Driving force and pathway in polyelectrolyte complex coacervation.

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Shape changes and cooperativity in the folding of the central domain of the 16S ribosomal RNA.

Both the small and large subunits of the ribosome, the molecular machine that synthesizes proteins, are complexes of ribosomal RNAs (rRNAs) and a number of proteins. In bacteria, the small subunit has a single 16S rRNA whose folding is the first step in its assembly. The central domain of the 16S rRNA folds independently, driven either by Mg2+ ions or by interaction with ribosomal proteins. To provide a quantitative description of ion-induced folding of the ∼350-nucleotide rRNA, we carried out extensive coarse-grained molecular simulations spanning Mg2+ concentration between 0 and 30 mM. The Mg2+ dependence of the radius of gyration shows that globally the rRNA folds cooperatively. Surprisingly, various structural elements order at different Mg2+ concentrations, indicative of the heterogeneous assembly even within a single domain of the rRNA. Binding of Mg2+ ions is highly specific, with successive ion condensation resulting in nucleation of tertiary structures. We also predict the Mg2+-dependent protection factors, measurable in hydroxyl radical footprinting experiments, which corroborate the specificity of Mg2+-induced folding. The simulations, which agree quantitatively with several experiments on the folding of a three-way junction, show that its folding is preceded by formation of other tertiary contacts in the central junction. Our work provides a starting point in simulating the early events in the assembly of the small subunit of the ribosome.

Extended conformational states dominate the Hsp90 chaperone dynamics.

The heat shock protein 90 (Hsp90) is a molecular chaperone central to client protein folding and maturation in eukaryotic cells. During its chaperone cycle, Hsp90 undergoes ATPase-coupled large-scale conformational changes between open and closed states, where the N-terminal and middle domains of the protein form a compact dimerized conformation. However, the molecular principles of the switching motion between the open and closed states remain poorly understood. Here we show by integrating atomistic and coarse-grained molecular simulations with small-angle X-ray scattering experiments and NMR spectroscopy data that Hsp90 exhibits rich conformational dynamics modulated by the charged linker, which connects the N-terminal with the middle domain of the protein. We show that the dissociation of these domains is crucial for the conformational flexibility of the open state, with the separation distance controlled by a ß-sheet motif next to the linker region. Taken together, our results suggest that the conformational ensemble of Hsp90 comprises highly extended states, which could be functionally crucial for client processing.

Anatomy of a selectively coassembled ß-sheet peptide nanofiber.

Peptide self-assembly, wherein molecule A associates with other A molecules to form fibrillar ß-sheet structures, is common in nature and widely used to fabricate synthetic biomaterials. Selective coassembly of peptide pairs A and B with complementary partial charges is gaining interest due to its potential for expanding the form and function of biomaterials that can be realized. It has been hypothesized that charge-complementary peptides organize into alternating ABAB-type arrangements within assembled ß-sheets, but no direct molecular-level evidence exists to support this interpretation. We report a computational and experimental approach to characterize molecular-level organization of the established peptide pair, CATCH. Discontinuous molecular dynamics simulations predict that CATCH(+) and CATCH(-) peptides coassemble but do not self-assemble. Two-layer ß-sheet amyloid structures predominate, but off-pathway ß-barrel oligomers are also predicted. At low concentration, transmission electron microscopy and dynamic light scattering identified nonfibrillar ∼20-nm oligomers, while at high concentrations elongated fibers predominated. Thioflavin T fluorimetry estimates rapid and near-stoichiometric coassembly of CATCH(+) and CATCH(-) at concentrations ≥100 µM. Natural abundance 13C NMR and isotope-edited Fourier transform infrared spectroscopy indicate that CATCH(+) and CATCH(-) coassemble into two-component nanofibers instead of self-sorting. However, 13C-13C dipolar recoupling solid-state NMR measurements also identify nonnegligible AA and BB interactions among a majority of AB pairs. Collectively, these results demonstrate that strictly alternating arrangements of ß-strands predominate in coassembled CATCH structures, but deviations from perfect alternation occur. Off-pathway ß-barrel oligomers are also suggested to occur in coassembled ß-strand peptide systems.

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers.

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.

Thermodynamic phase diagram of amyloid-ß (16-22) peptide.

The aggregation of monomeric amyloid ß protein (Aß) peptide into oligomers and amyloid fibrils in the mammalian brain is associated with Alzheimer's disease. Insight into the thermodynamic stability of the Aß peptide in different polymeric states is fundamental to defining and predicting the aggregation process. Experimental determination of Aß thermodynamic behavior is challenging due to the transient nature of Aß oligomers and the low peptide solubility. Furthermore, quantitative calculation of a thermodynamic phase diagram for a specific peptide requires extremely long computational times. Here, using a coarse-grained protein model, molecular dynamics (MD) simulations are performed to determine an equilibrium concentration and temperature phase diagram for the amyloidogenic peptide fragment Aß16-22 Our results reveal that the only thermodynamically stable phases are the solution phase and the macroscopic fibrillar phase, and that there also exists a hierarchy of metastable phases. The boundary line between the solution phase and fibril phase is found by calculating the temperature-dependent solubility of a macroscopic Aß16-22 fibril consisting of an infinite number of ß-sheet layers. This in silico determination of an equilibrium (solubility) phase diagram for a real amyloid-forming peptide, Aß16-22, over the temperature range of 277-330 K agrees well with fibrillation experiments and transmission electron microscopy (TEM) measurements of the fibril morphologies formed. This in silico approach of predicting peptide solubility is also potentially useful for optimizing biopharmaceutical production and manufacturing nanofiber scaffolds for tissue engineering.

Coarse-grained simulations of phase separation driven by DNA and its sensor protein cGAS.

The enzyme cGAS functions as a sensor that recognizes the cytosolic DNA from foreign pathogen. The activation of the protein triggers the transcription of inflammatory genes, leading into the establishment of an antipathogen state. An interesting new discovery is that the detection of DNA by cGAS induced the formation of liquid-like droplets. However how cells regulate the formation of these droplets is still not fully understood. In order to unravel the molecular mechanism beneath the DNA-mediated phase separation of cGAS, we developed a polymer-based coarse-grained model which takes into accounts the basic structural organization in DNA and cGAS, as well as the binding properties between these biomolecules. This model was further integrated into a hybrid simulation algorithm. With this computational method, a multi-step kinetic process of aggregation between cGAS and DNA was observed. Moreover, we systematically tested the model under different concentrations and binding parameters. Our simulation results show that phase separation requires both cGAS dimerization and protein-DNA interactions, whereas polymers can be kinetically trapped in small aggregates under strong binding affinities. Additionally, we demonstrated that supramolecular assembly can be facilitated by increasing the number of functional modules in protein or DNA polymers, suggesting that multivalency and intrinsic disordered regions play positive roles in regulating phase separation. This is consistent to previous experimental evidences. Taken together, this is, to the best of our knowledge, the first computational model to study condensation of cGAS-DNA complexes. While the method can reach the timescale beyond the capability of atomic-level MD simulations, it still includes information about spatial arrangement of functional modules in biopolymers that is missing in the mean-field theory. Our work thereby adds a useful dimension to a suite of existing experimental and computational techniques to study the dynamics of phase separation in biological systems.

Direct observation and rational design of nucleation behavior in addressable self-assembly.

To optimize a self-assembly reaction, it is essential to understand the factors that govern its pathway. Here, we examine the influence of nucleation pathways in a model system for addressable, multicomponent self-assembly based on a prototypical "DNA-brick" structure. By combining temperature-dependent dynamic light scattering and atomic force microscopy with coarse-grained simulations, we show how subtle changes in the nucleation pathway profoundly affect the yield of the correctly formed structures. In particular, we can increase the range of conditions over which self-assembly occurs by using stable multisubunit clusters that lower the nucleation barrier for assembling subunits in the interior of the structure. Consequently, modifying only a small portion of a structure is sufficient to optimize its assembly. Due to the generality of our coarse-grained model and the excellent agreement that we find with our experimental results, the design principles reported here are likely to apply generically to addressable, multicomponent self-assembly.

Inchworm stepping of Myc-Max heterodimer protein diffusion along DNA.

Oncogenic protein Myc serves as a transcription factor to control cell metabolisms. Myc dimerizes via leucine zipper with its associated partner protein Max to form a heterodimer structure, which then binds target DNA sequences to regulate gene transcription. The regulation depends on Myc-Max binding to DNA and searching for target sequences via diffusional motions along DNA. Here, we conduct structure-based molecular dynamics (MD) simulations to investigate the diffusion dynamics of the Myc-Max heterodimer along DNA. We found that the heterodimer protein slides on the DNA in a rotation-uncoupled manner in coarse-grained simulations, as its two helical DNA binding basic regions (BRs) alternate between open and closed conformations via inchworm stepping motions. In such motions, the two BRs of the heterodimer step across the DNA strand one by one, with step sizes reaching about half of a DNA helical pitch length. Atomic MD simulations of the Myc-Max heterodimer in complex with DNA have also been conducted. Hydrogen bond interactions are revealed between the two BRs and two complementary DNA strands, respectively. In the non-specific DNA binding, the BR from Myc shows an onset of stepping on one association DNA strand and starts detaching from the other strand. Overall, our simulation studies suggest that the inchworm stepping motions of the Myc-Max heterodimer can be achieved during the protein diffusion along DNA.

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials.

The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer-polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to enhance the physical properties of composite materials by the strategic design of the "molecular architecture" of constituents to benefit from synergistic effects relating to the organization of the polymer component.

Martini Coarse-Grained Model of Hyaluronic Acid for the Structural Change of Its Gel in the Presence of Monovalent and Divalent Salts.

Hyaluronic acid (HA) has a wide range of biomedical applications including the formation of hydrogels, microspheres, sponges, and films. The modeling of HA to understand its behavior and interaction with other biomolecules at the atomic level is of considerable interest. The atomistic representation of long HA polymers for the study of the macroscopic structural formation and its interactions with other polyelectrolytes is computationally demanding. To overcome this limitation, we developed a coarse grained (CG) model for HA adapting the Martini scheme. A very good agreement was observed between the CG model and all-atom simulations for both local (bonded interactions) and global properties (end-to-end distance, a radius of gyration, RMSD). Our CG model successfully demonstrated the formation of HA gel and its structural changes at high salt concentrations. We found that the main role of CaCl2 is screening the electrostatic repulsion between chains. HA gel did not collapse even at high CaCl2 concentrations, and the osmotic pressure decreased, which agrees well with the experimental results. This is a distinct property of HA from other proteins or polynucleic acids which ensures the validity of our CG model. Our HA CG model is compatible with other CG biomolecular models developed under the Martini scheme, which allows for large-scale simulations of various HA-based complex systems.

Structural characterization of cardiolipin-driven activation of cytochrome c into a peroxidase and membrane perturbation.

The interaction between cardiolipin (CL) and cytochrome c (cyt-c) results in a gain of function of peroxidase activity by cyt-c. Despite intensive research, disagreements on nature and molecular details of this interaction remain. In particular, it is still not known how the interaction triggers the onset of apoptosis. Enzymatic characterization of peroxidase activity has highlighted the need for a critical threshold concentration of CL, a finding of profound physiological relevance in vivo. Using solution NMR, fluorescence spectroscopy, and in silico modeling approaches we here confirm that full binding of cyt-c to the membrane requires a CL:cyt-c threshold ratio of 5:1. Among three binding sites, the simultaneous binding of two sites, at two opposing sides of the heme, provides a mechanism to open the heme crevice to substrates. This results in "productive binding" in which cyt-c then sequesters CL, inducing curvature in the membrane. Membrane perturbation along with lipid peroxidation, due to interactions of heme/CL acyl chains, initiates the next step in the apoptotic pathway of making the membrane leaky. The third CL binding site while allowing interaction with the membrane, does not cluster CL or induce subsequent events, making this interaction "unproductive".

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models.

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

Coarse-grained simulations of hemolytic peptide δ-lysin interacting with a POPC bilayer.

δ-lysin, secreted by a Gram-positive bacterium Staphylococcus aureus, is a 26-residue membrane active peptide that shares many common features with antimicrobial peptides (AMPs). However, it possesses a few unique features that differentiate itself from typical AMPs. In particular, δ-lysin has zero net charge, even though it has many charged residues, and it preferentially lyses eukaryotic cells over bacterial cells. Here, we present the results of coarse-grained molecular dynamics simulations of δ-lysin interacting with a zwitterionic membrane over a wide range of peptide concentrations. When the peptides concentration is low, spontaneous dimerization of peptides is observed on the membrane surface, but deep insertion of peptides or pore formation was not observed. However, the calculated free energy of peptide insertion suggests that a small fraction of peptides is likely to be present inside the membrane at the peptide concentrations typically seen in dye efflux experiments. When the simulations with multiple peptides are carried out with a single pre-inserted transmembrane peptide, spontaneous pore formation occurs with a peptide-to-lipid ratio (P/L) as low as P/L=1:42. Inter-peptide salt bridges among the transmembrane peptides seem to play a role in creating compact pores with very low level of hydration. More importantly, the transmembrane peptides making up the pore are constantly pushed to the opposite side of the membrane when the mass imbalance between the two sides of membrane is significant. Thus, the pore is very dynamic, allowing multiple peptides to translocate across the membrane simultaneously.

Membrane pore formation in atomistic and coarse-grained simulations.

Biological cells and their organelles are protected by ultra thin membranes. These membranes accomplish a broad variety of important tasks like separating the cell content from the outer environment, they are the site for cell-cell interactions and many enzymatic reactions, and control the in- and efflux of metabolites. For certain physiological functions e.g. in the fusion of membranes and also in a number of biotechnological applications like gene transfection the membrane integrity needs to be compromised to allow for instance for the exchange of polar molecules across the membrane barrier. Mechanisms enabling the transport of molecules across the membrane involve membrane proteins that form specific pores or act as transporters, but also so-called lipid pores induced by external fields, stress, or peptides. Recent progress in the simulation field enabled to closely mimic pore formation as supposed to occur in vivo or in vitro. Here, we review different simulation-based approaches in the study of membrane pores with a focus on lipid pore properties such as their size and energetics, poration mechanisms based on the application of external fields, charge imbalances, or surface tension, and on pores that are induced by small molecules, peptides, and lipids. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

CHARMM-GUI 10 years for biomolecular modeling and simulation.

CHARMM-GUI, http://www.charmm-gui.org, is a web-based graphical user interface that prepares complex biomolecular systems for molecular simulations. CHARMM-GUI creates input files for a number of programs including CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Since its original development in 2006, CHARMM-GUI has been widely adopted for various purposes and now contains a number of different modules designed to set up a broad range of simulations: (1) PDB Reader & Manipulator, Glycan Reader, and Ligand Reader & Modeler for reading and modifying molecules; (2) Quick MD Simulator, Membrane Builder, Nanodisc Builder, HMMM Builder, Monolayer Builder, Micelle Builder, and Hex Phase Builder for building all-atom simulation systems in various environments; (3) PACE CG Builder and Martini Maker for building coarse-grained simulation systems; (4) DEER Facilitator and MDFF/xMDFF Utilizer for experimentally guided simulations; (5) Implicit Solvent Modeler, PBEQ-Solver, and GCMC/BD Ion Simulator for implicit solvent related calculations; (6) Ligand Binder for ligand solvation and binding free energy simulations; and (7) Drude Prepper for preparation of simulations with the CHARMM Drude polarizable force field. Recently, new modules have been integrated into CHARMM-GUI, such as Glycolipid Modeler for generation of various glycolipid structures, and LPS Modeler for generation of lipopolysaccharide structures from various Gram-negative bacteria. These new features together with existing modules are expected to facilitate advanced molecular modeling and simulation thereby leading to an improved understanding of the structure and dynamics of complex biomolecular systems. Here, we briefly review these capabilities and discuss potential future directions in the CHARMM-GUI development project. © 2016 Wiley Periodicals, Inc.

CHARMM-GUI Martini Maker for modeling and simulation of complex bacterial membranes with lipopolysaccharides.

A complex cell envelope, composed of a mixture of lipid types including lipopolysaccharides, protects bacteria from the external environment. Clearly, the proteins embedded within the various components of the cell envelope have an intricate relationship with their local environment. Therefore, to obtain meaningful results, molecular simulations need to mimic as far as possible this chemically heterogeneous system. However, setting up such systems for computational studies is far from trivial, and consequently the vast majority of simulations of outer membrane proteins still rely on oversimplified phospholipid membrane models. This work presents an update of CHARMM-GUI Martini Maker for coarse-grained modeling and simulation of complex bacterial membranes with lipopolysaccharides. The qualities of the outer membrane systems generated by Martini Maker are validated by simulating them in bilayer, vesicle, nanodisc, and micelle environments (with and without outer membrane proteins) using the Martini force field. We expect this new feature in Martini Maker to be a useful tool for modeling large, complicated bacterial outer membrane systems in a user-friendly manner. © 2017 Wiley Periodicals, Inc.

Exploring Protein-Nanoparticle Interactions with Coarse-Grained Protein Folding Models.

Understanding the fundamental biophysics behind protein-nanoparticle (NP) interactions is essential for the design and engineering bio-NP systems. The authors describe the development of a coarse-grained protein-NP model that utilizes a structure centric protein model. A key feature of the protein-NP model is the quantitative inclusion of the hydrophobic character of residues in the protein and their interactions with the NP surface. In addition, the curvature of the NP is taken into account, capturing the protein behavior on NPs of different size. The authors evaluate this model by comparison with experimental results for structure and adsorption of a model protein interacting with an NP. It is demonstrated that the simulation results recapitulate the structure of the small α/ß protein GB1 on the NP for data from circular dichroism and fluorescence spectroscopy. In addition, the calculated protein adsorption free energy agrees well with the experimental value. The authors predict the dependence of protein folding on the NP size, surface chemistry, and temperature. The model has the potential to guide NP design efforts by predicting protein behavior on NP surfaces with various chemical properties and curvatures.

Interplay between partner and ligand facilitates the folding and binding of an intrinsically disordered protein.

Protein-protein interactions are at the heart of regulatory and signaling processes in the cell. In many interactions, one or both proteins are disordered before association. However, this disorder in the unbound state does not prevent many of these proteins folding to a well-defined, ordered structure in the bound state. Here we examine a typical system, where a small disordered protein (PUMA, p53 upregulated modulator of apoptosis) folds to an α-helix when bound to a groove on the surface of a folded protein (MCL-1, induced myeloid leukemia cell differentiation protein). We follow the association of these proteins using rapid-mixing stopped flow, and examine how the kinetic behavior is perturbed by denaturant and carefully chosen mutations. We demonstrate the utility of methods developed for the study of monomeric protein folding, including ß-Tanford values, Leffler α, Φ-value analysis, and coarse-grained simulations, and propose a self-consistent mechanism for binding. Folding of the disordered protein before binding does not appear to be required and few, if any, specific interactions are required to commit to association. The majority of PUMA folding occurs after the transition state, in the presence of MCL-1. We also examine the role of the side chains of folded MCL-1 that make up the binding groove and find that many favor equilibrium binding but, surprisingly, inhibit the association process.

Linear aggregation of proteins on the membrane as a prelude to membrane remodeling.

Adhesion and insertion of curvature-mediating proteins can induce dramatic structural changes in cell membranes, allowing them to participate in several key cellular tasks. The way proteins interact to generate curvature remains largely unclear, especially at early stages of membrane remodeling. Using a coarse-grained model of Bin/amphiphysin/Rvs domain with an N-terminal helix (N-BAR) interacting with flat membranes and vesicles, we demonstrate that at low protein surface densities, binding of N-BAR domain proteins to the membrane is followed by a linear aggregation and the formation of meshes on the surface. In this process, the proteins assemble at the base of emerging membrane buds. Our work shows that beyond a more straightforward scaffolding mechanism at high bound densities, the interplay of anisotropic interactions and the local stress imposed by the N-BAR proteins results in deep invaginations and endocytic vesicular bud-like deformations, an order of magnitude larger than the size of the individual protein. Our results imply that by virtue of this mechanism, cell membranes may achieve rapid local increases in protein concentration.