Prof Natsuhiko Yoshinaga

Geometric control of wave instability in Min oscillations

Emergence of patterns in biological systems has attracted much attention
among broad areas in science to understand the generic mechanism of
biological functions associated with these patterns. Example includes
cell motility with active waves, Min oscillations for cell division,
cytoplasmic flows, and so on. Among them, the Min systems have been
studied intensively due to their robust realisation both in vivo and
vitro systems. Stimulated by these experiments, several theoretical
models have been proposed. These models share some aspects of the
oscillation; it is widely accepted that this phenomenon is described by
the cyclic processes in which MinD proteins are recruited on a membrane,
then MinE proteins are recruited, and finally both proteins detach from
the membrane. What distinguishes one model from another is
cooperativity. Without cooperativity, the system does not exhibit
patterns. The two mechanisms have been proposed; one is that MinD and
MinE are able to form aggregates that result in phase separation on a
membrane. The second possibility is cooperative attachment and/or
detachment. In this approach, the nonlinear reaction terms are included
in the models so to reproduce the waves of the concentration of Min
proteins.

Within both approaches, there are many choices for explicit forms of
aggregation and nonlinear terms. In this work, we consider the effect of
the shape of the membrane. We found that an ellipsoidal shape selects
the standing wave by its anisotropic geometry. This is in contrast with
a spherical membrane in which the rotating wave is stable. We able to
compute the threshold between these two types of the waves on varying
aspect ratio and compare with the numerical results. The result suggests
that the standing wave occurring in E-coli is dominated by its elongated
anisotropic shape, and may be controlled by changing the shape.