Prion is a misfolded protein that has a unique propagation system by the change of the tertiary structure. The concept of prion is conserved among various species, such as bacteria, yeast, anaspidea, sheep, and human. A kind of prions, such as mammalian PrP, causes a serious disease by widespread neuronal dysfunction. However, it remains unclear why the hallmark concept of prions has been preserved across diverse species form prokaryotes to eukaryotes. Here we summarize the researches of prion proteins about the function of the cellular prion or the dysfunction triggering neurotoxicity. We also highlight key findings that liquid-liquid phase separation (LLPS) of proteins plays a crucial role for the existence of prion proteins in living organisms. The LLPS of protein is expected as a new research target for polymer science, solution thermodynamics, biophysics, spectroscopy, and drug discovery.
The idea of synthetic dimensions is to use nonspatial degrees of freedom, such as spin or angular momentum degrees of freedom, as effective dimensions and to simulate high dimensional models using low dimensional physical platforms. We review recent progress of the study of topological lattice models using synthetic dimensions in various atomic, molecular, and optical systems such as ultracold atomic gases and photonics.
The Atiyah–Patodi–Singer index theorem is related to the bulk-edge correspondence of symmetry protected topological insulators. The mathematical set-up for this theorem is, however, unnatural since it imposes on the fermion fields a non-local boundary condition known as the “APS boundary condition” by hand, which is unlikely to be realized in the condensed matter systems. In 2017, we showed that the same integer as the APS index can be given by the eta-invariant of the domain-wall fermion Dirac operator. Recently, we invited three mathematicians, Mikio Furuta, Shinichiroh Matsuo, and Mayuko Yamashita to our group and proved that this correspondence is not a coincidence but generally true.
Variety of non-living self-propelled particles have been reported, for example, metal particles moving in hydrogen peroxide solution, oil droplets swimming in surfactant aqueous solution, and solid particles sliding on water. The self-propelled particles change the environmental condition around them and spontaneously break spacial symmetry by themselves resulting in stably generating driving force. In addition, the self-propelled particles interact each other, and thus, induce transition of collective behaviors depending on number density. Recently, mode change of self-propelled motion sliding on water, that is camphor disk, was observed with increase in the number density. The circular camphor disks showed continuous motion with low number density. With overcoming threshold value, the disks motion change to oscillatory motion, where the disks alternate rest and rapid motion. The mode-bifurcation was explained using mathematical model, where the essential factor was the coupling of slow dynamics of mean camphor concentration field and fast process of disk motion.