Two concurrent processes—a cell-related interdivision cycle and a chromosome cycle—compete to determine cell division.

Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to chemicals, such as nutrients and toxins. Many of the pathway's remarkable sensing and signaling properties are now concisely summarized in terms of design (or engineering) principles. More recently, new approaches from information theory and stochastic thermodynamics have begun to address how pathways process environmental stimuli and what the limiting factors are. However, to fully capitalize on these theoretical advances, a closer connection with single-cell experiments will be required. IntroductionAll living organisms from animals to unicellular bacteria live under constant evolutionary pressure. To stay ahead in the game of evolution, organisms need to process noisy information, allowing them to make survival decisions quickly. However, to process information and move organisms also require energy. Thus the final behavior of any organism has to be an outcome which produces strong advantages under likely occurring environments. Chemotaxis of Escherichia coli is particularly well understood in terms of its molecular components, allowing this bacterium to migrate towards food and away from toxins [1][2][3][4][5]. Indeed, an ever increasing amount of studies has highlighted several design principles, i.e. engineering blue prints, ensuring exquisite sensitivity, efficiency, robustness, and wide dynamic range at all levels of the pathway.This review focuses on recent findings in E. coli chemotaxis, in particular on how molecular mechanisms give rise to information processing, its associated thermodynamic cost, and the resulting swimming behavior. What new design principles will be discovered next? Classical view of Escherichia coli chemotaxisEscherichia coli is a Gram-negative bacterium inhabiting soil, as well as the animal and human gastrointestinal tracts. Inside the host, it contributes to the digestion of food and enhances resistance against pathogens [6]. This bacterium has a relatively simple chemotactic pathway (Fig. 1 1A). External stimuli are processed at the receptor level, where receptors sense and memorize chemical concentrations from the past by their adapted methylation level (Fig. 1A, see red box for 'sensing module'). The receptor-signaling activity can be monitored experimentally by tagging the CheY and CheZ proteins with a fluorescence-resonance-energy-transfer (FRET) reporter pair to follow their phosphorylation-dependent interaction. To swim cells are equipped with 5-8 flagellar rotary motors (Fig. 1A, blue box for 'motility module'), each of which rotates either clockwise (CW) or counterclockwise (CCW). Taking together these flagella determine cell movement, given either by a 'run' or a random reorientation in a 'tumble' [7][8][9]. The phosphorylated protein CheY-p links sensing and motility (Fig. 1A). In absence of any chemical gradient E. coli per...

Understanding the classic problem of how single E. coli cells coordinate cell division with genome replication would open the way to addressing cellcycle progression at the single-cell level. Recent studies produced new data, but the contrast in their conclusions and proposed mechanisms makes the emerging picture fragmented and unclear. Here, we re-evaluate available data and models, including generalizations based on the same assumptions. We show that although they provide useful insights, none of the proposed models captures all correlation patterns observed in data. We conclude that the assumption that replication is the bottleneck process for cell division is too restrictive. Instead, we propose that two concurrent cycles responsible for division and initiation of DNA replication set the time of cell division. This framework allows us to select a nearly constant added size per origin between subsequent initiations as the most likely mechanism setting initiation of replication.

In physics, it is customary to represent the fluctuations of a stochastic system at steady state in terms of linear response to small random perturbations. Previous work has shown that the same framework describes effectively the trade-off between cell-to-cell variability and correction in the control of cell division of single E. coli cells. However, previous analyses were motivated by specific models and limited to a subset of the measured variables. For example, most analyses neglected the role of growth rate variability. Here, we take a comprehensive approach and consider several sets of available data from both microcolonies and microfluidic devices in different growth conditions. We evaluate all the coupling coefficients between the three main measured variables (interdivision times, cell sizes and individual-cell growth rates). The linear-response framework correctly predicts consistency relations between a priori independent experimental measurements, which confirms its validity. Additionally, the couplings between the cell-specific growth rate and the other variables are typically non zero. Finally, we use the framework to detect signatures of mechanisms in experimental data involving growth rate fluctuations, finding that (1) noise-generating coupling between size and growth rate is a consequence of inter-generation growth rate correlations and (2) the correlation patterns agree with a near-adder model where the added size has a dependence on the single-cell growth rate. Our findings define relevant constraints that any theoretical description should reproduce, and will help future studies aiming to falsify some of the competing models of the cell cycle existing today in the literature.

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.

A cell can divide only upon completion of chromosome segregation, or its daughters would lose genetic material [1,2]. In E. coli bacteria, the prevalent view is that cells divide a fixed amount of time after they start to copy the chromosomes [3,4], and a known pathway prevents cells from dividing if the chromosomes interfere with the cytokinesis machinery [5]. However, whether completion of segregation is typically the bottleneck process for the decision to divide has never been stringently tested on single cells. We show how key trends in single-cell data lead to challenge the classic idea of replication-segregation limiting cell division. Instead, the data agree with a model where two concurrent processes (setting replication initiation and inter-division time) set cell division on competing time scales. During each cell cycle, division is set by the slowest process (an "AND" gate). The concept of transitions between cell-cycle stages as decisional processes integrating multiple inputs instead of cascading from orchestrated steps can affect the way we think of the cell cycle in general.Dynamic single-cell data revived the classic debate on the determinants of cell division, but the recent literature is fragmented into different and contrasting models [3]. Most studies take the classic view that a fixed "C+D period", comprising a "C period" to copy the genome and a "D period", needed to complete segregation and running from termination to cell division (Fig. 1a) is rate-limiting for cell division (Fig. 1b), but these studies do not agree on the underlying mechanisms [6,7]. A recent study by Harris and Theriot formulates the opposite hypothesis [8]. The main assumption of this alternative view is that the rate-limiting process for cell division is instead the completion of the septum (Fig. 1b), and consequently chromosome segregation is never rate-limiting for cell division.More specifically, the authors provide evidence that surface synthesis rate is proportional to volume, and they propose a model where division is set by a threshold surface to synthesize the septum [8]. This model recapitulates the empirical size-control strategy followed by Replication initiation occurs after a "B period" followed by the C (replication) and D (termination to division) periods, the B and C + D period can be measured in single cells by proxies of replication initiation [6,11]. b) Classically, replicationsegregation is believed to be rate-limiting for cell division; a recent hypothesis by Harris and Theriot [8] states that the rate-limiting process might be instead the formation of the septum. c) Our concurrent-processes hypothesis states that cell division is the result of the slowest between an interdivision cycle (setting division when, e.g., the septum machinery is ready) and a replication-related processes (setting division when replication-segregation is complete). Hence, the circuit is analogous to an AND gate. d) Scheme of the mathematical model.these cells, whereby the added size is nearly constant, regardless of init...

Cells must control the cell cycle to ensure that key processes are brought to completion. In Escherichia coli, it is controversial whether cell division is tied to chromosome replication or to a replication-independent inter-division process. A recent model suggests instead that both processes may limit cell division with comparable odds in single cells. Here, we tested this possibility experimentally by monitoring single-cell division and replication over multiple generations at slow growth. We then perturbed cell width, causing an increase of the time between replication termination and division. As a consequence, replication became decreasingly limiting for cell division, while correlations between birth and division and between subsequent replication-initiation events were maintained. Our experiments support the hypothesis that both chromosome replication and a replication-independent inter-division process can limit cell division: the two processes have balanced contributions in non-perturbed cells, while our width perturbations increase the odds of the replication-independent process being limiting.

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.