Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy-speed-accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance tradeoffs for cellular regulatory functions and information processing.

Control over the scaffolding activity of FtsZ probably represents a universal regulatory mechanism of bacterial cytokinesis.

Forces are important in biological systems for accomplishing key cell functions, such as motility, organelle transport, and cell division. Currently, known force generation mechanisms typically involve motor proteins. In bacterial cells, no known motor proteins are involved in cell division. Instead, a division ring (Z-ring) consists of mostly FtsZ, FtsA, and ZipA is used to exerting a contractile force. The mechanism of force generation in bacterial cell division is unknown. Using computational modeling, we show that Z-ring formation results from the colocalization of FtsZ and FtsA mediated by the favorable alignment of FtsZ polymers. The model predicts that the Z-ring undergoes a condensation transition from a lowdensity state to a high-density state and generates a sufficient contractile force to achieve division. FtsZ GTP hydrolysis facilitates monomer turnover during the condensation transition, but does not directly generate forces. In vivo fluorescence measurements show that FtsZ density increases during division, in accord with model results. The mechanism is akin to van der Waals picture of gas-liquid condensation, and shows that organisms can exploit microphase transitions to generate mechanical forces.force generation ͉ modeling ͉ Z-ring C ytokinesis is the final step of cell division. For bacterial cells, FtsZ filaments and several related proteins form a contractile ring (Z-ring) and drive cytokinesis (1-3). FtsZ is a tubulin homologue that hydrolyzes GTP (4, 5), although GTP hydrolysis activity is not essential for bacterial division (6). Recently, force generation by membrane-bound FtsZ in vesicles was observed (7). Thus, the role of the Z-ring seems to be 2-fold: It recruits cell wall synthesis proteins, facilitating cell wall growth and remodeling (2, 3), and it exerts a weak mechanical force to direct cell wall growth (8). Bacterial genome does not appear to code for contractile molecular motors, thus prompting the question: what is the mechanism of Z-ring formation and ensuing force generation?Earlier studies of FtsZ polymerization showed that FtsZ monomers can form polymer bonds and lateral bundling bonds (9-13). FtsZ forms proto-filament under low concentration and these proto-filaments interact with each other and form long but narrow bundles when FtsZ concentration is high (14). Quantitative analysis of in vitro polymerization kinetics indicated that the polymer bond is Ϫ17 Ϸ Ϫ20 k B T, and the lateral bond is Ϫ0.2 Ϸ Ϫ0.5 k B T, depending on the buffer condition (13). (k B T is 4.2 pNnm.) A GTP hydrolysis-associated conformational change has been observed for FtsZ filaments (9). However, it can be shown that the conformational change is unlikely to generate sufficient contractile force (see Discussion). A different mechanism of force generation must be at play.FtsA and ZipA are 2 proteins essential for the formation and maintenance of the Z-ring. Spatial regulation of the ring positioning is achieved in part through the action of the MinCDE system. MinC is a negative regulator of FtsZ poly...

The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli) is sufficient to accomplish division.bacterial cell division ͉ FtsZ-ring ͉ mathematical model ͉ peptidoglycan synthesis I n rod-like bacteria, such as Escherichia coli and Bacillus subtilis, a conserved cell division gene is FtsZ, which forms a filamentous ring structure (Z-ring) at the mid cell before division (1, 2). The positioning of the Z-ring at the mid cell in E. coli is related to spatial-temporal oscillations in the MinCDE system (3-5). For the actual division step, the radius of the Z-ring is seen to decrease over several minutes, after which a septum is formed and the bacterium separates into two daughter cells (1, 6). It has been postulated that the Z-ring generates forces and ''pinches'' the cell into halves (7), although whether FtsZ generates force is debatable. In addition to the Fts family of proteins, other proteins are also essential for cell division. In particular, disabling peptidoglycan (PG) synthesis proteins or penicillin binding proteins (PBP) just before division stops cytokinesis (8, 9). A systematic study showed that some PBPs are localized near the Z-ring during division (10). Therefore, cell wall synthesis is important in cell division. The mechanics and the dynamics of the cell wall must be considered on an equal footing for quantifying bacterial cell division.Growth and synthesis of the bacterial cell wall is a complex process. The wall is composed of saccharide strands interconnected by polypeptides (7,(11)(12)(13). Indeed, families of PBPs are found in bacteria, with some localized near the furrow during division and some uniformly distributed (10,14,15). Coordinated activity of PBPs synthesizes new PG strands, cross-linking them into the existing wall structure. In a proposed growth model, old strands are also depolymerized, thereby removing them from the wall structure (a process that we will generically call ''turnover'') (7, 11, 16), although models for E. coli growth without turnover also have been proposed (12, 13). Using radio-active labeling, turnover in the PG layer has been investigated (17-19). It was found that the c...