Pattern formation inside bacteria: fluctuations due to low copy number of proteins

We examine fluctuation effects due to the low copy number of proteins involved in pattern-forming dynamics within a bacterium. We focus on a stochastic model of the oscillating MinCDE protein system regulating accurate cell division in E. coli. We find that, for some parameter regions, the protein concentrations are low enough that fluctuations are essential for the generation of patterns. We also examine the role of fluctuations in constraining protein concentration levels.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

We calculate the exact autocorrelation exponent lambda and persistence exponent theta, and also amplitudes, in the dilute limit of phase ordering for dimensions d >= 2. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics we find theta = gamma_d*epsilon, a universal constant times the volume fraction. For autocorrelations, lambda = d at intermediate times, with a late time crossover to lambda >= d/2 + 2. We also derive lambda and theta for globally conserved dynamics and relate these to the q->infinity -state Potts model and soap froths, proposing new poisoning exponents.Comment: 4 pages, revtex. References added, abstract shortene

A storage-based model of heterocyst commitment and patterning in cyanobacteria

When deprived of fixed nitrogen (fN), certain filamentous cyanobacteria differentiate nitrogen-fixing heterocysts. There is a large and dynamic fraction of stored fN in cyanobacterial cells, but its role in directing heterocyst commitment has not been identified. We present an integrated computational model of fN transport, cellular growth, and heterocyst commitment for filamentous cyanobacteria. By including fN storage proportional to cell length, but without any explicit cell-cycle effect, we are able to recover a broad and late range of heterocyst commitment times and we observe a strong indirect cell-cycle effect. We propose that fN storage is an important component of heterocyst commitment and patterning in filamentous cyanobacteria. The model allows us to explore both initial and steady-state heterocyst patterns. The developmental model is hierarchical after initial commitment: our only source of stochasticity is observed growth rate variability. Explicit lateral inhibition allows us to examine $\Delta$patS, $\Delta$hetN, and $\Delta$patN phenotypes. We find that $\Delta$patS leads to adjacent heterocysts of the same generation, while $\Delta$hetN leads to adjacent heterocysts only of different generations. With a shortened inhibition range, heterocyst spacing distributions are similar to those in experimental $\Delta$patN systems. Step-down to non-zero external fixed nitrogen concentrations is also investigated.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version will be available onlin

Maximally-fast coarsening algorithms

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are accessible for similar unconditionally stable algorithms. We compare the scaling structure obtained from our maximally-fast conserved systems directly against the standard fixed-timestep Euler algorithm, and find that the error scales as $\sqrt{A}$ -- so arbitrary accuracy can be achieved.Comment: 5 pages, 3 postscript figures, Late

Scaling state of dry two-dimensional froths: universal angle deviations and structure

We characterize the late-time scaling state of dry, coarsening, two-dimensional froths using a detailed, force-based vertex model. We find that the slow evolution of bubbles leads to systematic deviations from 120degree angles at three-fold vertices in the froth, with an amplitude proportional to the vertex speed, v ~ sqrt(t), but with a side-number dependence that is independent of time. We also find that a significant number of T1 side-switching processes occur for macroscopic bubbles in the scaling state, though most bubble annihilations involve four-sided bubbles at microscopic scales.Comment: 7 pages, 7 figure

Steady-state MreB helices inside bacteria: dynamics without motors

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasi-static evolution of the helical pitch with cell growth, as well as timescales of helix turnover and denovo establishment. We find that while the body of a polarized MreB helix treadmills towards its slow-growing end, the fast-growing tips of laterally associated protofilaments move towards the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.Comment: 7 figures, 1 tabl