Coarse-grained Representation Research Articles

Reconstructing Protein Structure and Dynamics from Experimental Observables

Single-molecule experimental techniques track the real-time dynamics of molecules by recording a small number of experimental observables. Following these observables provides a coarse-grained representation of the conformational dynamics but does not furnish an atomistic representation of the instantaneous molecular structure. Remarkably, a theorem from dynamical systems asserts that these time series can, under quite general conditions, contain sufficient information to reconstruct the atomistic structure of the molecule.

Native-like membrane models of E. coli polar lipid extract shed light on the importance of lipid composition complexity

BackgroundLipid-protein interactions stabilize protein oligomers, shape their structure, and modulate their function. Whereas in vitro experiments already account for the functional importance of lipids by using natural lipid extracts, in silico methods lack behind by embedding proteins in single component lipid bilayers. However, to accurately complement in vitro experiments with molecular details at very high spatio-temporal resolution, molecular dynamics simulations have to be performed in natural(-like) lipid environments.ResultsTo enable more accurate MD simulations, we have prepared four membrane models of E. coli polar lipid extract, a typical model organism, each at all-atom (CHARMM36) and coarse-grained (Martini3) representations. These models contain all main lipid headgroup types of the E. coli inner membrane, i.e., phosphatidylethanolamines, phosphatidylglycerols, and cardiolipins, symmetrically distributed between the membrane leaflets. The lipid tail (un)saturation and propanylation stereochemistry represent the bacterial lipid tail composition of E. coli grown at 37∘C until 3/4 of the log growth phase. The comparison of the Simple three lipid component models to the complex 14-lipid component model Avanti over a broad range of physiologically relevant temperatures revealed that the balance of lipid tail unsaturation and propanylation in different positions and inclusion of lipid tails of various length maintain realistic values for lipid mobility, membrane area compressibility, lipid ordering, lipid volume and area, and the bilayer thickness. The only Simple model that was able to satisfactory reproduce most of the structural properties of the complex Avanti model showed worse agreement of the activation energy of basal water permeation with the here performed measurements. The Martini3 models reflect extremely well both experimental and atomistic behavior of the E. coli polar lipid extract membranes. Aquaporin-1 embedded in our native(-like) membranes causes partial lipid ordering and membrane thinning in its vicinity. Moreover, aquaporin-1 attracts and temporarily binds negatively charged lipids, mainly cardiolipins, with a distinct cardiolipin binding site in the crevice at the contact site between two monomers, most probably stabilizing the tetrameric protein assembly.ConclusionsThe here prepared and validated membrane models of E. coli polar lipids extract revealed that lipid tail complexity, in terms of double bond and cyclopropane location and varying lipid tail length, is key to stabilize membrane properties over a broad temperature range. In addition, they build a solid basis for manifold future simulation studies on more realistic lipid membranes bridging the gap between simulations and experiments.

Modal Analysis of the Lysozyme Protein Considering All-Atom and Coarse-Grained Finite Element Models

Proteins are the fundamental entities of several organic activities. They are essential for a broad range of tasks in a way that their shapes and folding processes are crucial to achieving proper biological functions. Low-frequency modes, generally associated with collective movements at terahertz (THz) and sub-terahertz frequencies, have been appointed as critical for the conformational processes of many proteins. Dynamic simulations, such as molecular dynamics, are vastly applied by biochemical researchers in this field. However, in the last years, proposals that define the protein as a simplified elastic macrostructure have shown appealing results when dealing with this type of problem. In this context, modal analysis based on different modelization techniques, i.e., considering both an all-atom (AA) and coarse-grained (CG) representation, is proposed to analyze the hen egg-white lysozyme. This work presents new considerations and conclusions compared to previous analyses. Experimental values for the B-factor, considering all the heavy atoms or only one representative point per amino acid, are used to evaluate the validity of the numerical solutions. In general terms, this comparison allows the assessment of the regional flexibility of the protein. Besides, the low computational requirements make this approach a quick method to extract the protein’s dynamic properties under scrutiny.

STransFuse: Fusing Swin Transformer and Convolutional Neural Network for Remote Sensing Image Semantic Segmentation

The applied research in remote sensing images has been pushed by convolutional neural network (CNN). Because of the fixed size of the perceptual field, CNN is unable to model global semantic relevance. Modeling global semantic information is possible with the self-attentive Transformer-based model. However, the method of patch computation used by Transformer for self-attentive computation ignores the spatial information inside each patch. To address these issues, we offer the STransFuse model as a new semantic segmentation method for remote sensing images. It is a model that combines the benefits of Transformer with CNN to improve the segmentation quality of various remote sensing images. We employ a staged model to extract coarse-grained and fine-grained feature representations at various semantic scales, unlike earlier techniques based on Transformer model fusion. In order to take full advantage of the features acquired at different stages, we designed an adaptive fusion module. This module adaptively fuses the semantic information between features at different scales employing a self-attentive mechanism. The overall accuracy (OA) of our proposed model on the Vaihingen dataset is 1.36% higher than the baseline, and 1.27% improvement in OA over baseline on the Potsdam dataset. When compared to other advanced models, the STransFuse model performs admirably.

Limitations of the ABEGO-based backbone design: ambiguity between αα-corner and αα-hairpin.

ABEGO is a coarse-grained representation for poly­peptide backbone dihedral angles. The Ramachandran map is divided into four segments denoted as A, B, E, and G to represent the local conformation of poly­peptide chains in the character strings. Although the ABEGO representation is widely used in backbone building simulation for de novo protein design, it cannot capture minor differences in backbone dihedral angles, which potentially leads to ambiguity between two structurally distinct fragments. Here, I show a nontrivial example of two local motifs that could not be distinguished by their ABEGO representations. I found that two well-known local motifs αα-hairpins and αα-corners are both represented as α-GBB-α and thus indistinguishable in the ABEGO representation, although they show distinct arrangements of the flanking α-helices. I also found that α-GBB-α motifs caused a loss of efficiency in the ABEGO-based fragment-assembly simulations for de novo protein backbone design. Nevertheless, I was able to design amino-acid sequences that were predicted to fold into the target topologies that contained these α-GBB-α motifs, which suggests such topologies that are difficult to build by ABEGO-based simulations are designable once the backbone structures are modeled by some means. The finding that certain local motifs bottleneck the ABEGO-based fragment-assembly simulations for construction of backbone structures suggests that finer representations of backbone torsion angles are required for efficiently generating diverse topologies containing such indistinguishable local motifs.

A coarse-grained xDLVO model for colloidal protein-protein interactions.

Colloidal protein-protein interactions (PPIs) of attractive and repulsive nature modulate the solubility of proteins, their aggregation, precipitation and crystallization. Such interactions are very important for many biotechnological processes, but are complex and hard to control, therefore, difficult to be understood in terms of measurements alone. In diluted protein solutions, PPIs can be estimated from the osmotic second virial coefficient, B22, which has been calculated using different methods and levels of theory. The most popular approach is based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and its extended versions, i.e. xDLVO. Despite much efforts, these models are not fully quantitative and must be fitted to experiments, which limits their predictive value. Here, we report an extended xDLVO-CG model, which extends existing models by a coarse-grained representation of proteins and the inclusion of an additional ion-protein dispersion interaction term. We demonstrate for four proteins, i.e. lysozyme (LYZ), subtilisin (Subs), bovine serum albumin (BSA) and immunoglobulin (IgG1), that semi-quantitative agreement with experimental values without the need to fit to experimental B22 values. While most likely not the final step in the nearly hundred years of research in PPIs, xDLVO-CG is a step towards predictive PPIs calculations that are transferable to different proteins.

Data-driven selection of coarse-grained models of coupled oscillators

Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to obtain using solely analytical methods. Rigorous methodologies for finding such coarse-grained representations of multi-scale phenomena would enable accelerated computational simulations and provide fundamental insights into the complex dynamics of interest. We focus on a heterogeneous population of oscillators of Kuramoto type as a canonical model of complex dynamics, and develop a data-driven approach for inferring its coarse-grained description. Our method is based on a numerical optimization of the coefficients in a general equation of motion informed by analytical derivations in the thermodynamic limit. We show that certain assumptions are required to obtain an autonomous coarse-grained equation of motion. However, optimizing coefficient values enables coarse-grained models with conceptually disparate functional forms, yet comparable quality of representation, to provide accurate reduced-order descriptions of the underlying system.

Using coarse-grained models to examine structure-property relationships of diblock-arm star polymers

Molecular dynamics simulations were used to verify that diblock-arm star polymers (SPs) can be accurately described using coarse-grained models. Each arm of the SPs examined consist of an inner polyethylene block and an outer polyethylene oxide block. A sixteen-arm SP with arm chemistry -CH224-CH2OCH26-H was mapped to a MARTINI coarse-grained representation and compared to results from atomistic simulations of an identical chemistry and architecture. Results for radius of gyration, radial distribution functions, and occupied volumes all show agreement with the atomistic model and reproduce general trends with respect to temperature. Additional measurements of interfacial area and anisotropy reveal that our model does not demonstrate crystallization of the polyethylene blocks at low temperatures as observed in the atomistic model which can be ascribed to the reduction in degrees of freedom that follow from coarse-graining. Calculated values for relaxation times agree with the general trends from the atomistic simulations. Nineteen additional coarse-grained star polymers were examined in order to investigate structure-property relationships that arise by varying arm number and arm length. The ability to model these chemical species at this resolution will allow for simulations of polymeric nanocarriers in more complex environments including at increased concentrations and near surfaces. This work demonstrates an important first step in work that will enable improved design of these polymeric nanoparticles for drug delivery applications.

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.

Implicit Modeling of the Impact of Adsorption on Solid Surfaces for Protein Mechanics and Activity with a Coarse-Grained Representation.

Surface immobilized enzymes play a key role in numerous biotechnological applications such as biosensors, biofuel cells, or biocatalytic synthesis. As a consequence, the impact of adsorption on the enzyme structure, dynamics, and function needs to be understood on the molecular level as it is critical for the improvement of these technologies. With this perspective in mind, we used a theoretical approach for investigating local protein flexibility on the residue scale that couples a simplified protein representation with an elastic network and Brownian dynamics simulations. The impact of protein adsorption on a solid surface is implicitly modeled via additional external constraints between the residues in contact with the surface. We first performed calculations on a redox enzyme, bilirubin oxidase (BOD) from M.verrucaria, to study the impact of adsorption on its mechanical properties. The resulting rigidity profiles show that, in agreement with the available experimental data, the mechanical variations observed in the adsorbed BOD will depend on its orientation and its anchor residues (i.e., residues that are in contact with the functionalized surface). Additional calculations on ribonuclease A and nitroreductase shed light on how seemingly stable adsorbed enzymes can nonetheless display an important decrease in their catalytic activity resulting from a perturbation of their mechanics and internal dynamics.

Effective aspect ratio of helices in shear flow.

We report the results of simulations of rigid colloidal helices suspended in a shear flow, using dissipative particle dynamics for a coarse-grained representation of the suspending fluid, as well as deterministic trajectories of non-Brownian helices calculated from the resistance tensor derived under the slender-body approximation. The shear flow produces nonuniform rotation of the helices, similarly to other high aspect ratio particles, such that more elongated helices spend more time aligned with the fluid velocity. We introduce a geometric effective aspect ratio calculated directly from the helix geometry and a dynamical effective aspect ratio derived from the trajectories of the particles and find that the two effective aspect ratios are approximately equal over the entire parameter range tested. We also describe observed transient deflections of the helical axis into the vorticity direction that can occur when the helix is rotating through the gradient direction and that depend on the rotation of the helix about its axis.

Thermal Compaction of Disordered and Elastin-like Polypeptides: A Temperature-Dependent, Sequence-Specific Coarse-Grained Simulation Model.

Elastin-like polypeptides (ELPs) undergo a sharp solubility transition from low-temperature solvated phases to coacervates at elevated temperatures, driven by the increased strength of hydrophobic interactions at higher temperatures. The transition temperature, or "cloud point", critically depends on sequence composition, sequence length, and concentration of the ELPs. In this work, we present a temperature-dependent, implicit solvent, sequence-specific coarse-grained (CG) simulation model that reproduces the transition temperatures as a function of sequence length and guest residue identity of various experimentally probed ELPs to appreciable accuracy. Our model builds upon the self-organized polymer model introduced recently for intrinsically disordered polypeptides (SOP-IDP) and introduces a semi-empirical functional form for the temperature dependence of hydrophobic interactions. In addition to the fine performance for various ELPs, we demonstrate the ability of our model to capture the thermal compactions in dominantly hydrophobic IDPs, consistent with experimental scattering data. With the high computational efficiency afforded by the CG representation, we envisage that the model will be ideally suited for simulations of large-scale structures such as ELP networks and hydrogels, as well as agglomerates of IDPs.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications.

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Predicting optical spectra for optoelectronic polymers using coarse-grained models and recurrent neural networks

Coarse-grained modeling of conjugated polymers has become an increasingly popular route to investigate the physics of organic optoelectronic materials. While ultraviolet (UV)-vis spectroscopy remains one of the key experimental methods for the interrogation of these materials, a rigorous bridge between simulated coarse-grained structures and spectroscopy has not been established. Here, we address this challenge by developing a method that can predict spectra of conjugated polymers directly from coarse-grained representations while avoiding repetitive procedures such as ad hoc back-mapping from coarse-grained to atomistic representations followed by spectral computation using quantum chemistry. Our approach is based on a generative deep-learning model: the long-short-term memory recurrent neural network (LSTM-RNN). The latter is suggested by the apparent similarity between natural languages and the mathematical structure of perturbative expansions of, in our case, excited-state energies perturbed by conformational fluctuations. We also use this model to explore the level of sensitivity of spectra to the coarse-grained representation back-mapping protocol. Our approach presents a tool uniquely suited for improving postsimulation analysis protocols, as well as, potentially, for including spectral data as input in the refinement of coarse-grained potentials.

Influence of Charge Regulation and Charge Heterogeneity on Complexation between Polyelectrolytes and Proteins.

We employed a combination of single chain in mean field methodology and constant pH Monte Carlo framework to compare the influence of charge regulation and charge heterogeneity on the adsorption and bridging characteristics of polyelectrolytes in solution on proteins. By adopting a coarse-grained representation of the proteins as spherical particles and embedding a simple framework for probing charge heterogeneities, we probe the influence of charge patches, net charge of the particle, the ratio of positive to negative charges on the proteins on the net adsorption, and bridging probabilities of polyelectrolytes. Our results demonstrate that charge regulation increases the probability of bridging between two particles when compared to proteins with the same fixed charge. The influence of charge regulation first increases and then decreases with an increase in the number of charge patches of proteins. An increase in the ratio of positive to negative charges and the net charge of the protein are also seen to increase the propensity for polyelectrolyte adsorption and bridging.

Over What Length Scale Does an Inorganic Substrate Perturb the Structure of a Glassy Organic Semiconductor?

While the bulk structure of vapor-deposited glasses has been extensively studied, structure at buried interfaces has received little attention, despite being important for organic electronic applications. To learn about glass structure at buried interfaces, we study the structure of vapor-deposited glasses of the organic semiconductor DSA-Ph (1,4-di-[4-(N,N-diphenyl)amino]styrylbenzene) as a function of film thickness; the structure is probed with grazing incidence X-ray scattering. We deposit on silicon and gold substrates and span a film thickness range of 10-600 nm. Our experiments demonstrate that interfacial molecular packing in vapor-deposited glasses of DSA-Ph is more disordered compared to the bulk. At a deposition temperature near room temperature, we estimate ∼8 nm near the substrate can have modified molecular packing. Molecular dynamics simulations of a coarse-grained representation of DSA-Ph reveal a similar length scale. In both the simulations and the experiments, deposition temperature controls glass structure beyond this interfacial layer of a few nanometers.

Disorder-Order Transitions in Conformational Selection of a Peptide by Ebola Virus Nucleoprotein.

This study presents parallel-tempering lattice Monte Carlo simulations based on the side-chain-only (SICHO) model for calculating the conformational landscape of a 28-residue intrinsically disordered peptide extracted from the Ebola virus protein VP35. The central issue is the applicability of the SICHO potential energy function and in general coarse-grained (CG) representations of intermediate resolution for modeling large-scale conformational heterogeneity that includes both folded and unstructured peptide states. Crystallographic data shows that the peptide folds in a 410-helix-turn-310-helix topology upon complex formation with the Ebola virus nucleoprotein, whereas in isolation, the peptide transitions to a disordered conformational ensemble as observed in circular dichroism experiments. The simulation reveals a potential of mean force that displays conformational diversity along the helix-forming reaction coordinate consistent with disorder–order transitions, yet unexpectedly the bound topology is poorly sampled, and a population shift to an unstructured state incurs a significant free-energy penalty. Applying an elastic network interpolation model suggests a hybrid binding mechanism through conformational selection of the 410-helix followed by an induced fit of the 310-helix. A comparison of the CG model with previously reported all-atom CHARMM-based simulations highlights a lattice-based approach that is computationally fast and with the correct parameterization yields good resolution to modeling conformational plasticity.

Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians.

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled-cluster wave functions to rigorously derive effective Hamiltonians in Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that Hubbard's and Heisenberg's Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

Microcanonical coarse-graining of the kinetic Ising model.

We propose a scheme for coarse-graining the dynamics of the 2-D kinetic Ising model onto the microcanonical ensemble. At subcritical temperatures, 2-D and higher-dimensional Ising lattices possess two basins of attraction separated by a free energy barrier. Projecting onto the microcanonical ensemble has the advantage that the dependence of the crossing rate constant on environmental conditions can be obtained from a single Monte Carlo trajectory. Using various numerical methods, we computed the forward rate constants of coarse-grained representations of the Ising model and compared them with the true value obtained from brute force simulation. While coarse-graining preserves detailed balance, the computed rate constants for barrier heights between 5 kT and 9 kT were consistently 50% larger than the true value. Markovianity testing revealed loss of dynamical memory, which we propose accounts for coarse-graining error. Committor analysis did not support the alternative hypothesis that microcanonical projection is incompatible with an optimal reaction coordinate. The correct crossing rate constant was obtained by spectrally decomposing the diffusion coefficient near the free energy barrier and selecting the slowest (reactive) component. The spectral method also yielded the correct rate constant in the 3-D Ising lattice, where coarse-graining error was 6% and memory effects were diminished. We conclude that microcanonical coarse-graining supplemented by spectral analysis of short-term barrier fluctuations provides a comprehensive kinetic description of barrier crossing in a non-inertial continuous-time jump process.

OSIRIS: A model for integrating the effects of multiple stressors on marine ecosystems

While much has been learnt about the impacts of specific stressors on individual marine organisms, considerable debate exists over the nature and impact of multiple simultaneous stressors on both individual species and marine ecosystems. We describe a modelling tool (OSIRIS) for integrating the effects of multiple simultaneous stressors. The model is relatively computationally light, and demonstrated using a coarse-grained, non-spatial and simplified representation of a temperate marine ecosystem. This version is capable of reproducing a wide range of dynamic responses. Results indicate the degree to which interactions are synergistic is crucial in determining sensitivity to forcing, particularly for the higher trophic levels, which can respond non-linearly to stronger forcing. Stronger synergistic interactions sensitize the system to variability in forcing, and combinations of stronger forcing, noise and synergies between effects are particularly potent. This work also underlines the significant potential risk incurred in treating stressors on ecosystems as individual and additive.