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.

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

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 conformational sampling is important even with a coarse-grained model which has smoother energy landscapes and reach longer time scales than atomistic models. The lipid bilayer in the un-tilted gel state is a little thicker than that in the tilted gel state, while the area of the lipid bilayer is quite similar. Tilt angle distributions are also analyzed, and the tilt angle of the tilted gel phase is around 30 .

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.

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 ST's 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.