A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Molecularly informed field theory for estimating critical micelle concentrations of intrinsically disordered protein surfactants

The critical micelle concentration (CMC) is a crucial parameter in understanding the self-assembly behavior of surfactants. In this study, we combine simulation and experiment to demonstrate the predictive capability of molecularly informed field theories in estimating the CMC of biologically based protein surfactants. Our simulation approach combines the relative entropy coarse-graining of small-scale atomistic simulations with large-scale field-theoretic simulations, allowing us to efficiently compute the free energy of micelle formation necessary for the CMC calculation while preserving chemistry-specific information about the underlying surfactant building blocks. We apply this methodology to a unique intrinsically disordered protein platform capable of a wide variety of tailored sequences that enable tunable micelle self-assembly. The computational predictions of the CMC closely match experimental measurements, demonstrating the potential of molecularly informed field theories as a valuable tool to investigate self-assembly in bio-based macromolecules systematically.

Mapping the configurational landscape and aggregation phase behavior of the tau protein fragment PHF6

The PHF6 (Val-Gln-Ile-Val-Tyr-Lys) motif, found in all isoforms of the microtubule-associated protein tau, forms an integral part of ordered cores of amyloid fibrils formed in tauopathies and is thought to play a fundamental role in tau aggregation. Because PHF6 as an isolated hexapeptide assembles into ordered fibrils on its own, it is investigated as a minimal model for insight into the initial stages of aggregation of larger tau fragments. Even for this small peptide, however, the large length and time scales associated with fibrillization pose challenges for simulation studies of its dynamic assembly, equilibrium configurational landscape, and phase behavior. Here, we develop an accurate, bottom-up coarse-grained model of PHF6 for large-scale simulations of its aggregation, which we use to uncover molecular interactions and thermodynamic driving forces governing its assembly. The model, not trained on any explicit information about fibrillar structure, predicts coexistence of formed fibrils with monomers in solution, and we calculate a putative equilibrium phase diagram in concentration-temperature space. We also characterize the configurational and free energetic landscape of PHF6 oligomers. Importantly, we demonstrate with a model of heparin that this widely studied cofactor enhances the aggregation propensity of PHF6 by ordering monomers during nucleation and remaining associated with growing fibrils, consistent with experimentally characterized heparin-tau interactions. Overall, this effort provides detailed molecular insight into PHF6 aggregation thermodynamics and pathways and, furthermore, demonstrates the potential of modern multiscale modeling techniques to produce predictive models of amyloidogenic peptides simultaneously capturing sequence-specific effects and emergent aggregate structures.

Principles Governing the Phase Separation of Multidomain Proteins

A variety of membraneless organelles, often termed "biological condensates", play an important role in the regulation of cellular processes such as gene transcription, translation, and protein quality control. On the basis of experimental and theoretical investigations, liquid-liquid phase separation (LLPS) has been proposed as a possible mechanism for the origin of biological condensates. LLPS requires multivalent macromolecules that template the formation of long-range, intermolecular interaction networks and results in the formation of condensates with defined composition and material properties. Multivalent interactions driving LLPS exhibit a wide range of modes from highly stereospecific to nonspecific and involve both folded and disordered regions. Multidomain proteins serve as suitable macromolecules for promoting phase separation and achieving disparate functions due to their potential for multivalent interactions and regulation. Here, we aim to highlight the influence of the domain architecture and interdomain interactions on the phase separation of multidomain protein condensates. First, the general principles underlying these interactions are illustrated on the basis of examples of multidomain proteins that are predominantly associated with nucleic acid binding and protein quality control and contain both folded and disordered regions. Next, the examples showcase how LLPS properties of folded and disordered regions can be leveraged to engineer multidomain constructs that form condensates with the desired assembly and functional properties. Finally, we highlight the need for improvements in coarse-grained computational models that can provide molecular-level insights into multidomain protein condensates in conjunction with experimental efforts.

Broad chemical transferability in structure-based coarse-graining

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher-resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parametrizations. Here we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parametrization of 3,441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parametrization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parametrization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules, while retaining the benefits of a structure-based parametrization.

SPICA Force Field for Proteins and Peptides

A coarse-grained (CG) model for peptides and proteins was developed as an extension of the Surface Property fItting Coarse grAined (SPICA) force field (FF). The model was designed to examine membrane proteins that are fully compatible with the lipid membranes of the SPICA FF. A preliminary version of this protein model was created using thermodynamic properties, including the surface tension and density in the SPICA (formerly called SDK) FF. In this study, we improved the CG protein model to facilitate molecular dynamics (MD) simulations with a reproduction of multiple properties from both experiments and all-atom (AA) simulations. An elastic network model was adopted to maintain the secondary structure within a single chain. The side-chain analogues reproduced the transfer free energy profiles across the lipid membrane and demonstrated reasonable association free energy (potential of mean force) in water compared to those from AA MD. A series of peptides/proteins adsorbed onto or penetrated into the membrane simulated by the CG MD correctly predicted the penetration depths and tilt angles of peripheral and transmembrane peptides/proteins as comparable to those in the orientations of proteins in membranes (OPM) database. In addition, the dimerization free energies of several transmembrane helices within a lipid bilayer were comparable to those from experimental estimation. Application studies on a series of membrane protein assemblies, scramblases, and poliovirus capsids demonstrated the good performance of the SPICA FF.

Accelerating Protein Folding Molecular Dynamics Using Inter-Residue Distances from Machine Learning Servers

Recently, predicting the native structures of proteins has become possible using computational molecular physics (CMP)─physics-based force fields sampled with proper statistics─but only for small proteins. Algorithms with better scaling are needed. We describe ML x MELD x MD, a molecular dynamics (MD) method that inputs residue contacts derived from machine learning (ML) servers into MELD, a Bayesian accelerator that preserves detailed-balance statistics. Contacts are derived from trRosetta-predicted distance histograms (distograms) and are integrated into MELD's atomistic MD as spatial restraints through parametrized potential functions. In the CASP14 blind prediction event, ML x MELD x MD predicted 13 native structures to better than 4.5 Å error, including for 10 proteins in the range of 115-250 amino acids long. Also, the scaling of simulation time vs protein length is much better than unguided MD: tsim ∼ e0.023N for ML x MELD x MD vs tsim ∼ e0.168N for MD alone. This shows how machine learning information can be leveraged to advance physics-based modeling of proteins.

A generic force field for simulating native protein structures using dissipative particle dynamics

A coarse-grained force field for molecular dynamics simulations of the native structures of proteins in a dissipative particle dynamics (DPD) framework is developed. The parameters for bonded interactions are derived by mapping the bonds and angles for 20 amino acids onto target distributions obtained from fully atomistic simulations in explicit solvent. A dual-basin potential is introduced for stabilizing backbone angles, to cover a wide spectrum of protein secondary structures. The backbone dihedral potential enables folding of the protein from an unfolded initial state to the folded native structure. The proposed force field is validated by evaluating the structural properties of several model peptides and proteins including the SARS-CoV-2 fusion peptide, consisting of α-helices, β-sheets, loops and turns. Detailed comparisons with fully atomistic simulations are carried out to assess the ability of the proposed force field to stabilize the different secondary structures present in proteins. The compact conformations of the native states were evident from the radius of gyration and the high intensity peaks of the root mean square deviation histograms, which were found to be within 0.4 nm. The Ramachandran-like energy landscape on the phase space of backbone angles (θ) and dihedrals (ϕ) effectively captured the conformational phase space of α-helices at ∼(ϕ = 50°,θ = 90°) and β-strands at ∼(ϕ = ±180°,θ = 90-120°). Furthermore, the residue-residue native contacts were also well reproduced by the proposed DPD model. The applicability of the model to multidomain complexes was assessed using lysozyme and a large α-helical bacterial pore-forming toxin, cytolysin A. Our study illustrates that the proposed force field is generic, and can potentially be extended for efficient in silico investigations of membrane bound polypeptides and proteins using DPD simulations.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Biomolecular response to hour-long ultralow field microwave radiation: An effective coarse-grained model simulation

Various electronic devices, which we commonly use, radiate microwaves. Such external perturbation influences the functionality of biomolecules. In an ultralow field, the cumulative response of a molecule is expected only over a time scale of hours. To study the structural dynamics of biomolecules over hours, we adopt a simple methodology for constructing the coarse-grained structure of the protein molecule and solve the Langevin equation under different working potentials. In this approach, each amino acid residue of a biomolecule is mapped onto a number of beads, a few for the backbone, and few for the side chain, depending on the complexity of its chemical structure. We choose the force field in such a way that the dynamics of the protein molecule in the presence of ultralow radiation field of microvolt/nm could be followed over the time frame of 2 h. We apply the model to describe a biomolecule, hen egg white lysozyme, and simulate its structural evolution under ultralow strength electromagnetic radiation. The simulation revealed the finer structural details, like the extent of exposure of bioactive residues and the state of the secondary structures of the molecule, further confirmed from spectroscopic measurements [details are available in Phys. Rev. E 97, 052416 (2018)10.1103/PhysRevE.97.052416 and briefly described here]. Though tested for a specific system, the model is quite general. We believe that it harnesses the potential in studying the structural dynamics of any biopolymer under external perturbation over an extended time scale.

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.

Investigating the energetic and entropic components of effective potentials across a glass transition

By eliminating unnecessary details, coarse-grained (CG) models provide the necessary efficiency for simulating scales that are inaccessible to higher resolution models. However, because they average over atomic details, the effective potentials governing CG degrees of freedom necessarily incorporate significant entropic contributions, which limit their transferability and complicate the treatment of thermodynamic properties. This work employs a dual-potential approach to consider the energetic and entropic contributions to effective interaction potentials for CG models. Specifically, we consider one- and three-site CG models for ortho-terphenyl (OTP) both above and below its glass transition. We employ the multiscale coarse-graining (MS-CG) variational principle to determine interaction potentials that accurately reproduce the structural properties of an all-atom (AA) model for OTP at each state point. We employ an energy-matching variational principle to determine an energy operator that accurately reproduces the intra- and inter-molecular energy of the AA model. While the MS-CG pair potentials are almost purely repulsive, the corresponding pair energy functions feature a pronounced minima that corresponds to contacting benzene rings. These energetic functions then determine an estimate for the entropic component of the MS-CG interaction potentials. These entropic functions accurately predict the MS-CG pair potentials across a wide range of liquid state points at constant density. Moreover, the entropic functions also predict pair potentials that quite accurately model the AA pair structure below the glass transition. Thus, the dual-potential approach appears a promising approach for modeling AA energetics, as well as for predicting the temperature-dependence of CG effective potentials.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.

The Effects of p-Azidophenylalanine Incorporation on Protein Structure and Stability

Functionalization is often needed to harness the power of proteins for beneficial use but can cause losses to stability and/or activity. State of the art methods to limit these deleterious effects accomplish this by substituting an amino acid in the wild-type molecule into an unnatural amino acid, such as p-azidophenylalanine (pAz), but selecting the residue for substitution a priori remains an elusive goal of protein engineering. The results of this work indicate that all-atom molecular dynamics simulation can be used to determine whether substituting pAz for a natural amino acid will be detrimental to experimentally determined protein stability. These results offer significant hope that local deviations from wild-type structure caused by pAz incorporation observed in simulations can be a predictive metric used to reduce the number of costly experiments that must be done to find active proteins upon substitution with pAz and subsequent functionalization.

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model

Intrinsically disordered proteins (IDPs) play an important role in an array of biological processes but present a number of fundamental challenges for computational modeling. Recently, simple polymer models have regained popularity for interpreting the experimental characterization of IDPs. Homopolymer theory provides a strong foundation for understanding generic features of phenomena ranging from single-chain conformational dynamics to the properties of entangled polymer melts, but is difficult to extend to the copolymer context. This challenge is magnified for proteins due to the variety of competing interactions and large deviations in side-chain properties. In this work, we apply a simple physics-based coarse-grained model for describing largely disordered conformational ensembles of peptides, based on the premise that sampling sterically forbidden conformations can compromise the faithful description of both static and dynamical properties. The Hamiltonian of the employed model can be easily adjusted to investigate the impact of distinct interactions and sequence specificity on the randomness of the resulting conformational ensemble. In particular, starting with a bead–spring-like model and then adding more detailed interactions one by one, we construct a hierarchical set of models and perform a detailed comparison of their properties. Our analysis clarifies the role of generic attractions, electrostatics, and side-chain sterics, while providing a foundation for developing efficient models for IDPs that retain an accurate description of the hierarchy of conformational dynamics, which is nontrivially influenced by interactions with surrounding proteins and solvent molecules.