Directing Min protein patterns with advective bulk flow

Abstract

The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.

Fig. 1. Min models and simulation results.

A Basic illustration of setup used for simulations as well as experiments. B Illustration of the effect of bulk flow on pattern formation. MinD advection in the bulk shifts its concentration profile in the bulk relative to the membrane pattern, leading to an increase in the bulk concentration on the upstream side of wave crests relative to the downstream side. This enhances the recruitment rate (green arrows) on the upstream side relative to the downstream side and thus, results in a movement of the membrane pattern (but not the individual proteins) in the upstream direction. C Diagram depicting the interactions in the full switch model. This model includes the MinE switch. MinD-ATP binds the membrane, recruiting more MinD-ATP as well as reactive MinE. After MinE stimulates ATP-hydrolysis, MinD-ADP and MinE detach from the membrane. MinD needs to ADP for ATP in the bulk. MinE temporarily assumes a latent state before rebinding to the membrane. D, E Typical spatial pattern (snapshots) and kymograph of the membrane protein density found in the full switch model at high E:D ratios (D) and at low E:D ratio (E). F For high E:D ratios the full switch model can be simplified into the reduced switch model. MinE bulk gradients become negligible. G At low E:D ratios, the behavior of the Min system is captured well by the skeleton model. This model does not include the MinE switch.

Fig. 2. Experimental data showing how patterns respond to flow at different E:D ratios.

Data are for MinE-wildtype (A, B) and MinE-L3E/I24N (C), with bulk flow directed left-to-right. Min patterns (outer left and outer right columns) show MinD-Cy3 in magenta and MinE-Cy5 in green. All scale bars are 100 μm. The results of wave-propagation analysis calculated for MinD-Cy3 data are represented as 2D histograms (center columns) with binning size (25 nm/s) × (25 nm/s), showing counts for directionality (v_x, v_y). Left half of the figures displays an exemplary image as well as wave-propagation analysis for the no-flow case. Right half of the figures displays an exemplary image as well as wave-propagation analysis with flow. Images were stitched from 3 × 3 fields of view. A Upstream propagation was observed in experiments for high E:D ratio (initial 10). B Downstream propagation observed for low E:D ratio (initial 2, corrected 1.3). C Downstream propagation observed for the MinE-L3E/I24N mutant at E:D = 0.05.

Fig. 3. Phase diagram displaying the predicted direction of pattern propagation.

A Phase diagram displaying the predicted direction of pattern propagation. Red and blue regions indicate the parts of the parameter space where exclusively downstream or upstream patterns are observed, respectively. Green region indicates the multistability regime, where the propagation direction depends on the initial conditions. If simulations are initiated from the homogeneous steady state, the observed propagation direction is downstream below the black dashed line, and upstream above it. Details on the adiabatic parameter sweeps and the data points underlying the phase diagram are provided in SI Sec. S1.5 and Fig. S6. B Schematic visualizing that the transition flow velocity depends on the wavelength of the pattern. Upon increasing the flow velocity, larger wavelength patterns reverse the propagation direction at a higher flow velocity.

Fig. 4. Experimental data showing how Min patterns respond to a sequence of flow rates.

A Min patterns for different flow velocities at initial ratio E:D = 5 (corrected 3.6) sampled at the same location within the flow channel. Channel MinD-Cy3 in cyan, scale bars 100 μm. Images stitched from 3 × 3 fields of view. B Polar histogram showing counts per angular segment for initial ratio E:D = 3 (corrected 2.1). C Idem for initial ratio E:D = 3 (corrected 2.1). D Idem for initial ratio E:D = 5 (corrected 3.6). E Idem for initial ratio E:D = 5 (corrected 4.3). F Peak velocity magnitude ± FWHM/2 (calculated from histogram with binning size 10 nm/s) shown as function of flow rate for different E:D ratios. G Overview of experiments done for wildtype MinE. Downstream and upstream fractions are obtained from histogram counts per angular segment, with one series (horizontal line) representing one experiment. Size of fraction is given by the segment’s radius. Red indicates downstream flowing patterns, blue indicates upstream patterns. Source data are provided as a Source Data file. Full experimental analysis is shown in the SI.