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Cells rely on their cytoskeleton for key processes including division and directed motility. Actin filaments are a primary constituent of the cytoskeleton. Although actin filaments can create a variety of network architectures linked to distinct cell functions, the microscale molecular interactions that give rise to these macroscale structures are not well understood. In this work, we investigate the microscale mechanisms that produce different branched actin network structures using an iterative classification approach. First, we employ a simple yet comprehensive agent-based model that produces synthetic actin networks with precise control over the microscale dynamics. Then we apply machine learning techniques to classify actin networks based on measurable network density and geometry, identifying key mechanistic processes that lead to particular branched actin network architectures. Extensive computational experiments reveal that the most accurate method uses a combination of supervised learning based on network density and unsupervised learning based on network symmetry. This framework can potentially serve as a powerful tool to discover the molecular interactions that produce the wide variety of actin network configurations associated with normal development as well as pathological conditions such as cancer.

The epithelial mesenchymal transition (EMT) is a process by which cells lose their adhesive nature and gain the migratory properties associated with mesenchymal cells. This transition allows cells to migrate away from a primary tumor while maintaining their newly acquired invasive behavior, suggesting that there is a bistable switch between the epithelial and mesenchymal phenotypes. In recent experimental work, we found evidence of this bistability in the MCF7 breast carcinoma cell line (Gasior et al., 2019). Underlying the complex processes governing EMT, we identify a feedback loop between E-cadherin, a protein involved in cellular adhesion, and Slug, a transcription factor that is upregulated during EMT. Here, we present a simple mathematical model that examines the relationship between E-cadherin and Slug in response to pro-epithelial and pro-mesenchymal factors, cell-cell contact and TGF-β, respectively. We hypothesize that cell-cell contact is a critical component in the transition from the epithelial to the mesenchymal phenotype and that it is possible to initiate EMT with the loss of cell-cell contact or the activation of the TGF-β signaling pathway. We propose a reversible bistable switch in response to a loss of cell-cell contact but an irreversible bistable switch when the cell is exposed to TGF-β. Taken together, this model shows that acquiring and retaining invasive behavior by cells with high levels of cell-cell contact is not impossible but, instead, depends on the cooperation between the two switches. The predictions of this model for E-cadherin and Slug levels were compared against relative gene expression data from our recent experiments with MCF7 cells (Gasior et al., 2019). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments, while also highlighting issues that arise when comparing experimental results to theoretical predictions.

The standard protocol for studying the spiking properties of single neurons is the application of current steps while monitoring the voltage response. Although this is informative, the jump in applied current is artificial. A more physiological input is where the applied current is ramped up, reflecting chemosensory input. Unsurprisingly, neurons can respond differently to the two protocols, since ion channel activation and inactivation are affected differently. Understanding the effects of current ramps, and changes in their slopes, is facilitated by mathematical models. However, techniques for analyzing current ramps are under-developed. In this article, we demonstrate how current ramps can be analyzed in single neuron models. The primary issue is the presence of gating variables that activate on slow time scales and are therefore far from equilibrium throughout the ramp. The use of an appropriate fast-slow analysis technique allows one to fully understand the neural response to ramps of different slopes. This study is motivated by data from olfactory bulb dopamine neurons, where both fast ramp (tens of milliseconds) and slow ramp (tens of seconds) protocols are used to understand the spiking profiles of the cells. The slow ramps generate experimental bifurcation diagrams with the applied current as a bifurcation parameter, thereby establishing asymptotic spiking activity patterns. The faster ramps elicit purely transient behavior that is of relevance to most physiological inputs, which are short in duration. The two protocols together provide a broader understanding of the neuron’s spiking profile and the role that slowly activating ion channels can play.

The makings of anisosomes Phase separation of proteins within the cell can produce a liquid-inside-a-liquid phase resembling oil droplets in water. Yu et al. now report that an RNA-binding protein called TDP-43, in which mutation and aggregation are linked to amyotrophic lateral sclerosis and frontotemporal dementia, phase separates into complex droplets, which they named anisosomes. This process occurred when TDP-43 lost its ability to bind RNA through disease-causing mutation or posttranslational acetylation. Anisosomes have spherical shells of TDP-43 (with properties of a liquid crystal) surrounding centers of the protein chaperone HSP70. Chaperone activity was required to maintain liquidity. Anisosomes formed in neurons in vivo when proteasome activity was inhibited and were converted into aggregates when adenosine triphosphate (ATP) levels fell. Science , this issue p. eabb4309

Actin is an intracellular protein that constitutes a primary component of the cellular cytoskeleton and is accordingly crucial for various cell functions. Actin assembles into semi-flexible filaments that cross-link to form higher order structures within the cytoskeleton. In turn, the actin cytoskeleton regulates cell shape, and participates in cell migration and division. A variety of theoretical models have been proposed to investigate actin dynamics across distinct scales, from the stochastic nature of protein and molecular motor dynamics to the deterministic macroscopic behavior of the cytoskeleton. Yet, the relationship between molecular-level actin processes and cellular-level actin network behavior remains understudied, where prior models do not holistically bridge the two scales together.

The RNA binding protein TDP-43 naturally phase separates within cell nuclei and forms cytoplasmic aggregates in age-related neurodegenerative diseases. Here we show that acetylation-mediated inhibition of TDP-43 binding to RNA produces co-de-mixing of acetylated and unmodified TDP-43 into symmetrical, intranuclear spherical annuli whose shells and cores have liquid properties. Shells are anisotropic, like liquid crystals. Consistent with our modelling predictions that annulus formation is driven by components with strong self-interactions but weak interaction with TDP-43, the major components of annuli cores are identified to be HSP70 family proteins, whose chaperone activity is required to maintain liquidity of the core. Proteasome inhibition, mimicking reduction in proteasome activity during aging, induces TDP-43-containing annuli in neurons in rodents. Thus, we identify that TDP-43 phase separation is regulated by acetylation, proteolysis, and ATPase-dependent chaperone activity of HSP70.One Sentence SummaryAcetylation of TDP-43 drives its phase separation into spherical annuli that form a liquid-inside-a-liquid-inside-a-liquid.

Background Following the formation of a primary carcinoma, neoplastic cells metastasize by undergoing the epithelial mesenchymal transition (EMT), which is triggered by cues from inflammatory and stromal cells in the microenvironment. EMT allows epithelial cells to lose their highly adhesive nature and instead adopt the spindle-like appearance, as well as the invasive and migratory behavior, of mesenchymal cells. We hypothesize that a bistable switch between the epithelial and mesenchymal phenotypes governs EMT, allowing the cell to maintain its mesenchymal phenotype even after it leaves the primary tumor microenvironment and EMT-inducing extracellular signal. Results This work presents a simple mathematical model of EMT, specifically the roles played by four key proteins in the Wnt signaling pathway: Dishevelled (Dvl), E-cadherin, β-catenin, and Slug. The model predicts that following activation of the Wnt pathway, an epithelial cell in the primary carcinoma must attain a threshold level of membrane-bound Dvl to convert to the mesenchymal-like phenotype and maintain that phenotype once it has migrated away from the primary tumor. Furthermore, sensitivity analysis of the model suggests that in both the epithelial and the mesenchymal states, the steady state behavior of E-cadherin and the transcription factor Slug are sensitive to changes in the degradation rate of Slug, while E-cadherin is also sensitive to the IC50 (half-maximal) concentration of Slug necessary to inhibit E-cadherin production. The steady state behavior of Slug exhibits sensitivity to changes in the rate at which it is induced by β-catenin upon activation of the Wnt pathway. In the presence of sufficient amount of Wnt ligand, E-cadherin levels are sensitive to the ratio of the rate of Slug activation via β-catenin to the IC50 concentration of Slug necessary to inhibit E-cadherin production. Conclusions The sensitivity of E-cadherin to the degradation rate of Slug, as well as the IC50 concentration of Slug necessary to inhibit E-cadherin production, shows how the adhesive nature of the cell depends on finely-tuned regulation of Slug. By highlighting the role of β-catenin in the activation of EMT and the relationship between E-cadherin and Slug, this model identifies critical parameters of therapeutic concern, such as the threshold level of Dvl necessary to inactivate the GSK-3β complex mediating β-catenin degradation, the rate at which β-catenin translocates to the nucleus, and the IC50 concentration of Slug needed to inhibit E-cadherin production. Electronic supplementary material The online version of this article (10.1186/s12976-017-0064-7) contains supplementary material, which is available to authorized users.

An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquid-like droplets condense to create compartments that are thought to promote and inhibit specific biochemistry. In this work, a multiphase, Cahn-Hilliard diffuse interface model is used to examine RNA-protein interactions driving LLPS. We create a bivalent system that allows for two different species of protein-RNA complexes and model the competition that arises for a shared binding partner, free protein. With this system we demonstrate that the binding and unbinding of distinct RNA-protein complexes leads to diverse spatial pattern formation and dynamics within droplets. Both the initial formation and transient behavior of spatial patterning are subject to the exchange of free proteins between RNA-protein complexes. This study illustrates that spatiotemporal heterogeneity can emerge within phase-separated biological condensates with simple binding reactions and competition. Intra-droplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.