Sorting of multiple molecular species on cell membranes.

Eukaryotic cells maintain their inner order by a hectic process of sorting and distillation of molecular factors taking place on their lipid membranes. A similar sorting process is implied in the assembly and budding of enveloped viruses. To understand the properties of this molecular sorting process, we have recently proposed a physical model [Zamparo et al., Phys. Rev. Lett. 126, 088101 (2021)]10.1103/PhysRevLett.126.088101, based on (1) the phase separation of a single, initially dispersed molecular species into spatially localized sorting domains on the lipid membrane and (2) domain-induced membrane bending leading to the nucleation of submicrometric lipid vesicles, naturally enriched in the molecules of the engulfed sorting domain. The analysis of the model showed the existence of an optimal region of parameter space where sorting is most efficient. Here the model is extended to account for the simultaneous distillation of a pool of distinct molecular species. We find that the mean time spent by sorted molecules on the membrane increases with the heterogeneity of the pool (i.e., the number of distinct molecular species sorted) according to a simple scaling law, and that a large number of distinct molecular species can in principle be sorted in parallel on cell membranes without significantly interfering with each other. Moreover, sorting is found to be most efficient when the distinct molecular species have comparable homotypic affinities. We also consider how valence (i.e., the average number of interacting neighbors of a molecule in a sorting domain) affects the sorting process, finding that higher-valence molecules can be sorted with greater efficiency than lower-valence molecules.

Phase separation and critical size in molecular sorting.

Molecular sorting is a fundamental process that allows eukaryotic cells to distill and concentrate specific chemical factors in appropriate cell membrane subregions, thus endowing them with different chemical identities and functional properties. A phenomenological theory of this molecular distillation process has recently been proposed [M. Zamparo, D. Valdembri, G. Serini, I. V. Kolokolov, V. V. Lebedev, L. Dall'Asta, and A. Gamba, Phys. Rev. Lett. 126, 088101 (2021)0031-900710.1103/PhysRevLett.126.088101], based on the idea that molecular sorting emerges from the combination of (a) phase separation driven formation of sorting domains and (b) domain-induced membrane bending, leading to the production of submicrometric lipid vesicles enriched in the sorted molecules. In this framework, a natural parameter controlling the efficiency of molecular distillation is the critical size of phase separated domains. In the experiments, sorting domains appear to fall into two classes: unproductive domains, characterized by short lifetimes and low probability of extraction, and productive domains, that evolve into vesicles that ultimately detach from the membrane system. It is tempting to link these two classes to the different fates predicted by classical phase separation theory for subcritical and supercritical phase separated domains. Here, we discuss the implication of this picture in the framework of the previously introduced phenomenological theory of molecular sorting. Several predictions of the theory are verified by numerical simulations of a lattice-gas model. Sorting is observed to be most efficient when the number of sorting domains is close to a minimum. To help in the analysis of experimental data, an operational definition of the critical size of sorting domains is proposed. Comparison with experimental results shows that the statistical properties of productive and unproductive domains inferred from experimental data are in agreement with those predicted from numerical simulations of the model, compatibly with the hypothesis that molecular sorting is driven by a phase separation process.

Physics of compartmentalization: How phase separation and signaling shape membrane and organelle identity.

Compartmentalization of cellular functions is at the core of the physiology of eukaryotic cells. Recent evidences indicate that a universal organizing process - phase separation - supports the partitioning of biomolecules in distinct phases from a single homogeneous mixture, a landmark event in both the biogenesis and the maintenance of membrane and non-membrane-bound organelles. In the cell, 'passive' (non energy-consuming) mechanisms are flanked by 'active' mechanisms of separation into phases of distinct density and stoichiometry, that allow for increased partitioning flexibility and programmability. A convergence of physical and biological approaches is leading to new insights into the inner functioning of this driver of intracellular order, holding promises for future advances in both biological research and biotechnological applications.

Optimality in Self-Organized Molecular Sorting.

We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations of a lattice-gas realization of the model and with experimental observations. The efficiency of the distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal conditions are realized in living cells.

Rac signal adaptation controls neutrophil mobilization from the bone marrow.

Mobilization of neutrophils from the bone marrow determines neutrophil blood counts and thus is medically important. Balanced neutrophil mobilization from the bone marrow depends on the retention-promoting chemokine CXCL12 and its receptor CXCR4 and the egression-promoting chemokine CXCL2 and its receptor CXCR2. Both pathways activate the small guanosine triphosphatase Rac, leaving the role of this signaling event in neutrophil retention and egression ambiguous. On the assumption that active Rac determines persistent directional cell migration, we generated a mathematical model to link chemokine-mediated Rac modulation to neutrophil egression time. Our computer simulation indicated that, in the bone marrow, where the retention signal predominated, egression time strictly depended on the time it took Rac to return to its basal activity (namely, adaptation). This prediction was validated in mice lacking the Rac inhibitor ArhGAP15. Neutrophils in these mice showed prolonged Rac adaptation and cell-autonomous retention in the bone marrow. Our model thus demonstrates that mobilization in the presence of two spatially defined opposing chemotactic cues strictly depends on inhibitors shaping the time course of signal adaptation. Furthermore, our findings might help to find new modes of intervention to treat conditions characterized by excessively low or high circulating neutrophils.

Three-dimensional chemotaxis-driven aggregation of tumor cells.

One of the most important steps in tumor progression involves the transformation from a differentiated epithelial phenotype to an aggressive, highly motile phenotype, where tumor cells invade neighboring tissues. Invasion can occur either by isolated mesenchymal cells or by aggregates that migrate collectively and do not lose completely the epithelial phenotype. Here, we show that, in a three-dimensional cancer cell culture, collective migration of cells eventually leads to aggregation in large clusters. We present quantitative measurements of cluster velocity, coalescence rates, and proliferation rates. These results cannot be explained in terms of random aggregation. Instead, a model of chemotaxis-driven aggregation - mediated by a diffusible attractant - is able to capture several quantitative aspects of our results. Experimental assays of chemotaxis towards culture conditioned media confirm this hypothesis. Theoretical and numerical results further suggest an important role for chemotactic-driven aggregation in spreading and survival of tumor cells.

Single-cell states in the estrogen response of breast cancer cell lines.

Estrogen responsive breast cancer cell lines have been extensively studied to characterize transcriptional patterns in hormone-responsive tumors. Nevertheless, due to current technological limitations, genome-wide studies have typically been limited to population averaged data. Here we obtain, for the first time, a characterization at the single-cell level of the states and expression signatures of a hormone-starved MCF-7 cell system responding to estrogen. To do so, we employ a recently proposed model that allows for dissecting single-cell states from time-course microarray data. We show that within 32 hours following stimulation, MCF-7 cells traverse, most likely, six states, with a faster early response followed by a progressive deceleration. We also derive the genome-wide transcriptional profiles of such single-cell states and their functional characterization. Our results support a scenario where estrogen promotes cell cycle progression by controlling multiple, sequential regulatory steps, whose single-cell events are here identified.

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures.

The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell-cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell-cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis.

Critical behavior and axis defining symmetry breaking in Hydra embryonic development.

The formation of a hollow cellular sphere is often one of the first steps of multicellular embryonic development. In the case of Hydra, the sphere breaks its initial symmetry to form a foot-head axis. During this process a gene, ks1, is increasingly expressed in localized cell domains whose size distribution becomes scale-free at the axis-locking moment. We show that a physical model based solely on the production and exchange of ks1-promoting factors among neighboring cells robustly reproduces the scaling behavior as well as the experimentally observed spontaneous and temperature-directed symmetry breaking.

Unraveling the influence of endothelial cell density on VEGF-A signaling.

Vascular endothelial growth factor-A (VEGF) is the master determinant for the activation of the angiogenic program leading to the formation of new blood vessels to sustain solid tumor growth and metastasis. VEGF specific binding to VEGF receptor-2 (VEGFR-2) triggers different signaling pathways, including phospholipase C-γ (PLC-γ) and Akt cascades, crucial for endothelial proliferation, permeability, and survival. By combining biologic experiments, theoretical insights, and mathematical modeling, we found that: (1) cell density influences VEGFR-2 protein level, as receptor number is 2-fold higher in long-confluent than in sparse cells; (2) cell density affects VEGFR-2 activation by reducing its affinity for VEGF in long-confluent cells; (3) despite reduced ligand-receptor affinity, high VEGF concentrations provide long-confluent cells with a larger amount of active receptors; (4) PLC-γ and Akt are not directly sensitive to cell density but simply transduce downstream the upstream difference in VEGFR-2 protein level and activation; and (5) the mathematical model correctly predicts the existence of at least one protein tyrosine phosphatase directly targeting PLC-γ and counteracting the receptor-mediated signal. Our data-based mathematical model quantitatively describes VEGF signaling in quiescent and angiogenic endothelium and is suitable to identify new molecular determinants and therapeutic targets.

A bistable model of cell polarity.

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

A simulation environment for directional sensing as a phase separation process.

The ability of eukaryotic cells to navigate along spatial gradients of extracellular guidance cues is crucial for embryonic development, tissue regeneration, and cancer progression. One proposed model for chemotaxis is a phosphoinositide-based phase separation process, which takes place at the plasma membrane upon chemoattractant stimulation and triggers directional motility of eukaryotic cells. Here, we make available virtual-cell software that allows the execution and spatiotemporal analysis of in silico chemotaxis experiments, in which the user can control physical and chemical parameters as well as the number and position of chemoattractant sources.

Diffusion-limited phase separation in eukaryotic chemotaxis.

The ability of cells to sense spatial gradients of chemoattractant factors governs the development of complex eukaryotic organisms. Cells exposed to shallow chemoattractant gradients respond with strong accumulation of the enzyme phosphatidylinositol 3-kinase (PI3K) and its D3-phosphoinositide product (PIP(3)) on the plasma membrane side exposed to the highest chemoattractant concentration, whereas PIP(3)-degrading enzyme PTEN and its product PIP(2) localize in a complementary pattern. Such an early symmetry-breaking event is a mandatory step for directed cell movement elicited by chemoattractants, but its physical origin is still mysterious. Here, we propose that directional sensing is the consequence of a phase-ordering process mediated by phosphoinositide diffusion and driven by the distribution of chemotactic signal. By studying a realistic reaction-diffusion lattice model that describes PI3K and PTEN enzymatic activity, recruitment to the plasma membrane, and diffusion of their phosphoinositide products, we show that the effective enzyme-enzyme interaction induced by catalysis and diffusion introduces an instability of the system toward phase separation for realistic values of physical parameters. In this framework, large reversible amplification of shallow chemotactic gradients, selective localization of chemical factors, macroscopic response timescales, and spontaneous polarization arise naturally. The model is robust with respect to order-of-magnitude variations of the parameters.

Modeling the early stages of vascular network assembly.

In vertebrates, networks of capillary vessels supply tissues with nutrients. Capillary patterns are closely mimicked by endothelial cells cultured on basement membrane proteins that allow single randomly dispersed cells to self-organize into vascular networks. Here we provide a model including chemoattraction as the fundamental mechanism for cell-to-cell communication in order to identify key parameters in the complexity of the formation of vascular patterns. By flanking biological experiments, theoretical insights and numerical simulations, we provide strong evidence that endothelial cell number and the range of activity of a chemoattractant factor regulate vascular network formation and size. We propose a mechanism linking the scale of formed endothelial structures to the range of cell-to-cell interaction mediated by the release of chemoattractants.