Temperature dependence of MinD oscillation in Escherichia coli: running hot and fast

Mechanistic origins of temperature scaling in the early embryonic cell cycle

Temperature profoundly impacts organismal physiology and ecological dynamics, particularly affecting ectothermic species and making them especially vulnerable to climate changes. Although complex physiological processes usually involve dozens of enzymes, empirically it is found that the rates of these processes often obey the Arrhenius equation, which was originally proposed for individual chemical reactions. Here we have examined the temperature scaling of the early embryonic cell cycle, with the goal of understanding why the Arrhenius equation approximately holds and why it breaks down at temperature extremes. Using experimental data from Xenopus laevis, Xenopus tropicalis, and Danio rerio, plus published data from Caenorhabditis elegans, Caenorhabditis briggsae, and Drosophila melanogaster, we find that the apparent activation energies (E a values) for the early embryonic cell cycle for diverse ectotherms are all similar, 75 ± 7 kJ/mol (mean ± std.dev., n = 6), which corresponds to aQ 10 value at 20°C of 2.8 ± 0.2 (mean ± std.dev., n = 6). Using computational models, we find that the approximate Arrhenius scaling and the deviations from it at high and low temperatures can be accounted for by biphasic temperature scaling in critical individual components of the cell cycle oscillator circuit, by imbalances in theE a values for different partially rate-determining enzymes, or by a combination of both. Experimental studies of cycling Xenopus extracts indicate that both of these mechanisms contribute to the general scaling of temperature, and in vitro studies of individual cell cycle regulators confirm that there is in fact a substantial imbalance in theirE a values. These findings provide mechanistic insights into the dynamic interplay between temperature and complex biochemical processes, and into why biological systems fail at extreme temperatures.

Growth-dependent concentration gradient of the oscillating Min system in Escherichia coli

Cell division in Escherichia coli is intricately regulated by the MinD and MinE proteins, which form oscillatory waves between cell poles. These waves manifest as concentration gradients that reduce MinC inhibition at the cell center, thereby influencing division site placement. This study explores the plasticity of the MinD gradients resulting from the interdependent interplay between molecular interactions and diffusion in the system. Through live cell imaging, we observed that as cells elongate, the gradient steepens, the midcell concentration decreases, and the oscillation period stabilizes. A one-dimensional model investigates kinetic rate constants representing various molecular interactions, effectively recapitulating our experimental findings. The model reveals the nonlinear dynamics of the system and a dynamic equilibrium among these constants, which underlie variable concentration gradients in growing cells. This study enhances quantitative understanding of MinD oscillations within the cellular environment. Furthermore, it emphasizes the fundamental role of concentration gradients in cellular processes.

Mutual Dependence between Membrane Phase Separation and Bacterial Division Protein Dynamics in Synthetic Cell Models

Cell membranes in bacteria are laterally polarized to produce specific environments for membrane proteins, e.g., proteins involved in cell division which accumulate at mid-cell or the cell poles. An interesting result of such membrane-lipid interplay is the reorganization of lipid domains together with membrane-bound proteins at the onset of cell division, suggesting functional significance of membrane compartments in the cell cycle. Here, by adopting the key bacterial division proteins MinC, MinD, MinE, FtsA and FtsZ as an archetypal spatial patterning system, we present a simple vesicle-based in vitro model to explore the mutual dependence of protein pattern formation and membrane heterogeneity. Like many other peripheral membrane proteins, Min proteins exhibit preferential binding and macro-scale pattern formation at Ld domains, which leads to altered oscillation mode selection in phase-separated membrane compartments (GUVs). Moreover, incorporating bacterial division proteins within phase-separated GUVs leads to blebbing-like membrane deformations followed by the reorganization of Lo domains aligning at the neck region of the bleb, which agrees well with the domain rearrangement in bacterial membranes immediately preceding the radial constriction process. Overall, the presented in vitro model system showcases a basic framework to better comprehend the cellular division mechanism in consideration of complex cellular lipid environments.

Bacterial filaments recover by successive and accelerated asymmetric divisions that allow rapid post-stress cell proliferation

Filamentation is a reversible morphological change triggered in response to various stresses that bacteria might encounter in the environment, during host infection or antibiotic treatments. Here we re-visit the dynamics of filament formation and recovery using a consistent framework based on live-cells microscopy. We compare the fate of filamentous Escherichia coli induced by cephalexin that inhibits cell division or by UV-induced DNA-damage that additionally perturbs chromosome segregation. We show that both filament types recover by successive and accelerated rounds of divisions that preferentially occur at the filaments' tip, thus resulting in the rapid production of multiple daughter cells with tightly regulated size. The DNA content, viability and further division of the daughter cells essentially depends on the coordination between chromosome segregation and division within the mother filament. Septum positioning at the filaments' tip depends on the Min system, while the nucleoid occlusion protein SlmA regulates the timing of division to prevent septum closure on unsegregated chromosomes. Our results not only recapitulate earlier conclusions but provide a higher level of detail regarding filaments division and the fate of the daughter cells. Together with previous reports, this work uncovers how filamentation recovery allows for a rapid cell proliferation after stress treatment.

Controlling the Periodicity of a Reaction-Diffusion Wave in Artificial Cells by a Two-Way Energy Supplier

Reaction-diffusion (RD) waves, which are dynamic self-organization structures generated by nanosize molecules, are a fundamental mechanism from patterning in nano- and micromaterials to spatiotemporal regulations in living cells, such as cell division and motility. Although the periods of RD waves are the critical element for these functions, the development of a system to control their period is challenging because RD waves result from nonlinear physical dynamics under far-from-equilibrium conditions. Here, we developed an artificial cell system with tunable period of an RD-driven wave (Min protein wave), which determines a cell division site plane in living bacterial cells. The developed system is based on our finding that Min waves are generated by energy consumption of either ATP or dATP, and the period of the wave is different between these two energy suppliers. We showed that the Min-wave period was modulated linearly by the mixing ratio of ATP and dATP and that it was also possible to estimate the mixing ratio of ATP and dATP from the period. Our findings illuminated a previously unidentified principle to control the dissipative dynamics of biomolecules and, simultaneously, built an important framework to construct molecular robots with spatiotemporal units.

Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells

Reaction-diffusion coupling (RDc) generates spatiotemporal patterns, including two dynamic wave modes: traveling and standing waves. Although mode selection plays a substantial role in the spatiotemporal organization of living cell molecules, the mechanism for selecting each wave mode remains elusive. Here, we investigated a wave mode selection mechanism using Min waves reconstituted in artificial cells, emerged by the RDc of MinD and MinE. Our experiments and theoretical analysis revealed that the balance of membrane binding and dissociation from the membrane of MinD determines the mode selection of the Min wave. We successfully demonstrated that the transition of the wave modes can be regulated by controlling this balance and found hysteresis characteristics in the wave mode transition. These findings highlight a previously unidentified role of the balance between activators and inhibitors as a determinant of the mode selection of waves by RDc and depict an unexplored mechanism in intracellular spatiotemporal pattern formations.

Min Oscillations as Real-time Reporter of Sublethal Effects in Photodynamic Treatment of Bacteria

The Min protein system is a cell division regulator in Escherichia coli. Under normal growth conditions, MinD is associated with the membrane and undergoes pole-to-pole oscillations. The period of these oscillations has been previously proposed as a reporter for the bacterial physiological state at the single-cell level and has been used to monitor the response to sublethal challenges from antibiotics, temperature, or mechanical fatigue. Using real-time single-cell fluorescence imaging, we explore here the effect of photodynamic treatment on MinD oscillations. Irradiation of bacteria in the presence of the photosensitizer methylene blue disrupts the MinD oscillation pattern depending on its concentration. In contrast to antibiotics, which slow down the oscillation, photodynamic treatment results in an abrupt interruption, reflecting divergent physiological mechanisms leading to bacterial death. We show that MinD oscillations are sensitive to mild photodynamic effects that are overlooked by traditional methods, expanding the toolbox for mechanistic studies in antimicrobial photodynamic therapy.

Dynamics of the Bacillus subtilis Min System

The molecular mechanisms that help to place the division septum in bacteria is of fundamental importance to ensure cell proliferation and maintenance of cell shape and size. The Min protein system, found in many rod-shaped bacteria, is thought to play a major role in division site selection.

Division site selection is a vital process to ensure generation of viable offspring. In many rod-shaped bacteria, a dynamic protein system, termed the Min system, acts as a central regulator of division site placement. The Min system is best studied in Escherichia coli, where it shows a remarkable oscillation from pole to pole with a time-averaged density minimum at midcell. Several components of the Min system are conserved in the Gram-positive model organism Bacillus subtilis. However, in B. subtilis, it is commonly believed that the system forms a stationary bipolar gradient from the cell poles to midcell. Here, we show that the Min system of B. subtilis localizes dynamically to active sites of division, often organized in clusters. We provide physical modeling using measured diffusion constants that describe the observed enrichment of the Min system at the septum. Mathematical modeling suggests that the observed localization pattern of Min proteins corresponds to a dynamic equilibrium state. Our data provide evidence for the importance of ongoing septation for the Min dynamics, consistent with a major role of the Min system in controlling active division sites but not cell pole areas.

Mechanically Induced Bacterial Death Imaged in Real Time: A Simultaneous Nanoindentation and Fluorescence Microscopy Study

Mechano-bactericidal nanomaterials rely on their mechanical or physical interactions with bacteria and are promising antimicrobial strategies that overcome bacterial resistance. However, the real effect of mechanical versus chemical action on their activity is under debate. In this paper, we quantify the forces necessary to produce critical damage to the bacterial cell wall by performing simultaneous nanoindentation and fluorescence imaging of single bacterial cells. Our experimental setup allows puncturing the cell wall of an immobilized bacterium with the tip of an atomic force microscope (AFM) and following in real time the increase in the fluorescence signal from a cell membrane integrity marker. We correlate the forces exerted by the AFM tip with the fluorescence dynamics for tens of cells, and we find that forces above 20 nN are necessary to exert critical damage. Moreover, a similar experiment is performed in which bacterial viability is assessed through physiological activity, in order to gain a more complete view of the effect of mechanical forces on bacteria. Our results contribute to the quantitative understanding of the interaction between bacteria and nanomaterials.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

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.

Regulation of Pom cluster dynamics in Myxococcus xanthus

Precise positioning of the cell division site is essential for the correct segregation of the genetic material into the two daughter cells. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a cluster on the chromosome that performs a biased random walk to midcell and positively regulates cell division there. PomZ, an ATPase, is necessary for tethering of the cluster to the nucleoid and regulates its movement towards midcell. It has remained unclear how the cluster dynamics change when the biochemical parameters, such as the attachment rates of PomZ dimers to the nucleoid and the cluster, the ATP hydrolysis rate of PomZ or the mobility of PomZ interacting with the nucleoid and cluster, are varied. To answer these questions, we investigate a one-dimensional model that includes the nucleoid, the Pom cluster and PomZ proteins. We find that a mechanism based on the diffusive PomZ fluxes on the nucleoid into the cluster can explain the latter's midnucleoid localization for a broad parameter range. Furthermore, there is an ATP hydrolysis rate that minimizes the time the cluster needs to reach midnucleoid. If the dynamics of PomZ on the nucleoid is slow relative to the cluster's velocity, we observe oscillatory cluster movements around midnucleoid. To understand midnucleoid localization, we developed a semi-analytical approach that dissects the net movement of the cluster into its components: the difference in PomZ fluxes into the cluster from either side, the force exerted by a single PomZ dimer on the cluster and the effective friction coefficient of the cluster. Importantly, we predict that the Pom cluster oscillates around midnucleoid if the diffusivity of PomZ on the nucleoid is reduced. A similar approach to that applied here may also prove useful for cargo localization in ParABS systems.

The PomXYZ Proteins Self-Organize on the Bacterial Nucleoid to Stimulate Cell Division

Cell division site positioning is precisely regulated to generate correctly sized and shaped daughters. We uncover the strategy used by the social bacterium Myxococcus xanthus to position the FtsZ cytokinetic ring at midcell. PomX, PomY, and the nucleoid-binding ParA/MinD ATPase PomZ self-assemble forming a large nucleoid-associated complex that localizes at the division site before FtsZ to directly guide and stimulate division. PomXYZ localization is generated through self-organized biased random motion on the nucleoid toward midcell and constrained motion at midcell. Experiments and theory show that PomXYZ motion is produced by diffusive PomZ fluxes on the nucleoid into the complex. Flux differences scale with the intracellular asymmetry of the complex and are converted into a local PomZ concentration gradient across the complex with translocation toward the higher PomZ concentration. At midcell, fluxes equalize resulting in constrained motion. Flux-based mechanisms may represent a general paradigm for positioning of macromolecular structures in bacteria.

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

Temperature-Dependent Model of Multi-step Transcription Initiation in Escherichia coli Based on Live Single-Cell Measurements

Transcription kinetics is limited by its initiation steps, which differ between promoters and with intra- and extracellular conditions. Regulation of these steps allows tuning both the rate and stochasticity of RNA production. We used time-lapse, single-RNA microscopy measurements in live Escherichia coli to study how the rate-limiting steps in initiation of the P_lac/ara-1 promoter change with temperature and induction scheme. For this, we compared detailed stochastic models fit to the empirical data in maximum likelihood sense using statistical methods. Using this analysis, we found that temperature affects the rate limiting steps unequally, as nonlinear changes in the closed complex formation suffice to explain the differences in transcription dynamics between conditions. Meanwhile, a similar analysis of the P_tetA promoter revealed that it has a different rate limiting step configuration, with temperature regulating different steps. Finally, we used the derived models to explore a possible cause for why the identified steps are preferred as the main cause for behavior modifications with temperature: we find that transcription dynamics is either insensitive or responds reciprocally to changes in the other steps. Our results suggests that different promoters employ different rate limiting step patterns that control not only their rate and variability, but also their sensitivity to environmental changes.

Temperature affects the behavior of cells, such as their growth rate. However, it is not well understood how these changes result from the changes at the single molecule level. We observed the production of individual RNA molecules in live cells under a wide range of temperatures. This allowed us to determine not only how fast they are produced, but also how much variability there is in this process. Next, we fit a stochastic model to the data to identify which rate-limiting steps during RNA production are responsible for the observed differences between conditions. We found that genes differ in how their RNA production is limited by different steps and in how these are affected by the temperature, which explains why different genes respond differently to temperature fluctuations.

Physics of Intracellular Organization in Bacteria

With the realization that bacteria achieve exquisite levels of spatiotemporal organization has come the challenge of discovering the underlying mechanisms. In this review, we describe three classes of such mechanisms, each of which has physical origins: the use of landmarks, the creation of higher-order structures that enable geometric sensing, and the emergence of length scales from systems of chemical reactions coupled to diffusion. We then examine the diversity of geometric cues that exist even in cells with relatively simple geometries, and end by discussing both new technologies that could drive further discovery and the implications of our current knowledge for the behavior, fitness, and evolution of bacteria. The organizational strategies described here are employed in a wide variety of systems and in species across all kingdoms of life; in many ways they provide a general blueprint for organizing the building blocks of life.

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self-organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during growth up to defined large dimensions. De novo formation of patterns from homogenous starting conditions is observed and studied both experimentally and in simulations. A new theoretical approach is developed for probing pattern stability under perturbations. Quantitative experiments and simulations show that, once established, Min oscillations tolerate a large degree of intracellular heterogeneity, allowing distinctly different patterns to persist in different cells with the same geometry. Min patterns maintain their axes for hours in experiments, despite imperfections, expansion, and changes in cell shape during continuous cell growth. Transitions between multistable Min patterns are found to be rare events induced by strong intracellular perturbations. The instances of multistability studied here are the combined outcome of boundary growth and strongly nonlinear kinetics, which are characteristic of the reaction-diffusion patterns that pervade biology at many scales.

Oscillating behavior of Clostridium difficile Min proteins in Bacillus subtilis

In rod‐shaped bacteria, the proper placement of the division septum at the midcell relies, at least partially, on the proteins of the Min system as an inhibitor of cell division. The main principle of Min system function involves the formation of an inhibitor gradient along the cell axis; however, the establishment of this gradient differs between two well‐studied gram‐negative and gram‐positive bacteria. While in gram‐negative Escherichia coli, the Min system undergoes pole‐to‐pole oscillation, in gram‐positive Bacillus subtilis, proper spatial inhibition is achieved by the preferential attraction of the Min proteins to the cell poles. Nevertheless, when E.coli Min proteins are inserted into B.subtilis cells, they still oscillate, which negatively affects asymmetric septation during sporulation in this organism. Interestingly, homologs of both Min systems were found to be present in various combinations in the genomes of anaerobic and endospore‐forming Clostridia, including the pathogenic Clostridium difficile. Here, we have investigated the localization and behavior of C.difficile Min protein homologs and showed that MinDE proteins of C.difficile can oscillate when expressed together in B.subtilis cells. We have also investigated the effects of this oscillation on B.subtilis sporulation, and observed decreased sporulation efficiency in strains harboring the MinDE genes. Additionally, we have evaluated the effects of C.difficile Min protein expression on vegetative division in this heterologous host.

An Optimal Free Energy Dissipation Strategy of the MinCDE Oscillator in Regulating Symmetric Bacterial Cell Division

Sustained molecular oscillations are ubiquitous in biology. The obtained oscillatory patterns provide vital functions as timekeepers, pacemakers and spacemarkers. Models based on control theory have been introduced to explain how specific oscillatory behaviors stem from protein interaction feedbacks, whereas the energy dissipation through the oscillating processes and its role in the regulatory function remain unexplored. Here we developed a general framework to assess an oscillator’s regulation performance at different dissipation levels. Using the Escherichia coli MinCDE oscillator as a model system, we showed that a sufficient amount of energy dissipation is needed to switch on the oscillation, which is tightly coupled to the system’s regulatory performance. Once the dissipation level is beyond this threshold, unlike stationary regulators’ monotonic performance-to-cost relation, excess dissipation at certain steps in the oscillating process damages the oscillator’s regulatory performance. We further discovered that the chemical free energy from ATP hydrolysis has to be strategically assigned to the MinE-aided MinD release and the MinD immobilization steps for optimal performance, and a higher energy budget improves the robustness of the oscillator. These results unfold a novel mode by which living systems trade energy for regulatory function.

This paper presents a unique dissipation mode of converting biochemical free energy in ATP to regulatory function through the MinCDE bio-oscillator that marks the mid-cell position for symmetric bacterial cell division. Through assessing the oscillator’s performance-to-cost relation, we demonstrate that some dissipation threshold needs to be satisfied to switch on the oscillation, but the oscillator’s performance can be damaged by excess free energy dissipation, which is distinct from the known monotonic tradeoff relation of stationary regulators. An optimal dissipation strategy has been unveiled: the ATP free energy must be precisely allocated to specific reaction steps for accurate mid-cell recognition, which also coincides with the dynamic requirements for robust oscillation to occur. These discoveries identify an optimizable operation scheme of free energy consumption in biological systems and provide deep insights into the evolution of dynamic regulatory networks.

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.

The Min system and other nucleoid-independent regulators of Z ring positioning

Rod-shaped bacteria such as E. coli have mechanisms to position their cell division plane at the precise center of the cell, to ensure that the daughter cells are equal in size. The two main mechanisms are the Min system and nucleoid occlusion (NO), both of which work by inhibiting assembly of FtsZ, the tubulin-like scaffold that forms the cytokinetic Z ring. Whereas NO prevents Z rings from constricting over unsegregated nucleoids, the Min system is nucleoid-independent and even functions in cells lacking nucleoids and thus NO. The Min proteins of E. coli and B. subtilis form bipolar gradients that inhibit Z ring formation most at the cell poles and least at the nascent division plane. This article will outline the molecular mechanisms behind Min function in E. coli and B. subtilis, and discuss distinct Z ring positioning systems in other bacterial species.

Oscillations of Min-proteins in micropatterned environments: a three-dimensional particle-based stochastic simulation approach

The Min-proteins from E. coli and other bacteria are the best characterized pattern forming system in cells and their spatiotemporal oscillations have been successfully reconstituted in vitro. Different mathematical and computational models have been used to better understand these oscillations. Here we use particle-based stochastic simulations to study Min-oscillations in patterned environments. We simulate a rectangular box of length 10 μm and width 5 μm that is filled with grid or checkerboard patterns of different patch sizes and distances. For this geometry, we find different stable oscillation patterns, typically pole-to-pole oscillations along the minor axis and striped oscillations along the major axis. The Min-oscillations can switch from one pattern to the other, either effected by changes in pattern geometry or stochastically. By automatic analysis of large-scale computer simulations, we show quantitatively how the perturbing effect of increased patch distance can be rescued by increased patch size. We also show that striped oscillations occur robustly in arbitrarily shaped filamentous E. coli cells. Our results highlight the robustness and variability of Min-oscillations, put limits on the effect of putative division sites, and provide a powerful computational framework for future studies of protein self-organization in patterned environments.

Highly canalized MinD transfer and MinE sequestration explain the origin of robust MinCDE-protein dynamics

Min-protein oscillations in Escherichia coli are characterized by the remarkable robustness with which spatial patterns dynamically adapt to variations of cell geometry. Moreover, adaption, and therefore proper cell division, is independent of temperature. These observations raise fundamental questions about the mechanisms establishing robust Min oscillations, and about the role of spatial cues, as they are at odds with present models. Here, we introduce a robust model based on experimental data, consistently explaining the mechanisms underlying pole-to-pole, striped, and circular patterns, as well as the observed temperature dependence of the oscillation period. Contrary to prior conjectures, the model predicts that MinD and cardiolipin domains are not colocalized. The transient sequestration of MinE and highly canalized transfer of MinD between polar zones are the key mechanisms underlying oscillations. MinD channeling enhances midcell localization and facilitates stripe formation, revealing the potential optimization process from which robust Min-oscillations originally arose.

An oscillating Min system in Bacillus subtilis influences asymmetrical septation during sporulation

The Min system plays an important role in ensuring that cell division occurs at mid-cell in rod-shaped bacteria. In Escherichia coli, pole-to-pole oscillation of the Min proteins specifically inhibits polar septation. This system also prevents polar division in Bacillus subtilis during vegetative growth; however, the Min proteins do not oscillate in this organism. The Min system of B. subtilis plays a distinct role during sporulation, a process of differentiation which begins with an asymmetrical cell division. Here, we show that oscillation of the E. coli Min proteins can be reproduced following their introduction into B. subtilis cells. Further, we present evidence that the oscillatory behaviour of the Min system inhibits sporulation. We propose that an alternative Min system mechanism avoiding oscillation is evolutionarily important because oscillation of the Min system is incompatible with efficient asymmetrical septum formation and sporulation.

Changes in the Min oscillation pattern before and after cell birth

The Min system regulates the positioning of the cell division site in many bacteria. In Escherichia coli, MinD migrates rapidly from one cell pole to the other. In conjunction with MinC, MinD helps to prevent unwanted FtsZ rings from assembling at the poles and to stabilize their positioning at midcell. Using time-lapse microscopy of growing and dividing cells expressing a gfp-minD fusion, we show that green fluorescent protein (GFP)-MinD often paused at midcell in addition to at the poles, and the frequency of midcell pausing increased as cells grew longer and cell division approached. At later stages of septum formation, GFP-MinD often paused specifically on only one side of the septum, followed by migration to the other side of the septum or to a cell pole. About the time of septum closure, this irregular pattern often switched to a transient double pole-to-pole oscillation in the daughter cells, which ultimately became a stable double oscillation. The splitting of a single MinD zone into two depends on the developing septum and is a potential mechanism to explain how MinD is distributed equitably to both daughter cells. Septal pausing of GFP-MinD did not require MinC, suggesting that MinC-FtsZ interactions do not drive MinD-septal interactions, and instead MinD recognizes a specific geometric, lipid, and/or protein target at the developing septum. Finally, we observed regular end-to-end oscillation over very short distances along the long axes of minicells, supporting the importance of geometry in MinD localization.

Effects of poly(L-lysine) substrates on attached Escherichia coli bacteria

Poly(L-lysine) (PLL) is a cationic polymer that is often used for attaching and immobilizing cells to glass substrates for further investigation by, e.g., AFM techniques. Because of their small size, bacterial attachment is most easily done using thick air-dried PLL coatings--though thinner PLL coatings are also used and are commercially available. Nevertheless, the antimicrobial activity of PLL is well-established. Accordingly, we have investigated the physiological effects of suspended PLL and of PLL coatings on individual Escherichia coli bacteria through the pole-to-pole oscillations of cytoplasmic MinD-GFP fusion proteins. For planktonic bacteria, suspended PLL concentrations at the micromolar level quenched MinD-GFP oscillations and inhibited bacterial growth. On coverslips with PLL coatings prepared by short exposures of the slides to PLL solutions, followed by rinsing, only a fraction of available bacteria attached after hours of settling time. Min oscillations in the attached bacteria, however, were strong and only moderately slowed. On thick PLL coatings, prepared by drying drops on the slides followed by a brief rinse with deionized water, cells attached well within 15 min. With thick coatings, average oscillation periods for bacteria increased significantly, and considerable cell-to-cell variability was also observed; subsequent replacement of buffer with distilled water led to much larger period increases and/or fading of fluorescence intensity. We demonstrate that Min oscillations are a useful metric for bacteria attached to adhesion layers. We suggest that thick PLL coatings should probably be avoided for bacterial attachment, and that even thin PLL coatings can have significant effects on bacterial physiology.

Predictions from a stochastic polymer model for the MinDE protein dynamics in Escherichia coli

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations--both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

Subcellular Min oscillations as a single-cell reporter of the action of polycations, protamine, and gentamicin on Escherichia coli

Background

In Escherichia coli, MinD-GFP fusion proteins show rapid pole to pole oscillations. The objective was to investigate the effects of extracellular cations on the subcellular oscillation of cytoplasmic MinD within Escherichia coli.

Methodology/Principal Findings

We exposed bacteria to the extracellular cations Ca⁺⁺, Mg⁺⁺, the cationic antimicrobial peptide (CAP) protamine, and the cationic aminoglycoside gentamicin. We found rapid and substantial increases in the average MinD oscillation periods in the presence of any of these polyvalent cations. For Ca⁺⁺ and Mg⁺⁺ the increases in period were transient, even with a constant extracellular concentration, while increases in period for protamine or gentamicin were apparently irreversible. We also found striking interdependence in the action of the small cations with protamine or gentamicin, distorted oscillations under the action of intermediate levels of gentamicin and Ca⁺⁺, and reversible freezing of the Min oscillation at high cationic concentrations.

Conclusions/Significance

Intracellular Min oscillations provide a fast single-cell reporter of bacterial response to extracellular polycations, which can be explained by the penetration of polycations into cells.

Self-organization of the MinE protein ring in subcellular Min oscillations

We model the self-organization of the MinE ring that is observed during subcellular oscillations of the proteins MinD and MinE within the rod-shaped bacterium Escherichia coli. With a steady-state approximation, we can study the MinE ring generically--apart from the other details of the Min oscillation. Rebinding of MinE to depolymerizing MinD-filament tips controls MinE-ring formation through a scaled cell shape parameter r. We find two types of E-ring profiles near the filament tip: either a strong plateaulike E ring controlled by one-dimensional diffusion of MinE along the bacterial length or a weak cusplike E ring controlled by three-dimensional diffusion near the filament tip. While the width of a strong E ring depends on r, the occupation fraction of MinE at the MinD-filament tip is saturated and hence the depolymerization speed does not depend strongly on r. Conversely, for weak E rings both r and the MinE to MinD stoichiometry strongly control the tip occupation and hence the depolymerization speed. MinE rings in vivo are close to the threshold between weak and strong, and so MinD-filament depolymerization speed should be sensitive to cell shape, stoichiometry, and MinE-rebinding rate. We also find that the transient to MinE-ring formation is quite long in the appropriate open geometry for assays of ATPase activity in vitro, explaining the long delays of ATPase activity observed for smaller MinE concentrations in those assays without the need to invoke cooperative MinE activity.

A plant MinD homologue rescues Escherichia coli HL1 mutant (DeltaMinDE) in the absence of MinE

Background

In E. coli, the Min operon (MinCDE) plays a key role in determining the site of cell division. MinE oscillates from the middle to one pole or another to drive the MinCD complex to the end of the cell. The MinCD complex prevents FtsZ ring formation and the subsequent cell division at cell ends. In Arabidopsis thaliana, a homologue of MinD has been shown to be involved in the positioning of chloroplast division site.

Results

To learn whether the MinD homologue in plants is functional in bacteria, AtMinD was expressed in E. coli. Surprisingly, AtMinD can rescue the minicell phenotype of E. coli HL1 mutant (ΔMinDE) in the absence of EcMinE. This rescue requires EcMinC. AtMinD was localized to puncta at the poles of E. coli cells and puncta in chloroplasts without oscillation. AtMinD expressed in the HL1 mutant can cause a punctate localization pattern of GFP-EcMinC at cell ends. Yeast two hybrid and BiFC analysis showed that AtMinD can interact with EcMinC.

Conclusion

Similar to the MinD in Bacillus subtilis, AtMinD is localized to the polar region in E. coli and interacts with EcMinC to confine EcFtsZ polymerization and cell division at the midpoint of the cell.