Multiple modes of interconverting dynamic pattern formation by bacterial cell division proteins

A programmable reaction-diffusion system for spatiotemporal cell signaling circuit design

Cells self-organize molecules in space and time to generate complex behaviors, but we lack synthetic strategies for engineering spatiotemporal signaling. We present a programmable reaction-diffusion platform for designing protein oscillations, patterns, and circuits in mammalian cells using two bacterial proteins, MinD and MinE (MinDE). MinDE circuits act like "single-cell radios," emitting frequency-barcoded fluorescence signals that can be spectrally isolated and analyzed using digital signal processing tools. We define how to genetically program these signals and connect their spatiotemporal dynamics to cell biology using engineerable protein-protein interactions. This enabled us to construct sensitive reporter circuits that broadcast endogenous cell signaling dynamics on a frequency-barcoded imaging channel and to build control signal circuits that synthetically pattern activities in the cell, such as protein condensate assembly and actin filamentation. Our work establishes a paradigm for visualizing, probing, and engineering cellular activities at length and timescales critical for biological function.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Meiosis: Dances Between Homologs

The raison d'être of meiosis is shuffling of genetic information via Mendelian segregation and, within individual chromosomes, by DNA crossing-over. These outcomes are enabled by a complex cellular program in which interactions between homologous chromosomes play a central role. We first provide a background regarding the basic principles of this program. We then summarize the current understanding of the DNA events of recombination and of three processes that involve whole chromosomes: homolog pairing, crossover interference, and chiasma maturation. All of these processes are implemented by direct physical interaction of recombination complexes with underlying chromosome structures. Finally, we present convergent lines of evidence that the meiotic program may have evolved by coupling of this interaction to late-stage mitotic chromosome morphogenesis.

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

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.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Interaction of the bacterial division regulator MinE with lipid bicelles studied by NMR spectroscopy

The bacterial MinE and MinD division regulatory proteins form a standing wave enabling MinC, which binds MinD, to inhibit FtsZ polymerization everywhere except at the midcell, thereby assuring correct positioning of the cytokinetic septum and even distribution of contents to daughter cells. The MinE dimer undergoes major structural rearrangements between a resting six-stranded state present in the cytoplasm, a membrane-bound state, and a four-stranded active state bound to MinD on the membrane, but it is unclear which MinE motifs interact with the membrane in these different states. Using NMR, we probe the structure and global dynamics of MinE bound to disc-shaped lipid bicelles. In the bicelle-bound state, helix α1 no longer sits on top of the six-stranded β-sheet, losing any contact with the protein core, but interacts directly with the bicelle surface; the structure of the protein core remains unperturbed and also interacts with the bicelle surface via helix α2. Binding may involve a previously identified excited state of free MinE in which helix α1 is disordered, thereby allowing it to target the membrane surface. Helix α1 and the protein core undergo nanosecond rigid body motions of differing amplitudes in the plane of the bicelle surface. Global dynamics on the sub-millisecond time scale between a ground state and a sparsely populated excited state are also observed and may represent a very early intermediate on the transition path between the resting six-stranded and active four-stranded conformations. In summary, our results provide insights into MinE structural rearrangements important during bacterial cell division.

Directing Min protein patterns with advective bulk flow

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.

Distinct architectural requirements for the parS centromeric sequence of the pSM19035 plasmid partition machinery

Three-component ParABS partition systems ensure stable inheritance of many bacterial chromosomes and low-copy-number plasmids. ParA localizes to the nucleoid through its ATP-dependent nonspecific DNA-binding activity, whereas centromere-like parS-DNA and ParB form partition complexes that activate ParA-ATPase to drive the system dynamics. The essential parS sequence arrangements vary among ParABS systems, reflecting the architectural diversity of their partition complexes. Here, we focus on the pSM19035 plasmid partition system that uses a ParB_pSM of the ribbon-helix-helix (RHH) family. We show that parS_pSM with four or more contiguous ParB_pSM-binding sequence repeats is required to assemble a stable ParA_pSM-ParB_pSM complex and efficiently activate the ParA_pSM-ATPase, stimulating complex disassembly. Disruption of the contiguity of the parS_pSM sequence array destabilizes the ParA_pSM-ParB_pSM complex and prevents efficient ATPase activation. Our findings reveal the unique architecture of the pSM19035 partition complex and how it interacts with nucleoid-bound ParA_pSM-ATP.

Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at small scales. Here, we present a semiphenomenological approach which exploits mass conservation in pattern formation, and enables reconstruction of information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction-diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can, in principle, be applied to a wide range of systems with an underlying conservation law.

Catching a Walker in the Act-DNA Partitioning by ParA Family of Proteins

Partitioning the replicated genetic material is a crucial process in the cell cycle program of any life form. In bacteria, many plasmids utilize cytoskeletal proteins that include ParM and TubZ, the ancestors of the eukaryotic actin and tubulin, respectively, to segregate the plasmids into the daughter cells. Another distinct class of cytoskeletal proteins, known as the Walker A type Cytoskeletal ATPases (WACA), is unique to Bacteria and Archaea. ParA, a WACA family protein, is involved in DNA partitioning and is more widespread. A centromere-like sequence parS, in the DNA is bound by ParB, an adaptor protein with CTPase activity to form the segregation complex. The ParA ATPase, interacts with the segregation complex and partitions the DNA into the daughter cells. Furthermore, the Walker A motif-containing ParA superfamily of proteins is associated with a diverse set of functions ranging from DNA segregation to cell division, cell polarity, chemotaxis cluster assembly, cellulose biosynthesis and carboxysome maintenance. Unifying principles underlying the varied range of cellular roles in which the ParA superfamily of proteins function are outlined. Here, we provide an overview of the recent findings on the structure and function of the ParB adaptor protein and review the current models and mechanisms by which the ParA family of proteins function in the partitioning of the replicated DNA into the newly born daughter cells.

CTP and parS coordinate ParB partition complex dynamics and ParA-ATPase activation for ParABS-mediated DNA partitioning

ParABS partition systems, comprising the centromere-like DNA sequence parS, the parS-binding ParB-CTPase, and the nucleoid-binding ParA-ATPase, ensure faithful segregation of bacterial chromosomes and low-copy-number plasmids. F-plasmid partition complexes containing ParB_F and parS_F move by generating and following a local concentration gradient of nucleoid-bound ParA_F. However, the process through which ParB_F activates ParA_F-ATPase has not been defined. We studied CTP- and parS_F-modulated ParA_F-ParB_F complex assembly, in which DNA-bound ParA_F-ATP dimers are activated for ATP hydrolysis by interacting with two ParB_F N-terminal domains. CTP or parS_F enhances the ATPase rate without significantly accelerating ParA_F-ParB_F complex assembly. Together, parS_F and CTP accelerate ParA_F-ParB_F assembly without further significant increase in ATPase rate. Magnetic-tweezers experiments showed that CTP promotes multiple ParB_F loading onto parS_F-containing DNA, generating condensed partition complex-like assemblies. We propose that ParB_F in the partition complex adopts a conformation that enhances ParB_F-ParB_F and ParA_F-ParB_F interactions promoting efficient partitioning.

CTP and parS coordinate ParB partition complex dynamics and ParA-ATPase activation for ParABS-mediated DNA partitioning

ParABS partition systems, comprising the centromere-like DNA sequence parS, the parS-binding ParB-CTPase, and the nucleoid-binding ParA-ATPase, ensure faithful segregation of bacterial chromosomes and low-copy-number plasmids. F-plasmid partition complexes containing ParB_F and parS_F move by generating and following a local concentration gradient of nucleoid-bound ParA_F. However, the process through which ParB_F activates ParA_F-ATPase has not been defined. We studied CTP- and parS_F-modulated ParA_F-ParB_F complex assembly, in which DNA-bound ParA_F-ATP dimers are activated for ATP hydrolysis by interacting with two ParB_F N-terminal domains. CTP or parS_F enhances the ATPase rate without significantly accelerating ParA_F-ParB_F complex assembly. Together, parS_F and CTP accelerate ParA_F-ParB_F assembly without further significant increase in ATPase rate. Magnetic-tweezers experiments showed that CTP promotes multiple ParB_F loading onto parS_F-containing DNA, generating condensed partition complex-like assemblies. We propose that ParB_F in the partition complex adopts a conformation that enhances ParB_F-ParB_F and ParA_F-ParB_F interactions promoting efficient partitioning.

Bulk-surface coupling identifies the mechanistic connection between Min-protein patterns in vivo and in vitro

Self-organisation of Min proteins is responsible for the spatial control of cell division in Escherichia coli, and has been studied both in vivo and in vitro. Intriguingly, the protein patterns observed in these settings differ qualitatively and quantitatively. This puzzling dichotomy has not been resolved to date. Using reconstituted proteins in laterally wide microchambers with a well-controlled height, we experimentally show that the Min protein dynamics on the membrane crucially depend on the micro chamber height due to bulk concentration gradients orthogonal to the membrane. A theoretical analysis shows that in vitro patterns at low microchamber height are driven by the same lateral oscillation mode as pole-to-pole oscillations in vivo. At larger microchamber height, additional vertical oscillation modes set in, marking the transition to a qualitatively different in vitro regime. Our work reveals the qualitatively different mechanisms of mass transport that govern Min protein-patterns for different bulk heights and thus shows that Min patterns in cells are governed by a different mechanism than those in vitro.

Delayed global feedback in the genesis and stability of spatiotemporal excitation patterns in paced biological excitable media

Biological excitable media, such as cardiac or neural cells and tissue, exhibit memory in which a change in the present excitation may affect the behaviors in the next excitation. For example, a change in calcium (Ca²⁺) concentration in a cell in the present excitation may affect the Ca²⁺ dynamics in the next excitation via bi-directional coupling between voltage and Ca²⁺, forming a delayed feedback loop. Since the Ca²⁺ dynamics inside the excitable cells are spatiotemporal while the membrane voltage is a global signal, the feedback loop is then a delayed global feedback (DGF) loop. In this study, we investigate the roles of DGF in the genesis and stability of spatiotemporal excitation patterns in periodically-paced excitable media using mathematical models with different levels of complexity: a model composed of coupled FitzHugh-Nagumo units, a 3-dimensional physiologically-detailed ventricular myocyte model, and a coupled map lattice model. We investigate the dynamics of excitation patterns that are temporal period-2 (P2) and spatially concordant or discordant, such as subcellular concordant or discordant Ca²⁺alternans in cardiac myocytes or spatially concordant or discordant Ca²⁺ and repolarization alternans in cardiac tissue. Our modeling approach allows both computer simulations and rigorous analytical treatments, which lead to the following results and conclusions. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions with the discordant P2 patterns being spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. The theoretical analyses of the coupled map lattice model reveal the underlying instabilities and bifurcations for the genesis, selection, and stability of spatiotemporal excitation patterns.

Understanding the mechanisms of pattern formation in biological systems is of great importance. Here we investigate the dynamical mechanisms by which delayed global feedback affects excitation pattern formation and stability in periodically-paced biological excitable media, such as cardiac or neural cells and tissue. We focus on the formation and stability of the temporal period-2 and spatially in-phase and out-of-phase excitation patterns. Using models of different levels of complexity, we show that when the delayed global feedback is negative, only the spatially in-phase patterns are stable. When the feedback is positive, both spatially in-phase and out-of-phase patterns are stable, and the out-of-phase patterns are spatially random but satisfy that the global signals are temporal period-1 solutions.

Morphology engineering: a new strategy to construct microbial cell factories

Currently, synthetic biology approaches have been developed for constructing microbial cell factories capable of efficient synthesis of high value-added products. Most studies have focused on the construction of novel biosynthetic pathways and their regulatory processes. Morphology engineering has recently been proposed as a novel strategy for constructing efficient microbial cell factories, which aims at controlling cell shape and cell division pattern by manipulating the cell morphology-related genes. Morphology engineering strategies have been exploited for improving bacterial growth rate, enlarging cell volume and simplifying downstream separation. This mini-review summarizes cell morphology-related proteins and their function, current advances in manipulation tools and strategies of morphology engineering, and practical applications of morphology engineering for enhanced production of intracellular product polyhydroxyalkanoate and extracellular products. Furthermore, current limitations and the future development direction using morphology engineering are proposed.

Flow Induced Symmetry Breaking in a Conceptual Polarity Model

Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein reactions and protein transport. Since Turing’s seminal work, the formation of protein patterns resulting from the interplay between reactions and diffusive transport has been widely studied. Over the last few years, increasing evidence shows that also advective transport, resulting from cytosolic and cortical flows, is present in many cells. However, it remains unclear how and whether these flows contribute to protein-pattern formation. To address this question, we use a minimal model that conserves the total protein mass to characterize the effects of cytosolic flow on pattern formation. Combining a linear stability analysis with numerical simulations, we find that membrane-bound protein patterns propagate against the direction of cytoplasmic flow with a speed that is maximal for intermediate flow speed. We show that the mechanism underlying this pattern propagation relies on a higher protein influx on the upstream side of the pattern compared to the downstream side. Furthermore, we find that cytosolic flow can change the membrane pattern qualitatively from a peak pattern to a mesa pattern. Finally, our study shows that a non-uniform flow profile can induce pattern formation by triggering a regional lateral instability.

Probing transient excited states of the bacterial cell division regulator MinE by relaxation dispersion NMR spectroscopy

Bacterial MinD and MinE form a standing oscillatory wave which positions the cell division inhibitor MinC, that binds MinD, everywhere on the membrane except at the midpoint of the cell, ensuring midcell positioning of the cytokinetic septum. During this process MinE undergoes fold switching as it interacts with different partners. We explore the exchange dynamics between major and excited states of the MinE dimer in 3 forms using ¹⁵N relaxation dispersion NMR: the full-length protein (6-stranded β-sheet sandwiched between 4 helices) representing the resting state; a 10-residue N-terminal deletion (Δ10) mimicking the membrane-binding competent state where the N-terminal helix is detached to interact with membrane; and N-terminal deletions of either 30 (Δ30) or 10 residues with an I24N mutation (Δ10/I24N), in which the β1-strands at the dimer interface are extruded and available to bind MinD, leaving behind a 4-stranded β-sheet. Full-length MinE samples 2 "excited" states: The first is similar to a full-length/Δ10 heterodimer; the second, also sampled by Δ10, is either similar to or well along the pathway toward the 4-stranded β-sheet form. Both Δ30 and Δ10/I24N sample 2 excited species: The first may involve destabilization of the β3- and β3'-strands at the dimer interface; changes in the second are more extensive, involving further disruption of secondary structure, possibly representing an ensemble of states on the pathway toward restoration of the resting state. The quantitative information on MinE conformational dynamics involving these excited states is crucial for understanding the oscillation pattern self-organization by MinD-MinE interaction dynamics on the membrane.

Design of biochemical pattern forming systems from minimal motifs

Although molecular self-organization and pattern formation are key features of life, only very few pattern-forming biochemical systems have been identified that can be reconstituted and studied in vitro under defined conditions. A systematic understanding of the underlying mechanisms is often hampered by multiple interactions, conformational flexibility and other complex features of the pattern forming proteins. Because of its compositional simplicity of only two proteins and a membrane, the MinDE system from Escherichia coli has in the past years been invaluable for deciphering the mechanisms of spatiotemporal self-organization in cells. Here, we explored the potential of reducing the complexity of this system even further, by identifying key functional motifs in the effector MinE that could be used to design pattern formation from scratch. In a combined approach of experiment and quantitative modeling, we show that starting from a minimal MinE-MinD interaction motif, pattern formation can be obtained by adding either dimerization or membrane-binding motifs. Moreover, we show that the pathways underlying pattern formation are recruitment-driven cytosolic cycling of MinE and recombination of membrane-bound MinE, and that these differ in their in vivo phenomenology.

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid-cell zone for division. The universality of pattern-forming mechanisms in divisome placement is currently unclear. We examined the location of the division plane in two pleomorphic archaea, Haloferax volcanii and Haloarcula japonica, and showed that it correlates with the predictions of Turing patterning. Time-lapse analysis of H. volcanii shows that divisome locations after successive rounds of division are dynamically determined by daughter cell shape. For H. volcanii, we show that the location of DNA does not influence division plane location, ruling out nucleoid occlusion. Triangular cells provide a stringent test for Turing patterning, where there is a bifurcation in division plane orientation. For the two archaea examined, most triangular cells divide as predicted by a Turing mechanism; however, in some cases multiple division planes are observed resulting in cells dividing into three viable progeny. Our results suggest that the division site placement is consistent with a Turing patterning system in these archaea.

Active Transport of Membrane Components by Self-Organization of the Min Proteins

Heterogeneous distribution of components in the biological membrane is critical in the process of cell polarization. However, little is known about the mechanisms that can generate and maintain the heterogeneous distribution of the membrane components. Here, we report that the propagating wave patterns of the bacterial Min proteins can impose steric pressure on the membrane, resulting in transport and directional accumulation of the component in the membrane. Therefore, the membrane component waves represent transport of the component in the membrane that is caused by the steric pressure gradient induced by the differential levels of binding and dissociation of the Min proteins in the propagating waves on the membrane surface. The diffusivity, majorly influenced by the membrane anchor of the component, and the repulsed ability, majorly influenced by the steric property of the membrane component, determine the differential spatial distribution of the membrane component. Thus, transportation of the membrane component by the Min proteins follows a simple physical principle, which resembles a linear peristaltic pumping process, to selectively segregate and maintain heterogeneous distribution of materials in the membrane. VIDEO ABSTRACT.

Reverse and forward engineering of protein pattern formation

Living systems employ protein pattern formation to regulate important life processes in space and time. Although pattern-forming protein networks have been identified in various prokaryotes and eukaryotes, their systematic experimental characterization is challenging owing to the complex environment of living cells. In turn, cell-free systems are ideally suited for this goal, as they offer defined molecular environments that can be precisely controlled and manipulated. Towards revealing the molecular basis of protein pattern formation, we outline two complementary approaches: the biochemical reverse engineering of reconstituted networks and the de novo design, or forward engineering, of artificial self-organizing systems. We first illustrate the reverse engineering approach by the example of the Escherichia coli Min system, a model system for protein self-organization based on the reversible and energy-dependent interaction of the ATPase MinD and its activating protein MinE with a lipid membrane. By reconstituting MinE mutants impaired in ATPase stimulation, we demonstrate how large-scale Min protein patterns are modulated by MinE activity and concentration. We then provide a perspective on the de novo design of self-organizing protein networks. Tightly integrated reverse and forward engineering approaches will be key to understanding and engineering the intriguing phenomenon of protein pattern formation.This article is part of the theme issue 'Self-organization in cell biology'.

The Min-protein oscillations in Escherichia coli: an example of self-organized cellular protein waves

In the rod-shaped bacterium Escherichia coli, selection of the cell centre as the division site involves pole-to-pole oscillations of the proteins MinC, MinD and MinE. This spatio-temporal pattern emerges from interactions among the Min proteins and with the cytoplasmic membrane. Combining experimental studies in vivo and in vitro together with theoretical analysis has led to a fairly good understanding of Min-protein self-organization. In different geometries, the system can, in addition to standing waves, also produce travelling planar and spiral waves as well as coexisting stable stationary distributions. Today it stands as one of the best-studied examples of cellular self-organization of proteins.This article is part of the theme issue 'Self-organization in cell biology'.

Minimal in vitro systems shed light on cell polarity

Cell polarity - the morphological and functional differentiation of cellular compartments in a directional manner - is required for processes such as orientation of cell division, directed cellular growth and motility. How the interplay of components within the complexity of a cell leads to cell polarity is still heavily debated. In this Review, we focus on one specific aspect of cell polarity: the non-uniform accumulation of proteins on the cell membrane. In cells, this is achieved through reaction-diffusion and/or cytoskeleton-based mechanisms. In reaction-diffusion systems, components are transformed into each other by chemical reactions and are moving through space by diffusion. In cytoskeleton-based processes, cellular components (i.e. proteins) are actively transported by microtubules (MTs) and actin filaments to specific locations in the cell. We examine how minimal systems - in vitro reconstitutions of a particular cellular function with a minimal number of components - are designed, how they contribute to our understanding of cell polarity (i.e. protein accumulation), and how they complement in vivo investigations. We start by discussing the Min protein system from Escherichia coli, which represents a reaction-diffusion system with a well-established minimal system. This is followed by a discussion of MT-based directed transport for cell polarity markers as an example of a cytoskeleton-based mechanism. To conclude, we discuss, as an example, the interplay of reaction-diffusion and cytoskeleton-based mechanisms during polarity establishment in budding yeast.

Stationary Patterns in a Two-Protein Reaction-Diffusion System

Patterns formed by reaction-diffusion mechanisms are crucial for the development or sustenance of most organisms in nature. Patterns include dynamic waves, but are more often found as static distributions, such as animal skin patterns. Yet, a simplistic biological model system to reproduce and quantitatively investigate static reaction-diffusion patterns has been missing so far. Here, we demonstrate that the Escherichia coli Min system, known for its oscillatory behavior between the cell poles, is under certain conditions capable of transitioning to quasi-stationary protein distributions on membranes closely resembling Turing patterns. We systematically titrated both proteins, MinD and MinE, and found that removing all purification tags and linkers from the N-terminus of MinE was critical for static patterns to occur. At small bulk heights, dynamic patterns dominate, such as in rod-shaped microcompartments. We see implications of this work for studying pattern formation in general, but also for creating artificial gradients as downstream cues in synthetic biology applications.

In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers

Many aspects of the fundamental spatiotemporal organization of cells are governed by reaction-diffusion type systems. In vitro reconstitution of such systems allows for detailed studies of their underlying mechanisms which would not be feasible in vivo. Here, we provide a protocol for the in vitro reconstitution of the MinCDE system of Escherichia coli, which positions the cell division septum in the cell middle. The assay is designed to supply only the components necessary for self-organization, namely a membrane, the two proteins MinD and MinE and energy in the form of ATP. We therefore fabricate an open reaction chamber on a coverslip, on which a supported lipid bilayer is formed. The open design of the chamber allows for optimal preparation of the lipid bilayer and controlled manipulation of the bulk content. The two proteins, MinD and MinE, as well as ATP, are then added into the bulk volume above the membrane. Imaging is possible by many optical microscopies, as the design supports confocal, wide-field and TIRF microscopy alike. In a variation of the protocol, the lipid bilayer is formed on a patterned support, on cell-shaped PDMS microstructures, instead of glass. Lowering the bulk solution to the rim of these compartments encloses the reaction in a smaller compartment and provides boundaries that allow mimicking of in vivo oscillatory behavior. Taken together, we describe protocols to reconstitute the MinCDE system both with and without spatial confinement, allowing researchers to precisely control all aspects influencing pattern formation, such as concentration ranges and addition of other factors or proteins, and to systematically increase system complexity in a relatively simple experimental setup.

Mechanistic insights of the Min oscillator via cell-free reconstitution and imaging

The MinD and MinE proteins of Escherichia coli self-organize into a standing-wave oscillator on the membrane to help align division at mid-cell. When unleashed from cellular confines, MinD and MinE form a spectrum of patterns on artificial bilayers-static amoebas, traveling waves, traveling mushrooms, and bursts with standing-wave dynamics. We recently focused our cell-free studies on bursts because their dynamics recapitulate many features of Min oscillation observed in vivo. The data unveiled a patterning mechanism largely governed by MinE regulation of MinD interaction with membrane. We proposed that the MinD to MinE ratio on the membrane acts as a toggle switch between MinE-stimulated recruitment and release of MinD from the membrane. In this review, we summarize cell-free data on the Min system and expand upon a molecular mechanism that provides a biochemical explanation as to how these two 'simple' proteins can form the remarkable spectrum of patterns.

Optical Control of a Biological Reaction-Diffusion System

Patterns formed by reaction and diffusion are the foundation for many phenomena in biology. However, the experimental study of reaction-diffusion (R-D) systems has so far been dominated by chemical oscillators, for which many tools are available. In this work, we developed a photoswitch for the Min system of Escherichia coli, a versatile biological in vitro R-D system consisting of the antagonistic proteins MinD and MinE. A MinE-derived peptide of 19 amino acids was covalently modified with a photoisomerizable crosslinker based on azobenzene to externally control peptide-mediated depletion of MinD from the membrane. In addition to providing an on-off switch for pattern formation, we achieve frequency-locked resonance with a precise 2D spatial memory, thus allowing new insights into Min protein action on the membrane. Taken together, we provide a tool to study phenomena in pattern formation using biological agents.

Dissecting the role of conformational change and membrane binding by the bacterial cell division regulator MinE in the stimulation of MinD ATPase activity

The bacterial cell division regulators MinD and MinE together with the division inhibitor MinC localize to the membrane in concentrated zones undergoing coordinated pole-to-pole oscillation to help ensure that the cytokinetic division septum forms only at the mid-cell position. This dynamic localization is driven by MinD-catalyzed ATP hydrolysis, stimulated by interactions with MinE's anti-MinCD domain. This domain is buried in the 6-β-stranded MinE "closed" structure, but is liberated for interactions with MinD, giving rise to a 4-β-stranded "open" structure through an unknown mechanism. Here we show that MinE-membrane interactions induce a structural change into a state resembling the open conformation. However, MinE mutants lacking the MinE membrane-targeting sequence stimulated higher ATP hydrolysis rates than the full-length protein, indicating that binding to MinD is sufficient to trigger this conformational transition in MinE. In contrast, conformational change between the open and closed states did not affect stimulation of ATP hydrolysis rates in the absence of membrane binding, although the MinD-binding residue Ile-25 is critical for this conformational transition. We therefore propose an updated model where MinE is brought to the membrane through interactions with MinD. After stimulation of ATP hydrolysis, MinE remains bound to the membrane in a state that does not catalyze additional rounds of ATP hydrolysis. Although the molecular basis for this inhibited state is unknown, previous observations of higher-order MinE self-association may explain this inhibition. Overall, our findings have general implications for Min protein oscillation cycles, including those that regulate cell division in bacterial pathogens.

Reconstitutions of plasmid partition systems and their mechanisms

Bacterial plasmid and chromosome segregation systems ensure that genetic material is efficiently transmitted to progeny cells. Cell-based studies have shed light on the dynamic nature and the molecular basis of plasmid partition systems. In vitro reconstitutions, on the other hand, have proved to be an invaluable tool for studying the minimal components required to elucidate the mechanism of DNA segregation. This allows us to gain insight into the biological and biophysical processes that enable bacterial cells to move and position DNA. Here, we review the reconstitutions of plasmid partition systems in cell-free reactions, and discuss recent work that has begun to challenge long standing models of DNA segregation in bacteria.

FtsZ-ring Architecture and Its Control by MinCD

In bacteria and archaea, the most widespread cell division system is based on the tubulin homologue FtsZ protein, whose filaments form the cytokinetic Z-ring. FtsZ filaments are tethered to the membrane by anchors such as FtsA and SepF and are regulated by accessory proteins. One such set of proteins is responsible for Z-ring's spatiotemporal regulation, essential for the production of two equal-sized daughter cells. Here, we describe how our still partial understanding of the FtsZ-based cell division process has been progressed by visualising near-atomic structures of Z-rings and complexes that control Z-ring positioning in cells, most notably the MinCDE and Noc systems that act by negatively regulating FtsZ filaments. We summarise available data and how they inform mechanistic models for the cell division process.

E. coli Cell Cycle Machinery

Cytokinesis in E. coli is organized by a cytoskeletal element designated the Z ring. The Z ring is formed at midcell by the coalescence of FtsZ filaments tethered to the membrane by interaction of FtsZ's conserved C-terminal peptide (CCTP) with two membrane-associated proteins, FtsA and ZipA. Although interaction between an FtsZ monomer and either of these proteins is of low affinity, high affinity is achieved through avidity - polymerization linked CCTPs interacting with the membrane tethers. The placement of the Z ring at midcell is ensured by antagonists of FtsZ polymerization that are positioned within the cell and target FtsZ filaments through the CCTP. The placement of the ring is reinforced by a protein network that extends from the terminus (Ter) region of the chromosome to the Z ring. Once the Z ring is established, additional proteins are recruited through interaction with FtsA, to form the divisome. The assembled divisome is then activated by FtsN to carry out septal peptidoglycan synthesis, with a dynamic Z ring serving as a guide for septum formation. As the septum forms, the cell wall is split by spatially regulated hydrolases and the outer membrane invaginates in step with the aid of a transenvelope complex to yield progeny cells.

Mapping out Min protein patterns in fully confined fluidic chambers

The bacterial Min protein system provides a major model system for studying reaction-diffusion processes in biology. Here we present the first in vitro study of the Min system in fully confined three-dimensional chambers that are lithography-defined, lipid-bilayer coated and isolated through pressure valves. We identify three typical dynamical behaviors that occur dependent on the geometrical chamber parameters: pole-to-pole oscillations, spiral rotations, and traveling waves. We establish the geometrical selection rules and show that, surprisingly, Min-protein spiral rotations govern the larger part of the geometrical phase diagram. Confinement as well as an elevated temperature reduce the characteristic wavelength of the Min patterns, although even for confined chambers with a bacterial-level viscosity, the patterns retain a ~5 times larger wavelength than in vivo. Our results provide an essential experimental base for modeling of intracellular Min gradients in bacterial cell division as well as, more generally, for understanding pattern formation in reaction-diffusion systems.

DOI:http://dx.doi.org/10.7554/eLife.19271.001

Some proteins can spontaneously organize themselves into ordered patterns within living cells. One widely studied pattern is made in a rod-shaped bacterium called Escherichia coli by a group of proteins called the Min proteins. The pattern formed by the Min proteins allows an E. coli cell to produce two equally sized daughter cells when it divides by ensuring that the division machinery correctly assembles at the center of the parent cell. These proteins move back and forth between the two ends of the parent cell so that the levels of Min proteins are highest at the ends and lowest in the middle. Since the Min proteins act to inhibit the assembly of the cell division machinery, this machinery only assembles in locations where the level of Min proteins is at its lowest, that is, at the middle of the cell.

When Min proteins are purified and placed within an artificial compartment that contains a source of chemical energy and is covered by a membrane similar to the membranes that surround cells, they spontaneously form traveling waves on top of the membrane in many directions along to surface. It is not clear how these waves relate to the oscillations seen in E. coli. Caspi and Dekker now analyze the behavior of purified Min proteins inside chambers of various sizes that are fully enclosed by a membrane.

The results show that in narrow chambers, Min proteins move back and forth (i.e. oscillate) from one side to the other. However, in wider containers the wave motion is more common. In containers of medium width the Min proteins rotate in a spiral fashion. Caspi and Dekker propose that the spiral rotations are the underlying pattern formed by Min proteins and that the back and forth motion is caused by spirals being cut short. In other words, if a spiral cannot form because the compartment is too small then the back and forth motion emerges. Similarly, Caspi and Dekker propose that the waves emerge in larger containers when multiple spirals come together.

These findings suggest that the different patterns that Min proteins form in bacterial cells and artificial compartments arise from different underlying mechanisms. The next step will be to investigate other differences in how the patterns of Min proteins form in E. coli and in artificial compartments.

DOI:http://dx.doi.org/10.7554/eLife.19271.002

Membrane-bound MinDE complex acts as a toggle switch that drives Min oscillation coupled to cytoplasmic depletion of MinD

The Escherichia coli Min system self-organizes into a cell-pole to cell-pole oscillator on the membrane to prevent divisions at the cell poles. Reconstituting the Min system on a lipid bilayer has contributed to elucidating the oscillatory mechanism. However, previous in vitro patterns were attained with protein densities on the bilayer far in excess of those in vivo and failed to recapitulate the standing wave oscillations observed in vivo. Here we studied Min protein patterning at limiting MinD concentrations reflecting the in vivo conditions. We identified "burst" patterns--radially expanding and imploding binding zones of MinD, accompanied by a peripheral ring of MinE. Bursts share several features with the in vivo dynamics of the Min system including standing wave oscillations. Our data support a patterning mechanism whereby the MinD-to-MinE ratio on the membrane acts as a toggle switch: recruiting and stabilizing MinD on the membrane when the ratio is high and releasing MinD from the membrane when the ratio is low. Coupling this toggle switch behavior with MinD depletion from the cytoplasm drives a self-organized standing wave oscillator.

MinC/MinD copolymers are not required for Min function

In Escherichia coli, precise placement of the cytokinetic Z ring at midcell requires the concerted action of the three Min proteins. MinD activates MinC, an inhibitor of FtsZ, at least in part, by recruiting it to the membrane and targeting it to the Z ring, while MinE stimulates the MinD ATPase inducing an oscillation that directs MinC/MinD activity away from midcell. Recently, MinC and MinD were shown to form copolymers of alternating dimers of MinC and MinD, and it was suggested that these copolymers are the active form of MinC/MinD. Here, we use MinD mutants defective in binding MinC to generate heterodimers with wild-type MinD that are unable to form MinC/MinD copolymers. Similarly, MinC mutants defective in binding to MinD were used to generate heterodimers with wild-type MinC that are unable to form copolymers. Such heterodimers are active and in the case of MinC were shown to mediate spatial regulation of the Z ring demonstrating that MinC/MinD copolymer formation is not required. Our results are consistent with a model in which a membrane anchored MinC/MinD complex is targeted to the Z ring through the conserved carboxy tail of FtsZ leading to breakage of FtsZ filaments.

Critical waves and the length problem of biology

It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large or small scales using echo timing and fringe counting. It is shown that suitable linear chemical potential waves can, in fact, be manufactured by tuning to criticality conventional reaction-diffusion with a small number substance. Min oscillations in Escherichia coli are cited as precedent resonant length measurement using chemical potential waves analogous to laser detection. Mitotic structures in eukaryotes are identified as candidates for such an effect at higher frequency. The engineering principle is shown to be very general and functionally the same as that used by hearing organs.

Collaborative protein filaments

It is now well established that prokaryotic cells assemble diverse proteins into dynamic cytoskeletal filaments that perform essential cellular functions. Although most of the filaments assemble on their own to form higher order structures, growing evidence suggests that there are a number of prokaryotic proteins that polymerise only in the presence of a matrix such as DNA, lipid membrane or even another filament. Matrix-assisted filament systems are frequently nucleotide dependent and cytomotive but rarely considered as part of the bacterial cytoskeleton. Here, we categorise this family of filament-forming systems as collaborative filaments and introduce a simple nomenclature. Collaborative filaments are frequent in both eukaryotes and prokaryotes and are involved in vital cellular processes including chromosome segregation, DNA repair and maintenance, gene silencing and cytokinesis to mention a few. In this review, we highlight common principles underlying collaborative filaments and correlate these with known functions.

Symmetry and scale orient Min protein patterns in shaped bacterial sculptures

The boundary of a cell defines the shape and scale of its subcellular organization. However, the effects of the cell's spatial boundaries as well as the geometry sensing and scale adaptation of intracellular molecular networks remain largely unexplored. Here, we show that living bacterial cells can be 'sculpted' into defined shapes, such as squares and rectangles, which are used to explore the spatial adaptation of Min proteins that oscillate pole-to-pole in rod-shaped Escherichia coli to assist cell division. In a wide geometric parameter space, ranging from 2 × 1 × 1 to 11 × 6 × 1 μm(3), Min proteins exhibit versatile oscillation patterns, sustaining rotational, longitudinal, diagonal, stripe and even transversal modes. These patterns are found to directly capture the symmetry and scale of the cell boundary, and the Min concentration gradients scale with the cell size within a characteristic length range of 3-6 μm. Numerical simulations reveal that local microscopic Turing kinetics of Min proteins can yield global symmetry selection, gradient scaling and an adaptive range, when and only when facilitated by the three-dimensional confinement of the cell boundary. These findings cannot be explained by previous geometry-sensing models based on the longest distance, membrane area or curvature, and reveal that spatial boundaries can facilitate simple molecular interactions to result in far more versatile functions than previously understood.

Molecular Interactions of the Min Protein System Reproduce Spatiotemporal Patterning in Growing and Dividing Escherichia coli Cells

Oscillations of the Min protein system are involved in the correct midcell placement of the divisome during Escherichia coli cell division. Based on molecular interactions of the Min system, we formulated a mathematical model that reproduces Min patterning during cell growth and division. Specifically, the increase in the residence time of MinD attached to the membrane as its own concentration increases, is accounted for by dimerisation of membrane-bound MinD and its interaction with MinE. Simulation of this system generates unparalleled correlation between the waveshape of experimental and theoretical MinD distributions, suggesting that the dominant interactions of the physical system have been successfully incorporated into the model. For cells where MinD is fully-labelled with GFP, the model reproduces the stationary localization of MinD-GFP for short cells, followed by oscillations from pole to pole in larger cells, and the transition to the symmetric distribution during cell filamentation. Cells containing a secondary, GFP-labelled MinD display a contrasting pattern. The model is able to account for these differences, including temporary midcell localization just prior to division, by increasing the rate constant controlling MinD ATPase and heterotetramer dissociation. For both experimental conditions, the model can explain how cell division results in an equal distribution of MinD and MinE in the two daughter cells, and accounts for the temperature dependence of the period of Min oscillations. Thus, we show that while other interactions may be present, they are not needed to reproduce the main characteristics of the Min system in vivo.

Spatial coordination between chromosomes and cell division proteins in Escherichia coli

To successfully propagate, cells need to coordinate chromosomal replication and segregation with cell division to prevent formation of DNA-less cells and cells with damaged DNA. Here, we review molecular systems in Escherichia coli that are known to be involved in positioning the divisome and chromosome relative to each other. Interestingly, this well-studied micro-organism has several partially redundant mechanisms to achieve this task; none of which are essential. Some of these systems determine the localization of the divisome relative to chromosomes such as SlmA-dependent nucleoid occlusion, some localize the chromosome relative to the divisome such as DNA translocation by FtsK, and some are likely to act on both systems such as the Min system and newly described Ter linkage. Moreover, there is evidence that E. coli harbors other divisome-chromosome coordination systems in addition to those known. The review also discusses the minimal requirements of coordination between chromosomes and cell division proteins needed for cell viability. Arguments are presented that cells can propagate without any dedicated coordination between their chromosomes and cell division machinery at the expense of lowered fitness.

Reconstituting ParA/ParB-mediated transport of DNA cargo

Protein gradients play key roles in subcellular spatial organization. In bacteria, ParA adenosine triphosphatases, or ATPases, form dynamic gradients on the nucleoid surface, which imparts positional information for the segregation, transport, and positioning of chromosomes, plasmids, and large protein assemblies. Despite the apparent simplicity of these minimal and self-organizing systems, the mechanism remains unclear. The small size of bacteria along with the number of physical and biochemical processes involved in subcellular organization makes it difficult to study these systems under controlled conditions in vivo. We developed a cell-free reconstitution technique that allows for the visualization of ParA-mediated cargo transport on a DNA carpet, which acts as a biomimetic of the nucleoid surface. Here, we present methods to express, purify, and visualize the dynamic properties of the SopABC system from F plasmid, considered a paradigm for the study of ParA-type systems. We hope similar cell-free studies will be used to address the biochemical and biophysical underpinnings of this ubiquitous transport scheme in bacteria.

Physics, emergence, and the connectome

Experience with complex systems more primitive than the brain teaches important lessons about big data in biology. Chief among them is that physical laws, relationships among measured things that are always true, emerge out of chaos, not the other way around. Correct prediction (as opposed to incorrect prediction) from large data sets requires understanding of these laws. The reason is that the same processes that make them also make the system wildly error-intolerant if the errors are too large. This instability routinely causes computer simulations of even primitive systems to fail by enabling mistakes to cascade into ever worsening falsehoods. The more complex and sophisticated the system is, the more intolerant to errors it becomes.

Meiotic crossover patterns: obligatory crossover, interference and homeostasis in a single process

During meiosis, crossover recombination is tightly regulated. A spatial patterning phenomenon known as interference ensures that crossovers are well-spaced along the chromosomes. Additionally, every pair of homologs acquires at least one crossover. A third feature, crossover homeostasis, buffers the system such that the number of crossovers remains steady despite decreases or increases in the number of earlier recombinational interactions. Here we summarize recent work from our laboratory supporting the idea that all 3 of these aspects are intrinsic consequences of a single basic process and suggesting that the underlying logic of this process corresponds to that embodied in a particular (beam-film) model.

Programmable chemical reaction networks: emulating regulatory functions in living cells using a bottom-up approach

Living cells are able to produce a wide variety of biological responses when subjected to biochemical stimuli.

MinCD cell division proteins form alternating copolymeric cytomotive filaments

During bacterial cell division, filaments of the tubulin-like protein FtsZ assemble at midcell to form the cytokinetic Z-ring. Its positioning is regulated by the oscillation of MinCDE proteins. MinC is activated by MinD through an unknown mechanism and prevents Z-ring assembly anywhere but midcell. Here, using X-ray crystallography, electron microscopy and in vivo analyses we show that MinD activates MinC by forming a new class of alternating copolymeric filaments that show similarity to eukaryotic septin filaments A non-polymerising mutation in MinD causes aberrant cell division in E. coli. MinCD copolymers bind to membrane, interact with FtsZ, and are disassembled by MinE. Imaging a functional msfGFP-MinC fusion protein in MinE deleted cells reveals filamentous structures. EM imaging of our reconstitution of the MinCD-FtsZ interaction on liposome surfaces reveals a plausible mechanism for regulation of FtsZ ring assembly by MinCD copolymers.

Toward Spatially Regulated Division of Protocells: Insights into the E. coli Min System from in Vitro Studies

For reconstruction of controlled cell division in a minimal cell model, or protocell, a positioning mechanism that spatially regulates division is indispensable. In Escherichia coli, the Min proteins oscillate from pole to pole to determine the division site by inhibition of the primary divisome protein FtsZ anywhere but in the cell middle. Remarkably, when reconstituted under defined conditions in vitro, the Min proteins self-organize into spatiotemporal patterns in the presence of a lipid membrane and ATP. We review recent progress made in studying the Min system in vitro, particularly focusing on the effects of various physicochemical parameters and boundary conditions on pattern formation. Furthermore, we discuss implications and challenges for utilizing the Min system for division site placement in protocells.