A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium _Escherichia coli_, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the _in vivo_ MinDE localization dynamics by accounting for the established properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally

Continuous and Long-Term Volume Measurements with a Commercial Coulter Counter

We demonstrate a method to enhance the time resolution of a commercial Coulter counter and enable continuous and long-term cell size measurements for growth rate analyses essential to understanding basic cellular processes, such as cell size regulation and cell cycle progression. Our simple modifications to a commercial Coulter counter create controllable cell culture conditions within the sample compartment and combine temperature control with necessary adaptations to achieve measurement stability over several hours. We also wrote custom software, detailed here, to analyze instrument data files collected by either this continuous method or standard, periodic sampling. We use the continuous method to measure the growth rate of yeast in G1 during a prolonged arrest and, in different samples, the dependency of growth rate on cell size and cell cycle position in arrested and proliferating cells. We also quantify with high time resolution the response of mouse lymphoblast cell culture to drug treatment. This method provides a technique for continuous measurement of cell size that is applicable to a large variety of cell types and greatly expands the set of analysis tools available for the Coulter counter.National Institutes of Health (U.S.) (EUREKA Exceptional, Unconventional Research Enabling Knowledge Acceleration (R01GM085457))National Institutes of Health (U.S.) (contract R21CA137695)National Cancer Institute (U.S.). Physical Sciences-Oncology Center (U54CA143874

An Easy-To-Use Simulation Program Demonstrates Variations in Bacterial Cell Cycle Parameters Depending on Medium and Temperature

Many studies are performed on chromosome replication and segregation in Escherichia coli and other bacteria capable of complex replication with C phases spanning several generations. For such investigations an understanding of the replication patterns, including copy numbers of origins and replication forks, is crucial for correct interpretation of the results

The Min System and Nucleoid Occlusion Are Not Required for Identifying the Division Site in Bacillus subtilis but Ensure Its Efficient Utilization

Precise temporal and spatial control of cell division is essential for progeny survival. The current general view is that precise positioning of the division site at midcell in rod-shaped bacteria is a result of the combined action of the Min system and nucleoid (chromosome) occlusion. Both systems prevent assembly of the cytokinetic Z ring at inappropriate places in the cell, restricting Z rings to the correct site at midcell. Here we show that in the bacterium Bacillus subtilis Z rings are positioned precisely at midcell in the complete absence of both these systems, revealing the existence of a mechanism independent of Min and nucleoid occlusion that identifies midcell in this organism. We further show that Z ring assembly at midcell is delayed in the absence of Min and Noc proteins, while at the same time FtsZ accumulates at other potential division sites. This suggests that a major role for Min and Noc is to ensure efficient utilization of the midcell division site by preventing Z ring assembly at potential division sites, including the cell poles. Our data lead us to propose a model in which spatial regulation of division in B. subtilis involves identification of the division site at midcell that requires Min and nucleoid occlusion to ensure efficient Z ring assembly there and only there, at the right time in the cell cycle

A Model for Damage Load and Its Implications for the Evolution of Bacterial Aging

Deleterious mutations appearing in a population increase in frequency until stopped by natural selection. The ensuing equilibrium creates a stable frequency of deleterious mutations or the mutational load. Here I develop the comparable concept of a damage load, which is caused by harmful non-heritable changes to the phenotype. A damage load also ensues when the increase of damage is opposed by selection. The presence of a damage load favors the evolution of asymmetrical transmission of damage by a mother to her daughters. The asymmetry is beneficial because it increases fitness variance, but it also leads to aging or senescence. A mathematical model based on microbes reveals that a cell lineage dividing symmetrically is immortal if lifetime damage rates do not exceed a threshold. The evolution of asymmetry allows the lineage to persist above the threshold, but the lineage becomes mortal. In microbes with low genomic mutation rates, it is likely that the damage load is much greater than the mutational load. In metazoans with higher genomic mutation rates, the damage and the mutational load could be of the same magnitude. A fit of the model to experimental data shows that Escherichia coli cells experience a damage rate that is below the threshold and are immortal under the conditions examined. The model estimates the asymmetry level of E. coli to be low but sufficient for persisting at higher damage rates. The model also predicts that increasing asymmetry results in diminishing fitness returns, which may explain why the bacterium has not evolved higher asymmetry

Polar Flagellar Biosynthesis and a Regulator of Flagellar Number Influence Spatial Parameters of Cell Division in Campylobacter jejuni

Spatial and numerical regulation of flagellar biosynthesis results in different flagellation patterns specific for each bacterial species. Campylobacter jejuni produces amphitrichous (bipolar) flagella to result in a single flagellum at both poles. These flagella confer swimming motility and a distinctive darting motility necessary for infection of humans to cause diarrheal disease and animals to promote commensalism. In addition to flagellation, symmetrical cell division is spatially regulated so that the divisome forms near the cellular midpoint. We have identified an unprecedented system for spatially regulating cell division in C. jejuni composed by FlhG, a regulator of flagellar number in polar flagellates, and components of amphitrichous flagella. Similar to its role in other polarly-flagellated bacteria, we found that FlhG regulates flagellar biosynthesis to limit poles of C. jejuni to one flagellum. Furthermore, we discovered that FlhG negatively influences the ability of FtsZ to initiate cell division. Through analysis of specific flagellar mutants, we discovered that components of the motor and switch complex of amphitrichous flagella are required with FlhG to specifically inhibit division at poles. Without FlhG or specific motor and switch complex proteins, cell division occurs more often at polar regions to form minicells. Our findings suggest a new understanding for the biological requirement of the amphitrichous flagellation pattern in bacteria that extend beyond motility, virulence, and colonization. We propose that amphitrichous bacteria such as Campylobacter species advantageously exploit placement of flagella at both poles to spatially regulate an FlhG-dependent mechanism to inhibit polar cell division, thereby encouraging symmetrical cell division to generate the greatest number of viable offspring. Furthermore, we found that other polarly-flagellated bacteria produce FlhG proteins that influence cell division, suggesting that FlhG and polar flagella may function together in a broad range of bacteria to spatially regulate division

Noise Contributions in an Inducible Genetic Switch: A Whole-Cell Simulation Study

Stochastic expression of genes produces heterogeneity in clonal populations of bacteria under identical conditions. We analyze and compare the behavior of the inducible lac genetic switch using well-stirred and spatially resolved simulations for Escherichia coli cells modeled under fast and slow-growth conditions. Our new kinetic model describing the switching of the lac operon from one phenotype to the other incorporates parameters obtained from recently published in vivo single-molecule fluorescence experiments along with in vitro rate constants. For the well-stirred system, investigation of the intrinsic noise in the circuit as a function of the inducer concentration and in the presence/absence of the feedback mechanism reveals that the noise peaks near the switching threshold. Applying maximum likelihood estimation, we show that the analytic two-state model of gene expression can be used to extract stochastic rates from the simulation data. The simulations also provide mRNA–protein probability landscapes, which demonstrate that switching is the result of crossing both mRNA and protein thresholds. Using cryoelectron tomography of an E. coli cell and data from proteomics studies, we construct spatial in vivo models of cells and quantify the noise contributions and effects on repressor rebinding due to cell structure and crowding in the cytoplasm. Compared to systems without spatial heterogeneity, the model for the fast-growth cells predicts a slight decrease in the overall noise and an increase in the repressors rebinding rate due to anomalous subdiffusion. The tomograms for E. coli grown under slow-growth conditions identify the positions of the ribosomes and the condensed nucleoid. The smaller slow-growth cells have increased mRNA localization and a larger internal inducer concentration, leading to a significant decrease in the lifetime of the repressor–operator complex and an increase in the frequency of transcriptional bursts