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.

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.

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.

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.

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.

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.

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.

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.

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).

Lateral density of receptor arrays in the membrane plane influences sensitivity of the E. coli chemotaxis response.

In chemotactic bacteria, transmembrane chemoreceptors, CheA and CheW form the core signalling complex of the chemotaxis sensory apparatus. These complexes are organized in extended arrays in the cytoplasmic membrane that allow bacteria to respond to changes in concentration of extracellular ligands via a cooperative, allosteric response that leads to substantial amplification of the signal induced by ligand binding. Here, we have combined cryo-electron tomographic studies of the 3D spatial architecture of chemoreceptor arrays in intact E. coli cells with computational modelling to develop a predictive model for the cooperativity and sensitivity of the chemotaxis response. The predictions were tested experimentally using fluorescence resonance energy transfer (FRET) microscopy. Our results demonstrate that changes in lateral packing densities of the partially ordered, spatially extended chemoreceptor arrays can modulate the bacterial chemotaxis response, and that information about the molecular organization of the arrays derived by cryo-electron tomography of intact cells can be translated into testable, predictive computational models of the chemotaxis response.

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.

A common molecular basis for exogenous and endogenous cannabinoid potentiation of glycine receptors.

Both exogenous and endogenous cannabinoids can allosterically modulate glycine receptors (GlyRs). However, little is known about the molecular basis of cannabinoid-GlyR interactions. Here we report that sustained incubation with the endocannabinoid anandamide (AEA) substantially increased the amplitude of glycine-activated current in both rat cultured spinal neurons and in HEK-293 cells expressing human α1, rat α2 and α3 GlyRs. While the α1 and α3 subunits were highly sensitive to AEA-induced potentiation, the α2 subunit was relatively insensitive to AEA. Switching a serine at 296 and 307 in the TM3 (transmembrane domain 3) of the α1 and α3 subunits with an alanine (A) at the equivalent position in the α2 subunit converted the α1/α3 AEA-sensitive receptors to sensitivity resembling that of α2. The S296 residue is also critical for exogenous cannabinoid-induced potentiation of I(Gly). The magnitude of AEA potentiation decreased with removal of either the hydroxyl or oxygen groups on AEA. While desoxy-AEA was significantly less efficacious in potentiating I(Gly), desoxy-AEA inhibited potentiation produced by both Δ(9)-tetrahydrocannabinol (THC), a major psychoactive component of marijuana, and AEA. Similarly, didesoxy-THC, a modified THC with removal of both hydroxyl/oxygen groups, did not affect I(Gly) when applied alone but inhibited the potentiation of I(Gly) induced by AEA and THC. These findings suggest that exogenous and endogenous cannabinoids potentiate GlyRs via a hydrogen bonding-like interaction. Such a specific interaction likely stems from a common molecular basis involving the S296 residue in the TM3 of the α1 and α3 subunits.

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.

Weak intra-ring allosteric communications of the archaeal chaperonin thermosome revealed by normal mode analysis.

Chaperonins are molecular machines that use ATP-driven cycles to assist misfolded substrate proteins to reach the native state. During the functional cycle, these machines adopt distinct nucleotide-dependent conformational states, which reflect large-scale allosteric changes in individual subunits. Distinct allosteric kinetics has been described for the two chaperonin classes. Bacterial (group I) chaperonins, such as GroEL, undergo concerted subunit motions within each ring, whereas archaeal and eukaryotic chaperonins (group II) undergo sequential subunit motions. We study these distinct mechanisms through a comparative normal mode analysis of monomer and double-ring structures of the archaeal chaperonin thermosome and GroEL. We find that thermosome monomers of each type exhibit common low-frequency behavior of normal modes. The observed distinct higher-frequency modes are attributed to functional specialization of these subunit types. The thermosome double-ring structure has larger contribution from higher-frequency modes, as it is found in the GroEL case. We find that long-range intersubunit correlation of amino-acid pairs is weaker in the thermosome ring than in GroEL. Overall, our results indicate that distinct allosteric behavior of the two chaperonin classes originates from different wiring of individual subunits as well as of the intersubunit communications.

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling.

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

Maintain rigid structures in Verlet based cartesian molecular dynamics simulations.

An algorithm is presented to maintain rigid structures in Verlet based cartesian molecular dynamics (MD) simulations. After each unconstrained MD step, the coordinates of selected particles are corrected to maintain rigid structures through an iterative procedure of rotation matrix computation. This algorithm, named as SHAPE and implemented in CHARMM program suite, avoids the calculations of Lagrange multipliers, so that the complexity of computation does not increase with the number of particles in a rigid structure. The implementation of this algorithm does not require significant modification of propagation integrator, and can be plugged into any cartesian based MD integration scheme. A unique feature of the SHAPE method is that it is interchangeable with SHAKE for any object that can be constrained as a rigid structure using multiple SHAKE constraints. Unlike SHAKE, the SHAPE method can be applied to large linear (with three or more centers) and planar (with four or more centers) rigid bodies. Numerical tests with four model systems including two proteins demonstrate that the accuracy and reliability of the SHAPE method are comparable to the SHAKE method, but with much more applicability and efficiency.

Force-momentum-based self-guided Langevin dynamics: a rapid sampling method that approaches the canonical ensemble.

The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.

Toward canonical ensemble distribution from self-guided Langevin dynamics simulation.

This work derives a quantitative description of the conformational distribution in self-guided Langevin dynamics (SGLD) simulations. SGLD simulations employ guiding forces calculated from local average momentums to enhance low-frequency motion. This enhancement in low-frequency motion dramatically accelerates conformational search efficiency, but also induces certain perturbations in conformational distribution. Through the local averaging, we separate properties of molecular systems into low-frequency and high-frequency portions. The guiding force effect on the conformational distribution is quantitatively described using these low-frequency and high-frequency properties. This quantitative relation provides a way to convert between a canonical ensemble and a self-guided ensemble. Using example systems, we demonstrated how to utilize the relation to obtain canonical ensemble properties and conformational distributions from SGLD simulations. This development makes SGLD not only an efficient approach for conformational searching, but also an accurate means for conformational sampling.