Narutoshi Kamiya

Structural views of the ligand-binding cores of a metabotropic glutamate receptor complexed with an antagonist and both glutamate and Gd3+

Crystal structures of the extracellular ligand-binding region of the metabotropic glutamate receptor, complexed with an antagonist, (S)-(α)-methyl-4-carboxyphenylglycine, and with both glutamate and Gd3+ ion, have been determined by x-ray crystallographic analyses. The structure of the complex with the antagonist is similar to that of the unliganded resting dimer. The antagonist wedges the protomer to maintain an inactive open form. The glutamate/Gd3+ complex is an exact 2-fold symmetric dimer, where each bi-lobed protomer adopts the closed conformation. The surface of the C-terminal domain contains an acidic patch, whose negative charges are alleviated by the metal cation to stabilize the active dimeric structure. The structural comparison between the active and resting dimers suggests that glutamate binding tends to induce domain closing and a small shift of a helix in the dimer interface. Furthermore, an interprotomer contact including the acidic patch inhibited dimer formation by the two open protomers in the active state. These findings provide a structural basis to describe the link between ligand binding and the dimer interface.

α,β-Unsaturated Ketone Is a Core Moiety of Natural Ligands for Covalent Binding to Peroxisome Proliferator-activated Receptor γ

Peroxisome proliferator-activated receptor γ (PPARγ) functions in various biological processes, including macrophage and adipocyte differentiation. Several natural lipid metabolites have been shown to activate PPARγ. Here, we report that some PPARγ ligands, including 15-deoxy-Δ12,14-prostaglandin J2, covalently bind to a cysteine residue in the PPARγ ligand binding pocket through a Michael addition reaction by an α,β-unsaturated ketone. Using rhodamine-maleimide as well as mass spectroscopy, we showed that the binding of these ligands is covalent and irreversible. Consistently, mutation at the cysteine residue abolished abilities of these ligands to activate PPARγ, but not of BRL49653, a non-covalent synthetic agonist, indicating that covalent binding of the α,β-unsaturated ketone in the natural ligands was required for their transcriptional activities. Screening of lipid metabolites containing the α,β-unsaturated ketone revealed that several other oxidized metabolites of hydroxyeicosatetraenoic acid, hydroxyeicosadecaenoic acid, and prostaglandins can also function as novel covalent ligands for PPARγ. We propose that PPARγ senses oxidation of fatty acids by recognizing such an α,β-unsaturated ketone as a common moiety.

Conformational transition states of a β‐hairpin peptide between the ordered and disordered conformations in explicit water

The conformational transition states of a β‐hairpin peptide in explicit water were identified from the free energy landscapes obtained from the multicanonical ensemble, using an enhanced conformational sampling calculation. The β‐hairpin conformations were significant at 300 K in the landscape, and the typical nuclear Overhauser effect signals were reproduced, consistent with the previously reported experiment. In contrast, the disordered conformations were predominant at higher temperatures. Among the stable conformations at 300 K, there were several free energy barriers, which were not visible in the landscapes formed with the conventional parameters. We identified the transition states around the saddle points along the putative folding and unfolding paths between the β‐hairpin and the disordered conformations in the landscape. The characteristic features of these transition states are the predominant hydrophobic contacts and the several hydrogen bonds among the side‐chains, as well as some of the backbone hydrogen bonds. The unfolding simulations at high temperatures, 400 K and 500 K, and their principal component analyses also provided estimates for the transition state conformations, which agreed well with those at 400 K and 500 K deduced from the current free energy landscapes at 400 K and 500 K, respectively. However, the transition states at high temperatures were much more widely distributed on the landscape than those at 300 K, and their conformations were different.

Application of MDGRAPE‐3, a special purpose board for molecular dynamics simulations, to periodic biomolecular systems

We describe the application of a special purpose board for molecular dynamics simulations, named MDGRAPE‐3, to the problem of simulating periodic bio‐molecular systems. MDGRAPE‐3 is the latest board in a series of hardware accelerators designed to calculate the nonbonding long‐range interactions much more rapidly than normal processors. So far, MDGRAPEs were mainly applied to isolated systems, where very many nonbonded interactions were calculated without any distance cutoff. However, in order to regulate the density and pressure during simulations of membrane embedded protein systems, one has to evaluate interactions under periodic boundary conditions. For this purpose, we implemented the Particle–Mesh Ewald (PME) method, and its approximation with distance cutoffs and charge neutrality as proposed by Wolf et al., using MDGRAPE‐3. When the two methods were applied to simulations of two periodic biomolecular systems, a single MDGRAPE‐3 achieved 30–40 times faster computation times than a single conventional processor did in the both cases. Both methods are shown to have the same molecular structures and dynamics of the systems.

Molecular Dynamics Simulations Accelerated by GPU for Biological Macromolecules with a Non-Ewald Scheme for Electrostatic Interactions

A molecular dynamics (MD) simulation program for biological macromolecules was implemented with a non-Ewald scheme for long-ranged electrostatic interactions and run on a general purpose graphics processing unit (GPU). We recently developed several non-Ewald methods to compute the electrostatic energies with high precision. In particular, the zero-dipole summation (ZD) method, which takes into account the neutralities of charges and dipoles in a truncated subset, enables the calculation of electrostatic interactions with high accuracy and low computational cost, and its algorithm is simple enough to be implemented in a GPU. We developed an MD program with the space decomposition algorithm, myPresto/psygene, and applied it to several biological macromolecular systems with GPUs implementing the ZD method. Rapid computing performance with high accuracy was obtained.

Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes

Protein folding and protein–ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein–ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent.

Simple and accurate scheme to compute electrostatic interaction : Zero-dipole summation technique for molecular system and application to bulk water

The zero-dipole summation method was extended to general molecular systems, and then applied to molecular dynamics simulations of an isotropic water system. In our previous paper [I. Fukuda, Y. Yonezawa, and H. Nakamura, J. Chem. Phys. 134, 164107 (2011)], for evaluating the electrostatic energy of a classical particle system, we proposed the zero-dipole summation method, which conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. Here, we consider the application of this scheme to molecular systems, as well as some fundamental aspects of general cutoff truncation protocols. Introducing an idea to harmonize the bonding interactions and the electrostatic interactions in the scheme, we develop a specific algorithm. As in the previous study, the resulting energy formula is represented by a simple pairwise function sum, enabling facile applications to high-performance computation. The accuracy of the electrostatic energies calculated by the zero-dipole summation method with the atom-based cutoff was numerically investigated, by comparison with those generated by the Ewald method. We obtained an electrostatic energy error of less than 0.01% at a cutoff length longer than 13 Å for a TIP3P isotropic water system, and the errors were quite small, as compared to those obtained by conventional truncation methods. The static property and the stability in an MD simulation were also satisfactory. In addition, the dielectric constants and the distance-dependent Kirkwood factors were measured, and their coincidences with those calculated by the particle mesh Ewald method were confirmed, although such coincidences are not easily attained by truncation methods. We found that the zero damping-factor gave the best results in a practical cutoff distance region. In fact, in contrast to the zero-charge scheme, the damping effect was insensitive in the zero-charge and zero-dipole scheme, in the molecular system we treated. We discussed the origin of this difference between the two schemes and the dependence of this fact on the physical system. The use of the zero damping-factor will enhance the efficiency of practical computations, since the complementary error function is not employed. In addition, utilizing the zero damping-factor provides freedom from the parameter choice, which is not trivial in the zero-charge scheme, and eliminates the error function term, which corresponds to the time-consuming Fourier part under the periodic boundary conditions.

Protein‐inhibitor flexible docking by a multicanonical sampling: Native complex structure with the lowest free energy and a free‐energy barrier distinguishing the native complex from the others

Flexible docking between a protein (lysozyme) and an inhibitor (tri‐N‐acetyl‐D‐glucosamine, tri‐NAG) was carried out by an enhanced conformational sampling method, multicanonical molecular dynamics simulation. We used a flexible all‐atom model to express lysozyme, tri‐NAG, and water molecules surrounding the two bio‐molecules. The advantages of this sampling method are as follows: the conformation of system is widely sampled without trapping at energy minima, a thermally equilibrated conformational ensemble at an arbitrary temperature can be reconstructed from the simulation trajectory, and the thermodynamic weight can be assigned to each sampled conformation. During the simulation, exchanges between the binding and free (i.e., unbinding) states of the protein and the inhibitor were repeatedly observed. The conformational ensemble reconstructed at 300 K involved various conformational clusters. The main outcome of the current study is that the most populated conformational cluster (i.e., the cluster of the lowest free energy) was assigned to the native complex structure (i.e., the X‐ray complex structure). The simulation also produced non‐native complex structures, where the protein and the inhibitor bound with different modes from that of the native complex structure, as well as the unbinding structures. A free‐energy barrier (i.e., activation free energy) was clearly detected between the native complex structures and the other structures. The thermal fluctuations of tri‐NAG in the lowest free‐energy complex correlated well with the X‐ray B‐factors of tri‐NAG in the X‐ray complex structure. The existence of the free‐energy barrier ensures that the lowest free‐energy structure can be discriminated naturally from the other structures. In other words, the multicanonical molecular dynamics simulation can predict the native complex structure without any empirical objective function. The current study also manifested that the flexible all‐atom model and the physico‐chemically defined atomic‐level force field can reproduce the native complex structure. A drawback of the current method is that it requires a time consuming computation due to the exhaustive conformational sampling. We discussed a possibility for combining the current method with conventional docking methods. Proteins 2008.

Theory for trivial trajectory parallelization of multicanonical molecular dynamics and application to a polypeptide in water

Trivial trajectory parallelization of multicanonical molecular dynamics (TTP‐McMD) explores the conformational space of a biological system with multiple short runs of McMD starting from various initial structures. This method simply connects (i.e., trivially parallelizes) the short trajectories and generates a long trajectory. First, we theoretically prove that the simple trajectory connection satisfies a detailed balance automatically. Thus, the resultant long trajectory is regarded as a single multicanonical trajectory. Second, we applied TTP‐McMD to an alanine decapeptide with an all‐atom model in explicit water to compute a free‐energy landscape. The theory imposes two requirements on the multiple trajectories. We have demonstrated that TTP‐McMD naturally satisfies the requirements. The TTP‐McMD produces the free‐energy landscape considerably faster than a single‐run McMD does. We quantitatively showed that the accuracy of the computed landscape increases with increasing the number of multiple runs. Generally, the free‐energy landscape of a large biological system is unknown a priori. The current method is suitable for conformational sampling of such a large system to reduce the waiting time to obtain a canonical ensemble statistically reliable.

Free Energy Landscapes of Alanine Dipeptide in Explicit Water Reproduced by the Force-Switching Wolf Method.

Precise and rapid calculation of long-range interactions is of crucial importance for molecular dynamics (MD) and Monte Carlo simulations. Instead of the Ewald method or its high speed variant, PME, we applied our novel method, called the force-switching Wolf method, to computation of the free energy landscapes of a short peptide in explicit water. Wolf and co-workers showed that long-range electrostatic energy under a periodic boundary condition can be well reproduced even by truncating the contribution from the distant charges, when the charge neutrality is taken into account. We recently applied the procedure proposed by Wolf and co-workers to a mathematically consistent MD theory by means of a force-switching scheme, and we show that the total electrostatic energy for sodium chloride liquid was well conserved and stable during the MD simulation with the force-switching Wolf method. Our current results for an aqueous peptide solution with a series of canonical and multicanonical molecular dynamics simulations show that the force-switching Wolf method is not only in good accordance with the energies and forces calculated by the conventional PME method but also properly reproduces the solvation and the free energy landscapes of the peptide at 300 K.