Topological turbulence on the membrane of a living cell
Signaling protein waves during cell development often carry the vital role of laying out organizational information that needs to be spatially and temporally well-structured. With the building blocks being nanometer-size protein molecules and the target range often the tens-of or hundreds-of-micron-size the whole cell, how as physicists can we understand such propagation of order? The fact that cells are constantly comsuming energy to maintain such structures poses extra interests as well as challenges, since we then deal with an out-of-equilibrium system and there are no well-established order parameters in sight.
We investigated this question by combining topological analysis with experimental studies in the sea star egg cell. During the early egg cell development, Rho-GTP signaling proteins are capable of forming a variety of steady-state wave patterns that maintain coherent spatial and temporal periodicity. Studying the evolution of reconstructed phase fields, we identified the underlying topological defect dynamics that exhibit characteristic statistics and scaling laws. By a multi-scale analysis of the accompanying phase velocity field, we further found out the unexpected close correspondence between organization of phase information flow on cell membrane and an universal class of two-dimensional turbulence.
Check here for the published project: T. H. Tan1, J. Liu1, P. W. Miller1, M. Tekant, J. Dunkel, N. Fakhri..