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

Unwinding Scaling Violations in Phase Ordering

The one-dimensional $O(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length, $L \sim t^{1/z}$, and the phase winding length, $L_{w} \sim L^{\chi}$. We derive the scaling law $z=2+\mu\chi$, where $\mu=0$ ($\mu=2$) for nonconserved (conserved) dynamics and $\chi=1/2$ for uncorrelated initial orientations. From hard-spin equations of motion, we consider the evolution of the topological defect density and recover a simple scaling description. (please email [email protected] for a hard copy by mail)Comment: 4 pages, LATeX, uuencoded figure file appended: needs epsf.sty, [resubmitted since postscript version did not work well], M/C.TH.94/21,NI9402

Triangular anisotropies in Driven Diffusive Systems: reconciliation of Up and Down

Deterministic coarse-grained descriptions of driven diffusive systems (DDS) have been hampered by apparent inconsistencies with kinetic Ising models of DDS. In the evolution towards the driven steady-state, ``triangular'' anisotropies in the two systems point in opposite directions with respect to the drive field. We show that this is non-universal behavior in the sense that the triangular anisotropy ``flips'' with local modifications of the Ising interactions. The sign and magnitude of the triangular anisotropy also vary with temperature. We have also flipped the anisotropy of coarse-grained models, though not yet at the latest stages of evolution. Our results illustrate the comparison of deterministic coarse-grained and stochastic Ising DDS studies to identify universal phenomena in driven systems. Coarse-grained systems are particularly attractive in terms of analysis and computational efficiency.Comment: 6 pages, 7 figure

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