Yasushige Yonezawa

An Insight into the pathway of the amyloid fibril formation of hen egg white lysozyme obtained from a small-angle X-ray and neutron scattering study.

It is known that hen egg white lysozyme (HEWL) forms amyloid fibrils. Since HEWL is one of the proteins that have been studied most extensively and is closely related to human lysozyme, the variants of which form the amyloid fibrils that are related to hereditary systemic amyloidosis, this protein is an ideal model to study the mechanism of amyloid fibril formation. In order to gain an insight into the mechanism of amyloid fibril formation, systematic and detailed studies to detect and characterize various structural states of HEWL were conducted. Since HEWL forms amyloid fibrils in highly concentrated ethanol solutions, solutions of various concentrations of HEWL in various concentrations of ethanol were prepared, and the structures of HEWL in these solutions were investigated by small-angle X-ray and neutron scattering. It was shown that the structural states of HEWL were distinguished as the monomer state, the state of the dimer formation, the state of the protofilament formation, the protofilament state, and the state towards the formation of amyloid fibrils. A phase diagram of these structural states was obtained as a function of protein, water and ethanol concentrations. It was found that under the monomer state the structural changes of HEWL were not gross changes in shape but local conformational changes, and the dimers, formed by the association at the end of the long axis of HEWL, had an elongated shape. Circular dichroism measurements showed that the large changes in the secondary structures of HEWL occurred during dimer formation. The protofilaments were formed by stacking of the dimers with their long axis (nearly) perpendicular to and rotated around the protofilament axis to form a helical structure. These protofilaments were characterized by their radius of gyration of the cross-section of 2.4nm and the mass per unit length of 16,000(+/-2300)Da/nm. It was shown that the changes of the structural states towards the amyloid fibril formation occurred via lateral association of the protofilaments. A pathway of the amyloid fibril formation of HEWL was proposed from these results.

Denaturation and aggregation of hen egg lysozyme in aqueous ethanol solution studied by dynamic light scattering.

We applied dynamic light scattering technique on the model system of hen egg lysozyme in salt-free aqueous ethanol solution to study the mechanism of denaturation and aggregation of protein. At low ethanol concentration [0-63% (v/v)], the fast relaxation mode was observed, which was caused by lysozyme molecules in the solution interacting with each other with strong repulsive electrostatic force. At 45 and 63% (v/v) ethanol, the slow relaxation mode was also observed, which showed translational diffusive nature, similar to that observed in salt-free polyelectrolyte solution. At 72 or 81% (v/v) ethanol, the slow mode disappeared, leaving only the fast mode. However, the mutual diffusion coefficients obtained from the fast mode at 72 and 81% (v/v) ethanol decreased by about one order of magnitude compared with those from the fast mode at 0-63% (v/v). The reported alcohol-induced conformational transformation of lysozyme molecules at >60% (v/v) ethanol from their native structure to an alpha-helix-rich structure might cause such drastic decrease in the mutual diffusion coefficients. At the highest ethanol concentration of 90% (v/v), the slow mode reappeared, and its relaxation rate was decreasing with elapsed time, which is possibly due to the growth of aggregates of lysozyme molecules. X-ray diffraction results suggested that the intermolecular beta-sheet formation caused the aggregation. Thus, our results indicated that the change in molecular structure of lysozyme closely relates to the diffusion of molecules and their aggregation.

Molecular dynamics scheme for precise estimation of electrostatic interaction via zero-dipole summation principle

We propose a novel idea, zero-dipole summation, for evaluating the electrostatic energy of a classical particle system, and have composed an algorithm for effectively utilizing the idea for molecular dynamics. It conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. The resulting energy formula is nevertheless represented by a simple pairwise function sum, which enables facile application to high-performance computation. By following a heuristic approach to derive the current electrostatic energy formula, we developed an axiomatic approach to construct the method consistently. Explorations of the theoretical details of our method revealed the structure of the generated error, and we analyzed it by comparisons with other methods. A numerical simulation using liquid sodium chloride confirmed that the current method with a small damping factor yielded sufficient accuracy with a practical cutoff distance region. The current energy function also conducts stable numerical integration in a liquid MD simulation. Our method is an extension of the charge neutralized summation developed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)]. Furthermore, we found that the current method becomes a generalization of the preaveraged potential method proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)], which is based on a viewpoint different from the neutrality. The current study presents these relationships and suggests possibilities for their further applications.

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.

Effects of Salt Concentration on Association of the Amyloid Protofilaments of Hen Egg White Lysozyme Studied by Time-resolved Neutron Scattering

Various proteins have been shown to form various aggregated structures including the filamentous aggregates known as amyloid fibrils depending on the solution conditions. Hen egg white lysozyme (HEWL) is one of the proteins that form the amyloid fibrils. To gain insight into the mechanism of this polymorphism of the aggregated structures, we employed a model system consisting of HEWL, pure water, and ethanol, and investigated the kinetic process of the fibril formation in various salt concentrations with time-resolved neutron scattering. It was shown that by addition of NaCl in a range between 0.3 mM and 1.0 mM to HEWL solution in 90% ethanol, gelation occurred, and this gelation proceeded through a two-step process: the lateral association of the protofilaments, followed by the cross-linking of these fibrils formed. Both the structures of the fibrils and the rate of the gelation depended on NaCl concentration. The average structures of the fibrils formed at 1.0 mM NaCl were characterized by the radius of gyration of their cross-section (45.9(+/-0.4)A) and the number of the protofilaments within the fibril (4.10(+/-0.12)), corresponding to the mature amyloid fibrils. A range of intermediate structures was formed below 1 mM NaCl. Above 2 mM NaCl, precipitation occurred because of the formation of amorphous aggregates. Here the branch point to the formation of the mature amyloid fibrils or to the amorphous aggregates was after the formation of the protofilaments. Sensitivity of the aggregated structures to salt concentration suggests that electrostatic interaction plays an essential role in the formation of these structures. The structural diversity both in the fibrils and the aggregated structures of the fibrils can be interpreted in terms of the difference in the degree of the electrostatic shielding at different salt concentrations.

Intra- and intermolecular interaction inducing pyramidalization on both sides of a proline dipeptide during isomerization: an ab initio QM/MM molecular dynamics simulation study in explicit water.

The cis-trans isomerization of the peptide bond preceding a proline plays important roles in protein folding and biological function. Although many experimental and theoretical studies have been done, the mechanism has not yet been clearly elucidated. We studied the cis-trans isomerization of the proline dipeptide (Ace-Pro-NMe) in explicit water by molecular dynamics simulations using a combined potential derived from ab initio quantum mechanics and empirical molecular mechanics. We obtained the free energy landscape during the isomerization by using the umbrella sampling method. The free energy landscape is in good accordance with previous experimental and theoretical values. We observed that in the middle of the isomerization, the prolyl nitrogen transiently takes pyramidal conformations in two polarized directions and that, simultaneously, the prolyl C-N bond extends. We show that these geometrical changes cooperatively transform the prolyl nitrogen from a sp(2)-hybridized electronic state into a sp(3)-hybridized one, and thus realize a transition state that reduces the rotational barriers separating the cis- and trans-states. We also found that the hydration of the prolyl nitrogen stabilizes the negative pyramidal conformation, while an intramolecular interaction mainly stabilizes the positive one. Fluctuations in the polarity and magnitude of the pyramidal conformation during the isomerization are interpreted as a competition between the hydrogen-bonding partners for the prolyl nitrogen between different sides of the pyrrolidine ring.

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.