All-atom Protein Research Articles

RaFoSA: Random forests secondary structure assignment for coarse-grained and all-atom protein systems

Secondary structures (SS) of proteins are of great importance to structural, molecular, and computational biology and chemistry. Accurate and reliable method for automatic SS assignment when only c...

Simulated Force Spectroscopy of a Badly-Behaved Protein: on the Reliability of Protein Coarse-Grained Models

We used single-molecule pulling molecular dynamic simulations to capture the detailed structural mechanism of the unfolding process for a protein linked to neurodegenerative disease. In these simulations, a loop-truncated variant of superoxide dismutase 1 (SOD1) was pulled from the N- and C-Termini. Force-Extension Curves (FECS) and the predicted unfolding pathways of the protein were obtained for all-atom models in explicit solvent, and the results compared to several Coarse-Grained (CG) models in common use; including implicit solvent models, all-ATOM- 3-BEAD-, and Cα-based-Gō models, martini model, and associative memory hamiltonian models. In systematically comparing dynamic unfolding processes for all-atom and coarse-grained protein models, we had to resolve several problems including what energy and time means within a coarse-grained system. We describe our solution to this problem, and then discuss which cg models, if any, are most successful in predicting realistic force-induced unfolding pathways.

Structure and Dynamics of Intrinsically Disordered Proteins from a Physics-Based Model

There is significant interest in understanding the physical properties of intrinsically disordered proteins (IDPs) due to their functional relevance in diverse biochemical processes such as regulation, signaling, and pathogenesis of several disease conditions. Due to their flexibility and lack of well-defined structure, it is quite challenging to experimentally characterize the details of the heterogeneous equilibrium ensemble of IDPs. In principle, all-atom molecular simulations can provide sufficiently detailed spatiotemporal information on IDP properties. But as highlighted recently in the literature, physics-based computer models may not be able to describe the protein disordered states accurately. In this talk, I’ll discuss our recently proposed all-atom protein model (Amber03ws) that can provide accurate information on IDP structure and dynamics, without any experimental input. Results from several different example IDP sequences will be used to demonstrate the usefulness of this model.

A theoretical multiscale treatment of protein–protein electron transfer: The ferredoxin/ferredoxin-NADP+ reductase and flavodoxin/ferredoxin-NADP+ reductase systems

In the photosynthetic electron transfer (ET) chain, two electrons transfer from photosystem I to the flavin-dependent ferredoxin-NADP+ reductase (FNR) via two sequential independent ferredoxin (Fd) electron carriers. In some algae and cyanobacteria (as Anabaena), under low iron conditions, flavodoxin (Fld) replaces Fd as single electron carrier. Extensive mutational studies have characterized the protein–protein interaction in FNR/Fd and FNR/Fld complexes. Interestingly, even though Fd and Fld share the interaction site on FNR, individual residues on FNR do not participate to the same extent in the interaction with each of the protein partners, pointing to different electron transfer mechanisms. Despite of extensive mutational studies, only FNR/Fd X-ray structures from Anabaena and maize have been solved; structural data for FNR/Fld remains elusive. Here, we present a multiscale modelling approach including coarse-grained and all-atom protein–protein docking, the QM/MM e-Pathway analysis and electronic coupling calculations, allowing for a molecular and electronic comprehensive analysis of the ET process in both complexes. Our results, consistent with experimental mutational data, reveal the ET in FNR/Fd proceeding through a bridge-mediated mechanism in a dominant protein–protein complex, where transfer of the electron is facilitated by Fd loop-residues 40–49. In FNR/Fld, however, we observe a direct transfer between redox cofactors and less complex specificity than in Fd; more than one orientation in the encounter complex can be efficient in ET.

Folding thermodynamics of β‐hairpins studied by replica‐exchange molecular dynamics simulations

We study the differences in folding stability of β-hairpin peptides, including GB1 hairpin and a point mutant GB1 K10G, as well as tryptophan zippers (TrpZips): TrpZip1, TrpZip2, TrpZip3-1, and TrpZip4. By performing replica-exchange molecular dynamics simulations with Amber03* force field (a modified version of Amber ff03) in explicit solvent, we observe ab initio folding of all the peptides except TrpZip3-1, which is experimentally known to be the least stable among the peptides studied here. By calculating the free energies of unfolding of the peptides at room temperature and folding midpoint temperatures for thermal unfolding of peptides, we find that TrpZip4 and GB1 K10G peptides are the most stable β-hairpins followed by TrpZip1, GB1, and TrpZip2 in the given order. Hence, the proposed K10G mutation of GB1 peptide results in enhanced stability compared to wild-type GB1. An important goal of our study is to test whether simulations with Amber 03* model can reproduce experimentally predicted folding stability differences between these peptides. While the stabilities of GB1 and TrpZip1 yield close agreement with experiment, TrpZip2 is found to be less stable than predicted by experiment. However, as heterogenous folding of TrpZip2 may yield divergent thermodynamic parameters by different spectroscopic methods, mismatching of results with previous experimental values are not conclusive of model shortcomings. For most of the cases, molecular simulations with Amber03* can successfully reproduce experimentally known differences between the mutated peptides, further highlighting the predictive capabilities of current state-of-the-art all-atom protein force fields.

Molecular Simulations of Unfolded and Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack well-defined solution structure under physiological conditions but still have biologically relevant function in the cell. A significant fraction of eukaryotic proteins are fully or partially disordered. Additionally, the unfolded state of proteins has attracted prominent interest for decades, for better understanding of the protein folding problem. In this work we address the most fundamental question: are IDPs different from unfolded states of globular proteins? We simulated five different protein sequences in aqueous solution for the systematic investigation of their characteristic polymer properties. An accurate all-atom protein model with explicit solvent (Amber03w) is used, which naturally captures temperature-dependent solvation effects. We found that the qualitative scaling behavior of the protein chains matches expectations from theory under ambient conditions. We also observe experimentally known temperature-induced collapse of polypeptide chains in our simulations. Detailed analysis suggests that this collapse originates from the change in hydration propensity of individual residues as a function of temperature. Furthermore, we find that the unfolded ensembles of proteins at different temperatures are remarkably similar due to temperature-induced collapse.We also address a key issue in the single molecule Forster resonance energy transfer (FRET) experiments to study the properties of unfolded and intrinsically disordered proteins, i.e., are the properties of the unfolded chain affected by the presence of chromophore dyes? We find that the secondary structure and long-range contacts are largely the same in the presence or absence of the fluorophores, and that the dimensions of the chain with and without chromophores are similar. We also find that the dye orientational factor, kappa2, has an average value and equilibrium distribution very close to that expected for isotropic orientations, which supports one of the assumptions frequently made when interpreting FRET efficiencies in terms of distances.

All-atom simulation study of protein PTH(1-34) by using the Wang-Landau sampling method

We perform simulations of the N-terminal 34-residue protein fragment PTH(1-34), consisting of 581 atoms, of the 84-residue human parathyroid hormone by using the all-atom ECEPP/3 force field and the Wang-Landau sampling method. Through a massive high-performance computation, the density of states and the partition function Z(T), as a continuous function of T, are obtained for PTH(1-34). From the continuous partition function Z(T), the partition function zeros of PTH(1-34) are evaluated for the first time. From both the specific heat and the partition function zeros, two characteristic transition temperatures are obtained for the all-atom protein PTH(1-34). The higher transition temperature T 1 and the lower transition temperature T 2 of PTH(1-34) can be interpreted as the collapse temperature T θ and the folding temperature T f , respectively.

A multiple minima genetic algorithm for protein structure prediction

Protein structure prediction (PSP) has a large potential for valuable biotechnological applications. However the prediction itself encompasses a difficult optimization problem with thousands of degrees of freedom and is associated with extremely complex energy landscapes. In this work a simplified three-dimensional protein model (hydrophobic-polar model, HP in a cubic lattice) was used in order to allow for the fast development of a robust and efficient genetic algorithm based methodology. The new methodology employs a phenotype based crowding mechanism for the maintenance of useful diversity within the populations, which resulted in increased performance and granted the algorithm multiple solutions capabilities. Tests against several benchmark HP sequences and comparative results showed that the proposed genetic algorithm is superior to other evolutionary algorithms. The proposed algorithm was then successfully adapted to an all-atom protein model and tested on poly-alanines. The native structure, an alpha helix, was found in all test cases as a local or a global minimum, in addition to other conformations with similar energies. The results showed that optimization strategies with multiple solutions capability present two advantages for PSP applications. The first one is a more efficient investigation of complex energy landscapes; the second one is an increase in the probability of finding native structures, even when they are not at the global optimum.

Absolute Quality Assessment of Protein Models

Modeling methods increasingly attempt to close the gap between the number of known protein-coding sequences to that of structurally resolved proteins, but the results of these methods have been of mixed success. Adequate models can be built for proteins with high sequence similarity to a structurally resolved protein and occasionally modeling even succeeds in the absence of a good template, but currently no method exists to reliably rate the quality of the models.Many protein structure prediction methods rate protein models using an established scoring function by comparing the energies of an ensemble of structures and choosing the lowest energy members of said ensemble as the prediction. The acceptance of theoretical protein models is limited in the life-sciences, as currently no method exists to rate the quality of a protein model a-priori, i.e. from the model alone.Here we investigate an approach to provide an a-priori estimator of the quality of a protein model using a free-energy scoring function[1], without comparing it to a competing ensemble. We devised a N-dimensional statistical test based on the per-residue energies of amino acids in a set of high-resolution experimental structures. The quality of the protein structures can be assessed by comparison against these statistics. We were able to discriminate the low quality models for 93% of the 160 proteins tested, which is increased further to 99%, when excluding proteins, which bind cofactors or DNA; interactions not considered by the energy model or the training set. In combination with bioinformatics based methods that exclude proteins that are not covered by the scoring function, this measure for quality assessment of protein models may help increase the acceptance of qualified theoretical protein models in the life-sciences.[1] Verma, A.,Wenzel, W. (2009). A Free-Energy Approach for All-Atom Protein Simulation. Biophys.J 96,3483-3494.

Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles.

While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large number of applications, limitations in the model with respect to the equilibrium between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non Gly, Pro) backbone CMAP potential has been refined against experimental solution NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mechanical energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mechanical energy surfaces, followed by additional empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against data not used to guide parametrization: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equilibrium folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for the modeling and simulation studies of proteins, including studies of protein folding, assembly and functionally relevant conformational changes.

Protein Kinase A (PKA) Phosphorylation of Na+/K+-ATPase Opens Intracellular C-terminal Water Pathway Leading to Third Na+-binding site in Molecular Dynamics Simulations

Phosphorylation is one of the major mechanisms for posttranscriptional modification of proteins. The addition of a compact, negatively charged moiety to a protein can significantly change its function and localization by affecting its structure and interaction network. We have used all-atom Molecular Dynamics simulations to investigate the structural consequences of phosphorylating the Na(+)/K(+)-ATPase (NKA) residue Ser(936), which is the best characterized phosphorylation site in NKA, targeted in vivo by protein kinase A (PKA). The Molecular Dynamics simulations suggest that Ser(936) phosphorylation opens a C-terminal hydrated pathway leading to Asp(926), a transmembrane residue proposed to form part of the third sodium ion-binding site. Simulations of a S936E mutant form, for which only subtle effects are observed when expressed in Xenopus oocytes and studied with electrophysiology, does not mimic the effects of Ser(936) phosphorylation. The results establish a structural association of Ser(936) with the C terminus of NKA and indicate that phosphorylation of Ser(936) can modulate pumping activity by changing the accessibility to the ion-binding site.

Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes.

Protein folding and protein–ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein–ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent.

Atomistic Kinetic Model for Population Shift and Allostery in Biomolecules

Allosteric signaling in biomolecules is a key mechanism for a myriad of cellular processes. We present a general yet compact model for protein allostery at atomic detail to quantitatively explain and predict structural-dynamics properties of allosteric signal propagation. The master equation-based approach for allostery by population shift (MAPS) is introduced that derives the time scales, amplitudes, and pathways of signal transmission in peptides and proteins from dihedral angle dynamics observed in extended molecular dynamics simulations. The MAPS approach is first applied to the alanine-pentapeptide, and the results are tested against an explicit simulation in the presence of local conformational constraints, confirming the validity and accuracy of the model. We then apply the approach to a larger Markovian system based on a millisecond all-atom protein molecular dynamics trajectory of BPTI (Shaw et al. Science 2010, 330, 341-346). We use MAPS to illustrate in silico the propagation of a local perturbation over medium- to long-range distances across a disulfide bridge linking loops L1 and L2, which constitute the binding interface of BPTI.

Transform and relax sampling for highly anisotropic systems: Application to protein domain motion and folding

Transform and relax sampling (TRS) is proposed as a conformational sampling method to enhance "soft" fluctuation in highly anisotropic systems using molecular dynamics simulation. This method consists of three stages; transform, relax, and sampling. In the transform stage, molecular dynamics simulation is performed with randomly assigned force bias to enhance the fluctuations along relatively soft collective movements, as expected from the linear response theory. After relaxing the heated system to equilibrium without force bias in the relax stage, Monte Carlo-type determination is made as to whether the generated state is accepted or not. The sampling stage is then conducted for conformational sampling by conventional molecular dynamics simulation. TRS is first applied for the idealized multidimensional double-well C(α) model to mimic protein open-close transition. Subsequently, it is applied to three different all-atom protein systems in an explicit solvent model; T4 lysozyme, glutamine binding protein, and a mini-protein chignolin. Investigation of structural variations in the hinge angle of T4 lysozyme in crystals is demonstrated by TRS. The liganded close structure of the glutamine binding protein is sampled starting from the unliganded open form. Chignolin is shown to fold into a native structure multiple times starting from highly extended structures within 100 ns. It is concluded that TRS sampled a reasonable conformational space within a relatively short simulation time in these cases. Possible future extensions of TRS are also discussed.

What Is the Time Scale for α-Helix Nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ∼0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.

Broad Ensemble Generator (BEG): Software to Generate Ensembles for Intrinsically Disordered Proteins

n this presentation the broad ensemble generator (BEG) software is introduced, designed to efficiently construct diverse all-atom protein structures from sequence information alone. The BEG software utilizes a build-up approach where the protein chain is grown one amino acid at a time. All generated structures follow random spatial patterns by varying phi-psi angles along the peptide bonds. There is also an option present to allow changes of amino-acid side-chain torsions. Only steric interactions are currently included, but the method is flexible enough to allow for other interaction types. The application of BEG to generating structural ensembles for intrinsically disordered proteins is also presented.

Slipknotting upon native-like loop formation in a trefoil knot protein

Protein knots and slipknots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Recent experimental results show that knotting, starting from a fully extended polypeptide, has not yet been observed. Understanding the nucleation process of folding knots is thus a natural challenge for both experimental and theoretical investigation. In this study, we employ energy landscape theory and molecular dynamics to elucidate the entire folding mechanism. The full free energy landscape of a knotted protein is mapped using an all-atom structure-based protein model. Results show that, due to the topological constraint, the protein folds through a three-state mechanism that contains (i) a precise nucleation site that creates a correctly twisted native loop (first barrier) and (ii) a rate-limiting free energy barrier that is traversed by two parallel knot-forming routes. The main route corresponds to a slipknot conformation, a collapsed configuration where the C-terminal helix adopts a hairpin-like configuration while threading, and the minor route to an entropically limited plug motion, where the extended terminus is threaded as through a needle. Knot formation is a late transition state process and results show that random (nonspecific) knots are a very rare and unstable set of configurations both at and below folding temperature. Our study shows that a native-biased landscape is sufficient to fold complex topologies and presents a folding mechanism generalizable to all known knotted protein topologies: knotting via threading a native-like loop in a preordered intermediate.

Reconstruction of Protein Backbone with the α-Carbon Coordinates

Given an amino acid sequence with the α-carbon 3D coordinates on its backbone, the all-atom protein backbone reconstruction problem (PBRP) is to rebuild the 3D coordinates of all major atoms (N, C and O atoms) on the backbone. In this paper, we first build a 4-residue fragment library extracted from PDB. Then, to solve PBRP, we search for fragments with similar structures based on the inner distances. To test the performance of our method, we use two testing sets of target proteins, one was proposed by Maupetit et al. and the other is a subset extracted from CASP7. We compare the experimental results of our method with three previous works, MaxSprout, Adcock's method and SABBAC proposed by Maupetit et al. The reconstruction accuracy of our method is comparable to these previous works. And the solution of our method is more stable than the previous works in most target proteins. These previous works contain complicated energy computation, while our method does not. Thus, our method requires much less execution time than the previous works.

Modeling and Simulation of Rodlet Assembly of Hydrophobin EAS in an All-Atom Free-Energy Forcefield

In this investigation we simulate the rodlet assembly of an Class-I hydrophobin mutant EAS D15D8 in all-atom free-energy Monte-Carlo simulations. Results show that rodlet assembly is possible without additional beta strand formation in the flexible loop regions.Hydrophobins are small amphipathic proteins characterized by their unique bond pattern of eight Cysteine amino acids and a resulting similar tertiary structure, although only marginal sequence conservation exists within the family. In this work we elucidate the structure of the assembled rodlets in Class-I hydrophobins.The initial model of the EAS mutant is created using homology modeling of the solution structure of EAS allowing for a rigid structure omitting most of the flexible loop regions. A large population of possible docking structures is further generated using a generic protein-protein docking approach and filtered for candidates with distinct amphipathicity to account for the presence of an air-water interface.The resulting structures are further relaxed in the all-atom-free energy forcefield PFF02[1] using the POEM (Protein Optimization using Energy Methods) program package in parallel relaxation runs. Relaxation of the whole population was possible using the distributed volunteer computing platform POEM@HOME (http://boinc.fzk.de/).[1] A.Verma, W.Wenzel, A Free-Energy Approach for All-Atom Protein Simulation, Biophysical Journal, Volume 96, Issue 9, 2009, P. 3483

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Characterizing the equilibrium ensemble of folding pathways, including their relative probability, is one of the major challenges in protein folding theory today. Although this information is in principle accessible via all-atom molecular dynamics simulations, it is difficult to compute in practice because protein folding is a rare event and the affordable simulation length is typically not sufficient to observe an appreciable number of folding events, unless very simplified protein models are used. Here we present an approach that allows for the reconstruction of the full ensemble of folding pathways from simulations that are much shorter than the folding time. This approach can be applied to all-atom protein simulations in explicit solvent. It does not use a predefined reaction coordinate but is based on partitioning the state space into small conformational states and constructing a Markov model between them. A theory is presented that allows for the extraction of the full ensemble of transition pathways from the unfolded to the folded configurations. The approach is applied to the folding of a PinWW domain in explicit solvent where the folding time is two orders of magnitude larger than the length of individual simulations. The results are in good agreement with kinetic experimental data and give detailed insights about the nature of the folding process which is shown to be surprisingly complex and parallel. The analysis reveals the existence of misfolded trap states outside the network of efficient folding intermediates that significantly reduce the folding speed.