AmberTools.

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Determination of van der Waals Parameters Using a Double Exponential Potential for Nonbonded Divalent Metal Cations in TIP3P Solvent.

A double exponential (DE) functional form for Lennard-Jones (LJ) interactions, proposed in our previous study, has many advantages over LJ potentials including a natural softcore characteristic for the convenience of the pathway-based free-energy calculations, fast convergence, and flexibility in use. In this work, we put the first step on the application of the DE functional form by identifying a DE potential, coined DE-TIP3P, for molecular simulations using the TIP3P water model. The developed DE-TIP3 potential was better than LJ potential in reproducing the experimental water properties. Afterward, we developed the nonbonded models of 15 divalent metal ions, which frequently appear and play vital roles in biological systems, to be consistent with the DE-TIP3P potential and TIP3P water model. Our nonbonded models were as good as the complicated nonbonded dummy cationic models by Jiang et al. and the nonbonded 12-6-4 LJ models by Li and Merz in reproducing the experimental properties of those ions. Moreover, our nonbonded models achieved a better performance than the compromise (CM) LJ models and 12-6-4 LJ models, developed by Li and Merz, in reproducing the properties of MgCl2 in aqueous solution.

Reformulation of the self-guided molecular simulation method.

Self-guided molecular/Langevin dynamics (SGMD/SGLD) simulation methods were developed to enhance conformational sampling through promoting low frequency motion of molecular systems and have been successfully applied in many simulation studies. Quantitative understanding of conformational distribution in SGLD has been achieved by separating microscopic properties according to frequency. However, a missing link between the guiding factors and conformational distributions makes it highly empirical and system dependent when choosing the values of the guiding parameters. Based on the understanding that molecular interactions are the source of energy barriers and diffusion friction, this work reformulates the equation of the low frequency motion to resemble Langevin dynamics. This reformulation leads to new forms of guiding forces and establishes a relation between the guiding factors and conformational distributions. We call simulations with these new guiding forces the generalized self-guided molecular/Langevin dynamics (SGMDg/SGLDg). In addition, we present a new way to calculate low frequency properties and an efficient algorithm to implement SGMDg/SGLDg that minimizes memory usage and inter-processor communication. Through example simulations with a skewed double well system, an argon fluid, and a cryo-EM map flexible fitting case, we demonstrate the guiding effects on conformational distributions and conformational searching.

Membrane cholesterol dependence of cannabinoid modulation of glycine receptor.

Cannabinoids exert therapeutic effects on several diseases such as chronic pain and startle disease by targeting glycine receptors (GlyRs). Our previous studies have shown that cannabinoids target a serine residue at position 296 in the third transmembrane helix of the α1/α3 GlyR. This site is located on the outside of the ion channel protein at the lipid interface where the cholesterol concentrates. However, whether membrane cholesterol regulates cannabinoid-GlyR interaction remains unknown. Here, we show that GlyRs are closely associated with cholesterol/caveolin-rich domains at subcellular levels. Membrane cholesterol reduction significantly inhibits cannabinoid potentiation of glycine-activated currents in cultured spinal neurons and in HEK 293T cells expressing α1/α3 GlyRs. Such inhibition is fully rescued by cholesterol replenishment in a concentration-dependent manner. Molecular docking calculations further reveal that cholesterol regulates cannabinoid enhancement of GlyR function through both direct and indirect mechanisms. Taken together, these findings suggest that cholesterol is critical for the cannabinoid-GlyR interaction in the cell membrane.

Protonation state of the selectivity filter of bacterial voltage-gated sodium channels is modulated by ions.

The selectivity filter (SF) of bacterial voltage-gated sodium channels consists of four glutamate residues arranged in a C4 symmetry. The protonation state population of this tetrad is unclear. To address this question, we simulate the pore domain of bacterial voltage-gated sodium channel of Magnetococcus sp. (Nav Ms) through constant pH methodology in explicit solvent and free energy perturbation calculations. We find that at physiological pH the fully deprotonated as well as singly and doubly protonated states of the SF appear feasible, and that the calculated pKa decreases with each additional bound ion, suggesting that a decrease in the number of ions in the pore can lead to protonation of the SF. Previous molecular dynamics simulations have suggested that protonation can lead to a decrease in the conductance, but no pKa calculations were performed. We confirm a decreased ionic population of the pore with protonation, and also observe structural symmetry breaking triggered by protonation; the SF of the deprotonated channel is closest to the C4 symmetry observed in crystal structures of the open state, while the SF of protonated states display greater levels of asymmetry which could lead to transition to the inactivated state which possesses a C2 symmetry in the crystal structure. We speculate that the decrease in the number of ions near the mouth of the channel, due to either random fluctuations or ion depletion due to conduction, could be a self-regulatory mechanism resulting in a nonconducting state that functionally resembles inactivated states.

A double exponential potential for van der Waals interaction.

Van der Waals (vdw) interaction is an important force between atoms and molecules. Many potential functions have been proposed to model vdw interaction such as the Lennard-Jones (L-J) potential. To overcome certain drawbacks of existing function forms, this work proposes a double exponential (DE) potential that contains a repulsive exponential term and an attractive exponential term. This potential decays faster than the L-J potential and has a soft core. The DE potential is very flexible and its two exponential parameters can be adjusted continuously to mimic many potential functions. Combined with the isotropic periodic sum (IPS) method, the DE potential can efficiently and accurately describe non-bonded interactions and is convenient for alchemical free energy calculation.

The homogeneity condition: A simple way to derive isotropic periodic sum potentials for efficient calculation of long-range interactions in molecular simulation.

Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential, which folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. Analytic solutions of IPS potentials have been solved for many interaction types. To further simplify the application of the IPS method, this work presents the homogeneity condition, which requires the sum of interaction energies for any particle to be independent of cutoff distances for a truly homogeneous system. Using the homogeneity condition, one can avoid the complicated mathematic work to solve analytic solutions and can instead use simple functions as IPS potentials. Example simulations are performed for model systems of a series of interaction types. Energies, volumes, and their fluctuations from these simulations demonstrate that simple IPS potentials obtained through the homogeneity condition can satisfactorily describe long-range interactions. The homogeneity condition makes the IPS method a convenient way to handle long-range interactions of any type.

Comparison of the umbrella sampling and the double decoupling method in binding free energy predictions for SAMPL6 octa-acid host-guest challenges.

We calculate the absolute binding free energies of tetra-methylated octa-acids host-guest systems as a part of the SAMPL6 blind challenge (receipt ID vq30p). We employed two different free energy simulation methods, i.e., the umbrella sampling (US) and double decoupling method (DDM). The US method was used with the weighted histogram analysis method (WHAM) (US-WHAM scheme). In the DDM scheme, Hamiltonian replica-exchange method (HREM) was combined with the Bennett acceptance ratio (BAR) (HREM-BAR scheme). We obtained initial binding poses via molecular docking using GalaxyDock-HG program, which is developed for the SAMPL challenge. The root mean square deviation (RMSD) and the mean absolute deviations (MAD) using US-WHAM scheme were 1.33 and 1.02 kcal/mol, respectively. The MAD was the top among all submissions, however the correlation with respect to experiment was unexceptional. While the RMSD and MAD via HREM-BAR scheme were greater than US-WHAM scheme, (i.e., 2.09 and 1.76 kcal/mol), their correlations were slightly better than US-WHAM. The correlation between the two methods was high. Further discussion on the DDM method can be found in a companion paper by Han et al. (receipt ID 3z83m) in the same issue.

Hydronium Ions Accompanying Buried Acidic Residues Lead to High Apparent Dielectric Constants in the Interior of Proteins.

Internal ionizable groups are known to play important roles in protein functions. A mystery that has attracted decades of extensive experimental and theoretical studies is the apparent dielectric constants experienced by buried ionizable groups, which are much higher than values expected for protein interiors. Many interpretations have been proposed, such as water penetration, conformational relaxation, local unfolding, protein intrinsic backbone fluctuations, etc. However, these interpretations conflict with many experimental observations. The virtual mixture of multiple states (VMMS) simulation method developed in our lab provides a direct approach for studying the equilibrium of multiple chemical states and can monitor p Ka values along simulation trajectories. Through VMMS simulations of staphylococcal nuclease (SNase) variants with internal Asp or Glu residues, we discovered that cations were attracted to buried deprotonated acidic groups and the presence of the nearby cations were essential to reproduce experimentally measured p Ka values. This finding, combined with structural analysis and validation simulations, suggests that the proton released from a deprotonation process stays near the deprotonated group inside proteins, possibly in the form of a hydronium ion. The existence of a proton near a buried charge has many implications in our understanding of protein functions.

Atomic Resolution Cryo-EM Structure of ß-Galactosidase.

The advent of direct electron detectors has enabled the routine use of single-particle cryo-electron microscopy (EM) approaches to determine structures of a variety of protein complexes at near-atomic resolution. Here, we report the development of methods to account for local variations in defocus and beam-induced drift, and the implementation of a data-driven dose compensation scheme that significantly improves the extraction of high-resolution information recorded during exposure of the specimen to the electron beam. These advances enable determination of a cryo-EM density map for ß-galactosidase bound to the inhibitor phenylethyl ß-D-thiogalactopyranoside where the ordered regions are resolved at a level of detail seen in X-ray maps at ∼ 1.5 Å resolution. Using this density map in conjunction with constrained molecular dynamics simulations provides a measure of the local flexibility of the non-covalently bound inhibitor and offers further opportunities for structure-guided inhibitor design.

Origin of pKa Shifts of Internal Lysine Residues in SNase Studied Via Equal-Molar VMMS Simulations in Explicit Water.

Protein internal ionizable groups can exhibit large shifts in pKa values. Although the environment and interaction changes have been extensively studied both experimentally and computationally, direct calculation of pKa values of these internal ionizable groups in explicit water is challenging due to energy barriers in solvent interaction and in conformational transition. The virtual mixture of multiple states (VMMS) method is a new approach designed to study chemical state equilibrium. This method constructs a virtual mixture of multiple chemical states in order to sample the conformational space of all states simultaneously and to avoid crossing energy barriers related to state transition. By applying VMMS to 25 variants of staphylococcal nuclease with lysine residues at internal positions, we obtained the pKa values of these lysine residues and investigated the physics underlining the pKa shifts. Our calculation results agree reasonably well with experimental measurements, validating the VMMS method for pKa calculation and providing molecular details of the protonation equilibrium for protein internal ionizable groups. Based on our analyses of protein conformation relaxation, lysine side chain flexibility, water penetration, and the microenvironment, we conclude that the hydrophobicity of the microenvironment around the lysine side chain (which affects water penetration differently for different protonation states) plays an important role in the pKa shifts.

Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole tensor.

Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential; it folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. It has been demonstrated that the IPS method produces consistent simulation results, including free energies, as the particle mesh Ewald (PME) method. By introducing the multipole homogeneous background approximation, this work derives multipole IPS potentials, abbreviated as IPSMm, with m being the maximum order of multipole interactions. To efficiently calculate the multipole interactions in Cartesian space, we propose a vector relation that calculates a multipole tensor as a dot product of a radial potential vector and a directional vector. Using model systems with charges, dipoles, and/or quadrupoles, with and without polarizability, we demonstrate that multipole interactions of order m can be described accurately with the multipole IPS potential of order 2 or m - 1, whichever is higher. Through simulations with the multipole IPS potentials, we examined energetic, structural, and dynamic properties of the model systems and demonstrated that the multipole IPS potentials produce very similar results as PME with a local region radius (cutoff distance) as small as 6 Å.

The ubiquitin ligase Ubr4 controls stability of podocin/MEC-2 supercomplexes.

The PHB-domain protein podocin maintains the renal filtration barrier and its mutation is an important cause of hereditary nephrotic syndrome. Podocin and its Caenorhabditis elegans orthologue MEC-2 have emerged as key components of mechanosensitive membrane protein signalling complexes. Whereas podocin resides at a specialized cell junction at the podocyte slit diaphragm, MEC-2 is found in neurons required for touch sensitivity. Here, we show that the ubiquitin ligase Ubr4 is a key component of the podocin interactome purified both from cultured podocytes and native glomeruli. It colocalizes with podocin and regulates its stability. In C. elegans, this process is conserved. Here, Ubr4 is responsible for the degradation of mislocalized MEC-2 multimers. Ubiquitylomic analysis of mouse glomeruli revealed that podocin is ubiquitylated at two lysine residues. These sites were Ubr4-dependent and were conserved across species. Molecular dynamics simulations revealed that ubiquitylation of one site, K301, do not only target podocin/MEC-2 for proteasomal degradation, but may also affect stability and disassembly of the multimeric complex. We suggest that Ubr4 is a key regulator of podocyte foot process proteostasis.

Self-guided Langevin dynamics via generalized Langevin equation.

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.

A Virtual Mixture Approach to the Study of Multistate Equilibrium: Application to Constant pH Simulation in Explicit Water.

Chemical and thermodynamic equilibrium of multiple states is a fundamental phenomenon in biology systems and has been the focus of many experimental and computational studies. This work presents a simulation method to directly study the equilibrium of multiple states. This method constructs a virtual mixture of multiple states (VMMS) to sample the conformational space of all chemical states simultaneously. The VMMS system consists of multiple subsystems, one for each state. The subsystem contains a solute and a solvent environment. The solute molecules in all subsystems share the same conformation but have their own solvent environments. Transition between states is implicated by the change of their molar fractions. Simulation of a VMMS system allows efficient calculation of relative free energies of all states, which in turn determine their equilibrium molar fractions. For systems with a large number of state transition sites, an implicit site approximation is introduced to minimize the cost of simulation. A direct application of the VMMS method is for constant pH simulation to study protonation equilibrium. Applying the VMMS method to a heptapeptide of 3 ionizable residues, we calculated the pKas of those residues both with all explicit states and with implicit sites and obtained consistent results. For mouse epidermal growth factor of 9 ionizable groups, our VMMS simulations with implicit sites produced pKas of all 9 ionizable groups and the results agree qualitatively with NMR measurement. This example demonstrates the VMMS method can be applied to systems of a large number of ionizable groups and the computational cost scales linearly with the number of ionizable groups. For one of the most challenging systems in constant pH calculation, SNase Δ+PHS/V66K, our VMMS simulation shows that it is the state-dependent water penetration that causes the large deviation in lysine66's pKa.

2.2 Å resolution cryo-EM structure of ß-galactosidase in complex with a cell-permeant inhibitor.

Cryo-electron microscopy (cryo-EM) is rapidly emerging as a powerful tool for protein structure determination at high resolution. Here we report the structure of a complex between Escherichia coli ß-galactosidase and the cell-permeant inhibitor phenylethyl ß-D-thiogalactopyranoside (PETG), determined by cryo-EM at an average resolution of ~2.2 angstroms (Å). Besides the PETG ligand, we identified densities in the map for ~800 water molecules and for magnesium and sodium ions. Although it is likely that continued advances in detector technology may further enhance resolution, our findings demonstrate that preparation of specimens of adequate quality and intrinsic protein flexibility, rather than imaging or image-processing technologies, now represent the major bottlenecks to routinely achieving resolutions close to 2 Å using single-particle cryo-EM.

Maturation of the HIV-1 core by a non-diffusional phase transition.

The formation of the HIV-1 core is the final step in the viral maturation pathway, resulting in the formation of infectious virus. Most current models for HIV-1 core formation suggest that, upon proteolytic cleavage from the immature Gag, capsid (CA) dissociates into the viral interior before reforming into the core. Here we present evidence for an alternate view of core formation by taking advantage of our serendipitous observation of large membrane-enclosed structures in HIV-1 supernatants from infected cells. Cryo-electron tomographic studies show that these structures, which contain ordered arrays of what is likely the membrane-associated matrix protein, contain multiple cores that can be captured at different stages of maturation. Our studies suggest that HIV maturation involves a non-diffusional phase transition in which the detaching layer of the cleaved CA lattice is gradually converted into a roll that ultimately forms the surface of the mature conical core.

Comparative phosphoproteomic analysis of mammalian glomeruli reveals conserved podocin C-terminal phosphorylation as a determinant of slit diaphragm complex architecture.

Glomerular biology is dependent on tightly controlled signal transduction networks that control phosphorylation of signaling proteins such as cytoskeletal regulators or slit diaphragm proteins of kidney podocytes. Cross-species comparison of phosphorylation events is a powerful mean to functionally prioritize and identify physiologically meaningful phosphorylation sites. Here, we present the result of phosphoproteomic analyses of cow and rat glomeruli to allow cross-species comparisons. We discovered several phosphorylation sites with potentially high biological relevance, e.g. tyrosine phosphorylation of the cytoskeletal regulator synaptopodin and the slit diaphragm protein neph-1 (Kirrel). Moreover, cross-species comparisons revealed conserved phosphorylation of the slit diaphragm protein nephrin on an acidic cluster at the intracellular terminus and conserved podocin phosphorylation on the very carboxyl terminus of the protein. We studied a highly conserved podocin phosphorylation site in greater detail and show that phosphorylation regulates affinity of the interaction with nephrin and CD2AP. Taken together, these results suggest that species comparisons of phosphoproteomic data may reveal regulatory principles in glomerular biology. All MS data have been deposited in the ProteomeXchange with identifier PXD001005 (http://proteomecentral.proteomexchange.org/dataset/PXD001005).

Phosphoproteomic analysis reveals regulatory mechanisms at the kidney filtration barrier.

Diseases of the kidney filtration barrier are a leading cause of ESRD. Most disorders affect the podocytes, polarized cells with a limited capacity for self-renewal that require tightly controlled signaling to maintain their integrity, viability, and function. Here, we provide an atlas of in vivo phosphorylated, glomerulus-expressed proteins, including podocyte-specific gene products, identified in an unbiased tandem mass spectrometry-based approach. We discovered 2449 phosphorylated proteins corresponding to 4079 identified high-confidence phosphorylated residues and performed a systematic bioinformatics analysis of this dataset. We discovered 146 phosphorylation sites on proteins abundantly expressed in podocytes. The prohibitin homology domain of the slit diaphragm protein podocin contained one such site, threonine 234 (T234), located within a phosphorylation motif that is mutated in human genetic forms of proteinuria. The T234 site resides at the interface of podocin dimers. Free energy calculation through molecular dynamic simulations revealed a role for T234 in regulating podocin dimerization. We show that phosphorylation critically regulates formation of high molecular weight complexes and that this may represent a general principle for the assembly of proteins containing prohibitin homology domains.

Targeted conformational search with map-restrained self-guided Langevin dynamics: application to flexible fitting into electron microscopic density maps.

We present a map-restrained self-guided Langevin dynamics (MapSGLD) simulation method for efficient targeted conformational search. The targeted conformational search represents simulations under restraints defined by experimental observations and/or by user specified structural requirements. Through map-restraints, this method provides an efficient way to maintain substructures and to set structure targets during conformational searching. With an enhanced conformational searching ability of self-guided Langevin dynamics, this approach is suitable for simulating large-scale conformational changes, such as the formation of macromolecular assemblies and transitions between different conformational states. Using several examples, we illustrate the application of this method in flexible fitting of atomic structures into density maps derived from cryo-electron microscopy.