Tetsuro Nagai

Synchronization of Circadian Oscillation of Phosphorylation Level of KaiC In Vitro

In recent experimental reports, robust circadian oscillation of the phosphorylation level of KaiC has been reconstituted by incubating three cyanobacterial proteins, KaiA, KaiB, and KaiC, with ATP in vitro. This reconstitution indicates that protein-protein interactions and the associated ATP hydrolysis suffice to generate the oscillation, and suggests that the rhythm arising from this protein-based system is the circadian clock pacemaker in cyanobacteria. The mechanism of this reconstituted oscillation, however, remains elusive. In this study, we extend our previous model of oscillation by explicitly taking two phosphorylation sites of KaiC into account and we apply the extended model to the problem of synchrony of two oscillatory samples mixed at different phases. The agreement between the simulated and observed data suggests that the combined mechanism of the allosteric transition of KaiC hexamers and the monomer shuffling between them plays a key role in synchronization among KaiC hexamers and hence underlies the population-level oscillation of the ensemble of Kai proteins. The predicted synchronization patterns in mixtures of unequal amounts of two samples provide further opportunities to experimentally check the validity of the proposed mechanism. This mechanism of synchronization should be important in vivo for the persistent oscillation when Kai proteins are synthesized at random timing in cyanobacterial cells.

Replica-exchange molecular dynamics simulation of a lipid bilayer system with a coarse-grained model

We performed a replica-exchange molecular dynamics (REMD) simulation of a lipid bilayer system in order to study sol-gel phase transitions. The REMD method allows one to enhance conformational sampling efficiency and to study the system in a wide temperature range at once. We used a coarse-grained model MARTINI. The results show a large jump in internal energy and thickness of the bilayer around 295 K, which suggests a sol-gel phase transition. The bilayer seems to have two states in the gel state. One is a tilted gel state and the other is an untilted gel state. A previous work with MARTINI force field reported only the untitled gel state. This indicates that conformational sampling efficiency is crucial even with a coarse-grained model, which has smoother energy landscapes and reaches longer time scales than atomistic models.

Phase Behavior of a Lipid Bilayer System Studied by a Replica-Exchange Molecular Dynamics Simulation

A replica-exchange molecular dynamics (REMD) simulation of a lipid bilayer system has been performed in order to study the sol–gel phase transitions. The REMD method enhances conformational sampling efficiency, and one can study the system in a wide temperature range at once. A coarse-grained model MARTINI was used. The results show sudden changes in enthalpy, bilayer thickness, and area of bilayer around 296 K. A peak in heat capacity was also observed around this temperature. These results suggest sol–gel phase transitions. We also investigated temperature dependences of composite energy terms. According to potential of mean force maps and tilt angle distributions, the bilayer is found to have two states in the gel phase. One is a tilted gel state and the other is an un-tilted gel state. A previous work with MARTINI force field reported only the un-titled gel state. Another previous work with MARTINI force field reported titled gel state only with externally applied tension. This suggests that enhanced ...

Simulated tempering and magnetizing: application of two-dimensional simulated tempering to the two-dimensional Ising model and its crossover.

We have performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional STs applicability to dealing with phase transitions and study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus this simulation can be referred to as simulated tempering and magnetizing (STM). We also performed simulated magnetizing (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. As discussed in previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Flipping of the entire magnetization did not occur in the SM simulations under the critical temperature T{c} in large-lattice-size simulations; however, the phase changed through the high-temperature region in the STM simulations. Thus the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study a wide area of the phase space. We discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior is clearly observed in the simulations, in agreement with the theoretical implications.

Mass-scaling replica-exchange molecular dynamics optimizes computational resources with simpler algorithm

We develop a novel method of replica-exchange molecular dynamics (REMD) simulation, mass-scaling REMD (MSREMD) method, which improves numerical stability of simulations. In addition, the MSREMD method can also simplify a replica-exchange routine by eliminating velocity scaling. As a pilot system, a Lennard-Jones fluid is simulated with the new method. The results suggest that the MSREMD method improves the numerical stability at high temperatures compared with the conventional REMD method. For the Nosé-Hoover thermostats, we analytically demonstrate that the MSREMD simulations can reproduce completely the same trajectories of the conventional REMD ones with shorter time steps at high temperatures. Accordingly, we can easily compare the computational costs of the REMD and MSREMD simulations. We conclude that the MSREMD method decreases the instability and optimizes the computational resources with simpler algorithm.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized‐ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass‐scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed.

Application of simulated tempering and magnetizing to a two-dimensional Potts model

We apply the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to investigate STM?s applicability further. The temperature and the external field are treated as dynamical variables updated during the STM simulations. On the basis of adequate information obtained by STM for several lattice sizes L???L (up to 160?160), we also perform a number of conventional canonical simulations of larger lattices in order to illustrate the crossover behavior of the Potts model in an external field with increasing L. The temperature and external field for the larger lattice size simulations are chosen by extrapolation of the detailed information obtained by STM. We present a careful analysis of the crossover-scaling behavior at the phase transitions with respect to the lattice size as well as the temperature and external field. The crossover behavior is clearly observed in the simulations in agreement with theoretical predictions.

Critical size dependence of domain formation observed in coarse-grained simulations of bilayers composed of ternary lipid mixtures

Model cellular membranes are known to form micro- and macroscale lipid domains dependent on molecular composition. The formation of macroscopic lipid domains by lipid mixtures has been the subject of many simulation investigations. We present a critical study of system size impact on lipid domain phase separation into liquid-ordered and liquid-disordered macroscale domains in ternary lipid mixtures. In the popular di-C16:0 PC:di-C18:2 PC:cholesterol at 35:35:30 ratio mixture, we find systems with a minimum of 1480 lipids to be necessary for the formation of macroscopic phase separated domains and systems of 10 000 lipids to achieve structurally converged conformations similar to the thermodynamic limit. To understand these results and predict the behavior of any mixture forming two phases, we develop and investigate an analytical Flory-Huggins model which is recursively validated using simulation and experimental data. We find that micro- and macroscale domains can coexist in ternary mixtures. Additionally, we analyze the distributions of specific lipid-lipid interactions in each phase, characterizing domain structures proposed based on past experimental studies. These findings offer guidance in selecting appropriate system sizes for the study of phase separations and provide new insights into the nature of domain structure for a popular ternary lipid mixture.

Momentum and Velocity Scaling Rules in Replica-Exchange Molecular Dynamics Simulations with Mass Manipulation

The authors have recently presented the mass-scaling replica-exchange molecular dynamics (MSREMD) method [J. Chem. Phys. 141, 114111 (2014)], in which all masses are scaled in proportion to temperature for better numerical stability with a large time step. In addition, the scaling of masses, performed in advance of the simulation, can be substituted for the velocity scaling necessary after every accepted replica-exchange attempt, and the algorithm can thereby be simplified. In this work, the authors present the mass-manipulating REMD (MMREMD) method, where arbitrary mass scaling is employed. Rules for momentum and velocity scaling are formalized for the MMREMD method, followed by a demonstration with two replicas. Adherence to these rules is crucial for sampling of the correct canonical distribution. The authors also review and discuss a previous study as a sample application of the MMREMD method.

Gaussian mixture model for coarse-grained modeling from XFEL

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.