The microbial rhodopsins are a class of membrane proteins with seven transmembrane helices harboring an all-trans retinal retinal chromophore. The functions of microbial rhodopsins are diverse, including light-driven cation and anion pumps, light-gated cation and anion channels, positive and negative phototaxis sensors, photochromic sensors, and light-activated enzymes. Here I focus on the ion-transporting rhodopsins and explain the mechanism of the pumps and the channels revealed by the electrophysiological studies. Characteristics of light-gated cation channel (channelrhodopsins) and proton-pumping rhodopsins are discussed.

Robustness and plasticity are important characteristics common to a variety of biological systems and have attracted much attention not only from biologists but also from physicists interested in biosystems. Whereas robustness concerns insensitivity to perturbations against external changes, plasticity concerns changeability upon external inputs. How these two properties are compatible with each other is an important question to be addressed. Recently we have uncovered universal reciprocity relationship between the robustness of period and plasticity of phase in biochemical oscillators such as circadian clocks. We review this relationship and discuss its theoretical origin and biological relevance.

Spiral waves are often observed in wide variety of reaction-diffusion systems. Those in cardiac tissues are important since they are related to serious disease that threatens human lives, such as atrial and ventricular fibrillation. We consider the unpinning of spiral waves around two types of defects using high-frequency pacing. The defects are classified into two kinds, i.e, that without any diffusive interaction with the environment, and that with diffusive interaction. We found that the threshold frequency is lower for the defect with diffusive interaction than for the one without it.