Highly Coarse-Grained Representations of Transmembrane Proteins

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.

Optimizing Coarse-Grained Models for Large-Scale Membrane Protein Simulation

Coarse-grained (CG) models have been developed for studying membrane proteins at physiologically relevant scales. Such methods, including popular CG lipid models, exhibit stability and efficiency at moderate scales, but they can become impractical or even unusable beyond a critical size due to various technical issues. Here, we report that these scale-dependent issues can arise from progressively slower relaxation dynamics and become confounded by unforeseen instabilities observed only at larger scales. To address these issues, we systemically optimized a 4-site solvent-free CG lipid model that is suitable for conducting micron-scale molecular dynamics simulations of membrane proteins under various membrane properties. We applied this lipid model to explore the long-range membrane deformation induced by a large mechanosensitive ion channel, PIEZO. We show that the optimized CG models are powerful in elucidating the structural and dynamic interplay between PIEZO and the membrane. Furthermore, we anticipate that our methodological insights can prove useful for resolving issues stemming from scale-dependent limitations of similar CG methodologies.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.

Cholesterol and M2 Rendezvous in Budding and Scission of Influenza A Virus

The cholesterol of the host cell plasma membrane and viral M2 protein plays a crucial role in multiple stages of infection and replication of the influenza A virus. Cholesterol is required for the formation of heterogeneous membrane microdomains (or rafts) in the budozone of the host cell that serves as assembly sites for the viral components. The raft microstructures act as scaffolds for several proteins. Cholesterol may further contribute to the mechanical forces necessary for membrane scission in the last stage of budding and help to maintain the stability of the virus envelope. The M2 protein has been shown to cause membrane scission in model systems by promoting the formation of curved lipid bilayer structures that, in turn, can lead to membrane vesicles budding off or scission intermediates. Membrane remodeling by M2 is intimately linked with cholesterol as it affects local lipid composition, fluidity, and stability of the membrane. Thus, both cholesterol and M2 protein contribute to the efficient and proper release of newly formed influenza viruses from the virus-infected cells.

Exploring the landscape of model representations

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon

An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) time scales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels.

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.

Entropic forces drive clustering and spatial localization of influenza A M2 during viral budding

The influenza A matrix 2 (M2) transmembrane protein facilitates virion release from the infected host cell. In particular, M2 plays a role in the induction of membrane curvature and/or in the scission process whereby the envelope is cut upon virion release. Here we show using coarse-grained computer simulations that various M2 assembly geometries emerge due to an entropic driving force, resulting in compact clusters or linearly extended aggregates as a direct consequence of the lateral membrane stresses. Conditions under which these protein assemblies will cause the lipid membrane to curve are explored, and we predict that a critical cluster size is required for this to happen. We go on to demonstrate that under the stress conditions taking place in the cellular membrane as it undergoes large-scale membrane remodeling, the M2 protein will, in principle, be able to both contribute to curvature induction and sense curvature to line up in manifolds where local membrane line tension is high. M2 is found to exhibit linactant behavior in liquid-disordered-liquid-ordered phase-separated lipid mixtures and to be excluded from the liquid-ordered phase, in near-quantitative agreement with experimental observations. Our findings support a role for M2 in membrane remodeling during influenza viral budding both as an inducer and a sensor of membrane curvature, and they suggest a mechanism by which localization of M2 can occur as the virion assembles and releases from the host cell, independent of how the membrane curvature is produced.

Computer Simulations Predict High Structural Heterogeneity of Functional State of NMDA Receptors

N-methyl-D-aspartate receptors (NMDARs)-i.e., transmembrane proteins expressed in neurons-play a central role in the molecular mechanisms of learning and memory formation. It is unclear how the known atomic structures of NMDARs determined by x-ray crystallography and electron cryomicroscopy (18 published Protein Data Bank entries) relate to the functional states of NMDARs inferred from electrophysiological recordings (multiple closed, open, preopen, etc. states). We address this problem by using molecular dynamics simulations at atomic resolution, a method successfully applied in the past to much smaller biomolecules. Our simulations predict that several conformations of NMDARs with experimentally determined geometries, including four "nonactive" electron cryomicroscopy structures, rapidly interconvert on submicrosecond timescales and therefore may correspond to the same functional state of the receptor (specifically, one of the closed states). This conclusion is not trivial because these conformational transitions involve changes in certain interatomic distances as large as tens of Å. The simulations also predict differences in the conformational dynamics of the apo and holo (i.e., agonist and coagonist bound) forms of the receptor on the microsecond timescale. To our knowledge, five new conformations of NMDARs, with geometries joining various features from different known experimental structures, are also predicted by the model. The main limitation of this work stems from its limited sampling (30 μs of aggregate length of molecular dynamics trajectories). Though this level significantly exceeds the sampling in previous simulations of parts of NMDARs, it is still much lower than the sampling recently achieved for smaller biomolecules (up to a few milliseconds), thus precluding, in particular, the observation of transitions between different functional states of NMDARs. Despite this limitation, such computational predictions may guide further experimental studies on the structure, dynamics, and function of NMDARs, for example by suggesting optimal locations of spectroscopic probes. Overall, atomic resolution simulations provide, to our knowledge, a novel perspective on the structure and dynamics of NMDARs, complementing information obtained by experimental methods.

Simulated Dynamics of Glycans on Ligand-Binding Domain of NMDA Receptors Reveals Strong Dynamic Coupling between Glycans and Protein Core

N-Methyl-d-aspartate (NMDA) receptors, key neuronal receptors playing the central role in learning and memory, are heavily glycosylated in vivo. Astonishingly little is known about the structure, dynamics, and physiological relevance of glycans attached to them. We recently demonstrated that certain glycans on the ligand binding domain (LBD) of NMDA receptors (NMDARs) can serve as intramolecular potentiators, changing EC50 of NMDAR coagonists. In this work, we use molecular dynamics trajectories, in aggregate 86.5 μs long, of the glycosylated LBD of the GluN1 subunit of the NMDAR to investigate the behavior of glycans on NMDARs. Though all glycans in our simulations were structurally the same (Man5), the dynamics of glycans at different locations on NMDARs was surprisingly different. The slowest-time scale motions that we detected in various glycans in some cases corresponded to a flipping of parts of glycans relative to each other, while in other cases they reduced to a head-to-tail bending of a glycan. We predict that time scales of conformational changes in glycans on the GluN1 LBD of NMDARs range from nanoseconds to at least hundreds of microseconds. Some of the conformational changes in the glycans correlate with the physiologically important clamshell-like opening and closing of the GluN1 LBD domain. Thus, glycans are an integral part of NMDARs, and computational models of NMDARs should include glycans to faithfully represent the structure and the dynamics of these receptors.