Mesoscale spatial patterning in the Escherichia coli Min system: Reaction–diffusion versus mechanical communication

Spatiotemporal patterning in biological systems is a fascinating subject. In this issue of PNAS, Ivanov and Mizuuchi (1) analyze patterning by Escherichia coli Min proteins in vitro.

In vivo, coordinated pole-to-pole oscillations of MinD, a membrane-binding ATPase, and its binding partner MinE specify cell division specifically at midcell (Fig. 1 A and B; reviewed in ref. 3). Prior studies modeled Min system patterning with a particular version of the Turing-style “reaction–diffusion” paradigm (4): reactions occur on the surface, generating solution inhomogeneities, which are counteracted by diffusion of the components in the solution (e.g., ref. 5). Ivanov and Mizuuchi (1) observe biologically relevant patterning in conditions where solution inhomogeneities cannot arise. Furthermore, because the surface-to-volume ratio of their system is orders of magnitude different from that present in vivo, bulk diffusion coefficients are unlikely to play critical roles. They conclude that patterning reactions are taking place exclusively on the surface, with the solution serving only as a homogeneous reservoir of components.

Fig. 1.

In vivo Min oscillations and relationship to in vitro amoebae. (A) Pole-to-pole oscillation of MinD-GFP. Time scale is in seconds. (Scale bar: 2 μm.) (Images courtesy of P. de Boer.) (B) E-ring dynamics. A peripheral ring defined by increased local density of MinE-GFP emerges at the edge of a MinD-rich polar zone (e.g., t = 0 s in A), which it then follows during poleward recession (see text). (Images adapted from ref. 2 with permission from Macmillan Publishers Ltd: EMBO J 20:1563–1572, Copyright 2001; http://www.nature.com/emboj/index.html.) (C and D) Analogy between amoeba forms observed in vitro (C Right and D) and the in vivo E-ring/MinD polar zone state (C Left and B). (Scale bar: 5 μm.) (Image in C Left adapted from ref. 9 with permission from Macmillan Publishers Ltd: EMBO J 20:1563–1572, Copyright 2001; http://www.nature.com/emboj/index.html; images in C Right and D reprinted from ref. 1 with permission from PNAS.)

A specific MinDE reaction pathway is proposed (1). A particular species binds to the membrane surface, nucleating a multistep series of MinD/E polymerization and depolymerization events that, ultimately, leaves behind the original nucleating species but in a different molecular form (e.g., ADP-bound versus ATP-bound). Intermediate transitions are proposed to be modulated by mechanical feedback from membrane–protein interactions. Mechanical inputs into biochemical reactions may not be uncommon (e.g., refs. 6 and 7).

Ivanov and Mizuuchi (1) propose a new approach to surface-mediated patterning. They speculate that particular protein–membrane complexes arising along the biochemical pathway create local deformations in the membrane structure, differently for different complexes. The spatial communication for patterning then arises by indirect mechanically based interactions among such species, rather than by direct protein–protein contacts and/or conventional two-dimensional diffusion of reactants. In accord with such a mechanism, the proposed locally evolving reaction sequence does not require direct interactions among components independently bound on the membrane. The potential for stressed deformations in the Min reaction is clear: helical MinD polymers are known to deform lipid bilayers into tubes, as modulated by MinE and nucleotide (e.g., ref. 8).

Ivanov and Mizuuchi (1) propose two specific effects: repulsive interactions between locally deformed protein–membrane complexes and mesoscale reorganization via redistribution of mechanical stress.

Oscillations and Waves

Fluorescently tagged MinD and MinE, and ATP, are introduced into a flow cell whose surfaces are coated with lipids of desired composition. MinD-rich zones emerge via local nucleation and expansion, and then fuse. The resulting broad area then undergoes temporal oscillations. Biochemical events of the reaction pathway occur in sequence over time, homogeneously and synchronously across the surface. The observed sequence implies existence of a reaction-based timing mechanism that operates over quite long time scales, of up to a few minutes. Oscillations eventually stall and are replaced by trains of waves. Biochemical reaction species are now displayed in sequence in 1D space across the wave band, rather than in time. Presumptively, at each location on the membrane, the same biochemical series is occurring as observed in oscillations.

In both patterns, the appearance of MinD-rich zones is inferred to involve autocatalytic binding of “initiation centers” (nature of autocatalysis not specified). Importantly, reaction centers sparsely occupy the surface. Because entropy might not suffice for this effect, the authors propose that each initiation center binding creates a local deformation of the membrane whose effects spread outward over distances of ∼100 nm, thereby discouraging other initiation center bindings in the immediate vicinity. A physically reasonable basis for a local zone of inhibitory deformation is not specified. Oscillations and waves also both have gaps between cycles. These gaps are proposed to arise because the molecular residuum of the biochemical cycle comprises a “dissociation center” that, via a local deformation, again inhibits initiation center binding in its vicinity. Slow unbinding of this species from the membrane would delay onset of a next cycle, creating the observed gaps.

Amoebae

The wave pattern also eventually stalls, leading to the appearance of amoebae, where a central MinD-rich zone containing reaction intermediates from early stages of the biochemical cycle is surrounded by a tight peripheral MinE-rich ring containing a species that arises later in the cycle (MinDE-ADP polymers) (Fig. 1D). Here, the continuous gradient of reaction species seen across wave bands has changed to a state involving more discrete spatial segregation. Formation of amoebae thus implies reorganization of reaction species in two-dimensional space. Amoebae arise abruptly at the trailing edge of a wave, via appearance of many similarly sized “cells”; amoebae also grow and divide, into the same similarly sized cells. Abrupt occurrence and resultant even spacing are characteristic of transitions provoked by mechanical stress, with relief of stress providing a lower energy state. Ivanov and Mizuuchi (1) propose that stress arises because sparsely distributed MinDE-ADP polymers, each generating a localized membrane deformation, together comprise an unstable higher-energy state. In contrast, after amoeba formation, high-density clustering of these complexes within the narrow peripheral ring would be a lower-energy state in which the system stabilizes. Irrespective of mechanism, the precise basis for the movements of reaction species required for spatial reorganization remains to be determined.

The appearance of amoebae can be explained because stalling of wave progression increases the surface density of the stress-inducing species, particularly at the trailing edge of the wave where they are most abundant, thereby triggering stress-promoted reorganization. The progression from oscillations to waves analogously increases spatial segregation of earlier and later reaction species and, like amoeba formation, might be triggered by stalling of the earlier form. In both transitions, stalling is proposed to result from progressive accumulation of dissociation centers deposited over previous cycles. This build-up, by its effects on initiation-center binding, decreases the likelihood of oscillation cycle onset or progression of a wave front.

How could the in vitro observations of Ivanov and Mizuuchi (1) relate to the MinDE oscillation cycle observed in vivo (Fig. 1 A and B)?

Events at a single pole are well recapitulated. (i) An in vivo cycle initiates by appearance of a MinD-rich zone at one cell pole, analogous to the autocatalytic spreading of MinD-rich zones in vitro. (ii) A MinE-rich E-ring now develops at the edge of the polar zone near the midcell, after which the entire zone, with E-ring, recedes toward its pole. Amoeba behaviors recapitulate these events almost exactly, in time and space (Fig. 1 C and D). Projection of the E-ring/polar zone membrane surface onto a perpendicular plane centered at the corresponding cell pole yields an amoeba morphology. The two forms have similar dimensions (micrometers). Small amoebae tend to shrink, analogous to polar zone recession, with the E-ring disappearing together with the MinD-rich zone in both cases. Amoebae sometimes grow; analogously, E-ring/polar zones sometimes extend toward the other pole before shrinking (2). Dynamic changes occur over time scales of seconds in both cases. E-ring appearance in vivo is preceded by a diffuse area of MinE enrichment similar to the trailing edge of an in vitro wave. (iii) Finally, as a polar zone recedes, the depolymerizing MinDE-ADP polymers in its E-ring would give rise to a trail of dissociation centers, thus ensuring delayed onset of the next cycle at that pole.

What about coordination of events between poles? Spatial coordination is explained by the fact that the residual presence of dissociation centers at one end will block spreading of a polar zone into that region from the opposite end. In contrast, temporal oscillation between the two poles of the cell is not recapitulated in vitro. However, Ivanov and Mizuuchi (1) do present evidence that initiation of an oscillation cycle requires prior interaction of an involved species with the membrane. Thus, initiation of a cycle at one end of the cell may require a certain concentration of a species that is released via depolymerization of membrane-associated reaction centers at the opposite end (K. Mizuuchi, personal communication). Such a model implies that a cycle at one end would initiate at a specific point in the cycle at the opposite pole. Correspondingly, the appearance of a MinD-rich polar zone at one end of the cell occurs just at the onset of recession of the E-ring/polar zone at the other end of the cell. The critical reaction species could be MinD-ATP dimers, which are released during biochemical depolymerization and are proposed to create initiation centers.

By this scenario, bulk diffusion coefficients and cellular surface-to-volume ratios would indeed play a critical role in Min oscillations, but only in determining temporal coordination. Spatial patterning and coordination would, instead, involve surface-only processes, where communication depends on redistribution of membrane deformations and accompanying mechanical stress.

General Implications: Mesoscale Patterning via Mechanical Repulsion

The presented findings (1) suggest that stress-mediated spatial reorganization can occur over large (mesoscale) distances. Furthermore, the spatial dimensions of a mechanical system are determined by its physical parameters. Thus, such effects could potentially be relevant to cellular or subcellular patterning in all types of cells and subcellular membrane compartments. In addition, the effects inferred here for protein–membrane interactions could be equally applicable to protein–DNA–chromatin–chromosome–RNA interactions. More generally, mechanical effects might govern mesoscale spatiotemporal patterning in chromosomal “compartments” (as proposed in ref. 10). It is interesting to note that Turing initially considered elasticity of substrates and mechanical stress as a part of the physical aspects of the system, although he ultimately decided that these could be ignored for his derivation (4).

The authors (1) also make the novel proposal of mechanical repulsion between locally deformed protein–membrane complexes. Repulsion would affect initiation center binding and provoke longer-scale reorganizations (and also, potentially, shorter-scale even spacing) along the surface. This provocative proposition, the precise basis for which is thus far unspecified, differs from more conventional mechanical models where, typically, a change involving imposition of stress autocatalytically favors the occurrence of further such changes or, oppositely, a stress-promoted change gives relief of stress that disfavors the occurrence of further stress-promoted changes.

Advances in analysis of the Min system from the Mizuuchi laboratory seem to set the stage for a new phase in our understanding of biopatterning at levels ranging from general paradigms to specific molecular mechanisms.