Modelling the effect of cell motility on mixing and invasion in epithelial monolayers.

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Transition from growth to decay of an epidemic due to lockdown.

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown health measures are introduced to reduce the probability of disease transmission. Although in the case of uniform lockdown, a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using the Gillespie stochastic simulation algorithm based on a connected set of stochastic susceptible-infected-removed/recovered networks representing the locked-down majority population (in which the reproduction number is less than 1) weakly coupled to a large set of small clusters in which the infection may propagate. We find that the presence of such active clusters can lead to slower than expected decay of the epidemic and significantly delayed onset of the decay phase. We study the relative contributions of these changes, caused by the active clusters within the population, to the additional total infected population. We also demonstrate that limiting the size of the inevitable active clusters can be efficient in reducing their impact on the overall size of the epidemic outbreak. The deceleration of the decay phase becomes apparent when the active clusters form at least 5% of the population.

Bimodal behaviour of interfollicular epidermal progenitors regulated by hair follicle position and cycling.

Interfollicular epidermal (IFE) homeostasis is a major physiological process allowing maintenance of the skin barrier function. Despite progress in our understanding of stem cell populations in different hair follicle compartments, cellular mechanisms of IFE maintenance, in particular, whether a hierarchy of progenitors exists within this compartment, have remained controversial. We here used multicolour lineage tracing with Brainbow transgenic labels activated in the epidermis to track individual keratinocyte clones. Two modes of clonal progression could be observed in the adult murine dorsal skin. Clones attached to hair follicles showed rapid increase in size during the growth phase of the hair cycle. On the other hand, clones distant from hair follicles were slow cycling, but could be mobilized by a proliferative stimulus. Reinforced by mathematical modelling, these data support a model where progenitor cycling characteristics are differentially regulated in areas surrounding or away from growing hair follicles. Thus, while IFE progenitors follow a non-hierarchical mode of development, spatiotemporal control by their environment can change their potentialities, with far-reaching implications for epidermal homeostasis, wound repair and cancer development.

Functional Definition of Progenitors Versus Mature Endothelial Cells Reveals Key SoxF-Dependent Differentiation Process.

BACKGROUND: During adult life, blood vessel formation is thought to occur via angiogenic processes involving branching from existing vessels. An alternate proposal suggests that neovessels form from endothelial progenitors able to assemble the intimal layers. We here aimed to define vessel-resident endothelial progenitors in vivo in a variety of tissues in physiological and pathological situations such as normal aorta, lungs, and wound healing, tumors, and placenta, as well. METHODS: Based on protein expression levels of common endothelial markers using flow cytometry, 3 subpopulations of endothelial cells could be identified among VE-Cadherin+ and CD45- cells. RESULTS: Lineage tracing by using Cdh5creERt2/Rosa-YFP reporter strategy demonstrated that the CD31-/loVEGFR2lo/intracellular endothelial population was indeed an endovascular progenitor (EVP) of an intermediate CD31intVEGFR2lo/intracellular transit amplifying (TA) and a definitive differentiated (D) CD31hiVEGFR2hi/extracellular population. EVP cells arose from vascular-resident beds that could not be transferred by bone marrow transplantation. Furthermore, EVP displayed progenitor-like status with a high proportion of cells in a quiescent cell cycle phase as assessed in wounds, tumors, and aorta. Only EVP cells and not TA and D cells had self-renewal capacity as demonstrated by colony-forming capacity in limiting dilution and by transplantation in Matrigel plugs in recipient mice. RNA sequencing revealed prominent gene expression differences between EVP and D cells. In particular, EVP cells highly expressed genes related to progenitor function including Sox9, Il33, Egfr, and Pdfgrα. Conversely, D cells highly expressed genes related to differentiated endothelium including Ets1&2, Gata2, Cd31, Vwf, and Notch. The RNA sequencing also pointed to an essential role of the Sox18 transcription factor. The role of SOX18 in the differentiation process was validated by using lineage-tracing experiments based on Sox18CreERt2/Rosa-YFP mice. Besides, in the absence of functional SOX18/SOXF, EVP progenitors were still present, but TA and D populations were significantly reduced. CONCLUSIONS: Our findings support an entirely novel endothelial hierarchy, from EVP to TA to D, as defined by self-renewal, differentiation, and molecular profiling of an endothelial progenitor. This paradigm shift in our understanding of vascular-resident endothelial progenitors in tissue regeneration opens new avenues for better understanding of cardiovascular biology.

The role of Allee effect in modelling post resection recurrence of glioblastoma.

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence.

Bistable front dynamics in a contractile medium: Travelling wave fronts and cortical advection define stable zones of RhoA signaling at epithelial adherens junctions.

Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.

Concise review: understanding clonal dynamics in homeostasis and injury through multicolor lineage tracing.

Lineage tracing is an essential tool to study stem cell fate. Although traditional lineage tracing techniques have considerably advanced our understanding of stem cell behavior, they pose significant limitations for identification and longitudinal tracking of the progeny of individual stem cells, to compare their behaviors. This is of importance given the well-established heterogeneity among stem cells both in terms of potentialities and proliferative capacities. The recent development of multicolor genetic reporters addressable to specific cell populations largely overcomes these issues. These new "rainbow" technologies provide increased resolution in clonal identification and offer the possibility to study the relative distribution, contacts, tiled arrangement, and competitive interactions among cells or groups of cells of the same type.

Self-organizing actomyosin patterns on the cell cortex at epithelial cell-cell junctions.

The behavior of actomyosin critically determines morphologically distinct patterns of contractility found at the interface between adherent cells. One such pattern is found at the apical region (zonula adherens) of cell-cell junctions in epithelia, where clusters of the adhesion molecule E-cadherin concentrate in a static pattern. Meanwhile, E-cadherin clusters throughout lateral cell-cell contacts display dynamic movements in the plane of the junctions. To gain insight into the principles that determine the nature and organization of these dynamic structures, we analyze this behavior by modeling the 2D actomyosin cell cortex as an active fluid medium. The numerical simulations show that the stability of the actin filaments influences the spatial structure and dynamics of the system. We find that in addition to static Turing-type patterns, persistent dynamic behavior occurs in a wide range of parameters. In the 2D model, mechanical stress-dependent actin breakdown is shown to produce a continuously changing network of actin bridges, whereas with a constant breakdown rate, more isolated clusters of actomyosin tend to form. The model qualitatively reproduces the dynamic and stable patterns experimentally observed at the junctions between epithelial cells.

Tactile interactions lead to coherent motion and enhanced chemotaxis of migrating cells.

When motile cells come into contact with one another their motion is often considerably altered. In a process termed contact inhibition of locomotion (CIL) cells reshape and redirect their movement as a result of cell-cell contact. Here we describe a mathematical model that demonstrates that CIL alone is sufficient to produce coherent, collective cell migration. Our model illustrates a possible mechanism behind collective cell migration that is observed, for example, in neural crest cells during development, and in metastasizing cancer cells. We analyse the effects of varying cell density and shape on the alignment patterns produced and the transition to coherent motion. Finally, we demonstrate that this process may have important functional consequences by enhancing the accuracy and robustness of the chemotactic response, and factors such as cell shape and cell density are more significant determinants of migration accuracy than the individual capacity to detect environmental gradients.

Modelling of Tissue Invasion in Epithelial Monolayers.

Mathematical and computational models are used to describe biomechanical processes in multicellular systems. Here, we develop a model to analyse how two types of epithelial cell layers interact during tissue invasion depending on their cellular properties, i.e., simulating cancer cells expanding into a region of normal cells. We model the tissue invasion process using the cellular Potts model and implement our two-dimensional computational simulations in the software package CompuCell3D. The model predicts that differences in mechanical properties of cells can lead to tissue invasion, even if the division rates and death rates of the two cell types are the same. We also show how the invasion speed varies depending on the cell division and death rates and the mechanical properties of the cells.

Context-dependent interaction leads to emergent search behavior in social aggregates.

Locating the source of an advected chemical signal is a common challenge facing many living organisms. When the advecting medium is characterized by either high Reynolds number or high Peclet number, the task becomes highly nontrivial due to the generation of heterogeneous, dynamically changing filamental concentrations that do not decrease monotonically with distance to the source. Defining search strategies that are effective in these environments has important implications for the understanding of animal behavior and for the design of biologically inspired technology. Here we present a strategy that is able to solve this task without the higher intelligence required to assess spatial gradient direction, measure the diffusive properties of the flow field, or perform complex calculations. Instead, our method is based on the collective behavior of autonomous individuals following simple social interaction rules which are modified according to the local conditions they are experiencing. Through these context-dependent interactions, the group is able to locate the source of a chemical signal and in doing so displays an awareness of the environment not present at the individual level. This behavior illustrates an alternative pathway to the evolution of higher cognitive capacity via the emergent, group-level intelligence that can result from local interactions.

Stirring effects in models of oceanic plankton populations.

We present an overview and extend previous results on the effects of large scale oceanic transport processes on plankton population dynamics, considering different types of ecosystem models. We find that increasing stirring rate in an environment where the carrying capacity is non-uniformly distributed leads to an overall decrease of the effective carrying capacity of the system. This may lead to sharp regime shifts induced by stirring in systems with multiple steady states. In prey-predator type systems, stirring leads to resonant response of the population dynamics to fluctuations enhancing the spatial variability-patchiness-in a certain range of stirring rates. Oscillatory population models produce strongly heterogeneous patchy distribution of plankton blooms when the stirring is weak, while strong stirring may either synchronise the oscillatory dynamics, when the inhomogeneity is relatively weak, or suppress oscillations completely (oscillator death) by reducing the effective carrying capacity below the bifurcation point.

Modelling the Collective Mechanical Regulation of the Structure and Morphology of Epithelial Cell Layers.

The morphology and function of epithelial sheets play an important role in healthy tissue development and cancer progression. The maintenance of structure of closely packed epithelial layers requires the coordination of various mechanical forces due to intracellular activities and interactions with other cells and tissues. However, a general model for the combination of mechanical properties which determine the cell shape and the overall structure of epithelial layers remains elusive. Here, we propose a computational model, based on the Cellular Potts Model, to analyse the interplay between mechanical properties of cells and dynamical transitions in epithelial cell shapes and structures. We map out phase diagrams as functions of cellular properties and the orientation of cell division. Results show that monolayers of squamous, cuboidal, and columnar cells are formed when the axis of cell proliferation is perpendicular to the substrate or along the major axis of the cells. Monolayer-to-multilayer transition is promoted via cell extrusion, depending on the mechanical properties of cells and the orientation of cell division. The results and model predictions are discussed in the context of experimental observations.

Integrating multiple signals into cell decisions by networks of protein modification cycles.

Posttranslational protein modifications play a key role in regulating cellular processes. We present a general model of reversible protein modification networks and demonstrate that a single protein modified by several enzymes is capable of integrating multiple signals into robust digital decisions by switching between multiple forms that can activate distinct cellular processes. First we consider two competing protein modification cycles and show that in the saturated regime, the protein is concentrated into a single form determined by the enzyme activities. We generalize this to protein modification networks with tree structure controlled by multiple enzymes that can be characterized by their phase diagram, which is a partition of the space of enzyme activities into regions corresponding to different dominant forms. We show that the phase diagram can be obtained analytically from the wiring diagram of the modification network by recursively solving a set of balance equations for the steady-state distributions and then applying a positivity condition to determine the regions corresponding to different responses. We also implement this method in a computer algebra system that automatically generates the phase diagram as a set of inequalities. Based on this theoretical framework, we determine some general properties of protein modification systems.

Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data.

A better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ([Formula: see text]) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

Contact inhibition of locomotion generates collective cell migration without chemoattractants in an open domain.

Neural crest cells are embryonic stem cells that migrate throughout embryos and, at different target locations, give rise to the formation of a variety of tissues and organs. The directional migration of the neural crest cells is experimentally described using a process referred to as contact inhibition of locomotion, by which cells redirect their movement upon the cell-cell contacts. However, it is unclear how the migration alignment is affected by the motility properties of the cells. Here, we theoretically model the migration alignment as a function of the motility dynamics and interaction of the cells in an open domain with a channel geometry. The results indicate that by increasing the influx rate of the cells into the domain a transition takes place from random movement to an organized collective migration, where the migration alignment is maximized and the migration time is minimized. This phase transition demonstrates that the cells can migrate efficiently over long distances without any external chemoattractant information about the direction of migration just based on local interactions with each other. The analysis of the dependence of this transition on the characteristic properties of cellular motility shows that the cell density determines the coordination of collective migration whether the migration domain is open or closed. In the open domain, this density is determined by a feedback mechanism between the flux and order parameter, which characterises the alignment of collective migration. The model also demonstrates that the coattraction mechanism proposed earlier is not necessary for collective migration and a constant flux of cells moving into the channel is sufficient to produce directed movement over arbitrary long distances.

Assessment of heterogeneity in collective endothelial cell behavior with multicolor clonal cell tracking to predict arteriovenous remodeling.

Arteries and veins form in a stepwise process that combines vasculogenesis and sprouting angiogenesis. Despite extensive data on the mechanisms governing blood vessel assembly at the single-cell level, little is known about how collective cell migration contributes to the organization of the balanced distribution between arteries and veins. Here, we use an endothelial-specific zebrafish reporter, arteriobow, to label small cohorts of arterial cells and trace their progeny from early vasculogenesis throughout arteriovenous remodeling. We reveal that the genesis of arteries and veins relies on the coordination of 10 types of collective cell dynamics. Within these behavioral categories, we identify a heterogeneity of collective cell motion specific to either arterial or venous remodeling. Using pharmacological blockade, we further show that cell-intrinsic Notch signaling and cell-extrinsic blood flow act as regulators in maintaining the heterogeneity of collective endothelial cell behavior, which, in turn, instructs the future territory of arteriovenous remodeling.

Formation of intracellular concentration landscapes by multisite protein modification.

Multiple cellular proteins are covalently modified (e.g., phosphorylated/dephosphorylated) at several sites, which leads to diverse signaling activities. Here, we consider a signaling cascade that is activated at the plasma membrane and composed of two-site protein modification cycles, and we focus on the radial profile of the concentration landscapes created by different protein forms in the cytoplasm. We show that under proper conditions, the concentrations of modified proteins generate a series of peaks that propagate into the cell interior. Proteins modified at both sites form activity gradients with long plateaus that abruptly decay at successive locations along the path from the membrane to the nucleus. We demonstrate under what conditions signals generated at the membrane stall in the vicinity of that membrane or propagate into the cell. We derive analytical approximations for the main characteristics of the protein concentration profiles and demonstrate what we believe to be a novel steady-state pattern formation mechanism capable of generating precise spatial guidance for diverse cellular processes.

Positional information generated by spatially distributed signaling cascades.

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus.

Processivity of molecular motors under vectorial loads.

Molecular motors are cellular machines that drive the spatial organization of the cells by transporting cargos along intracellular filaments. Although the mechanical properties of single molecular motors are relatively well characterized, it remains elusive how the geometry of a load imposed on a motor affects its processivity, i.e., the average distance that a motor moves per interaction with a filament. Here, we theoretically explore this question for a single-kinesin molecular motor by analyzing the load dependence of the stepping and detachment processes. We find that the processivity of the kinesin increases with lowering the load angle between the kinesin and the microtubule filament, due to the deceleration of the detachment rate. When the load angle is large, the processivity is predicted to enhance with accelerating the stepping rate through an optimal distribution of the load over the kinetic transition rates underlying a mechanical step of the motor. These results provide new insights into understanding of the design of potential synthetic biomolecular machines that can travel long distances with high velocities.