Andrew D. Rutenberg

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.

Microbial response to surface microtopography: the role of metabolism in localized mineral dissolution

Abstract We examine the role of microtopographical surface features on sulfide minerals in localizing and aligning bacterial adhesion. Experimental data shows strong correlation between bacterial cell alignment and principal crystallographic axes of pyrite (〈100〉 and 〈110〉). While bacteria often adhere to visible surface imperfections such as scratches, in many cases no associated surface features are visible. Additionally, the size of the surface imperfection does not unambiguously determine its effect in localizing and aligning bacterial cells. We theoretically model bacterial adhesion. We find that the depth of a surface feature such as a scratch is less important than its cross-sectional shape. Surface features that conform to the bacterial shape can strongly alter local bacterial adhesion energies, even with heights of only 10 nm. Hence, small local surface alterations due to bacterial metabolism could strongly affect local adhesion parameters, and may account for the observed bacterial distributions on mineral surfaces.

Pattern formation inside bacteria: Fluctuations due to the 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.

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 Eyres 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. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step Delta t that grows with time t as Delta t approximately 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 speedup relative to a fixed time step grows with N, the linear size of the system, as N/ln N. With conservative choices for the parameters controlling accuracy and finite-size effects we find that an 8192(2) lattice can be integrated 300 times faster than with the Euler method.

Effects of poly(L-lysine) substrates on attached escherichia coli bacteria

Poly(L-lysine) (PLL) is a cationic polymer that is often used for attaching and immobilizing cells to glass substrates for further investigation by, e.g., AFM techniques. Because of their small size, bacterial attachment is most easily done using thick air-dried PLL coatings--though thinner PLL coatings are also used and are commercially available. Nevertheless, the antimicrobial activity of PLL is well-established. Accordingly, we have investigated the physiological effects of suspended PLL and of PLL coatings on individual Escherichia coli bacteria through the pole-to-pole oscillations of cytoplasmic MinD-GFP fusion proteins. For planktonic bacteria, suspended PLL concentrations at the micromolar level quenched MinD-GFP oscillations and inhibited bacterial growth. On coverslips with PLL coatings prepared by short exposures of the slides to PLL solutions, followed by rinsing, only a fraction of available bacteria attached after hours of settling time. Min oscillations in the attached bacteria, however, were strong and only moderately slowed. On thick PLL coatings, prepared by drying drops on the slides followed by a brief rinse with deionized water, cells attached well within 15 min. With thick coatings, average oscillation periods for bacteria increased significantly, and considerable cell-to-cell variability was also observed; subsequent replacement of buffer with distilled water led to much larger period increases and/or fading of fluorescence intensity. We demonstrate that Min oscillations are a useful metric for bacteria attached to adhesion layers. We suggest that thick PLL coatings should probably be avoided for bacterial attachment, and that even thin PLL coatings can have significant effects on bacterial physiology.

PEX16 contributes to peroxisome maintenance by constantly trafficking PEX3 via the ER

ABSTRACT The endoplasmic reticulum (ER) is required for the de novo biogenesis of peroxisomes in mammalian cells. However, its role in peroxisome maintenance is unclear. To explore ER involvement in the maintenance of peroxisomes, we redirect a peroxisomal membrane protein (PMP), PEX3, to directly target to the ER using the N-terminal ER signal sequence from preprolactin. Using biochemical techniques and fluorescent imaging, we find that ER-targeting PEX3 (ssPEX3) is continuously imported into pre-existing peroxisomes. This suggests that the ER constitutively provides membrane proteins and associated lipids to pre-existing peroxisomes. Using quantitative time-lapse live-cell fluorescence microscopy applied to cells that were either depleted of or exogenously expressing PEX16, we find that PEX16 mediates the peroxisomal trafficking of two distinct peroxisomal membrane proteins, PEX3 and PMP34, via the ER. These results not only provide insight into peroxisome maintenance and PMP trafficking in mammalian cells but also highlight important similarities and differences in the mechanisms of PMP import between the mammalian and yeast systems.

Temperature Dependence of MinD Oscillation in Escherichia coli: Running Hot and Fast

We observed that the oscillation period of MinD within rod-like and filamentous cells of Escherichia coli varied by a factor of 4 in the temperature range from 20 degrees C to 40 degrees C. The detailed dependence was Arrhenius, with a slope similar to the overall temperature-dependent growth curve of E. coli. The detailed pattern of oscillation, including the characteristic wavelength in filamentous cells, remained independent of temperature. A quantitative model of MinDE oscillation exhibited similar behavior, with an activated temperature dependence of the MinE-stimulated MinD-ATPase rate.

Energy-scaling approach to phase-ordering growth laws

We present a simple, unified approach to determining the growth law for the characteristic length scale L(t) in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines L(t) self-consistently for purely dissipative dynamics by computig the time dependence of the energy in two ways. We derive growth laws for conserved and nonconserved O(n) models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.

Aging, frailty and complex networks

When people age their mortality rate increases exponentially, following Gompertz’s law. Even so, individuals do not die from old age. Instead, they accumulate age-related illnesses and conditions and so become increasingly vulnerable to death from various external and internal stressors. As a measure of such vulnerability, frailty can be quantified using the frailty index (FI). Larger values of the FI are strongly associated with mortality and other adverse health outcomes. This association, and the insensitivity of the FI to the particular health variables that are included in its construction, makes it a powerful, convenient, and increasingly popular integrative health measure. Still, little is known about why the FI works so well. Our group has recently developed a theoretical network model of health deficits to better understand how changes in health are captured by the FI. In our model, health-related variables are represented by the nodes of a complex network. The network has a scale-free shape or “topology”: a few nodes have many connections with other nodes, whereas most nodes have few connections. These nodes can be in two states, either damaged or undamaged. Transitions between damaged and non-damaged states are governed by the stochastic environment of individual nodes. Changes in the degree of damage of connected nodes change the local environment and make further damage more likely. Our model shows how age-dependent acceleration of the FI and of mortality emerges, even without specifying an age-damage relationship or any other time-dependent parameter. We have also used our model to assess how informative individual deficits are with respect to mortality. We find that the information is larger for nodes that are well connected than for nodes that are not. The model supports the idea that aging occurs as an emergent phenomenon, and not as a result of age-specific programming. Instead, aging reflects how damage propagates through a complex network of interconnected elements.

PEX5 and Ubiquitin Dynamics on Mammalian Peroxisome Membranes

Peroxisomes are membrane-bound organelles within eukaryotic cells that post-translationally import folded proteins into their matrix. Matrix protein import requires a shuttle receptor protein, usually PEX5, that cycles through docking with the peroxisomal membrane, ubiquitination, and export back into the cytosol followed by deubiquitination. Matrix proteins associate with PEX5 in the cytosol and are translocated into the peroxisome lumen during the PEX5 cycle. This cargo translocation step is not well understood, and its energetics remain controversial. We use stochastic computational models to explore different ways the AAA ATPase driven removal of PEX5 may couple with cargo translocation in peroxisomal importers of mammalian cells. The first model considered is uncoupled, in which translocation is spontaneous, and does not immediately depend on PEX5 removal. The second is directly coupled, in which cargo translocation only occurs when its PEX5 is removed from the peroxisomal membrane. The third, novel, model is cooperatively coupled and requires two PEX5 on a given importomer for cargo translocation — one PEX5 with associated cargo and one with ubiquitin. We measure both the PEX5 and the ubiquitin levels on the peroxisomes as we vary the matrix protein cargo addition rate into the cytosol. We find that both uncoupled and directly coupled translocation behave identically with respect to PEX5 and ubiquitin, and the peroxisomal ubiquitin signal increases as the matrix protein traffic increases. In contrast, cooperatively coupled translocation behaves dramatically differently, with a ubiquitin signal that decreases with increasing matrix protein traffic. Recent work has shown that ubiquitin on mammalian peroxisome membranes can lead to selective degradation by autophagy, or ‘pexophagy.’ Therefore, the high ubiquitin level for low matrix cargo traffic with cooperatively coupled protein translocation could be used as a disuse signal to mediate pexophagy. This mechanism may be one way that cells could regulate peroxisome numbers.