Extraction of accurate cytoskeletal actin velocity distributions from noisy measurements.

Dynamic remodeling of the actin cytoskeleton is essential for many cellular processes. Tracking the movement of individual actin filaments can in principle shed light on how this complex behavior arises at the molecular level. However, the information that can be extracted from these measurements is often limited by low signal-to-noise ratios. We developed a Bayesian statistical approach to estimate true, underlying velocity distributions from the tracks of individual actin-associated fluorophores with quantified localization uncertainties. We found that the motion of filamentous (F)-actin in fibroblasts and endothelial cells was better described by a statistical jump process than by models in which filaments undergo continuous, diffusive movement. In particular, a model with exponentially distributed jump length- and time-scales recapitulated actin filament velocity distributions measured for the cell cortex, integrin-based adhesions, and stress fibers, suggesting that a common physical model can potentially describe actin filament dynamics in a variety of cellular contexts.

The membrane-actin linker ezrin acts as a sliding anchor.

Protein linkages to filamentous (F)-actin provide the cell membrane with mechanical stability and support intricate membrane architectures. However, the actin cytoskeleton is highly dynamic and undergoes rapid changes in shape during cell motility and other processes. The molecular mechanisms that generate a mechanically robust yet fluid connection between the membrane and actin cytoskeleton remain poorly understood. Here, we adapted a single-molecule optical trap assay to examine how the prototypical membrane-actin linker ezrin acts to anchor F-actin to the cell membrane. We find that ezrin forms a complex that slides along F-actin over micrometer distances while resisting detachment by forces oriented perpendicular to the filament axis. The ubiquity of ezrin and analogous proteins suggests that sliding anchors such as ezrin may constitute an important but overlooked element in the construction of the actin cytoskeleton.

Tether-guided lamellipodia enable rapid wound healing.

Adhesion between animal cells and the underlying extracellular matrix is challenged during wounding, cell division, and a variety of pathological processes. How cells recover adhesion in the immediate aftermath of detachment from the extracellular matrix remains incompletely understood, due in part to technical limitations. Here, we used acute chemical and mechanical perturbations to examine how epithelial cells respond to partial delamination events. In both cases, we found that cells extended lamellipodia to establish readhesion within seconds of detachment. These lamellipodia were guided by sparse membrane tethers whose tips remained attached to their original points of adhesion, yielding lamellipodia that appear to be qualitatively distinct from those observed during cell migration. In vivo measurements in the context of a zebrafish wound assay showed a similar behavior, in which membrane tethers guided rapidly extending lamellipodia. In the case of mechanical wounding events, cells selectively extended tether-guided lamellipodia in the direction opposite of the pulling force, resulting in the rapid reestablishment of contact with the substrate. We suggest that membrane tether-guided lamellipodial respreading may represent a general mechanism to reestablish tissue integrity in the face of acute disruption.

High-order correlations in species interactions lead to complex diversity-stability relationships for ecosystems.

How ecosystems maintain stability is an active area of research. Inspired by applications of random matrix theory in nuclear physics, May showed decades ago that in an ecosystem model with many randomly interacting species, increasing species diversity decreases the stability of the ecosystem. There have since been many additions to May's efforts, one being an improved understanding the effect of mutualistic, competitive, or predator-prey-like correlations between pairs of species. Here we extend a random matrix technique developed in the context of spin-glass theory to study the effect of high-order correlations among species interactions. The resulting analytically solvable models include next-to-nearest-neighbor correlations in the species interaction network, such as the enemy of my enemy is my friend, as well as higher-order correlations. We find qualitative differences from May and others' models, including nonmonotonic diversity-stability relationships. Furthermore, inclusion of particular next-to-nearest-neighbor correlations in predator-prey as opposed to mutualist-competitive networks causes the former to transition to being more stable at higher species diversity. We discuss potential applicability of our results to microbiota engineering and to the ecology of interpredator interactions, such as cub predation between lions and hyenas as well as companionship between humans and dogs.

Limited dishevelled/Axin oligomerization determines efficiency of Wnt/ß-catenin signal transduction.

In Wnt/ß-catenin signaling, the transcriptional coactivator ß-catenin is regulated by its phosphorylation in a complex that includes the scaffold protein Axin and associated kinases. Wnt binding to its coreceptors activates the cytosolic effector Dishevelled (Dvl), leading to the recruitment of Axin and the inhibition of ß-catenin phosphorylation. This process requires interaction of homologous DIX domains present in Dvl and Axin, but is mechanistically undefined. We show that Dvl DIX forms antiparallel, double-stranded oligomers in vitro, and that Dvl in cells forms oligomers typically <10 molecules at endogenous expression levels. Axin DIX (DAX) forms small single-stranded oligomers, but its self-association is stronger than that of DIX. DAX caps the ends of DIX oligomers, such that a DIX oligomer has at most four DAX binding sites. The relative affinities and stoichiometry of the DIX-DAX interaction provide a mechanism for efficient inhibition of ß-catenin phosphorylation upon Axin recruitment to the Wnt receptor complex.

Stem cells can give rise to many types of specialized cells through a process called differentiation, which is partly regulated by changes in the levels of a protein known as ß-catenin. On one hand, a 'destruction complex' can keep ß-catenin levels low; this complex includes a protein called Axin and an enzyme known as GSK-3, which can tag ß-catenin for degradation. On the other hand, when ß-catenin levels need to increase, another protein called Dishevelled is activated. By binding to Axin, Dishevelled can bring the destruction complex in contact with other proteins, which leads to the deactivation of GSK-3. Dishevelled and Axin interact via a region that is similar in the two proteins, called DIX in Dishevelled and DAX in Axin. Studies of DIX and DAX have shown that both regions can form polymers ­ that is, a high number of similar units can bind together to form larger structures. However, these experiments were at higher concentrations than would be found in the cell. It was thought that, when combined, DIX and DAX might form these long chains together, preventing Axin from carrying out its role in destroying ß-catenin. Kan et al. set out to better understand this process by studying how DIX and DAX behave separately, and how they interact. The proteins were examined using a technique called cryo-electron microscopy, which allows scientists to dissect the structure of large proteins. When there was a high concentration of DIX in the sample, the molecules attached to one another to form long double-stranded helices. Similarly, DAX also formed helices, but these were shorter and only single-stranded. When the two proteins were combined, DAX bound only to the ends of short DIX chains, so that there are not more than four DAX chains attached to each DIX double helix. To see if this behaviour happens naturally, Kan et al. attached fluorescent tags to Dishevelled proteins and followed them in living cells: this showed that Dishevelled forms smaller chains with fewer than ten molecules. Together these results highlight how Dishevelled binds to Axin to deactivate GSK-3, to prevent the enzyme from promoting ß-catenin destruction. Mutations in the genes that encode ß-catenin or its regulators are associated with cancer. Ultimately, a better understanding of how ß-catenin is regulated could help to identify new opportunities for drug development.

Dynamics of translation can determine the spatial organization of membrane-bound proteins and their mRNA.

Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that encode inner-membrane proteins can be concentrated near the inner membrane. Cotranslational insertion of the nascent peptide into the membrane brings the translating ribosome and the mRNA close to the membrane. This suggests that kinetic properties of translation can determine the spatial organization of these mRNAs and proteins, which can be modulated through posttranscriptional regulation. Here we use a simple stochastic model of translation to characterize the effect of mRNA properties on the dynamics and statistics of its spatial distribution. We show that a combination of the rate of translation initiation, the availability of secretory apparatuses, and the composition of the coding region determines the abundance of mRNAs near the membrane, as well as their residence time. We propose that the spatiotemporal dynamics of mRNAs can give rise to protein clusters on the membrane and determine their size distribution.

Sub-cellular mRNA localization modulates the regulation of gene expression by small RNAs in bacteria.

Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that demonstrate that families of mRNAs show non-trivial sub-cellular distributions raise the question of how localization may affect the regulatory activity of sRNAs. Here we address this question within a simple mathematical model. We show that the non-uniform spatial distributions of mRNA can alter the threshold-linear response that characterizes sRNAs that act stoichiometrically, and modulate the hierarchy among targets co-regulated by the same sRNA. We also identify conditions where the sub-cellular organization of cofactors in the sRNA pathway can induce spatial heterogeneity on sRNA targets. Our results suggest that under certain conditions, interpretation and modeling of natural and synthetic gene regulatory circuits need to take into account the spatial organization of the transcripts of participating genes.