A New Mixed All-Atom/Coarse-Grained Model: Application to Melittin Aggregation in Aqueous Solution

Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins

For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.

Simulations of Functional Motions of Super Large Biomolecules with a Mixed-Resolution Model

Many large protein machines function through an interplay between large-scale movements and intricate conformational changes. Understanding functional motions of these proteins through simulations becomes challenging for both all-atom and coarse-grained (CG) modeling techniques because neither approach alone can readily capture the full details of these motions. In this study, we develop a multiscale model by employing the popular MARTINI CG model to represent a heterogeneous environment and structurally stable proteins and using the united-atom (UA) model PACE to describe proteins undergoing subtle conformational changes. PACE was previously developed to be compatible with the MARTINI solvent and membrane. Here, we couple the protein descriptions of the two models by directly mixing UA and CG interaction parameters to greatly simplify parameter determination. Through extensive validations with diverse protein systems in solution or membrane, we demonstrate that only additional parameter rescaling is needed to enable the resulting model to recover the stability of native structures of proteins under mixed representation. Moreover, we identify the optimal scaling factors that can be applied to various protein systems, rendering the model potentially transferable. To further demonstrate its applicability for realistic systems, we apply the model to a mechanosensitive ion channel Piezo1 that has peripheral arms for sensing membrane tension and a central pore for ion conductance. The model can reproduce the coupling between Piezo1's large-scale arm movement and subtle pore opening in response to membrane stress while consuming much less computational costs than all-atom models. Therefore, our model shows promise for studying functional motions of large protein machines.

From Milliseconds to Minutes: Melittin Self-Assembly from Concerted Non-Equilibrium Pressure-Jump and Equilibrium Relaxation Nuclear Magnetic Resonance

Non-equilibrium kinetics techniques like pressure-jump nuclear magnetic resonance (NMR) are powerful in tracking changes in oligomeric populations and are not limited by relaxation rates for the time scales of exchange that can be probed. However, these techniques are less sensitive to minor, transient populations than are Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments. We integrated non-equilibrium pressure-jump and equilibrium CPMG relaxation dispersion data to fully map the kinetic landscape of melittin tetramerization. While monomeric peptides weakly form dimers (Kd,D/M ≈ 26 mM) whose population never exceeds 1.6% at 288 K, dimers associate tightly to form stable tetrameric species (Kd,T/D ≈ 740 nM). Exchange between the monomer and dimer, along with exchange between the dimer and tetramer, occurs on the millisecond time scale. The NMR approach developed herein can be readily applied to studying the folding and misfolding of a wide range of oligomeric assemblies.

Multiscale Simulations to Discover Self-Assembled Oligopeptides: A Benchmarking Study

Peptide self-assembly is critical for biomedical and material discovery and production. While it is costly to experimentally test every possible peptide design, computational assessment provides an affordable solution to evaluate many designs and prioritize synthesis and characterization. Following a theoretical investigation, we present a systematic analysis of all-atom and coarse-grained simulations to predict peptide self-assembly. Benchmarking studies of two model dipeptides allow us to assess the impacts of intrinsic properties (such as amino acids and terminal modifications) and external environment (such as salinity) on the simulated aggregation. Further examination of 20 oligopeptides containing two to five amino acids shows good agreement among our theory, simulations, and prior experimental observations. The success rate of our prediction is 90%. Therefore, our theory, simulation, and analysis can be useful to identify peptide designs that can self-assemble and predict the potential nanostructures. These findings lay the ground for future virtual screening of peptide-assembled nanostructures and computer-aided biologics design.

Machine Learning-Guided Adaptive Parametrization for Coupling Terms in a Mixed United-Atom/Coarse-Grained Model for Diphenylalanine Self-Assembly in Aqueous Ionic Liquids

Precise regulation of the peptide self-assembly into ordered nanostructures with intriguing properties has attracted intense attention. However, predicting peptide assembly at atomic resolution is a challenge due to both the structural flexibility of peptides and the associated huge computational costs. A machine learning-guided adaptive parametrization method was proposed for developing a mixed atomic and coarse-grained (CG) model through a multiobjective optimization strategy. Our model incorporates the united-atom (UA) model for diphenylalanine (P) and the polarizable electrostatic-variable coarse-grained (VaCG) model for aqueous ionic liquid [BMIM]+[BF4]- solution. In this mixed model, the coupling van der Waals (vdW) interaction is addressed by introducing virtual sites (VS) in the UA model to interact with solvent CG beads. The coupling parameters, including the electrostatic parameter and vdW parameters, are automatically optimized through ML-guided adaptive parametrization. The performance of this model was tested by some microstructural properties, e.g., the average number of P-P intermolecular hydrogen bonds (HBs) and radius distribution functions (RDFs) between P and different fragments of IL, in comparison with all-atom (AA) simulations. The computational cost is significantly reduced using such a parametrization scheme, which could search tens of thousands of force-field parameter sets, while needing only a small fraction of them to be assessed with molecular dynamics (MD) simulations. We used such a mixed resolution model to investigate the self-assembly in IL-water mixtures with variants of IL concentration (X). The long-range-ordered fibril structure is formed in a pure water system (X = 0). With an increase of IL concentrations, the formation of an ordered self-assembly nanostructure is prohibited, instead forming branched fibril at X = 2 mol % or amorphous aggregates when X > 10 mol %, resulting from the interplay between π-stacking and HB interactions between P and IL. The qualitative agreement between the simulated structures and the observed morphologies in experiments indicates the applicability of ML-guided parametrization strategy in the study of complex systems, such as polymers, lipid bilayers, and polysaccharides.

Millisecond Time-Resolved Solid-State NMR Initiated by Rapid Inverse Temperature Jumps

Elucidation of the detailed mechanisms by which biological macromolecules undergo major structural conversions, such as folding, complex formation, and self-assembly, is a central concern of biophysical chemistry that will benefit from new experimental methods. We describe a simple technique for initiating a structural conversion process by a rapid decrease in the temperature of a solution, i.e., a rapid inverse temperature jump. By pumping solutions through copper capillary tubes that are thermally anchored to heated and cooled blocks, solution temperatures can be switched from 95 to 30 °C (or lower) in about 0.8 ms. For time-resolved solid-state nuclear magnetic resonance (ssNMR), solutions can then be frozen rapidly by spraying into cold isopentane after a variable structural evolution time τ_e. As an initial demonstration, we use this "inverse T-jump" technique to characterize the kinetics and mechanism by which the 26-residue peptide melittin converts from its primarily disordered, monomeric state at 95 °C to its α-helical, tetrameric state at 30 °C. One- and two-dimensional ssNMR spectra of frozen solutions with various values of τ_e, recorded at 25 K with signal enhancements from dynamic nuclear polarization, show that both helical secondary structure and intermolecular contacts develop on the same time scale of about 6 ms. The dependences on τ_e of both intraresidue crosspeak patterns and inter-residue crosspeak volumes in two-dimensional spectra can be fit with a unidirectional dimerization model, consistent with dimerization being the rate-limiting step for melittin tetramer formation.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model

A fully atomistic (AT) modeling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di-N-acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.

Calculating the absolute binding free energy of the insulin dimer in an explicit solvent

Insulin is a significant hormone in the regulation of glucose level in the blood. Its monomers bind to each other to form dimers or hexamers through a complex process. To study the binding of the insulin dimer, we first calculate its absolute binding free energy by the steered molecular dynamics method and the confinement method based on a fictitious thermodynamic cycle. After considering some special correction terms, the final calculated binding free energy at 298 K is −8.97 ± 1.41 kcal mol⁻¹, which is close to the experimental value of −7.2 ± 0.8 kcal mol⁻¹. Furthermore, we discuss the important residue–residue interactions between the insulin monomers, including hydrophobic interactions, π–π interactions and hydrogen bond interactions. The analysis reveals five key residues, Vla^B12, Tyr^B16, Phe^B24, Phe^B25, and Tyr^B26, for the dimerization of the insulin. We also perform MM-PBSA calculations for the wild-type dimer and some mutants and study the roles of the key residues by the change of the binding energy of the insulin dimer.

In this paper, we calculate the absolute binding free energy of an insulin dimer by steered MD method. The result of −8.97 kcal mol⁻¹ is close to the experimental value −7.2 kcal mol⁻¹. We also analyze the residue–residue interactions.

Application of millisecond time-resolved solid state NMR to the kinetics and mechanism of melittin self-assembly

Common experimental approaches for characterizing structural conversion processes such as protein folding and self-assembly do not report on all aspects of the evolution from an initial state to the final state. Here, we demonstrate an approach that is based on rapid mixing, freeze-trapping, and low-temperature solid-state NMR (ssNMR) with signal enhancements from dynamic nuclear polarization (DNP). Experiments on the folding and tetramerization of the 26-residue peptide melittin following a rapid pH jump show that multiple aspects of molecular structure can be followed with millisecond time resolution, including secondary structure at specific isotopically labeled sites, intramolecular and intermolecular contacts between specific pairs of labeled residues, and overall structural order. DNP-enhanced ssNMR data reveal that conversion of conformationally disordered melittin monomers at low pH to α-helical conformations at neutral pH occurs on nearly the same timescale as formation of antiparallel melittin dimers, about 6 to 9 ms for 0.3 mM melittin at 24 °C in aqueous solution containing 20% (vol/vol) glycerol and 75 mM sodium phosphate. Although stopped-flow fluorescence data suggest that melittin tetramers form quickly after dimerization, ssNMR spectra show that full structural order within melittin tetramers develops more slowly, in ∼60 ms. Time-resolved ssNMR is likely to find many applications to biomolecular structural conversion processes, including early stages of amyloid formation, viral capsid formation, and protein-protein recognition.

From quantum to subcellular scales: multi-scale simulation approaches and the SIRAH force field

Modern molecular and cellular biology profits from astonishing resolution structural methods, currently even reaching the whole cell level. This is encompassed by the development of computational methods providing a deep view into the structure and dynamics of molecular processes happening at very different scales in time and space. Linking such scales is of paramount importance when aiming at far-reaching biological questions. Computational methods at the interface between classical and coarse-grained resolutions are gaining momentum with several research groups dedicating important efforts to their development and tuning. An overview of such methods is addressed herein, with special emphasis on the SIRAH force field for coarse-grained and multi-scale simulations. Moreover, we provide proof of concept calculations on the implementation of a multi-scale simulation scheme including quantum calculations on a classical fine-grained/coarse-grained representation of double-stranded DNA. This opens the possibility to include the effect of large conformational fluctuations in chromatin segments on, for instance, the reactivity of particular base pairs within the same simulation framework.

Top-down Multiscale Approach To Simulate Peptide Self-Assembly from Monomers

Modeling peptide assembly from monomers on large time and length scales is often intractable at the atomistic resolution. To address this challenge, we present a new approach which integrates coarse-grained (CG), mixed-resolution, and all-atom (AA) modeling in a single simulation. We simulate the initial encounter stage with the CG model, while the further assembly and reorganization stages are simulated with the mixed-resolution and AA models. We have implemented this top-down approach with new tools to automate model transformations and to monitor oligomer formations. Further, a theory was developed to estimate the optimal simulation length for each stage using a model peptide, melittin. The assembly level, the oligomer distribution, and the secondary structures of melittin simulated by the optimal protocol show good agreement with prior experiments and AA simulations. Finally, our approach and theory have been successfully validated with three amyloid peptides (β-amyloid 16-22, GNNQQNY fragment from the yeast prion protein SUP35, and α-synuclein fibril 35-55), which highlight the synergy from modeling at multiple resolutions. This work not only serves as proof of concept for multiresolution simulation studies but also presents practical guidelines for further self-assembly simulations at more physically and chemically relevant scales.

Assessment of Conformational State Transitions of Class B GPCRs Using Molecular Dynamics

Class B G protein-coupled receptors (GPCRs) comprise a family of 15 peptide-binding members, which are crucial targets for endocrine, metabolic, and stress-related disorders. While their protein structures and dynamics remain largely unclear, computer modeling and simulations represent a promising means to help solve such puzzles. Herein, we present a basic introduction to the methodology of molecular dynamics (MD) simulations and two analytical methods to assess the conformational ensembles and transitions of Class B GPCRs, using our recent studies of the human pituitary adenylate cyclase activating polypeptide (PAC₁) receptor as an example. From long MD simulations, conformational ensembles with different roles in ligand binding and receptor activation are sampled to establish four states identified as either "open" or "closed" for the PAC₁ receptor. Next, the dynamical network can be applied to analyze the simulations and identify key features within each conformational ensemble, which help distinguish the ligand-bound states of the PAC₁ receptor from the ligand-free one. Further, the Markov State Model has emerged as a key approach to construct the transition network and connect the GPCR ensembles, providing detailed information for the transition pathways and kinetics. For the ligand-free PAC₁ receptor, the transitions within the closed states are near 10-30 times faster than the open-closed transitions, which is likely related to the activation mechanism of the receptor. Overall, long MD simulations and analyses are useful to assess conformational transitions for the Class B GPCRs and to gain mechanistic insight, which is difficult to obtain using other methods.

Multiscale Simulation of Protein Hydration Using the SWINGER Dynamical Clustering Algorithm

To perform computationally efficient concurrent multiscale simulations of biological macromolecules in solution, where the all-atom (AT) models are coupled to supramolecular coarse-grained (SCG) solvent models, previous studies resorted to modified AT water models, such as the bundled-simple point charge (SPC) models, that use semiharmonic springs to restrict the relative movement of water molecules within a cluster. Those models can have a significant impact on the simulated biomolecules and can lead, for example, to a partial unfolding of a protein. In this work, we employ the recently developed alternative approach with a dynamical clustering algorithm, SWINGER, which enables a direct coupling of original unmodified AT and SCG water models. We perform an adaptive resolution molecular dynamics simulation of a Trp-Cage miniprotein in multiscale water, where the standard SPC water model is interfaced with the widely used MARTINI SCG model, and demonstrate that, compared to the corresponding full-blown AT simulations, the structural and dynamic properties of the solvated protein and surrounding solvent are well reproduced by our approach.