It is known that there exist a lot of proteins in living cells, and some of them exhibit their function by the structural change. These active proteins do not propel themselves but induce hydrodynamic flow around them. Taking this into account, we assume that active proteins cyclically change their shapes and thus operate as oscillating force dipoles in low-Reynolds-number fluids. By introducing a stochastic equation for hydrodynamic flow induced by the ensemble of active proteins, we can derive the Fokker-Planck equation for the distribution of particles transported by the hydrodynamic flow. We discussed the dynamics of such particle transport, and found that passive particles can accumulate into a region with higher concentration of active proteins [1, 2]. We also consider the case that the active particles are also transported by the hydrodynamic flow. Finally, the recent preliminary results on the molecular dynamics approach are discussed. We consider the ensemble of dumbbell-shaped particles, in which activity is introduced by oscillating bond lengths [3]. This work is the collaboration with A.S. Mikhailov and Y. Koyano.

Ref.
1) Y. Koyano, H. Kitahata, and A. S. Mikhailov, Phys. Rev. E 94, 022416 (2016).
2) A. S. Mikhailov, Y. Koyano, and H. Kitahata, J. Phys. Soc. Jpn. 86, 101013 (2017).
3) Y. Koyano, H. Kitahata, and A. S. Mikhailov, arXiv:1909.03949 (2019).