Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses.

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Inferring local molecular dynamics from the global actin network structure: A case study of 2D synthetic branching actin networks.

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.

Modeling the influence of cell-cell contact and TGF-ß signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells.

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-ß, 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-ß 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-ß. 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.

Fast-slow analysis as a technique for understanding the neuronal response to current ramps.

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.

HSP70 chaperones RNA-free TDP-43 into anisotropic intranuclear liquid spherical shells.

The RNA binding protein TDP-43 forms intranuclear or cytoplasmic aggregates in age-related neurodegenerative diseases. In this study, we found that RNA binding-deficient TDP-43 (produced by neurodegeneration-causing mutations or posttranslational acetylation in its RNA recognition motifs) drove TDP-43 demixing into intranuclear liquid spherical shells with liquid cores. These droplets, which we named "anisosomes", have shells that exhibit birefringence, thus indicating liquid crystal formation. Guided by mathematical modeling, we identified the primary components of the liquid core to be HSP70 family chaperones, whose adenosine triphosphate (ATP)-dependent activity maintained the liquidity of shells and cores. In vivo proteasome inhibition within neurons, to mimic aging-related reduction of proteasome activity, induced TDP-43-containing anisosomes. These structures converted to aggregates when ATP levels were reduced. Thus, acetylation, HSP70, and proteasome activities regulate TDP-43 phase separation and conversion into a gel or solid phase.

Partial demixing of RNA-protein complexes leads to intradroplet patterning in phase-separated biological condensates.

An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquidlike 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. Intradroplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.

The role of cellular contact and TGF-beta signaling in the activation of the epithelial mesenchymal transition (EMT).

The epithelial mesenchymal transition (EMT) is one step in the process through which carcinoma cells metastasize by gaining the cellular mobility associated with mesenchymal cells. This work examines the dual influence of the TGF-ß pathway and intercellular contact on the activation of EMT in colon (SW480) and breast (MCF7) carcinoma cells. While the SW480 population revealed an intermediate state between the epithelial and mesenchymal states, the MC7 cells exhibited highly adhesive behavior. However, for both cell lines, an exogenous TGF-ß signal and a reduction in cellular confluence can push a subgroup of the population towards the mesenchymal phenotype. Together, these results highlight that, while EMT is induced by the synergy of multiple signals, this activation varies across cell types.

A Theoretical Model of the Wnt Signaling Pathway in the Epithelial Mesenchymal Transition.

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, ß-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 ß-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 ß-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 ß-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-3ß complex mediating ß-catenin degradation, the rate at which ß-catenin translocates to the nucleus, and the IC50 concentration of Slug needed to inhibit E-cadherin production.