Effects of surface water on protein dynamics studied by a novel coarse-grained normal mode approach

Coarse-Graining Waters: Unveiling The Effective Hydrophilicity/Hydrophobicity of Individual Protein Atoms and The Roles of Waters' Hydrogens

There have been many coarse-graining methods developed that aim to reduce the sizes of simulated systems and their computational costs. In this work, we develop a new coarse-graining method, called coarse-graining-delta (or δ-CG in short), that reduces the degrees of freedom of the potential energy surface by coarse-graining relative locations of atoms from their unit centers. Our method extends and generalizes the methods used in the coarse-grained normal mode analysis and enables us to study the roles of the individual removed atoms in a system, which have been difficult to study in molecular dynamics simulations. By applying δ-CG to coarse-grain three-point water molecules into single-point solvent particles, we successfully identify the effective hydrophilicity and hydrophobicity of all the individual protein atom types, which collectively correlate well with the known hydrophilic, hydrophobic, and amphipathic characteristics of amino acids. Moreover, our investigation shows that water's hydrogens have two roles in interacting with protein atoms. First, water molecules adjust their poses around different amino acids and their atoms, and the statistical preferences of the hydrogen poses near the atoms determine the effective hydrophilicity and hydrophobicity of the atoms, which have not been successfully addressed before. Second, the collective dynamics of the hydrogens assist the water molecules in escaping from the potential energy wells of the hydrophilic atoms. Our method also shows that coarse-graining a system mathematically leads to breaking antisymmetry of the nonbonded interactions; as a result, two interacting coarse-grained units exert different forces on each other. Our study indicates that the accuracy of coarse-grained force fields, such as the MARTINI force field and the UNRES force field, can be improved in two ways: (i) refining their potential energy functions and coefficients by analyzing the coarse-grained potential energy surface using δ-CG, and (ii) introducing non-antisymmetric interactions.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules

Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C _α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

Mitochondrial Ca(2+) uptake in skeletal muscle health and disease

Muscle uses Ca²⁺ as a messenger to control contraction and relies on ATP to maintain the intracellular Ca²⁺ homeostasis. Mitochondria are the major sub-cellular organelle of ATP production. With a negative inner membrane potential, mitochondria take up Ca²⁺ from their surroundings, a process called mitochondrial Ca²⁺ uptake. Under physiological conditions, Ca²⁺ uptake into mitochondria promotes ATP production. Excessive uptake causes mitochondrial Ca²⁺ overload, which activates downstream adverse responses leading to cell dysfunction. Moreover, mitochondrial Ca²⁺ uptake could shape spatio-temporal patterns of intracellular Ca²⁺ signaling. Malfunction of mitochondrial Ca²⁺ uptake is implicated in muscle degeneration. Unlike non-excitable cells, mitochondria in muscle cells experience dramatic changes of intracellular Ca²⁺ levels. Besides the sudden elevation of Ca²⁺ level induced by action potentials, Ca²⁺ transients in muscle cells can be as short as a few milliseconds during a single twitch or as long as minutes during tetanic contraction, which raises the question whether mitochondrial Ca²⁺ uptake is fast and big enough to shape intracellular Ca²⁺ signaling during excitation-contraction coupling and creates technical challenges for quantification of the dynamic changes of Ca²⁺ inside mitochondria. This review focuses on characterization of mitochondrial Ca²⁺ uptake in skeletal muscle and its role in muscle physiology and diseases.

Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models

Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations—how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Proteins and other biomolecules are not static but are constantly in motion. Moreover, they possess intrinsic collective motion patterns that are tightly linked to their functions. Thus, an accurate and detailed description of their motions can provide deep insights into their functional mechanisms. For large protein complexes with hundreds of thousands of atoms or more, an atomic level description of the motions can be computationally prohibitive, and so coarse-grained models with fewer structural details are often used instead. However, there can be a big gap between the quality of motions derived from atomic models and those from coarse-grained models. In this work, we solve an important problem in protein dynamics studies: how to preserve the atomic-level accuracy in describing molecular motions while using coarse-grained models? We accomplish this by developing a novel iterative matrix projection method that dramatically speeds up the computations. This method is significant since it promises accurate descriptions of protein motions approaching an all-atom level even for the largest biomolecular complexes. Results shown here for a large molecular chaperonin demonstrate how this can provide new insights into its functional process.

Aligning experimental and theoretical anisotropic B-factors: water models, normal-mode analysis methods, and metrics

The strength of X-ray crystallography in providing the information for protein dynamics has been under appreciated. The anisotropic B-factors (ADPs) from high-resolution structures are invaluable in studying the relationship among structure, dynamics, and function. Here, starting from an in-depth evaluation of the metrics used for comparing the overlap between two ellipsoids, we applied normal-mode analysis (NMA) to predict the theoretical ADPs and then align them with experimental results. Adding an extra layer of explicitly treated water on protein surface significantly improved the energy minimization results and better reproduced the anisotropy of experimental ADPs. In comparing experimental and theoretical ADPs, we focused on the overlap in shape, the alignment of dominant directions, and the similarity in magnitude. The choices of water molecules, NMA methods, and the metrics for evaluating the overlap of ADPs determined final results. This study provides useful information for exploring the physical basis and the application potential of experimental ADPs.

Progress in developing Poisson-Boltzmann equation solvers

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Normal-mode-analysis-guided investigation of crucial intersubunit contacts in the cAMP-dependent gating in HCN channels

Protein structures define a complex network of atomic interactions in three dimensions. Direct visualization of the structure and analysis of the interaction potential energy are not straightforward approaches to pinpoint the atomic contacts that are crucial for protein function. We used the tetrameric hyperpolarization-activated cAMP-regulated (HCN) channel as a model system to study the intersubunit contacts in cAMP-dependent gating. To obtain a systematic survey of the contacts between each pair of residues, we used normal-mode analysis, a computational approach for studying protein dynamics, and constructed the covariance matrix for C-α atoms. The significant contacts revealed by covariance analysis were further investigated by means of mutagenesis and functional assays. Among the mutant channels that show phenotypes different from those of the wild-type, we focused on two mutant channels that express opposite changes in cAMP-dependent gating. Subsequent biochemical assays on isolated C-terminal fragments, including the cAMP binding domain, revealed only minimal effects on cAMP binding, suggesting the necessity of interpreting the cAMP-dependent allosteric regulation at the whole-channel level. For this purpose, we applied the patch-clamp fluorometry technique and observed correlated changes in the dynamic, state-dependent cAMP binding in the mutant channels. This study not only provides further understanding of the intersubunit contacts in allosteric coupling in the HCN channel, it also illustrates an effective strategy for delineating important atomic contacts within a structure.

Normal mode analysis with molecular geometry restraints: bridging molecular mechanics and elastic models

A new method for normal mode analysis is reported for all-atom structures using molecular geometry restraints (MGR). Similar to common molecular mechanics force fields, the MGR potential contains short- and long-range terms. The short-range terms are defined by molecular geometry, i.e., bond lengths, angles and dihedrals; the long-range term is similar to that in elastic network models. Each interaction term uses a single force constant parameter, and is determined by fitting against a set of known structures. Tests on proteins/non-proteins show that MGR can produce low frequency eigenvectors closer to all-atom force-field-based methods than conventional elastic network models. Moreover, the "tip effect", found in low frequency eigenvectors in elastic network models, is reduced in MGR to the same level of the modes produced by force-field-based methods. The results suggest that molecular geometry plays an important role, in addition to molecular shape, in determining low frequency deformational motions. MGR does not require initial energy minimization, and is applicable to almost any structure, including the one with missing atoms, bad contacts, or bad geometries, frequently observed in low-resolution structure determination and refinement. The method bridges the two major representations in normal mode analyses, i.e., the molecular mechanics models and elastic network models.

Water evaporation and conformational changes from partially solvated ubiquitin

Using molecular dynamics simulation, we study the evaporation of water molecules off partially solvated ubiquitin. The evaporation and cooling rates are determined for a molecule at the initial temperature of 300 K. The cooling rate is found to be around 3 K/ns, and decreases with water temperature in the course of the evaporation. The conformation changes are monitored by studying a variety of intermediate partially solvated ubiquitin structures. We find that ubiquitin shrinks with decreasing hydration shell and exposes more of its hydrophilic surface area to the surrounding.

Comparative modeling of DNA and RNA polymerases from Moniliophthora perniciosa mitochondrial plasmid

BACKGROUND

The filamentous fungus Moniliophthora perniciosa (Stahel) Aime & Phillips-Mora is a hemibiotrophic Basidiomycota that causes witches' broom disease of cocoa (Theobroma cacao L.). This disease has resulted in a severe decrease in Brazilian cocoa production, which changed the position of Brazil in the market from the second largest cocoa exporter to a cocoa importer. Fungal mitochondrial plasmids are usually invertrons encoding DNA and RNA polymerases. Plasmid insertions into host mitochondrial genomes are probably associated with modifications in host generation time, which can be involved in fungal aging. This association suggests activity of polymerases, and these can be used as new targets for drugs against mitochondrial activity of fungi, more specifically against witches' broom disease. Sequencing and modeling: DNA and RNA polymerases of M. perniciosa mitochondrial plasmid were completely sequenced and their models were carried out by Comparative Homology approach. The sequences of DNA and RNA polymerase showed 25% of identity to 1XHX and 1ARO (pdb code) using BLASTp, which were used as templates. The models were constructed using Swiss PDB-Viewer and refined with a set of Molecular Mechanics (MM) and Molecular Dynamics (MD) in water carried out with AMBER 8.0, both working under the ff99 force fields, respectively. Ramachandran plots were generated by Procheck 3.0 and exhibited models with 97% and 98% for DNA and RNA polymerases, respectively. MD simulations in water showed models with thermodynamic stability after 2000 ps and 300 K of simulation.

CONCLUSION

This work contributes to the development of new alternatives for controlling the fungal agent of witches' broom disease.

Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach

In a previous paper [Ghysels et al., J. Chem. Phys. 126, 224102 (2007)] the mobile block Hessian (MBH) approach was presented. The method was designed to accurately compute vibrational modes of partially optimized molecular structures. The key concept was the introduction of several blocks of atoms, which can move as rigid bodies with respect to a local, fully optimized subsystem. The choice of the blocks was restricted in the sense that none of them could be connected, and also linear blocks were not taken into consideration. In this paper an extended version of the MBH method is presented that is generally applicable and allows blocks to be adjoined by one or two common atoms. This extension to all possible block partitions of the molecule provides a structural flexibility varying from very rigid to extremely relaxed. The general MBH method is very well suited to study selected normal modes of large macromolecules (such as proteins and polymers) because the number of degrees of freedom can be greatly reduced while still keeping the essential motions of the molecular system. The reduction in the number of degrees of freedom due to the block linkages is imposed here directly using a constraint method, in contrast to restraint methods where stiff harmonic couplings are introduced to restrain the relative motion of the blocks. The computational cost of this constraint method is less than that of an implementation using a restraint method. This is illustrated for the alpha-helix conformation of an alanine-20-polypeptide.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography

In this article, we report a method for coarse-grained normal mode analysis called the minimalist network model. The main features of the method are that it can deliver accurate low-frequency modes on structures without undergoing initial energy minimization and that it also retains the details of molecular interactions. The method does not require any additional adjustable parameters after coarse graining and is computationally very fast. Tests on modeling the experimentally measured anisotropic displacement parameters in biomolecular x-ray crystallography demonstrate that the method can consistently perform better than other commonly used methods including our own one. We expect this method to be effective for applications such as structural refinement and conformational sampling.

Structural and functional properties of hydration and confined water in membrane interfaces

The scope of the present review focuses on the interfacial properties of cell membranes that may establish a link between the membrane and the cytosolic components. We present evidences that the current view of the membrane as a barrier of permeability that contains an aqueous solution of macromolecules may be replaced by one in which the membrane plays a structural and functional role. Although this idea has been previously suggested, the present is the first systematic work that puts into relevance the relation water-membrane in terms of thermodynamic and structural properties of the interphases that cannot be ignored in the understanding of cell function. To pursue this aim, we introduce a new definition of interphase, in which the water is organized in different levels on the surface with different binding energies. Altogether determines the surface free energy necessary for the structural response to changes in the surrounding media. The physical chemical properties of this region are interpreted in terms of hydration water and confined water, which explain the interaction with proteins and could affect the modulation of enzyme activity. Information provided by several methodologies indicates that the organization of the hydration states is not restricted to the membrane plane albeit to a region extending into the cytoplasm, in which polar head groups play a relevant role. In addition, dynamic properties studied by cyclic voltammetry allow one to deduce the energetics of the conformational changes of the lipid head group in relation to the head-head interactions due to the presence of carbonyls and phosphates at the interphase. These groups are, apparently, surrounded by more than one layer of water molecules: a tightly bound shell, that mostly contributes to the dipole potential, and a second one that may be displaced by proteins and osmotic stress. Hydration water around carbonyl and phosphate groups may change by the presence of polyhydroxylated compounds or by changing the chemical groups esterified to the phosphates, mainly choline, ethanolamine or glycerol. Thus, surface membrane properties, such as the dipole potential and the surface pressure, are modulated by the water at the interphase region by changing the structure of the membrane components. An understanding of the properties of the structural water located at the hydration sites and the functional water confined around the polar head groups modulated by the hydrocarbon chains is helpful to interpret and analyze the consequences of water loss at the membranes of dehydrated cells. In this regard, a correlation between the effects of water activity on cell growth and the lipid composition is discussed in terms of the recovery of the cell volume and their viability. Critical analyses of the properties of water at the interface of lipid membranes merging from these results and others from the literature suggest that the interface links the membrane with the aqueous soluble proteins in a functional unit in which the cell may be considered as a complex structure stabilized by water rather than a water solution of macromolecules surrounded by a semi permeable barrier.