RESUMEN
The theory of polymer dynamics describes the intermediate scattering function for a polymer molecule in terms of relaxation modes defined by normal coordinates for the corresponding coarse-grained model. However, due to the difficulty of defining the normal coordinates for arbitrary polymer molecules, it is generally challenging to express the intermediate scattering function for a polymer molecule in terms of relaxation modes. To overcome this challenge, we propose a general method to calculate the intermediate scattering function for a polymer molecule on the basis of a relaxation mode analysis approach [Takano and Miyashita, J. Phys. Soc. Jpn. 64, 3688 (1995)]. In the proposed method, relaxation modes defined by eigenfunctions in a Markov process are evaluated on the basis of the simulation results for a polymer molecule and used to calculate the intermediate scattering function for that molecule. To demonstrate the effectiveness of the present method, we simulate the dynamics of a linear polymer molecule in a dilute solution and apply it to the calculation of the intermediate scattering function for the polymer molecule. The evaluation results regarding the relaxation modes reasonably describe the intermediate scattering function on the length scale of the radius of gyration of the polymer molecule. Accordingly, we examine the contributions of the pure relaxation and oscillatory relaxation processes to the entire intermediate scattering function.
RESUMEN
Stacked teacups inspired the idea that columnar assemblies of stacked bowl-shaped molecules may exhibit a unique dynamic behavior, unlike usual assemblies of planar disc- and rod-shaped molecules. On the basis of the molecular design concept for creating higher-order discotic liquid crystals, found in our group, we synthesized a sumanene derivative with octyloxycarbonyl side chains. This molecule forms an ordered hexagonal columnar mesophase, but unexpectedly, the columnar assembly is very soft, similar to sugar syrup. It displays, upon application of a shear force on solid substrates, a flexible bending motion with continuous angle variations of bowl-stacked columns while preserving the two-dimensional hexagonal order. In general, alignment control of higher-order liquid crystals is difficult to achieve due to their high viscosity. The present system that brings together higher structural order and mechanical softness will spark interest in bowl-shaped molecules as a component for developing higher-order liquid crystals with unique mechanical and stimuli-responsive properties.
RESUMEN
Recently, dynamic analysis methods in signal processing have been applied to the analysis of molecular dynamics (MD) trajectories of biopolymers. In the context of a relaxation mode analysis (RMA) method, based on statistical physics, it is explained why the signal-processing methods work well for the simulation trajectories of biopolymers. A distinctive difference between the RMA method and the signal-processing methods is the introduction of an additional parameter, called an evolution time parameter. This parameter enables us to better estimate the relaxation modes and rates, although it increases computational difficulty. In this paper, we propose a simple and effective extension of the RMA method, which is referred to as the positive definite RMA method, to introduce the evolution time parameter robustly. In this method, an eigenvalue problem for the time correlation matrix of physical quantities relevant to slow relaxation in a system is first solved to find the subspace in which the matrix is numerically positive definite. Then, we implement the RMA method in the subspace. We apply the method to the analysis of a 3-µs MD trajectory of a heterotrimer of an erythropoietin protein and two of its receptor proteins, and we demonstrate the effectiveness of the method.