The mechanism of MinD stability modulation by MinE in Min protein dynamics

Abstract

The patterns formed both in vivo and in vitro by the Min protein system have attracted much interest because of the complexity of their dynamic interactions given the apparent simplicity of the component parts. Despite both the experimental and theoretical attention paid to this system, the details of the biochemical interactions of MinD and MinE, the proteins responsible for the patterning, are still unclear. For example, no model consistent with the known biochemistry has yet accounted for the observed dual role of MinE in the membrane stability of MinD. Until now, a statistical comparison of models to the time course of Min protein concentrations on the membrane has not been carried out. Such an approach is a powerful way to test existing and novel models that are difficult to test using a purely experimental approach. Here, we extract time series from previously published fluorescence microscopy time lapse images of in vitro experiments and fit two previously described and one novel mathematical model to the data. We find that the novel model, which we call the Asymmetric Activation with Bridged Stability Model, fits the time-course data best. It is also consistent with known biochemistry and explains the dual MinE role via MinE-dependent membrane stability that transitions under the influence of rising MinE to membrane instability with positive feedback. Our results reveal a more complex network of interactions between MinD and MinE underlying Min-system dynamics than previously considered.

Forceful patterning: theoretical principles of mechanochemical pattern formation

“…The dynamics in the bulk are coupled to those on the surface through a boundary condition accounting for particle conservation: the flux of particles leaving and entering the cytosol is balanced by the rates of membrane binding and unbinding. Modeling details, including cooperative binding (Loose et al , 2008), further biochemical reactions (Meinhardt & Boer, 2001; Loose et al , 2011; Park et al , 2011; Ayed et al , 2017; preprint: Carlquist & Cytrynbaum, 2021), protein polymerization (Drew et al , 2005; Cytrynbaum & Marshall, 2007), interactions with particular lipids localized at the cell poles (Renner & Weibel, 2012), and advective cytoplasmic flows (Vecchiarelli et al , 2014; Meindlhumer et al , 2023), have been extensively studied and are proposed to play important roles in regulating Min patterns (Vecchiarelli et al , 2016; Wettmann & Kruse, 2018; Ramm et al , 2019; Takada et al , 2022).…”

“…Different groups have shown that the geometry of the cell may play a crucial role in the robust selection of standing wave patterns (Schweizer et al , 2012; Zieske & Schwille, 2013, 2014; Wu et al , 2015). Although the exact mechanism behind the emergence of patterns in different geometries is still under debate (Park et al , 2011; Halatek & Frey, 2012; Halatek et al , 2018; Wettmann & Kruse, 2018; Ramm et al , 2019; preprint: Carlquist & Cytrynbaum, 2021; Takada et al , 2022), protein depletion has been suggested to play an important role in the formation of standing waves (Vecchiarelli et al , 2016), and Brauns et al (2021) propose that this arises due to the narrow geometry of the cells. The boundary condition for the cytosolic concentrations enforces protein conservation.…”