In the living cell, proteins are able to organize space much larger than their dimensions. In return, changes of intracellular space can influence biochemical reactions, allowing cells to sense their size and shape. Despite the possibility to reconstitute protein selforganization with only a few purified components, we still lack knowledge of how geometrical boundaries affect spatiotemporal protein patterns. Following a minimal systems approach, we used purified proteins and photolithographically patterned membranes to study the influence of spatial confinement on the self-organization of the Min system, a spatial regulator of bacterial cytokinesis, in vitro. We found that the emerging protein pattern responds even to the lateral, two-dimensional geometry of the membrane such that, as in the three-dimensional cell, Min protein waves travel along the longest axis of the membrane patch. This shows that for spatial sensing the Min system does not need to be enclosed in a three-dimensional compartment. Using a computational model we quantitatively analyzed our experimental findings and identified persistent binding of MinE to the membrane as requirement for the Min system to sense geometry. Our results give insight into the interplay between geometrical confinement and biochemical patterns emerging from a nonlinear reaction-diffusion system. in vitro reconstitution | microstructures | supported lipid bilayers | spontaneous protein waves | Min oscillations P attern formation is one of the most intriguing features of biological systems. It takes place on many different spatial and temporal scales and several levels of complexity (1). Inside of the living cell, nonlinear reaction-diffusion dynamics allow proteins to encode for positional information (2-5), required to coordinate complex processes like cell division (6, 7), cell motility (8, 9), or give rise to information flow within the cell (5, 10). In reverse, cell geometry presumably affects such protein patterns, allowing processes within the cell to respond to changes in cell size and shape (11). However, how these reaction-diffusion systems sense the shape and the dimensions of the cell remains an outstanding question and requires decisive experimental testing.A well-studied example for a biochemical reaction-diffusion process is the spatiotemporal oscillations of the Min proteins in Escherichia coli (12, 13). The Min system positions the division septum in the cell to its center, such that it divides into two equally sized daughter cells. Oscillations emerge from the interactions of two proteins and the cytoplasmic membrane (14-16): MinD, a membrane-binding ATPase, and MinE, the activator of ATP hydrolysis and thus, antagonist of MinD in its membranebound state. In vivo, the intrinsic wavelength of Min protein oscillations is similar to the size of the E. coli cell, about 5 μm versus 3 μm cell length and 1 μm cell diameter (17). The ability of the Min system to sense the enclosed volume of the bacterial cell has been demonstrated in E. coli cells, which lost th...

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system's geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.

Conventional protein kinase Cs (cPKCs) are key signaling proteins for transducing intracellular Ca2+ signals into downstream phosphorylation events. However, the lifetime of individual membrane-bound activated cPKCs is an order of magnitude shorter than the average time needed for target-protein phosphorylation. Here, we employed intermolecular Förster resonance energy transfer (FRET) in living cells combined with computational analysis to study the spatial organization of cPKCs bound to the plasma membrane. We discovered Ca2+-dependent cPKC nano-clusters that significantly extend cPKC’s plasma-membrane residence time. These protein patterns resulted from self-assembly mediated by Ca2+-binding C2-domains, which are widely used for membrane-targeting of Ca2+-sensing proteins. We also established clustering of other unrelated C2-domain containing proteins, suggesting that nano-cluster formation is a key step for efficient cellular Ca2+-signaling.

In the rod-shaped bacterium Escherichia coli, the center is selected by the Min-proteins as the site of cell division. To this end, the proteins periodically translocate between the two cell poles, where they suppress assembly of the cell division machinery. Ample evidence notably obtained from in vitro reconstitution experiments suggests that the oscillatory pattern results from self-organization of the proteins MinD and MinE in presence of a membrane. A mechanism built on cooperative membrane attachment of MinD and persistent MinD removal from the membrane induced by MinE has been shown to be able to reproduce the observed Min-protein patterns in rod-shaped E. coli and on flat supported lipid bilayers. Here, we report our results of a numerical investigation of patterns generated by this mechanism in various geoemtries. Notably, we consider the dynamics on membrane patches of different forms, on topographically structured lipid bilayers, and in closed geometries of various shapes. We find that all previously described patterns can be reproduced by the mechanism. However, it requires different parameter sets for reproducing the patterns in closed and in open geometries.

The distributions of many proteins in rod-shaped bacteria are far from homogeneous. Often they accumulate at the cell poles or in the cell centre. At the same time, the copy number of proteins in a single cell is relatively small making the patterns noisy. To explore limits to protein patterns due to molecular noise, we studied a generic mechanism for spontaneous polar protein assemblies in rod-shaped bacteria, which are based on cooperative binding of proteins to the cytoplasmic membrane. For mono-polar assemblies, we find that the switching time between the two poles increases exponentially with the cell length and with the protein number. This feature could be beneficial to organelle maintenance in ageing bacteria.