations can be used to derive statistical (a.k.a. ‘knowledge-based’) potentials that can describe on a coarse-grained level the side chain–side chain interactions in peptides and proteins. The complexity of inter-residue interactions is reflected in a high degree of orientational anisotropy for the twenty amino acids. By including in this coarse-grained interaction model the possibility of quantifying the backbone–backbone and backbone–side chain interactions, important improvements are obtained in characterizing the native protein states. Results obtained from tests that involve the identification of native-like conformations from large sets of decoy structures are presented. The method for deriving orientation-dependent statistical potentials is also applied to obtain water–water interactions. Monte Carlo simulations using the new coarse-grained water model show that the locations of the minima and maxima of the oxygen–oxygen radial distribution function correspond well with experimental measurements.

Fibrous peptide networks, such as the structural framework of self-assembled fluorenylmethyloxycarbonyl diphenylalanine (Fmoc-FF) nanofibrils, have mechanical properties that could successfully mimic natural tissues, making them promising materials for tissue engineering scaffolds. These nanomaterials have been determined to exhibit shear piezoelectricity using piezoresponse force microscopy, as previously reported for FF nanotubes. Structural analyses of Fmoc-FF nanofibrils suggest that the observed piezoelectric response may result from the noncentrosymmetric nature of an underlying β-sheet topology. The observed piezoelectricity of Fmoc-FF fibrous networks is advantageous for a range of biomedical applications where electrical or mechanical stimuli are required. European Commission - European Regional Development Fund European Commission - Seventh Framework Programme (FP7) Science Foundation Ireland Programme for Research in Third Level Institutions

Protein phosphorylation is one of the most common post-translational modifications in cell regulatory mechanisms. Dimerization plays also a crucial role in the kinase activity of many kinases, including RAF, CDK2 (cyclin-dependent kinase 2) and EGFR (epidermal growth factor receptor), with heterodimers often being the most active forms. However, the structural and mechanistic details of how phosphorylation affects the activity of homo- and hetero-dimers are largely unknown. Experimentally, synthesizing protein samples with fully specified and homogeneous phosphorylation states remains a challenge for structural biology and biochemical studies. Typically, multiple changes in phosphorylation lead to activation of the same protein, which makes structural determination methods particularly difficult. It is also not well understood how the occurrence of phosphorylation and dimerization processes synergize to affect kinase activities. In the present article, we review available structural data and discuss how MD simulations can be used to model conformational transitions of RAF kinase dimers, in both their phosphorylated and unphosphorylated forms. Abbreviations: AL, activation loop; CDK, cyclin-dependent kinase; CL, catalytic loop; EGFR, epidermal growth factor receptor; ERK, extracellular-signal-regulated kinase; MEK, MAPK (mitogen-activated protein kinase)/ERK kinase; NtA, N-terminal acidic; PKA, cAMP-dependent protein kinase

The kinetics and thermodynamics of the coil-to-helix transition is studied using a one-dimensional “Zimm−Bragg” Ising model. The mean first-passage time for the coil-to-helix transition is estimated within the “mean sequence” approximation. A generalized mean first-passage time equation is derived where the transition rates may depend on the state of the system. The analytic expression for the mean first-passage time is evaluated, and the results are discussed as a function of energetic parameters, nucleation and propagation constants, peptide length, and the initial fraction of coil. The equilibrium thermodynamic properties of the model are shown to agree well with the Zimm−Bragg model, validating the mean sequence approximation. The time scales for helix formation are computed for a range of energetic parameters that determine the nucleation and propagation constants for the model. It is shown that, for a range of thermodynamically realistic parameters, the kinetic first-passage times are on the order o...

Accurate force fields are essential for the success of molecular dynamics simulations. In apparent contrast to the conformational preferences of most force fields, recent NMR experiments suggest that short polyalanine peptides in water populate the polyproline II structure almost exclusively. To investigate this apparent contradiction, with its ramifications for the assessment of molecular force fields and the structure of unfolded proteins, we performed extensive simulations of Ala(5) in water ( approximately 5 micros total time), using twelve different force fields and three different peptide terminal groups. Using either empirical or density-functional-based Karplus relations for the J-couplings, we find that most current force fields do overpopulate the alpha-region, with quantitative results depending on the choice of Karplus relation and on the peptide termini. Even after reweighting to match experiment, we find that Ala(5) retains significant alpha- and beta-populations. In fact, several force fields match the experimental data well before reweighting and have a significant helical population. We conclude that radical changes to the best current force fields are not necessary, based on the NMR data. Nevertheless, experiments on short peptides open the way toward the systematic improvement of current simulation models.

Amyloid fibrils and peptide oligomers play central roles in the pathology of Alzheimer's disease, type 2 diabetes, Parkinson's disease, Huntington's disease, and prion-related disease. Here, we investigate the molecular interactions between preformed amyloid β (Aβ) molecular protofilaments and lipid bilayer membranes, in the presence of explicit water molecules, using computational models and all-atom molecular dynamics. These interactions play an important role in the stability and function of both Aβ fibrils and the adjacent cellular membrane. Taking advantage of the symmetry-related and directional properties of the protofilaments, we build models that cover several relative protofilament-membrane orientations. Our molecular dynamics simulations reveal the relative contributions of different structural elements to the dynamics and stability of Aβ protofilament segments near membranes, and the first steps in the mechanism of fibril-membrane interactions. During this process, we observe a significant alteration of the side-chain contact pattern in protofilaments, although a fraction of the characteristic β-sheet content is preserved. As a major driving force, we identify the electrostatic interactions between Aβ charged side chains, including E22, D23, and K28, and lipid headgroups. Together with hydrogen bonding with atoms from lipid headgroups, these interactions can facilitate the penetration of hydrophobic C-terminal amino acids through the lipid headgroup region, which can finally lead both to further loss of the initial fibril structure and to local membrane-thinning effects. Our results may guide new experiments that could test the extent to which the structural features of water-formed amyloid fibrils are preserved, lost, or reshaped by membrane-mediated interactions.

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

We explore the effects of thermostats in replica exchange molecular dynamics (REMD) simulations. For thermostats that do not produce a canonical ensemble, REMD simulations are found to distort the configuration-space distributions. For bulk water, we find small deviations of the average potential energies, the buildup of tails in the potential energy distributions, and artificial correlations between the energies at different temperatures. If a solute is present, as in protein folding simulations, its conformational equilibrium can be altered. In REMD simulations of a helix-forming peptide with a weak-coupling (Berendsen) thermostat, we find that the folded state is overpopulated by about 10% at low temperatures, and underpopulated at high temperatures. As a consequence, the enthalpy of folding deviates by almost 3 kcal/mol from the correct value. The reason for this population shift is that non-canonical ensembles with narrowed potential energy fluctuations artificially bias toward replica exchanges between low-energy folded structures at the high temperature and high-energy unfolded structures at the low temperature. We conclude that REMD simulations should only be performed in conjunction with thermostats that produce a canonical ensemble.

We show how accurate kinetic information, such as the rates of protein folding and unfolding, can be extracted from replica-exchange molecular dynamics (REMD) simulations. From the brief and continuous trajectory segments between replica exchanges, we estimate short-time propagators in conformation space and use them to construct a master equation. For a helical peptide in explicit water, we determine the rates of transitions both locally between microscopic conformational states and globally for folding and unfolding. We show that accurate rates in the ~1/(100 ns) to ~1/(1 ns) range can be obtained from REMD with exchange times of 5 ps, in excellent agreement with results from long equilibrium molecular dynamics., Comment: 4 pages, 4 figures; v2: updated abstract and Fig. 3

Filamentous amyloid aggregates are central to the pathology of Alzheimer's disease. We use all-atom molecular dynamics (MD) simulations with explicit solvent and multiple force fields to probe the structural stability and the conformational dynamics of several models of Alzheimer's beta-amyloid fibril structures, for both wild-type and mutated amino acid sequences. The structural models are based on recent solid state NMR data. In these models, the peptides form in-register parallel beta-sheets along the fibril axis, with dimers of two U-shaped peptides located in layers normal to the fibril axis. Four different topologies are explored for stacking the beta-strand regions against each other to form a hydrophobic core. Our MD results suggest that all four NMR-based models are structurally stable, and we find good agreement with dihedral angles estimated from solid-state NMR experiments. Asp23 and Lys28 form buried salt-bridges, resulting in an alternating arrangement of the negatively and positively charged residues along the fibril axis that is reminiscent of a one-dimensional ionic crystal. Interior water molecules are solvating the buried salt-bridges. Based on data from NMR measurements and MD simulations of short amyloid fibrils, we constructed structural models of long fibrils. Calculated X-ray fiber diffraction patterns show the characteristics of packed beta-sheets seen in experiments, and suggest new experiments that could discriminate between various fibril topologies.

A new method is presented for extracting statistical potentials dependent on the relative side chain and backbone orientations in proteins. Coarse-grained, anisotropic potentials are constructed for short-, medium-, and long-range interactions using the Boltzmann method and a database of non-homologous protein structures. The new orientation-dependent potentials are analyzed using a spherical harmonics decomposition method with real eigenfunctions. This method permits a more realistic, continuous angular representation of the coarse-grained potentials. Results of tests for discriminating the native protein conformations from large sets of decoy proteins, show that the new continuous distance- and orientation-dependent potentials present significantly improved performance. Novel graphical representations are developed and used to depict the orientational dependence of the interaction potentials. These new continuous anisotropic statistical potentials could be instrumental in developing new computational methods for structure prediction, threading and coarse-grained simulations.

The need to perform large-scale studies of protein fold recognition, structure prediction and protein–protein interactions has led to novel developments of residue-level minimal models of proteins. A minimum requirement for useful protein force-fields is that they be successful in the recognition of native conformations. The balance between the level of detail in describing the specific interactions within proteins and the accuracy obtained using minimal protein models is the focus of many current protein studies. Recent results suggest that the introduction of explicit orientation dependence in a coarse-grained, residue-level model improves the ability of inter-residue potentials to recognize the native state. New statistical and optimization computational algorithms can be used to obtain accurate residue-dependent potentials for use in protein fold recognition and, more importantly, structure prediction.

We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial and angular correlation functions for a standard set of non-homologue protein structures, we construct the anisotropic pair potentials. The performance of the orientation dependent potentials was studied using a large database of decoy proteins. The results demonstrate that the new distance and orientation dependent residue-residue potentials present a significantly improved ability to recognize native folds from a set of native and decoy protein structures., Comment: Submitted to "The Journal of Chemical Physics"

We study two-state protein folding in the framework of a toy model of protein dynamics. This model has an important advantage: it allows for an analytical solution for the sum of folding and unfolding rate constants [A. M. Berezhkovskii, F. Tofoleanu, and N.-V. Buchete, J. Chem. Theory Comput. 7, 2370 (2011)10.1021/ct200281d] and hence for the reactive flux at equilibrium. We use the model to test the Kramers-type formula for the reactive flux, which was derived assuming that the protein dynamics is described by a Markov random walk on a network of complex connectivity [A. Berezhkovskii, G. Hummer, and A. Szabo, J. Chem. Phys. 130, 205102 (2009)10.1063/1.3139063]. It is shown that the Kramers-type formula leads to the same result for the reactive flux as the sum of the rate constants. AMS

Gleevec (a.k.a., imatinib) is an important anticancer (e.g., chronic myeloid leukemia) chemotherapeutic drug due to its inhibitory interaction with the Abl kinase. Here, we use atomically detailed simulations within the Milestoning framework to study the molecular dissociation mechanism of Gleevec from Abl kinase. We compute the dissociation free energy profile, the mean first passage time for unbinding, and explore the transition state ensemble of conformations. The milestones form a multidimensional network with average connectivity of about 2.93, which is significantly higher than the connectivity for a one-dimensional reaction coordinate. The free energy barrier for Gleevec dissociation is estimated to be ∼10 kcal/mol, and the exit time is ∼55 ms. We examined the transition state conformations using both, the committor and transition function. We show that near the transition state the highly conserved salt bridge K217 and E286 is transiently broken. Together with the calculated free energy profile, these calculations can advance the understanding of the molecular interaction mechanisms between Gleevec and Abl kinase and play a role in future drug design and optimization studies.

We explore the relative contributions of different structural elements to the stability of Abeta fibrils by molecular-dynamics simulations performed over a broad range of temperatures (298 K to 398 K). Our fibril structures are based on solid-state nuclear magnetic resonance experiments of Abeta(1-40) peptides, with sheets of parallel beta-strands connected by loops and stabilized by interior salt bridges. We consider models with different interpeptide interfaces, and different staggering of the N- and C-terminal beta-strands along the fibril axis. Multiple 10-20 ns molecular-dynamics simulations show that fibril segments with 12 peptides are stable at ambient temperature. The different models converge toward an interdigitated side-chain packing, and present water channels solvating the interior D23/K28 salt bridges. At elevated temperatures, we observe the early phases of fibril dissociation as a loss of order in the hydrophilic loops connecting the two beta-strands, and in the solvent-exposed N-terminal beta-sheets. As the most dramatic structural change, we observe collective sliding of the N- and C-terminal beta-sheets on top of each other. The interior C-terminal beta-sheets in the hydrophobic core remain largely intact, indicating that their formation and stability is crucial to the dissociation/elongation and stability of Abeta fibrils.