Multiscale coarse-graining of the protein energy landscape

NPEX: Never give up protein exploration with deep reinforcement learning

Elucidating unknown structures of proteins, such as metastable states, is critical in designing therapeutic agents. Protein structure exploration has been performed using advanced computational methods, especially molecular dynamics and Markov chain Monte Carlo simulations, which require untenably long calculation times and prior structural knowledge. Here, we developed an innovative method for protein structure determination called never give up protein exploration (NPEX) with deep reinforcement learning. The NPEX method leverages the soft actor-critic algorithm and the intrinsic reward system, effectively adding a bias potential without the need for prior knowledge. To demonstrate the method's effectiveness, we applied it to four models: a double well, a triple well, the alanine dipeptide, and the tryptophan cage. Compared with Markov chain Monte Carlo simulations, NPEX had markedly greater sampling efficiency. The significantly enhanced computational efficiency and lack of prior domain knowledge requirements of the NPEX method will revolutionize protein structure exploration.

Multiscale, Multiresolution Coarse-Grained Model via a Hybrid Approach: Solvation, Structure, and Self-Assembly of Aromatic Tripeptides

Short aromatic peptides have been observed to assemble into diverse nanostructures, including fibers, tubes, and vesicles, using computational techniques. However, the computational studies have employed top-down coarse-grained (CG) models, which are unable to capture the assembly along with the conformation, packing, and organization of the peptides within the aggregates in a manner that is consistent with the all atom (AA) representation of the molecules. In this study, a hybrid structure- and force-based approach is adapted to develop a bottom-up CG force field of triphenylalanine using reference data from AA trajectories. This approach follows a flexible methodology to approximate the chemical complexity of the underlying AA representation with the chosen CG representation. Two CG models are developed with distinct representations of the aromatic side chains. The first uses a simple single-bead representation, while the second uses a three-bead representation to more accurately represent the planarity of the ring. The one-bead model yields nanorods, while the three-bead model results in nanospheres. The role of different chemical groups in the assembly of nanostructures is identified, along with the importance of steric effects on the packing of the peptides within assemblies.

Machine learning coarse-grained potentials of protein thermodynamics

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

Host Cell Membrane Capture by the SARS-CoV-2 Spike Protein Fusion Intermediate

Cell entry by SARS-CoV-2 is accomplished by the S2 subunit of the spike S protein on the virion surface by capture of the host cell membrane and fusion with the viral envelope. Capture and fusion require the prefusion S2 to transit to its potent fusogenic form, the fusion intermediate (FI). However, the FI structure is unknown, detailed computational models of the FI are unavailable, and the mechanisms and timing of membrane capture and fusion are not established. Here, we constructed a full-length model of the SARS-CoV-2 FI by extrapolating from known SARS-CoV-2 pre- and postfusion structures. In atomistic and coarse-grained molecular dynamics simulations the FI was remarkably flexible and executed giant bending and extensional fluctuations due to three hinges in the C-terminal base. The simulated configurations and their giant fluctuations are quantitatively consistent with SARS-CoV-2 FI configurations measured recently using cryo-electron tomography. Simulations suggested a host cell membrane capture time of ∼2 ms. Isolated fusion peptide simulations identified an N-terminal helix that directed and maintained binding to the membrane but grossly underestimated the binding time, showing that the fusion peptide environment is radically altered when attached to its host fusion protein. The large configurational fluctuations of the FI generated a substantial exploration volume that aided capture of the target membrane, and may set the waiting time for fluctuation-triggered refolding of the FI that draws the viral envelope and host cell membrane together for fusion. These results describe the FI as machinery that uses massive configurational fluctuations for efficient membrane capture and suggest novel potential drug targets.

Machine learned coarse-grained protein force-fields: Are we there yet?

The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges.

A hybrid approach for coarse-graining helical peptoids: Solvation, secondary structure, and assembly

Protein mimics such as peptoids form self-assembled nanostructures whose shape and function are governed by the side chain chemistry and secondary structure. Experiments have shown that a peptoid sequence with a helical secondary structure assembles into microspheres that are stable under various conditions. The conformation and organization of the peptoids within the assemblies remains unknown and is elucidated in this study via a hybrid, bottom-up coarse-graining approach. The resultant coarse-grained (CG) model preserves the chemical and structural details that are critical for capturing the secondary structure of the peptoid. The CG model accurately captures the overall conformation and solvation of the peptoids in an aqueous solution. Furthermore, the model resolves the assembly of multiple peptoids into a hemispherical aggregate that is in qualitative agreement with the corresponding results from experiments. The mildly hydrophilic peptoid residues are placed along the curved interface of the aggregate. The composition of the residues on the exterior of the aggregate is determined by two conformations adopted by the peptoid chains. Hence, the CG model simultaneously captures sequence-specific features and the assembly of a large number of peptoids. This multiscale, multiresolution coarse-graining approach could help in predicting the organization and packing of other tunable oligomeric sequences of relevance to biomedicine and electronics.

Accurate and Efficient Estimation of Lennard-Jones Interactions for Coarse-Grained Particles via a Potential Matching Method

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

Key aspects of the past 30 years of protein design

Proteins are the workhorse of life. They are the building infrastructure of living systems; they are the most efficient molecular machines known, and their enzymatic activity is still unmatched in versatility by any artificial system. Perhaps proteins' most remarkable feature is their modularity. The large amount of information required to specify each protein's function is analogically encoded with an alphabet of just ∼20 letters. The protein folding problem is how to encode all such information in a sequence of 20 letters. In this review, we go through the last 30 years of research to summarize the state of the art and highlight some applications related to fundamental problems of protein evolution.

A hybrid coarse-grained model for structure, solvation and assembly of lipid-like peptides

Reconstituted photosynthetic proteins which are activated upon exposure to solar energy hold enormous potential for powering future solid state devices and solar cells. The functionality and integration of these proteins into such devices has been successfully enabled by lipid-like peptides. Yet, a fundamental understanding of the organization of these peptides with respect to the photosynthetic proteins and themselves remains unknown and is critical for guiding the design of such light-activated devices. This study investigates the relative organization of one such peptide sequence V₆K₂ (V: valine and K: lysine) within assemblies. Given the expansive spatiotemporal scales associated with this study, a hybrid coarse-grained (CG) model which captures the structure, conformation and aggregation of the peptide is adopted. The CG model uses a combination of iterative Boltzmann inversion and force matching to provide insight into the relative organization of V₆K₂ in assemblies. The CG model reproduces the structure of a V₆K₂ peptide sequence along with its all atom (AA) solvation structure. The relative organization of multiple peptides in an assembly, as captured by CG simulations, is in agreement with corresponding results from AA simulations. Also, a backmapping procedure reintroduces the AA details of the peptides within the aggregates captured by the CG model to demonstrate the relative organization of the peptides. Furthermore, a large number of peptides self-assemble into an elongated micelle in the CG simulation, which is consistent with experimental findings. The coarse-graining procedure is tested for transferability to longer peptide sequences, and hence can be extended to other amphiphilic peptide sequences.

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.

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy

Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π-π and hybrid cation-π/π-π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in-vitro phase diagrams; Mpipi predictions agree well with experiment on both fronts. Moreover, it can account for protein-RNA interactions, correctly predicts the multiphase behaviour of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental LLPS trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

Artificial Intelligence for Accelerating Time Integrations in Multiscale Modeling

We developed a novel data-driven Artificial Intelligence-enhanced Adaptive Time Stepping algorithm (AI-ATS) that can adapt timestep sizes to underlying biophysical dynamics. We demonstrated its values in solving a complex biophysical problem, at multiple spatiotemporal scales, that describes platelet dynamics in shear blood flow. In order to achieve a significant speedup of this computationally demanding problem, we integrated a framework of novel AI algorithms into the solution of the platelet dynamics equations. Our framework involves recurrent neural network-based autoencoders by the Long Short-Term Memory and the Gated Recurrent Units as the first step for memorizing the dynamic states in long-term dependencies for the input time series, followed by two fully-connected neural networks to optimize timestep sizes and step jumps. The computational efficiency of our AI-ATS is underscored by assessing the accuracy and speed of a multiscale simulation of the platelet with the standard time stepping algorithm (STS). By adapting the timestep size, our AI-ATS guides the omission of multiple redundant time steps without sacrificing significant accuracy of the dynamics. Compared to the STS, our AI-ATS achieved a reduction of 40% unnecessary calculations while bounding the errors of mechanical and thermodynamic properties to 3%.

Sampling of the conformational landscape of small proteins with Monte Carlo methods

Computer simulation provides an increasingly realistic picture of large-scale conformational change of proteins, but investigations remain fundamentally constrained by the femtosecond timestep of molecular dynamics simulations. For this reason, many biologically interesting questions cannot be addressed using accessible state-of-the-art computational resources. Here, we report the development of an all-atom Monte Carlo approach that permits the modelling of the large-scale conformational change of proteins using standard off-the-shelf computational hardware and standard all-atom force fields. We demonstrate extensive thermodynamic characterization of the folding process of the α-helical Trp-cage, the Villin headpiece and the β-sheet WW-domain. We fully characterize the free energy landscape, transition states, energy barriers between different states, and the per-residue stability of individual amino acids over a wide temperature range. We demonstrate that a state-of-the-art intramolecular force field can be combined with an implicit solvent model to obtain a high quality of the folded structures and also discuss limitations that still remain.

Molecular dynamics simulations in photosynthesis

Photosynthesis is regulated by a dynamic interplay between proteins, enzymes, pigments, lipids, and cofactors that takes place on a large spatio-temporal scale. Molecular dynamics (MD) simulations provide a powerful toolkit to investigate dynamical processes in (bio)molecular ensembles from the (sub)picosecond to the (sub)millisecond regime and from the Å to hundreds of nm length scale. Therefore, MD is well suited to address a variety of questions arising in the field of photosynthesis research. In this review, we provide an introduction to the basic concepts of MD simulations, at atomistic and coarse-grained level of resolution. Furthermore, we discuss applications of MD simulations to model photosynthetic systems of different sizes and complexity and their connection to experimental observables. Finally, we provide a brief glance on which methods provide opportunities to capture phenomena beyond the applicability of classical MD.

Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning

Accompanied with an increase of revealed biomolecular structures owing to advancements in structural biology, the molecular dynamics (MD) approach, especially coarse-grained (CG) MD suitable for macromolecules, is becoming increasingly important for elucidating their dynamics and behavior. In fact, CG-MD simulation has succeeded in qualitatively reproducing numerous biological processes for various biomolecules such as conformational changes and protein folding with reasonable calculation costs. However, CG-MD simulations strongly depend on various parameters, and selecting an appropriate parameter set is necessary to reproduce a particular biological process. Because exhaustive examination of all candidate parameters is inefficient, it is important to identify successful parameters. Furthermore, the successful region, in which the desired process is reproducible, is essential for describing the detailed mechanics of functional processes and environmental sensitivity and robustness. We propose an efficient search method for identifying the successful region by using two machine learning techniques, Bayesian optimization and active learning. We evaluated its performance using F1-ATPase, a biological rotary motor, with CG-MD simulations. We successfully identified the successful region with lower computational costs (12.3% in the best case) without sacrificing accuracy compared to exhaustive search. This method can accelerate not only parameter search but also biological discussion of the detailed mechanics of functional processes and environmental sensitivity based on MD simulation studies.

Identification of native protein structures captured by principal interactions

Background

Evaluation of protein structure is based on trustworthy potential function. The total potential of a protein structure is approximated as the summation of all pair-wise interaction potentials. Knowledge-based potentials (KBP) are one type of potential functions derived by known experimentally determined protein structures. Although several KBP functions with different methods have been introduced, the key interactions that capture the total potential have not studied yet.

Results

In this study, we seek the interaction types that preserve as much of the total potential as possible. We employ a procedure based on the principal component analysis (PCA) to extract the significant and key interactions in native protein structures. We call these interactions as principal interactions and show that the results of the model that considers only these interactions are very close to the full interaction model that considers all interactions in protein fold recognition. In fact, the principal interactions maintain the discriminative power of the full interaction model. This method was evaluated on 3 KBPs with different contact definitions and thresholds of distance and revealed that their corresponding principal interactions are very similar and have a lot in common. Additionally, the principal interactions consisted of 20 % of the full interactions on average, and they are between residues, which are considered important in protein folding.

Conclusions

This work shows that all interaction types are not equally important in discrimination of native structure. The results of the reduced model based on principal interactions that were very close to the full interaction model suggest that a new strategy is needed to capture the role of remaining interactions (non-principal interactions) to improve the power of knowledge-based potential functions.

MARTINI-Based Protein-DNA Coarse-Grained HADDOCKing

Modeling biomolecular assemblies is an important field in computational structural biology. The inherent complexity of their energy landscape and the computational cost associated with modeling large and complex assemblies are major drawbacks for integrative modeling approaches. The so-called coarse-graining approaches, which reduce the degrees of freedom of the system by grouping several atoms into larger “pseudo-atoms,” have been shown to alleviate some of those limitations, facilitating the identification of the global energy minima assumed to correspond to the native state of the complex, while making the calculations more efficient. Here, we describe and assess the implementation of the MARTINI force field for DNA into HADDOCK, our integrative modeling platform. We combine it with our previous implementation for protein-protein coarse-grained docking, enabling coarse-grained modeling of protein-nucleic acid complexes. The system is modeled using MARTINI topologies and interaction parameters during the rigid body docking and semi-flexible refinement stages of HADDOCK, and the resulting models are then converted back to atomistic resolution by an atom-to-bead distance restraints-guided protocol. We first demonstrate the performance of this protocol using 44 complexes from the protein-DNA docking benchmark, which shows an overall ~6-fold speed increase and maintains similar accuracy as compared to standard atomistic calculations. As a proof of concept, we then model the interaction between the PRC1 and the nucleosome (a former CAPRI target in round 31), using the same information available at the time the target was offered, and compare all-atom and coarse-grained models.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

The SIRAH 2.0 Force Field: Altius, Fortius, Citius

A new version of the coarse-grained (CG) SIRAH force field for proteins has been developed. Modifications to bonded and non-bonded interactions on the existing molecular topologies significantly ameliorate the structural description and flexibility of a non-redundant set of proteins. The SIRAH 2.0 force field has also been ported to the popular simulation package AMBER, which along with the former implementation in GROMACS expands significantly the potential range of users and performance of this CG force field on CPU/GPU codes. As a non-trivial example of its application, we undertook the structural and dynamical analysis of the most abundant and conserved calcium-binding protein, calmodulin (CaM). CaM is composed of two calcium-binding motifs called EF-hands, which in the presence of calcium specifically recognize a cognate peptide by embracing it. CG simulations of CaM bound to four calcium ions in the presence or absence of a binding peptide (holo and apo forms, respectively) resulted in good and stable ion coordination. The simulation of the holo form starting from an experimental structure sampled near-native conformations, retrieving quasi-atomistic precision. Removing the binding peptide enabled the EF-hands to perform large reciprocal movements, comparable to those observed in NMR structures. On the other hand, the isolated peptide starting from the helical conformation experienced spontaneous unfolding, in agreement with previous experimental data. However, repositioning the peptide in the neighborhood of one EF-hand not only prevented the peptide from unfolding but also drove CaM to a fully bound conformation, with both EF-hands embracing the cognate peptide, resembling the experimental holo structure. Therefore, SIRAH 2.0 shows the capacity to handle a number of structurally and dynamically challenging situations, including metal ion coordination, unbiased conformational sampling, and specific protein-peptide recognition.

Conformational preferences and phase behavior of intrinsically disordered low complexity sequences: insights from multiscale simulations

While many proteins and protein regions utilize a complex repertoire of amino acids to achieve their biological function, a subset of protein sequences are enriched in a reduced set of amino acids. These so-called low complexity (LC) sequences, specifically intrinsically disordered variants of LC sequences, have been the focus of recent investigations owing to their roles in a range of biological functions, specifically phase separation. Computational studies of LC sequences have provided rich insights into their behavior both as individual proteins in dilute solutions and as the drivers and modulators of higher-order assemblies. Here, we review how simulations performed across distinct resolutions have provided different types of insights into the biological role of LC sequences.

Molecular Mechanism of Uptake of Cationic Photoantimicrobial Phthalocyanine across Bacterial Membranes Revealed by Molecular Dynamics Simulations

Phthalocyanines are aromatic macrocyclic compounds, which are structurally related to porphyrins. In clinical practice, phthalocyanines are used in fluorescence imaging and photodynamic therapy of cancer and noncancer lesions. Certain forms of the substituted polycationic metallophthalocyanines have been previously shown to be active in photodynamic inactivation of both Gram-negative and Gram-positive bacteria; one of them is zinc octakis(cholinyl)phthalocyanine (ZnPcChol⁸⁺). However, the molecular details of how these compounds translocate across bacterial membranes still remain unclear. In the present work, we have developed a coarse-grained (CG) molecular model of ZnPcChol⁸⁺ within the framework of the popular MARTINI CG force field. The obtained model was used to probe the solvation behavior of phthalocyanine molecules, which agreed with experimental results. Subsequently, it was used to investigate the molecular details of interactions between phthalocyanines and membranes of various compositions. The results demonstrate that ZnPcChol⁸⁺ has high affinity to both the inner and the outer model membranes of Gram-negative bacteria, although this species does not show noticeable affinity to the 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphatidylcholine membrane. Furthermore, we found out that the process of ZnPcChol⁸⁺ penetration toward the center of the outer bacterial membrane is energetically favorable and leads to its overall disturbance and formation of the aqueous pore. Such intramembrane localization of ZnPcChol⁸⁺ suggests their twofold cytotoxic effect on bacterial cells: (1) via induction of lipid peroxidation by enhanced production of reactive oxygen species (i.e., photodynamic toxicity); (2) via rendering the bacterial membrane more permeable for additional Pc molecules as well as other compounds. We also found that the kinetics of penetration depends on the presence of phospholipid defects in the lipopolysaccharide leaflet of the outer membrane and the type of counterions, which stabilize it. Thus, the results of our simulations provide a detailed molecular view of ZnPcChol⁸⁺ "self-promoted uptake", the pathway previously proposed for some small molecules crossing the outer bacterial membrane.

Refining amino acid hydrophobicity for dynamics simulation of membrane proteins

Coarse-grained (CG) models have been successful in simulating the chemical properties of lipid bilayers, but accurate treatment of membrane proteins and lipid-protein molecular interactions remains a challenge. The CgProt force field, original developed with the multiscale coarse graining method, is assessed by comparing the potentials of mean force for sidechain insertion in a DOPC bilayer to results reported for atomistic molecular dynamics simulations. Reassignment of select CG sidechain sites from the apolar to polar site type was found to improve the attractive interfacial behavior of tyrosine, phenylalanine and asparagine as well as charged lysine and arginine residues. The solvation energy at membrane depths of 0, 1.3 and 1.7 nm correlates with experimental partition coefficients in aqueous mixtures of cyclohexane, octanol and POPC, respectively, for sidechain analogs and Wimley-White peptides. These experimental values serve as important anchor points in choosing between alternate CG models based on their observed permeation profiles, particularly for Arg, Lys and Gln residues where the all-atom OPLS solvation energy does not agree well with experiment. Available partitioning data was also used to reparameterize the representation of the peptide backbone, which needed to be made less attractive for the bilayer hydrophobic core region. The newly developed force field, CgProt 2.4, correctly predicts the global energy minimum in the potentials of mean force for insertion of the uncharged membrane-associated peptides LS3 and WALP23. CgProt will find application in studies of lipid-protein interactions and the conformational properties of diverse membrane protein systems.

Computational protein design: a review

Proteins are one of the most versatile modular assembling systems in nature. Experimentally, more than 110 000 protein structures have been identified and more are deposited every day in the Protein Data Bank. Such an enormous structural variety is to a first approximation controlled by the sequence of amino acids along the peptide chain of each protein. Understanding how the structural and functional properties of the target can be encoded in this sequence is the main objective of protein design. Unfortunately, rational protein design remains one of the major challenges across the disciplines of biology, physics and chemistry. The implications of solving this problem are enormous and branch into materials science, drug design, evolution and even cryptography. For instance, in the field of drug design an effective computational method to design protein-based ligands for biological targets such as viruses, bacteria or tumour cells, could give a significant boost to the development of new therapies with reduced side effects. In materials science, self-assembly is a highly desired property and soon artificial proteins could represent a new class of designable self-assembling materials. The scope of this review is to describe the state of the art in computational protein design methods and give the reader an outline of what developments could be expected in the near future.

Pipeline for inferring protein function from dynamics using coarse-grained molecular mechanics forcefield

Dynamics is integral to the function of proteins, yet the use of molecular dynamics (MD) simulation as a technique remains under-explored for molecular function inference. This is more important in the context of genomics projects where novel proteins are determined with limited evolutionary information. Recently we developed a method to match the query protein's flexible segments to infer function using a novel approach combining analysis of residue fluctuation-graphs and auto-correlation vectors derived from coarse-grained (CG) MD trajectory. The method was validated on a diverse dataset with sequence identity between proteins as low as 3%, with high function-recall rates. Here we share its implementation as a publicly accessible web service, named DynFunc (Dynamics Match for Function) to query protein function from ≥1 µs long CG dynamics trajectory information of protein subunits. Users are provided with the custom-developed coarse-grained molecular mechanics (CGMM) forcefield to generate the MD trajectories for their protein of interest. On upload of trajectory information, the DynFunc web server identifies specific flexible regions of the protein linked to putative molecular function. Our unique application does not use evolutionary information to infer molecular function from MD information and can, therefore, work for all proteins, including moonlighting and the novel ones, whenever structural information is available. Our pipeline is expected to be of utility to all structural biologists working with novel proteins and interested in moonlighting functions.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Cooperative Interactions between Different Classes of Disordered Proteins Play a Functional Role in the Nuclear Pore Complex of Baker's Yeast

Nucleocytoplasmic transport is highly selective, efficient, and is regulated by a poorly understood mechanism involving hundreds of disordered FG nucleoporin proteins (FG nups) lining the inside wall of the nuclear pore complex (NPC). Previous research has concluded that FG nups in Baker's yeast (S. cerevisiae) are present in a bimodal distribution, with the "Forest Model" classifying FG nups as either di-block polymer like "trees" or single-block polymer like "shrubs". Using a combination of coarse-grained modeling and polymer brush modeling, the function of the di-block FG nups has previously been hypothesized in the Di-block Copolymer Brush Gate (DCBG) model to form a higher-order polymer brush architecture which can open and close to regulate transport across the NPC. In this manuscript we work to extend the original DCBG model by first performing coarse grained simulations of the single-block FG nups which confirm that they have a single block polymer structure rather than the di-block structure of tree nups. Our molecular simulations also demonstrate that these single-block FG nups are likely cohesive, compact, collapsed coil polymers, implying that these FG nups are generally localized to their grafting location within the NPC. We find that adding a layer of single-block FG nups to the DCBG model increases the range of cargo sizes which are able to translocate the pore through a cooperative effect involving single-block and di-block FG nups. This effect can explain the puzzling connection between single-block FG nup deletion mutants in S. cerevisiae and the resulting failure of certain large cargo transport through the NPC. Facilitation of large cargo transport via single-block and di-block FG nup cooperativity in the nuclear pore could provide a model mechanism for designing future biomimetic pores of greater applicability.

Calculation of Enzyme Fluctuograms from All-Atom Molecular Dynamics Simulation

In this work, a computational framework is presented to compute the time evolution of force constants for a coarse grained (CG) elastic network model along an all-atom molecular dynamics trajectory of a protein system. Obtained via matching distance fluctuations, these force constants represent strengths of mechanical coupling between CG beads. Variation of coupling strengths with time is hence termed the fluctuogram of protein dynamics. In addition to the schematic procedure and implementation considerations, several ways of combining force constants and data analysis are presented to illustrate the potential application of protein fluctuograms. The unique angle provided by the fluctuogram expands the scope of atomistic simulations and is expected to impact upon fundamental understanding of protein dynamics as well as protein engineering technologies.

Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome's Facet

Bacterial microcompartments, BMCs, are organelles that exist within wide variety of bacteria and act as nanofactories. Among the different types of known BMCs, the carboxysome has been studied the most. The carboxysome plays an important role in the light-independent part of the photosynthesis process, where its icosahedral-like proteinaceous shell acts as a membrane that controls the transport of metabolites. Although a structural model exists for the carboxysome shell, it remains largely unknown how the shell proteins self-assemble. Understanding the self-assembly process can provide insights into how the shell affects the carboxysome's function and how it can be modified to create new functionalities, such as artificial nanoreactors and artificial protein membranes. Here, we describe a theoretical framework that employs Monte Carlo simulations with a coarse-grain potential that reproduces well the atomistic potential of mean force; employing this framework, we are able to capture the initial stages of the 2D self-assembly of CcmK2 hexamers, a major protein-shell component of the carboxysome's facet. The simulations reveal that CcmK2 hexamers self-assemble into clusters that resemble what was seen experimentally in 2D layers. Further analysis of the simulation results suggests that the 2D self-assembly of carboxysome's facets is driven by a nucleation-growth process, which in turn could play an important role in the hierarchical self-assembly of BMC shells in general.

The multiscale coarse-graining method. XI. Accurate interactions based on the centers of charge of coarse-grained sites

It is essential to be able to systematically construct coarse-grained (CG) models that can efficiently and accurately reproduce key properties of higher-resolution models such as all-atom. To fulfill this goal, a mapping operator is needed to transform the higher-resolution configuration to a CG configuration. Certain mapping operators, however, may lose information related to the underlying electrostatic properties. In this paper, a new mapping operator based on the centers of charge of CG sites is proposed to address this issue. Four example systems are chosen to demonstrate this concept. Within the multiscale coarse-graining framework, CG models that use this mapping operator are found to better reproduce the structural correlations of atomistic models. The present work also demonstrates the flexibility of the mapping operator and the robustness of the force matching method. For instance, important functional groups can be isolated and emphasized in the CG model.

Model parameters for simulation of physiological lipids

Coarse grain simulation of proteins in their physiological membrane environment can offer insight across timescales, but requires a comprehensive force field. Parameters are explored for multicomponent bilayers composed of unsaturated lipids DOPC and DOPE, mixed-chain saturation POPC and POPE, and anionic lipids found in bacteria: POPG and cardiolipin. A nonbond representation obtained from multiscale force matching is adapted for these lipids and combined with an improved bonding description of cholesterol. Equilibrating the area per lipid yields robust bilayer simulations and properties for common lipid mixtures with the exception of pure DOPE, which has a known tendency to form nonlamellar phase. The models maintain consistency with an existing lipid-protein interaction model, making the force field of general utility for studying membrane proteins in physiologically representative bilayers.

CAMELOT: A machine learning approach for coarse-grained simulations of aggregation of block-copolymeric protein sequences

We report the development and deployment of a coarse-graining method that is well suited for computer simulations of aggregation and phase separation of protein sequences with block-copolymeric architectures. Our algorithm, named CAMELOT for Coarse-grained simulations Aided by MachinE Learning Optimization and Training, leverages information from converged all atom simulations that is used to determine a suitable resolution and parameterize the coarse-grained model. To parameterize a system-specific coarse-grained model, we use a combination of Boltzmann inversion, non-linear regression, and a Gaussian process Bayesian optimization approach. The accuracy of the coarse-grained model is demonstrated through direct comparisons to results from all atom simulations. We demonstrate the utility of our coarse-graining approach using the block-copolymeric sequence from the exon 1 encoded sequence of the huntingtin protein. This sequence comprises of 17 residues from the N-terminal end of huntingtin (N17) followed by a polyglutamine (polyQ) tract. Simulations based on the CAMELOT approach are used to show that the adsorption and unfolding of the wild type N17 and its sequence variants on the surface of polyQ tracts engender a patchy colloid like architecture that promotes the formation of linear aggregates. These results provide a plausible explanation for experimental observations, which show that N17 accelerates the formation of linear aggregates in block-copolymeric N17-polyQ sequences. The CAMELOT approach is versatile and is generalizable for simulating the aggregation and phase behavior of a range of block-copolymeric protein sequences.