Session J40: Multi-cellular Processes and Development

A Quantitative Analysis of Axonal Growth and Connectivity in Cortical Neurons

Developing neurons extend processes (axons and dendrites), which are led by a distally positioned growth cone. The growth cone both secretes and senses signaling molecules, that may either attract or repel nearby growing processes. While knowledge on the qualitative effects of several secreted growth factors on axon development (e.g. axon length and number of neurons developing processes) are known, a more detailed mathematical model describing the process of axonal guidance remains to be developed. Towards this end, we have collected time-lapse microscopy data of the axonal development of cortical neurons. Image analysis provides information on the rate of growth, arc length, and curvature of the processes as a function of time and the spatial positioning of the neurons. These results will be discussed in relation to theoretical studies that model axon growth in response to varying gradients of attractive forces, representative of the effect that signaling molecules may have on axon guidance.   

Collective cell migration in a periodic potential

The strength of cell-substrate adhesion can be modulated by the elasticity of substrate material. Thus, a cell culture surface with periodically varying elasticity is analogous to a periodic potential for cell adhesion. Rich collective dynamics emerge in systems of adatoms on crystal lattice surfaces due to the mismatch between the preferred spacing of adatoms and the periodic potential associated with the crystal lattice. Here we explore a biological analog of atoms in a periodic potential; we study the collective dynamics of cells on a substrate with periodically patterned elasticity. Preliminary results will be presented.   

Collective Cell Migration on Deformable Substrates

In many biological processes, such as wound healing, tumor migration, or embryo development, cell migration is influenced by collective dynamics and coupling between cells. While cell-cell contact is one form of mechanical coupling, long-range interactions mediated by a deformable substrate lead to both spatial and temporal correlations during cell migration that extend over many cell lengths. While it is known that interactions between nearby but not contacted single cells are modified by substrate stiffness, it is not yet clear how changes to the substrate properties affect collective cell migration. This is especially important in the understanding of cancer cell migration since the mechanical properties of these cells change during disease progression; as such we expect that the influence of the substrate to change over time. To investigate this further, we study collective cell migration on deformable substrates of different stiffness to test whether changes in short range interactions between cells are correlated with changes in collective cell migration. Furthermore, we mix cells from different cancer stages and study their migration patterns to test whether correlations exist between different cell types during migration.   

Impact of jamming on collective cell migration

Multi-cellular migration plays an important role in physiological processes such as embryogenesis, cancer metastasis and tissue repair. During migration, single cells undergo cycles of extension, adhesion and retraction resulting in morphological changes. In a confluent monolayer, there are inter-cellular interactions and crowding, however, the impact of these interactions on the dynamics and elasticity of the monolayer at the multi-cellular and single cell level is not well understood. Here we study the dynamics of a confluent epithelial monolayer by simultaneously measuring cell motion at the multi-cellular and single cell level for various cell densities and tensile elasticity. At the multi-cellular level, the system exhibited spatial kinetic transitions from isotropic to anisotropic migration on long times and the velocity of the monolayer decreased with increasing cell density. Moreover, the dynamics was spatially and temporally heterogeneous. Interestingly, the dynamics was also heterogeneous in wound-healing assays and the correlation length was fitted by compressed exponential. On the single cell scale, we observed transient caging effects with increasing cage rearrangement times as the system age due to an increase in density. Also, the density dependent elastic modulus of the monolayer scaled as a weak power law. Together, these findings suggest that caging effects at the single cell level initiates a slow and heterogeneous dynamics at the multi-cellular level which is similar to the glassy dynamics of deformable colloidal systems.   

Self-rheology of cell monolayers

Collective migration of cell sheets is a central feature of fundamental biological processes including morphogenesis, tissue regeneration, and cancer invasion. The dynamics of such processes are heavily determined by the rheology of the sheet and of the constituent cells. Such material properties have been extensively measured using a broad variety of rheological techniques, but none of these techniques has probed the ultraslow time scales that are central to collective cell migration, and exceed thousands of seconds. Here we present a novel approach we call `Self rheology' that probes cell rheology using the pulses of strain rate that cells spontaneously generate. Using this approach, we show that stress and strain rate are in quadrature, thus indicating that the dominant stresses that govern collective cell migration are elastic. The monolayer's Young modulus is found to be an order of magnitude lower than the stiffness of single cells determined through active micro-rheology techniques at shorter time scales. This elastic behavior is followed by a fluidization regime at higher strains, which we interpret in terms of cell rearrangements. ``Self-rheology'' provides a new approach to study the dynamics of collective cellular processes at ultraslow time scales.   

Collective mechanics of undifferentiated cells drives ventral furrow formation in {\sl Drosophila} embryo

We propose a 2D mechanical model of ventral furrow formation in {\sl Drosophila} embryo that is based on undifferentiated epithelial cells of identical mechanical properties whose energy resides at their cortex. Depending on the relative tensions of the apical, basal, and lateral sides, the minimal-energy states of the embryo cross-section include circular and buckled furrow shapes. We discuss the possible shape transformation from a circular to an invaginated shape consistent with experimental observations, arguing that generic collective mechanics may contribute to the robustness of tissue shape changes in embryonic development. A small increase of the area of the mesoderm cells is sufficient to pin down the invagination. This agrees with experimental data which show that just before the outset of gastrulation, the apical, basal, and lateral sides of the mesoderm cells indeed are larger than in the rest of the embryo.   

Collective Cell Mechanics in 3D Scaffolds

Mechanical cell behavior is influential in tissue health and dynamic cellular processes such as wound healing, and angiogenesis. Traction force microscopy (TFM) is often used to measure cell generated forces while mechanical testing methods such as atomic force microscopy (AFM) are employed to determine materials properties of cells. Extant cell mechanics methods including TFM and AFM are optimal for cells cultured on flat, 2D surfaces. However, the development of new cell mechanics techniques in 3D systems is essential to elucidate the behavior of tissues. In this presentation we introduce results from live-cell time-lapse measurements of mechanical cell behavior in highly ordered 3-D scaffolds. Preliminary data will be presented.   

Biomechanics of the endothelium substrate influences leukocyte transmigration

The effects of shear flow and cytokines on leukocyte transmigration are well understood. However, the effects of substrate stiffness on transmigration remain unexplored. We have developed an in vitro model that allows us to study leukocyte transmigration as a function of varying physiological substrate stiffness. Interestingly, leukocyte transmigration increased with increasing substrate stiffness below the endothelium. intercellular adhesion molecule-1 expression, stiffness, cytoskeletal arrangement, morphology, and cell-substrate adhesion could not account for the dependence of transmigration on substrate stiffness. We also explored the role of cell contraction and observed that (1) neutrophil transmigration caused large hole formation in monolayers on stiff substrates. (2) Neutrophil transmigration on soft substrates was increased by decreasing cell-cell adhesion. (3) Inhibition of myosin light chain kinase normalized the effects of substrate stiffness by reducing cell contraction on stiff substrates. These results demonstrate that neutrophil transmigration is regulated by MLCK-mediated generation of gaps at cell borders through substrate stiffness-dependent endothelial cell contraction.   

Growth variability in a tissue governed by stress dependent growth

Cell wall mechanics lie at the heart of plant cell growth and tissue morphogenesis. Conversely, mechanical forces generated at tissue level can feedback on cellular dynamics. Differential growth of neighboring cells is one eminent origin of mechanical forces and stresses in tissues where cells adhere to each other. How can stresses arising from differential growth orchestrate large scale tissue growth? We show that cell growth coupled to the cell's main stress can reduce or increase tissue growth variability. Employing a cell-based two dimensional tissue model we investigate the dynamics of a tissue with stress depending growth dynamics. We find that the exact cell division rule strongly affects not only the tissue geometry and topology but also its growth dynamics. Our results should enable to infer underlying growth dynamics from live tissue statistics.   

Emergent mechanical behavior in a minimal model for embryonic tissues

We develop a minimal model for the mechanical properties of embryonic tissues that contains only three parameters and yet accurately reproduces many structural and dynamical features in zebrafish embryonic tissue explants. We verify model predictions for tissue surface tensiometer experiments and fusion assays, and contrast our model with existing models that are either difficult to constrain experimentally or insufficient to explain our experimental observations. The model tracks one degree of freedom per cell and introduces several types of interactions between cells to capture intracellular degrees of freedom, such as single cell viscoelasticity, adhesion, and active force generation. A key observation is that the motion of cells past one another, which must be generated by cells actively exerting tension on contacts, is best described by a special type of structured noise (both multiplicative and colored), instead of the white noise typically used in Brownian dynamics simulations. With such a noise term we can reproduce the glassy, viscoelastic dynamics in the bulk and explain how this new type of active ``droplet'' with very short-range interactions manages to have no ``vapor pressure.'' We discuss how this well-calibrated model can be used to study morphogenesis and pattern formation in developing tissues.   

Spatially limited growth of an epithelium

We present a study dealing with the growth of an epithelium on a spatially limited adhesive substrate. Adhesive patterns (typical size: 50$\mu$m to 500$\mu$m) are created by micro-fabrication techniques: A protein repellent polymeric gel homogeneously grafted on a coverslip is selectively ablated by plasma treatment through a thin layer of photoresist. The technique achieves a high resolution of patterning (around 2$\mu$m). After seeding cells (MDCK) on circular adhesive patterns, we let the monolayer grow for 30 hours after reaching the confluence. We use physical descriptors to describe migration and compaction. Two days after the confluence, we observe and characterize by confocal microscopy, the appearance of a tridimensionnal assembly of cells in the peripherical zone of the adhesive pattern (a ``rim''). Moreover using other patterns, the existence of a tissue line tension and internal pressure is investigated.   

Information propagation and nutrient flow in \textit{Physarum polycephalum}

Basal organisms such as slime mold and fungi grow as extended networks that can reach several square meters in size. Despite lacking a central coordination center, these organisms are able to globally reshape their morphology in response to local cues, such as the presence of a patch of nutrient. How are local signals integrated in these organisms, and how do they lead to an overall response? To answer this question, we focus on the flow of nutrients in the slime mold \textit{Physarum polycephalum}. This slime mold exhibits internal flow oscillations, as well as periodic contractions of its veins. Using plastic masks, we constrain network growth to simple geometries. This allows for an experimental characterization of the relationship between the contractions and the flow. We next describe the change in the overall oscillation pattern when a food source is presented locally to the slime mold, and its implication on the internal flow. Internal flows are both inferred from the contraction pattern and experimentally measured using fluorescent markers.   

Scaling of Traction Stresses with Size of Cohesive Cell Colonies

We explore the mechanical properties of colonies of cohesive cells adherent on soft substrates. Specifically, we image the spatial distribution of traction stresses exerted by colonies of primary mouse keratinocytes on fibronectin-coated silicone gels. These cells have strong cell-cell adhesions mediated by E-cadherin. We observe that the work performed by a colony on its substrate is concentrated at the colony's periphery. The total work is strongly correlated to the geometrical size of the colony but not to number of cells. In other words, the mechanical output of a large single cell mimics that of a cohesive colony with the same overall size. We compare our findings to a recent theoretical model that treats the cohesive colony as an active gel.   

Elasticity of adherent active cells on a compliant substrate

We present a continuum mechanical model of rigidity sensing by livings cells adhering to a compliant substrate. The cell or cell colony is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoelastic fluids. The coupling to the substrate enters as a boundary condition that relates the cell's deformation field to local stress gradients. In the presence of activity, the substrate induces spatially inhomogeneous contractile stresses and deformations, with a power law dependence of the total traction forces on cell or colony size. This is in agreement with recent experiments on keratinocyte colonies adhered to fibronectin coated surfaces. In the presence of acto-myosin activity, the substrate also enhances the cell polarization, breaking the cell's front-rear symmetry. Maximal polarization is observed when the substrate stiffness matches that of the cell, in agreement with experiments on stem cells.   

Wave transmission through cell-cell coupling

We previously found that waves of high boundary curvature travel from the front to the back of individual D. discoideum cells. We investigated the behavior of curvature waves in small groups of adherent cells, in particular, we investigated the transmission of the waves through cell-cell coupling. We analyzed the motion of individual cells in short streams of varying length, which are cells that follow one other. Furthermore, we developed a technique that uses holographic optical tweezers to grip cells indirectly and push them into one another, thereby forming artificial cell-cell contacts. Using that technique, we observed the affect of waves in coupled cells. We also compared the shape dynamics of groups of cells to the shape dynamics of cells within those groups. We extended these methods to suspended cells, which exhibit different wave dynamics.