We have developed a thermodynamic theory of stochastic phenomena. This theory reproduces the first and second law of thermodynamics and Helmholtz free energy, starting from the Langevin equation. Based on this theory, we have recently proposed a principal mechanism of autonomous free-energy transducers [1]. This principle, called bidirectional control, has been well accepted by the community. Next, this principle was applied to the molecular motors, especially to the myosin family and kinesin family. It turned out that (1) although a big apparent differences of the chemo-mechanical coupling cycles of these two motors, they undergo the same intra-molecular cycle; and that (2) the two motors uses the same parity, among the two possible ways of bidirectional regulation, [2]. By contrast, we have found that another principle of transduction, which is more or less complementary to the former one, works well for the membrane transpoters [3]. This transducer uses essentially only one allosteric degree of freedom, while the former used two. These findings will serve for the understanding of biological comprehension from the dynamics viewpoint. We have also developed a theoretical technique to analyze stochastic trajectories of anistropic objects [4].

[1] Ken Sekimoto: Physica D 205 242 (2005). .

[2] Ken Sekimoto: 6 Comptes Rendus Physique, 8 (2007) 650-660 .

[3] Eiro Muneyuki and Ken Sekimoto: (submitted to Phys. Rev. E) .

[4] Claire Ribrault, Antoine Triller and Ken Sekimoto: Phys. Rev. E 75, 021112 (2007) .