Double-Well Ultra-Coarse-Grained Model to Describe Protein Conformational Transitions

A double-well potential model for glass transition in a glassy hydrogel undergoing bi-stable interactions with water

The key mechanisms for achieving ultra-high mechanical properties of glassy hydrogels have not been fully understood, and it is commonly believed that their glass transitions are the crucial reasons due to the existence of significant bi-stable interactions between polymer macromolecules and water molecules. In this study, a double-well potential model is formulated to describe the mechanical properties of glassy hydrogels undergoing glass transition, by combining phase evolution theory and a rubber elasticity model. Bi-stable interactions between polymer macromolecules and water molecules (for both the trapped and free water) have been characterized using this double-well potential model, and various parameters are studied, including depth of well (for elasticity), distance between two wells (for yielding), and energy difference between two wells (for transition probability). Furthermore, constitutive stress-strain relationships are developed to explore the working principles for achieving ultra-high mechanical properties of these glassy hydrogels. Finally, the effectiveness of the proposed models is verified using finite element analysis (FEA) and also the experimental results reported in the literature, thus providing physical and mechanical insights into the ultra-high mechanical properties of glassy hydrogels.

Developing Hybrid All-Atom and Ultra-Coarse-Grained Models to Investigate Taxol-Binding and Dynein Interactions on Microtubules

Simulating the conformations and functions of biological macromolecules by using all-atom (AA) models is a challenging task due to expensive computational costs. One possible strategy to solve this problem is to develop hybrid all-atom and ultra-coarse-grained (AA/UCG) models of the biological macromolecules. In the AA/UCG scheme, the interest regions are described by AA models, while the other regions are described in the UCG representation. In this study, we develop the hybrid AA/UCG models and apply them to investigate the conformational changes of microtubule-bound tubulins. The simulation results of the hybrid models elucidated the mechanism of why the taxol molecules selectively bound microtubules but not tubulin dimers. In addition, we also explore the interactions of the microtubules and dyneins. Our study shows that the hybrid AA/UCG model has great application potential in studying the function of complex biological systems.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

From quantum-derived principles underlying cysteine reactivity to combating the COVID-19 pandemic

The COVID-19 pandemic poses a challenge in coming up with quick and effective means to counter its cause, the SARS-CoV-2. Here, we show how the key factors governing cysteine reactivity in proteins derived from combined quantum mechanical/continuum calculations led to a novel multi-targeting strategy against SARS-CoV-2, in contrast to developing potent drugs/vaccines against a single viral target such as the spike protein. Specifically, they led to the discovery of reactive cysteines in evolutionary conserved Zn2+-sites in several SARS-CoV-2 proteins that are crucial for viral polypeptide proteolysis as well as viral RNA synthesis, proofreading, and modification. These conserved, reactive cysteines, both free and Zn2+-bound, can be targeted using the same Zn-ejector drug (disulfiram/ebselen), which enables the use of broad-spectrum anti-virals that would otherwise be removed by the virus's proofreading mechanism. Our strategy of targeting multiple, conserved viral proteins that operate at different stages of the virus life cycle using a Zn-ejector drug combined with other broad-spectrum anti-viral drug(s) could enhance the barrier to drug resistance and antiviral effects, as compared to each drug alone. Since these functionally important nonstructural proteins containing reactive cysteines are highly conserved among coronaviruses, our proposed strategy has the potential to tackle future coronaviruses. This article is categorized under:Structure and Mechanism > Reaction Mechanisms and CatalysisStructure and Mechanism > Computational Biochemistry and BiophysicsElectronic Structure Theory > Density Functional Theory.

Coarse-Grained Water Model Development for Accurate Dynamics and Structure Prediction

Several coarse-graining (CG) methods have been combined to develop a CG model of water capable of the accurate prediction of structure and dynamics properties. The multiscale coarse-graining (MS-CG) method based on force matching and the PDF-based coarse-graining method were used for accurate dynamics prediction. The iterative Boltzmann inversion (IBI) method was added for accurate structure representation. The approach is applied to bulk water, and the results show close reproduction of the CG structure when compared with the reference atomistic data. The combination of MS-CG and IBI methods facilitates the development of CG force fields at different temperatures based on a single MS-CG coarse-graining procedure. The dynamic properties of the CG water model closely match those obtained from the reference atomistic system. The general application of this approach to any existing coarse-graining methods is discussed.

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.

Exploring the Binding Mechanism of a Supramolecular Tweezer CLR01 to 14-3-3σ Protein via Well-Tempered Metadynamics

Using supramolecules for protein function regulation is an effective strategy in chemical biology and drug discovery. However, due to the presence of multiple binding sites on protein surfaces, protein function regulation via selective binding of supramolecules is challenging. Recently, the functions of 14-3-3 proteins, which play an important role in regulating intracellular signaling pathways via protein–protein interactions, have been modulated using a supramolecular tweezer, CLR01. However, the binding mechanisms of the tweezer molecule to 14-3-3 proteins are still unclear, which has hindered the development of novel supramolecules targeting the 14-3-3 proteins. Herein, the binding mechanisms of the tweezer to the lysine residues on 14-3-3σ (an isoform in 14-3-3 protein family) were explored by well-tempered metadynamics. The results indicated that the inclusion complex formed between the protein and supramolecule is affected by both kinetic and thermodynamic factors. In particular, simulations confirmed that K214 could form a strong binding complex with the tweezer; the binding free energy was calculated to be −10.5 kcal·mol⁻¹ with an association barrier height of 3.7 kcal·mol⁻¹. In addition, several other lysine residues on 14-3-3σ were identified as being well-recognized by the tweezer, which agrees with experimental results, although only K214/tweezer was co-crystallized. Additionally, the binding mechanisms of the tweezer to all lysine residues were analyzed by exploring the representative conformations during the formation of the inclusion complex. This could be helpful for the development of new inhibitors based on tweezers with more functions against 14-3-3 proteins via modifications of CLR01. We also believe that the proposed computational strategies can be extended to understand the binding mechanism of multi-binding sites proteins with supramolecules and will, thus, be useful toward drug design.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Binding mechanism of inhibitors to p38α MAP kinase deciphered by using multiple replica Gaussian accelerated molecular dynamics and calculations of binding free energies

The p38α MAP Kinase has been an important target of drug design for treatment of inflammatory diseases and cancers. This work applies multiple replica Gaussian accelerated molecular dynamics (MR-GaMD) simulations and the molecular mechanics generalized Born surface area (MM-GBSA) method to probe the binding mechanism of inhibitors L51, R24 and 1AU to p38α. Dynamics analyses show that inhibitor bindings exert significant effect on conformational changes of the active helix α2 and the conserved DFG loop. The rank of binding free energies calculated with MM-GBSA not only agrees well with that determined by the experimental IC50 values but also suggests that mutual compensation between the enthalpy and entropy changes can improve binding of inhibitors to p38α. The analyses of free energy landscapes indicate that the L51, R24 and 1AU bound p38α display a DFG-out conformation. The residue-based free energy decomposition method is used to evaluate contributions of separate residues to the inhibitor-p38α binding and the results imply that residues V30, V38, L74, L75, I84, T106, H107, L108, M109, L167, F169 and D168 can be utilized as efficient targets of potent inhibitors toward p38α.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Mutation-Induced Impacts on the Switch Transformations of the GDP- and GTP-Bound K-Ras: Insights from Multiple Replica Gaussian Accelerated Molecular Dynamics and Free Energy Analysis

Mutations yield significant effect on the structural flexibility of two switch domains, SW1 and SW2, in K-Ras, which is considered as an important target of anticancer drug design. To unveil a molecular mechanism with regard to mutation-mediated tuning on the activity of K-Ras, multiple replica Gaussian accelerated molecular dynamics (MR-GaMD) simulations followed by analysis of free energy landscapes (FELs) are performed on the GDP- and GTP-bound wild-type (WT), G12V, and D33E K-Ras. The results suggest that G12V and D33E not only evidently change the flexibility of SW1 and SW2 but also greatly affect correlated motions of SW1 and SW2 separately relative to the P-loop and SW1, which exerts a certain tuning on the activity of K-Ras. The information stemming from the analyses of FELs reveals that the conformations of SW1 and SW2 are in high disorders in the GDP- and GTP-associated WT and mutated K-Ras, possibly producing significant effect on binding of guanine nucleotide exchange factors or effectors to K-Ras. The interaction networks of GDP and GTP with K-Ras are identified and the results uncover that the instability in hydrogen-bonding interactions of SW1 with GDP and GTP is mostly responsible for conformational disorder of SW1 and SW2 as well as tunes the activity of oncogenic K-Ras.

Optimizing Gō-MARTINI Coarse-Grained Model for F-BAR Protein on Lipid Membrane

Coarse-grained (CG) molecular dynamics (MD) simulations allow us to access much larger length and time scales than atomistic MD simulations, providing an attractive alternative to the conventional simulations. Based on the well-known MARTINI CG force field, the recently developed Gō-MARTINI model for proteins describes large-amplitude structural dynamics, which has not been possible with the commonly used elastic network model. Using the Gō-MARTINI model, we conduct MD simulations of the F-BAR Pacsin1 protein on lipid membrane. We observe that structural changes of the non-globular protein are largely dependent on the definition of the native contacts in the Gō model. To address this issue, we introduced a simple cutoff scheme and tuned the cutoff distance of the native contacts and the interaction strength of the Lennard-Jones potentials in the Gō-MARTINI model. With the optimized Gō-MARTINI model, we show that it reproduces structural fluctuations of the Pacsin1 dimer from atomistic simulations. We also show that two Pacsin1 dimers properly assemble through lateral interaction on the lipid membrane. Our work presents a first step towards describing membrane remodeling processes in the Gō-MARTINI CG framework by simulating a crucial step of protein assembly on the membrane.

Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.