arXiv subjects

Andrew D. Rutenberg

Publications and source records attributed to Andrew D. Rutenberg.

32 records · Page 2Linked to original sources

arXiv2012

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.

q-bio.SC↗

arXiv2012

Heterocyst placement strategies to maximize growth of cyanobacterial filaments

Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We examine three different heterocyst placement strategies by quantitatively modelling filament growth while varying both external fixed-nitrogen and leakage from the filament. We find that there is an optimum heterocyst frequency which maximizes the growth rate of the filament; the optimum frequency decreases as the external fixed-nitrogen concentration increases but increases as the leakage increases. In the presence of leakage, filaments implementing a local heterocyst placement strategy grow significantly faster than filaments implementing random heterocyst placement strategies. With no extracellular fixed-nitrogen, consistent with recent experimental studies of Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our local heterocyst placement strategy is qualitatively similar to experimentally observed patterns. As external fixed-nitrogen is increased, the spacing distribution for our local placement strategy retains the same shape while the average spacing between heterocysts continuously increases.

physics.bio-ph↗

arXiv2011

Reconciling cyanobacterial fixed-nitrogen distributions and transport experiments with quantitative modelling

Filamentous cyanobacteria growing in media with insufficient fixed nitrogen differentiate some cells into heterocysts, which fix nitrogen for the remaining vegetative cells. Transport studies have shown both periplasmic and cytoplasmic connections between cells that could transport fixed-nitrogen along the filament. Two experiments have imaged fixed-nitrogen distributions along filaments. In 1974,Wolk et al found a peaked concentration of fixed-nitrogen at heterocysts using autoradiographic techniques. In contrast, in 2007, Popa et al used nanoSIMS to show large dips at the location of heterocysts, with a variable but approximately level distribution between them. With an integrated model of fixed-nitrogen transport and cell growth, we recover the results of both Wolk et al and of Popa et al using the same model parameters. To do this, we account for immobile incorporated fixed-nitrogen and for the differing durations of labeled nitrogen fixation that occurred in the two experiments. The variations seen by Popa et al are consistent with the effects of cell-by-cell variations of growth rates, and mask diffusive gradients. We are unable to rule out a significant amount of periplasmic fN transport.

physics.bio-ph↗

arXiv2009

Self-organization of the MinE ring in subcellular Min oscillations

We model the self-organization of the MinE ring that is observed during subcellular oscillations of the proteins MinD and MinE within the rod-shaped bacterium {\it Escherichia coli}. With a steady-state approximation, we can study the MinE-ring generically -- apart from the other details of the Min oscillation. Rebinding of MinE to depolymerizing MinD filament tips controls MinE ring formation through a scaled cell shape parameter $\tilde{r}$. We find two types of E-ring profiles near the filament tip: a strong plateau-like E-ring controlled by 1D diffusion of MinE along the bacterial length, or a weak cusp-like E-ring controlled by 3D diffusion near the filament tip. While the width of a strong E-ring depends on $\tilde{r}$, the occupation fraction of MinE at the MinD filament tip is saturated and hence the depolymerization speed do not depend strongly on $\tilde{r}$. Conversely, for weak E-rings both $\tilde{r}$ and the MinE to MinD stoichiometry strongly control the tip occupation and hence the depolymerization speed. MinE rings {\em in vivo} are close to the threshold between weak and strong, and so MinD-filament depolymerization speed should be sensitive to cell shape, stoichiometry, and the MinE-rebinding rate. We also find that the transient to MinE-ring formation is quite long in the appropriate open geometry for assays of ATPase activity {\it in vitro}, explaining the long delays of ATPase activity observed for smaller MinE concentrations in those assays without the need to invoke cooperative MinE activity.

q-bio.SC↗

arXiv2007

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.

q-bio.SC↗

arXiv2007

Modeling partitioning of Min proteins between daughter cells after septation in Escherichia coli

Ongoing sub-cellular oscillation of Min proteins is required to block minicelling in E. coli. Experimentally, Min oscillations are seen in newly divided cells and no minicells are produced. In model Min systems many daughter cells do not oscillate following septation because of unequal partitioning of Min proteins between the daughter cells. Using the 3D model of Huang et al., we investigate the septation process in detail to determine the cause of the asymmetric partitioning of Min proteins between daughter cells. We find that this partitioning problem arises at certain phases of the MinD and MinE oscillations with respect to septal closure and it persists independently of parameter variation. At most 85% of the daughter cells exhibit Min oscillation following septation. Enhanced MinD binding at the static polar and dynamic septal regions, consistent with cardiolipin domains, does not substantially increase this fraction of oscillating daughters. We believe that this problem will be shared among all existing Min models and discuss possible biological mechanisms that may minimize partitioning errors of Min proteins following septation.

q-bio.SC↗

arXiv2005

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.

cond-mat.soft↗

arXiv2003

Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. We show that accuracy can be controlled with an unbounded time step Delta-t that grows with time t as Delta-t ~ t^alpha. We develop a classification scheme for the step exponent alpha and demonstrate that a class of simple linear algorithms gives alpha=1/3. For this class the speed up relative to a fixed time step grows with the linear size of the system as N/log N, and we estimate conservatively that an 8192^2 lattice can be integrated 300 times faster than with the Euler method.

cond-mat.stat-mech↗

arXiv2003

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.

cond-mat.stat-mech↗

arXiv2003

Diffusion of Asymmetric Swimmers

Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed curvature magnitude. At small speeds the diffusivity is independent of the speed. At larger particle speeds, the diffusivity depends on the speed through a novel exponent. We apply our results to intracellular transport of vesicles. In sharp contrast to thermal diffusion, the effective diffusivity increases with vesicle size and so may provide an effective means of intracellular transport.

cond-mat.soft↗

arXiv2001

Dynamic compartmentalization of bacteria: accurate division in E. coli

Positioning of the midcell division plane within the bacterium E. coli is controlled by the min system of proteins: MinC, MinD and MinE. These proteins coherently oscillate from end to end of the bacterium. We present a reaction--diffusion model describing the diffusion of min proteins along the bacterium and their transfer between the cytoplasmic membrane and cytoplasm. Our model spontaneously generates protein oscillations in good agreement with experiments. We explore the oscillation stability, frequency and wavelength as a function of protein concentration and bacterial length.

cond-mat.soft↗

arXiv1999

Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence

We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and hence is nonuniversal.

cond-mat.stat-mech↗

arXiv1998

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.

cond-mat.stat-mech↗

arXiv1997

Dynamical Multiscaling in Quenched Skyrme Systems

Strong dynamical scaling violations exist in quenched two-dimensional systems with vector O(3) order parameters. These systems support non-singular topologically stable configurations (skyrmions). By tuning the stability of isolated skyrmions to expand or shrink, we find dramatic differences in the dynamical multiscaling spectrum of decaying moments $< |ρ|^n >$ of the topological charge density distribution and in particular in the decay of the energy-density $ε\sim < |ρ| >$. We present a simple two-length-scale model for the observed exponents in the case when isolated skyrmions expand. No such simple model is found when isolated skyrmions shrink.

cond-mat.stat-mech↗