One of the most important steps in the developmental process of the bacteria cell at the cellular level is the determination of the middle of the cell and the proper placement of the septum, these being essential to the division of the cell. In E. coli, this step depends on the proteins MinC, MinD, and MinE. Exposure to a constant electric field may cause the bacteria cell division mechanism to change, resulting in an abnormal cytokinesis. To see the effects of an external field e.g., an electric or magnetic field on this process, we have solved a set of deterministic reaction diffusion equations, which incorporate the influence of an electric field. We have found some changes in the dynamics of the oscillations of the min proteins from pole to pole. The numerical results show some interesting effects, which are qualitatively in good agreement with some experimental results.
Cell division site positioning is precisely regulated to generate correctly sized and shaped daughters. We uncover a novel strategy to position the FtsZ cytokinetic ring at midcell in the social bacterium Myxococcus xanthus. 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 towards midcell and constrained motion at midcell. Experiments and theory sh…
Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in bacterial communities, also known as biofilm, remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is …
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple ($\approx$1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. S…
Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal measurements of protein content, showing accumulation and division across generations. Here we present a stochastic growth-and-division model with feedback which captures these observed properties. The limiting copy number distribution is calculated exactly, and a single parameter is found to determine the distribution shape and the variance-to-mean relation. E…
Colonies of rod-shaped bacteria constitute a system of colloidal active matter with nematic properties. As a single initial bacterium multiplies through repeated divisions, the resulting colony quickly loses long-range orientational order, but retains locally ordered domains. At the boundaries of these domains, topological defects emerge, which move around randomly as the colony grows. In both experiments and simulations, we find that these defects are created at a rate that corresponds to the exponential growth of the colony, resulting in a stable defect density. Both this defect density and …
The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial microcolonies comprising a few hundred cells. Using a combination of numerical simulations and analytical modeling, here we demonstrate that this transition originates from the competition between growth-induced in-plane active stresses and vertical restoring forces, due to the cell-substrate interactions. Using a simple chainlike colony of laterally confined …
This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We find that the cell size is expressed as a sum of independent lognormal variables. We show numerically that the quality of the lognormal approximation greatly depends on the distributions of the growth rate and cell cycle. Furthermore, we show that actual parameters of the growth rate and cell cycle take values that give a good lognormal approximation; thus, the…
The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings--despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading that incorporates the influence of confinement in promoting both cell-solid and c…
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential folding processes, and multifold structures extend over an agar plate. We report that the growth process from the exponential phase to the stationary phase is well described by the time evolution of fractal dimensions of the filament configuration. We propose a method of characterizing filament configurations using a set of lengths of multifold parts of a fila…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with …
We propose a computational framework to study the growth and spread of bacterial biofilms on interfaces, as well as the action of antibiotics on them. Bacterial membranes are represented by boundaries immersed in a fluid matrix and subject to interaction forces. Growth, division and death of bacterial cells follow dynamic energy budget rules, in response to variations in environmental concentrations of nutrients, toxicants and substances released by the cells. In this way, we create, destroy and enlarge boundaries, either spherical or rod-like. Appropriate forces represent details of the inter…
Essential Role of Extrinsic Noise in Models of E. coli Division Control
IFOM-ETS, The AIRC Institute of Molecular Oncology（IFOM-ETS，AIRC分子肿瘤学研究所）；Dipartimento di Matematica, Università di Pavia（帕维亚大学数学系）；Dipartimento di Fisica, Università degli studi di Milano（米兰大学物理系）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所米兰分部）；Department of Physics of Complex Systems, Weizmann Institute of Science（魏茨曼科学复杂系统物理系）
The plane of bacterial cell division must be precisely positioned. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a large cluster, which is tethered to the nucleoid by the ATPase PomZ and moves in a stochastic, but biased manner towards midcell, where it initiates cell division. Previously, a positioning mechanism based on the fluxes of PomZ on the nucleoid was proposed. However, the cluster dynamics was analyzed in a reduced, one-dimensional geometry. Here we introduce a mathematical model that accounts for the three-dimensional shape of the nucleoid, such that nucleoid-…
Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a longstanding question. Regulation of cell size and shape implies control mechanisms that couple the growth and division of bacteria to their cellular environment and macromolecular composition. In the past decade, simple quantitative laws have emerged that connect cell growth to proteomic composition and the nutrient availability. However, the relationships …
Signal propagation over long distances is a ubiquitous feature of multicellular communities. In biofilms of the bacterium Bacillus subtilis, we recently discovered that some, but not all, cells participate in the propagation of an electrical signal, and the ones that do are organized in a way that is statistically consistent with percolation theory. However, two key assumptions of percolation theory are violated in this system. First, we find here that the probability for a cell to signal is not independent from other cells but instead is correlated with its nearby neighbors. We develop a mech…
Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional structure with a vertically-aligned core. Here, we elucidate the physical mechanism underpinning this transition using a combination of agent-based and continuum modeling. We find that verticalization proceeds through a series of localized mechanical instabilities on the cellular scale. For short cells, these instabilities are primarily triggered by cell…
We observe that small drops of a Bacillus subtilis suspension deposited on agar strongly increase in volume while similar bacteria-void drops do not. By measuring the bacterial concentration within the drop at different heights, we show that the biomass increase due to the constant bacterial cell-division is too small to explain the drop bloating. Rather, the increased volume is caused by the presence of surfactin - a surfactant produced by the bacteria - which induces a water flow out of the environment by an osmotic capillary effect. The required concentration is very low (< 1 mM), four orde…
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule …
Optical tweezers are a technique in which microscopic-sized particles, including living cells and bacteria, can be non-intrusively trapped with high accuracy solely using focused light. The technique has therefore become a powerful tool in the field of biophysics. Optical tweezers thereby provide outstanding manipulation possibilities of cells as well as semi-transparent materials, both non-invasively and non-destructively, in biological systems. In addition, optical tweezers can measure minute forces (< 10-12 N), probe molecular interactions and their energy landscapes, and apply both static …
We develop a minimal model to describe growing dense active matter such as biological tissues, bacterial colonies and biofilms, that are driven by a competition between particle division and steric repulsion. We provide a detailed numerical analysis of collective and single particle dynamics. We show that the microscopic dynamics can be understood as the superposition of an affine radial component due to the global growth, and of a more complex non-affine component which displays features typical of driven soft glassy materials, such as aging, compressed exponential decay of time correlation f…
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over two orders of magnitude in kinetic energy, revealing a decrease…
Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking mechanical equilibrium and inducing collective dynamic responses. We report experiments and theory investigating the motion of immotile Vibrio cholerae, which can kill each other and reproduce in biofilms. We vary viscosity by using bacterial variants that secrete different amounts of extracellular matrix polymers, but are otherwise identical. Unlike thermally…
Current detection and identification of micro-organisms is based on either rather unspecific rapid microscopy or on more accurate complex, time-consuming procedures. In a medical context, the determination of the bacteria Gram type is of significant interest. The diagnostic of microbial infection often requires the identification of the microbiological agent responsible for the infection, or at least the identification of its family (Gram type), in a matter of minutes. In this work, we propose to use terahertz frequency range antennas for the enhanced selective detection of bacteria types. Sev…
One of the major challenges of bottom-up synthetic biology is rebuilding a minimal division machinery. The animal cell division apparatus is mechanically the simplest, in which an actin-based ring constricts the membrane, as compared to microbes and plant cells where a cell wall is involved. Furthermore, reconstitution of the actin division machinery helps to understand the physical and molecular mechanisms of cytokinesis in animal cells and thus our own cells. In this review, we describe the state-of-the-art research on reconstitution of minimal actin-mediated cytokinetic machineries. Based o…
Spontaneous oscillations and geometric cutoff in confined bacterial swarms
Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences (UCAS)（中国科学院大学材料科学与光电技术学院物质科学与光电工程中心）；Department of Physics, Hong Kong Baptist University（香港浸会大学物理系）；Center for Interdisciplinary Studies, Westlake University（西湖大学交叉研究中心）
We experimentally investigate the effects of polymer additives on the collective dynamics of swarming Serratia marcescens in quasi two-dimensional (2D) liquid films. We find that even minute amounts of polymers (< 20 ppm) can significantly enhance swimming speed and promote largescale coherent structures. Velocity statistics show that polymers suppress large velocity fluctuation, transforming the velocity distributions from super-Gaussian to Gaussian. Spatial and temporal correlation functions suggest that polymers increase both the size and lifetime of flow structures. The energy spectra show…
The use of biodegradation as a method for cleaning up soil that has been contaminated by spilt petroleum can be an effective strategy. So, this study investigated the existence of the wild microorganism in soil contaminated with oil and study their ability to degrade petroleum in vitro. Nineteen samples were collected from various locations near Taq Taq (TTOPCO) natural seeps in the Kurdistan Region of Iraq. Morphological, cultural, biochemical tests and molecular identification were used to identify the microbial communities, in addition, spore texture and the colour of the fungal isolates we…
As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as in quorum sensing, to achieve mutualism. Here, to achieve stable division of labor, three properties are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells, by achieving division of labor. Third, this cell aggregate is robust in the number distribution of…
Peritrichous bacteria synchronize and bundle their flagella to actively swim while disruption of the bundle leads to tumbling. It is still not known whether the number of flagella represents an evolutionary adaptation towards optimizing bacterial navigation. Here, we study the swimming dynamics of differentially flagellated Bacillus subtilis strains in a quasi-two-dimensional system. We find that decreasing the number of flagella N reduces the average turning angle between two successive run phases and enhances the duration and directional persistence of the run phase. As a result, having less…
During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description for these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experiment…
We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this mod…
The development of an aptamer-based impedimetric sensor for typing of bacteria (AIST-B) is presented. Highly specific DNA aptamers to Salmonella enteritidis were selected via Cell-SELEX technique. Twelve rounds of selection were performed; each comprises a positive selection step against S. enteritidis and a negative selection step against a mixture of related pathogens, including Salmonella typhimurium, Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa, and Citrobacter freundii to ensure the species-specificity of the selected aptamers. After sequencing of the pool showing the h…
Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available analyses generally neglect the coupling of regulatory circuits with the cellular "chassis" in which the circuits are embedded. For example, the intracellular macromolecular composition of fast-growing bacteria changes with growth rate. As a consequence, important parameters of gene expression, such as ribosome concentration or cell volume, are growth-rate depen…
