Session E66: Growth and Shapes

Tissue fracture and healing dynamics govern extreme plastic shape changes in the Trichoplax adhaerens, a simple, early divergent animal

While epithelial tissues provide robust mechanical support, they also exhibit local ‘flows’ during morphogenesis and development. In adults, epithelial tissues undergo repeated stretching (e.g. lungs), and an inability to withstand stretch can cause fractures leading to diseases. Tissue fractures so far have been associated with negative consequences, and we do not yet know if fractures can be beneficial. Here, we have discovered a novel fracture-based mechanism by which epithelial tissues can exhibit fast and extreme plastic shape changes in a simple, early divergent animal - the Trichoplax adhaerens (phylum Placozoa). Fracture dynamics play a critical role in the lifecycle of Placozoans by dictating asexual reproduction by binary fission. Using innovative experimental in-toto imaging and tagging techniques, we quantitatively demonstrate that innate mechanical forces (shear and tension) arising from organismal motility govern tissue fracture dynamics. These physiological fractures can either enlarge or ‘heal’ rapidly – leading to dramatic tissue shape change. These tissues exemplify a novel paradigm in soft-active-living-matter since they ‘fluidize’ by creating transient, local, stochastic ‘soft zones’ that exhibit glassy dynamics and a yield stress behavior in living animals.   

Cell Shape Dependent Motility During the Establishment of Tissue Structure

Mature epithelial tissues have distinct cellular architecture, which is maintained despite externally applied forces, wounding, and cell division or death. Here we investigate how a model tissue develops and maintains cellular structure by quantifying single cell dynamics and cell shape in newly formed MDCK monolayers. Over time cells in the monolayer become increasingly hexagonal and arrest at a final structure resembling a mature epithelium. Throughout this process we observe glassy dynamics controlled by cell shape, as predicted by vertex models. Varying substrate stiffness causes monolayers to form and evolve with different cell density, but a similar relationship between cell shape and dynamics. This suggests the changes in cell density often observed in tissue development may not directly impact cell motility. We find that inhibiting regulators of the actin cytoskeleton cause monolayers to arrest with elongated cell shapes. Interestingly, across a diverse set of conditions we find a relationship between the final cell shapes and velocity correlation length which we explore in vertex models by including cell alignment coupling. Our results demonstrate that multicellular coordination of motility affects the regulation of cell shape and determination of final tissue structure.   

Relationship between cell force, shape, and motion in collective cell migration

In biological tissues, collective cell groups exhibit a transition from a solid-like state, wherein cell positions remain fixed, to a fluid-like state, wherein cells flow freely and rearrange their positions with their neighbors. Recent theoretical models and experiments have demonstrated that this transition can be predicted by average cell shape, with cells having more elongated shapes and greater perimeters more easily sliding past their neighbors. Cell perimeter is hypothesized to be controlled by the cell surface tension which is an interplay of the cell’s cortical actomyosin contractility and cell-cell adhesions. However, the hypothesis is still experimentally unexplored. Here, we investigate the factors affecting cell perimeter, and we quantify the corresponding effects on collective migration. For this, we perturb actin and myosin-II in epithelial (MDCK) cell monolayers and study the effects on force, shape, and motion. We employ traction force microscopy, fluorescent imaging, and quantitative image analysis to measure forces, cell perimeters, and migration respectively. By combining these experimental measurements, our study provides experimental testing of the theoretical models and establishes new principles relating cell force, shape, and motion.   

Embryonic Inversion in Volvox carteri: The Flipping and Peeling of Elastic Lips

The embryos of the green alga Volvox are spherical sheets of cells that turn themselves inside out at the close of their development through a program of cell shape changes. This process of inversion is a simple model for the mathematical analysis of morphogenesis [1], yet shares many features with processes such as gastrulation in higher organisms. In Volvox carteri, inversion starts with four lips opening up at the anterior pole of the cell sheet, flipping over and peeling back to invert the embryo. Experimental studies have revealed that inversion in V. carteri is arrested if some cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. We analyse the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion [2].
[1] S Höhn, AR Honerkamp-Smith, PA Haas, P Khuc Trong, and RE Goldstein, Phys. Rev. Lett. 114, 178101 (2015); PA Haas, SSMH Höhn, AR Honerkamp-Smith, JB Kirkegaard, and RE Goldstein, PLOS Biol. 16, e2005536 (2018).
[2] PA Haas and RE Goldstein, Phys. Rev. E (2018, in press), arXiv:1808.00828.   

Morphogenesis of termite mounds

Several species of termites across Africa, Asia, Australia, and South America collectively construct meter-sized porous mound structures that regulate mound temperature, humidity, and gas concentrations. These mounds display varied yet distinctive morphologies that range widely in size and shape. To explain this morphological diversity, we introduce a mathematical model that couples environmental physics to insect behavior: the advection and diffusion of heat and pheromones through a porous medium are modified by the mound geometry and in turn modify that geometry through a minimal characterization of termite behavior. Our model captures the range of naturally observed mound shapes in terms of a minimal parameter set and suggests several simple scaling laws for mound morphology and construction time. An elaboration of our model that incorporates 3D internal nest structure gives rise to regularly spaced floors and pillars, as well as the spontaneous generation of helical ramps, as have been observed in scanned mounds across termite species. This framework makes testable hypotheses for the response of mound morphology to external temperature oscillations and internal odors.   

Pattern Selection in Brine Shrimp Swarms

Swarming is a ubiquitous self-organization phenomenon which occurs in many biological systems such as flocks of bird and insect, schools of fish, and collections of bacteria. This sort of behavior emerges spontaneously, arising without any sort of centralized control or leadership. Many crustaceans such as brine shrimp produce swarms, in which individuals cluster together rather than spreading out uniformly in their environment. The size and distribution of these swarms are governed by local interactions between individuals. We will discuss the three-dimensional patterns that can be observed in brine shrimp swarms, specifically of the Great Salt Lake strain of Artemia franciscana, at high concentration. These patterns can be easily observed with simple tabletop experiments; however, the causes of these patterns are unknown. We experimentally test the effects of certain environmental conditions on the development of these swarms. We then develop a model an agent based model of shrimp which yields the same sort of spatial patterns as those that are observed. The model reproduces the basic length and times scales of the patterns, the type patterns selected, and the stability of those patterns.   

Social insect aggregations as inspiration for mesoscopic active matter

Social insects such as ants and bees exhibit extraordinary co-operative behavior to form aggregations and are often called super-organisms due to their ability to achieve complex structures and functionalities. Individual interactions include attachment and detachment of legs, bodies and mandibles that result in active re-organization of the network that can drastically transform the aggregation from a solid-like to fluid-like material and vice-versa. As the interactions in these aggregations operate in the mesoscale, they are easily observable and are attractive candidates to emulate in synthetic systems. Drawing inspiration from insects, we have designed a synthetic mesoscopic aggregation in our lab made of particles resembling mini gears and interact through magnetic and shear forces to self-organize into a network. The aggregation is infused with leader particles containing battery powered motors that induce motion and activity in the entire network. The aggregation behavior can be tuned by varying the magnetic strength, motor activity of leaders and their positions and diversity in particle size. Using statistical mechanics, we show that the aggregation can be programmed to achieve specific shapes and even transport solid metal objects through them.   

Surface-mediated cell alignment using polymerized liquid crystal nanostructures

The microenvironment of cells affects their morphology and alignment. The physical characteristics of a cell are of extreme importance as the function and viability of a cell is closely linked to its morphology. In this work, we demonstrate the control of the orientation of cultured human dermal fibroblasts (hDFs) using polymerized liquid crystal (LC) periodic nano- and microstructures. The desired pattern is created by controlling the boundary conditions of the LC molecules which exhibit a smectic-A phase. Doping the LC with a small amount of reactive monomers allowed us to fix the molecular orientation and preserve the nano- and microstructures after photopolymerization and subsequent washing. The plated hDFs respond to the polymerized LC topography by changing their shape and aligning their long axis parallel to the patterned grooves. Though fibronectin treatment promotes proliferation of the cells, when comparing the hDFs grown on fibronectin and fibronectin-free patterned surfaces, the cells on fibronectin-free surface show improved alignment and elongation. The demonstrated LC-based surfaces will potentially find practical applications to preprogram cells to form specific kinds of tissues.   

Fluid to solid transition in muscles

Roboticists have long sought to develop actuators that emulate the performance of muscle. These have mostly centered on the power and force capacity of muscle and more recently on muscle's stiffness and damping characteristics. However, a critical aspect that remains missing in muscle-inspired actuators, and also poorly studied in muscle, is an activation-dependent fluid-to-solid transition in muscle's mechanical response. For example, a highly activated muscle resembles a solid-like material that maintains posture and provides stiff resistance, whereas muscle under low activation yields like a fluid without much resistance against rapid motions. Understanding how this transition may arise in muscle could guide the development of new muscle-like actuators that use similar principles as muscle to achieve a fluid-to-solid transition. Current understanding of the sarcomere is based on mean-field models of Huxley-based crossbridge cycles. We find that models of varying complexity, from two- to five-state models of actomyosin, all fail to capture the fluid-to-solid transition. In analogy with jamming transitions in disordered solids, we postulate potential nonequilibrium dynamics that may underlie the fluid-to-solid transition in muscle.   

A web-based application of the Cellular Force-Inference Toolkit (CellFIT)

Given an image of an epithelial cell sheet, CellFIT can infer cellular forces by segmenting the image into individual cells, constructing equilibrium equations for the points where cells meet at triple junctions, and finding a least-squares solution for the tensions at cell-cell interfaces. Similarly, cellular pressures can be estimated by constructing Laplace equations that relate the edge tensions, curvatures and cellular pressure differences. Despite these capabilities, the accessibility of CellFIT to scientists of all backgrounds is not yet optimized. We will present an updated web-based application of CellFIT that allows users to access the software from a browser. The updated version includes improved error handling and the implementation of additional functionality for reading and processing image stacks. Application of the web-based CellFIT to time-resolved image stacks of wound healing in Drosophila epithelia demonstrates spatial and temporal variations in cellular forces as the wounds close.   

Mechanical and Biochemical Simulations of Atherosclerosis

Atherosclerosis is a disease considered to be one of the leading causes of death. Understanding the behavior and dynamics of the vessel wall before and after atherosclerosis has been a motivation for many studies.
We investigate this phenomenon as a combination of mechanical deformation of the vessel wall along with the cell and chemical dynamics that happen inside of it.
We consider the vessel wall as a growing hyperelastic material with three layers, each having a different set of mechanical properties. To describe tissue growth we use morphoelasticity as the mathematical framework. To include the stiffening effect of collagen fibers we employ a Holzapfel-Gasser-Ogden anisotropic strain energy function.
In addition, we explore the distribution of oxidized lipids, macrophages, foam cells, oxygen and necrotic cells in the intima at each growth step via a system of PDEs.
All numerical simulations are carried out via the finite element method on the FENICS framework.
Altogether, this allows us to observe intimal thickening as a result of vessel growth along with histological changes within the wall such as the development of necrotic zones. Our simulations show results similar to the images acquired from ultrasounds scans.
  

Pattern formation and ecological feedback in antigen-immunity co-evolution

Immune systems manifest self-tolerance and respond to foreign invaders. Despite our knowledge of the molecular mechanisms involved in immune response and tolerance, an intuitive understanding of the immune-antigen relationship that determines the overall efficacy of immune control is lacking. We suggest that both features of natural immunity can be described by immune-antigen co-evolution. Extending ecological insights, we consider predator-prey interactions between immune cells and foreign or self antigen that can reach a dynamic balance through mutual adaptation. We present a minimal model of the co-evolutionary dynamics as a pair of reaction-diffusion processes in a phenotypic shape space, coupled by reciprocal interactions with finite cross-reactivity. We find that asymmetry in cross-reactivity can lead to pattern formation, indicating the emergence of antigen niches. We show in a phase diagram the regimes of balance breaking caused by pattern-forming instability: antigen extinction occurs as a result of co-localized population densities, whereas antigen escape follows the formation of alternating patterns under immune homeostasis. Thus, it is important to consider the feedback between population dynamics and pattern formation in understanding immune function and abnormality.