A stochastic model of Min oscillations in Escherichia coli and Min protein segregation during cell division

The Min system in Escherichia coli directs division to the centre of the cell through pole-to-pole oscillations of the MinCDE proteins. We present a one dimensional stochastic model of these oscillations which incorporates membrane polymerisation of MinD into linear chains. This model reproduces much of the observed phenomenology of the Min system, including pole-to-pole oscillations of the Min proteins. We then apply this model to investigate the Min system during cell division. Oscillations continue initially unaffected by the closing septum, before cutting off rapidly. The fractions of Min proteins in the daughter cells vary widely, from 50%-50% up to 85%-15% of the total from the parent cell, suggesting that there may be another mechanism for regulating these levels in vivo.Comment: 19 pages, 12 figures (25 figure files); published at http://www.iop.org/EJ/journal/physbi

Stuttering Min oscillations within E. coli bacteria: A stochastic polymerization model

We have developed a 3D off-lattice stochastic polymerization model to study subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding, and fragmentation of MinD filaments due to MinE. Each of processivity, protection, and fragmentation reduces stuttering, speeds oscillations, and reduces MinD filament lengths. Neither processivity or tip-protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations are consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization in experimental conditions.Comment: 21 pages, 7 figures, missing unit for k_f inserte

Fracture precursors in disordered systems

A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with respect to the control parameter (reduced stress) exhibits a singular behaviour. Our results are nevertheless compatible with previous experimental findings, if one restricts the comparison to the (limited) range accessible in the experiment. A power-law avalanche distribution is also found with an exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter

Treatment of tuberculosis in a region with high drug resistance: Outcomes, drug resistance amplification and re-infection

Introduction: Emerging antituberculosis drug resistance is a serious threat for tuberculosis (TB) control, especially in Eastern European countries. Methods: We combined drug susceptibility results and molecular strain typing data with treatment outcome reports to assess the influence of drug resistance on TB treatment outcomes in a prospective cohort of patients from Abkhazia (Georgia). Patients received individualized treatment regimens based on drug susceptibility testing (DST) results. Definitions for antituberculosis drug resistance and treatment outcomes were in line with current WHO recommendations. First and second line DST, and molecular typing were performed in a supranational laboratory for Mycobacterium tuberculosis (MTB) strains from consecutive sputum smear-positive TB patients at baseline and during treatment. Results: At baseline, MTB strains were fully drug-susceptible in 189/326 (58.0%) of patients. Resistance to at least H or R (PDR-TB) and multidrug-resistance (MDR-TB) were found in 69/326 (21.2%) and 68/326 (20.9%) of strains, respectively. Three MDR-TB strains were also extensively resistant (XDR-TB). During treatment, 3/189 (1.6%) fully susceptible patients at baseline were re-infected with a MDR-TB strain and 2/58 (3.4%) PDR-TB patients became MDR-TB due to resistance amplification. 5/ 47 (10.6%) MDR- patients became XDR-TB during treatment. Treatment success was observed in 161/189 (85.2%), 54/69 (78.3%) and 22/68 (32.3%) of patients with fully drug susceptible, PDR- and MDR-TB, respectively. Development of ofloxacin resistance was significantly associated with a negative treatment outcome. Conclusion: In Abkhazia, a region with high prevalence of drug resistant TB, the use of individualized MDR-TB treatment regimens resulted in poor treatment outcomes and XDR-TB amplification. Nosocomial transmission of MDR-TB emphasizes the importance of infection control in hospitals

Characteristics of drug-resistant tuberculosis in Abkhazia (Georgia), a high-prevalence area in Eastern Europe

Although multidrug-resistant (MDR) tuberculosis (TB) is a major public health problem in Eastern Europe, the factors contributing to emergence, spread and containment of MDR-TB are not well defined. Here, we analysed the characteristics of drug-resistant TB in a cross-sectional study in Abkhazia (Georgia) between 2003 and 2005, where standard short-course chemotherapy is supplemented with individualized drug-resistance therapy. Drug susceptibility testing (DST) and molecular typing were carried out for Mycobacterium tuberculosis complex strains from consecutive smear-positive TB patients. Out of 366 patients, 60.4% were resistant to any first-line drugs and 21% had MDR-TB. Overall, 25% of all strains belong to the Beijing genotype, which was found to be strongly associated with the risk of MDR-TB (OR 25.9, 95% CI 10.2-66.0) and transmission (OR 2.8, 95% CI 1.6-5.0). One dominant MDR Beijing clone represents 23% of all MDR-TB cases. The level of MDR-TB did not decline during the study period, coinciding with increasing levels of MDR Beijing strains among previously treated cases. Standard chemotherapy plus individualized drug-resistance therapy, guided by conventional DST, might be not sufficient to control MDR-TB in Eastern Europe in light of the spread of "highly transmissible" MDR Beijing strains circulating in the community

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

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl