Session J17: Focus Session: General Biological Patterns

Relating biophysical properties across scales: implications for early development and applications for tissue engineering

A distinguishing feature of a multicellular system is that it operates at various scales and levels of organization. Genes set up the conditions for physical mechanisms to act, in particular to shape the developing organism and establish its material characteristics. As development continues the changes brought about by the physical processes lead to changes in gene expression. It is through this interplay that the organism acquires its final structure and composition. It is natural to assume that in this multi-scale process the smaller defines the larger. In case of biophysical properties, in particular, those at the subcellular and cellular level are expected to give rise to those at the tissue level and beyond. Indeed, the physical characteristics of tissues vary greatly in physical properties: blood is liquid, bone is solid. In between these extremes lie most of the organs and tissues with intermediate viscoelastic properties. However, a blood cell is not the same as a liquid drop and a single bone-forming cell itself is not a solid. Little is known on how tissue and organ level properties are related to cell and subcellular properties. We introduce a novel combined theoretical-computational-experimental framework to address this question. The basis of our approach is a representation of a cell by a network of interacting `organelles' (i.e. modules) with cell-specific properties. Cells form tissues and eventually organs through interactions either directly with each other or through secreted substances. The experimental and theoretical inputs of the formalism are inseparable: it cannot even be set up without one or the either. The method can serve as the basis for ``computational tissue engineering''.   

Dynamics and Mechanics of Zebrafish Embryonic Tissues.

In early zebrafish embryonic development, complex flows of cell populations occur, which ultimately lead to the spatial organization of the three germ layers: Ectoderm, mesoderm and endoderm. Here, we study the material properties of these germ layer tissues which are important for their dynamics and spatial organization in the embryo. In general, tissues can be classified as inherently active complex fluids. However, here we present examples of observed tissue behavior, which can be described satisfactorily in terms of passive visco-elastic fluids. We determined the material properties of the germ layer tissues quantitatively and found that differences in their properties influence tissue interaction. Specifically, quantitative differences in tissue surface tension result in tissue immiscibility and cell sorting behavior analogous to that of ordinary immiscible liquids. Surface tensions were measured with a tissue surface tensiometer. Furthermore, by tracking individual cells in the developing zebrafish embryo, we found differences in the migratory behavior of the different tissue types, which are, to some extent, governed by their mechanical properties. Finally, we generated a 3D velocity flow profile describing the tissue movements during zebrafish embryonic organizer development.   

Laser Hole-Drilling as a Probe of Morphogenetic Stresses in Embryonic Epithelia: Experimental Observations

During the development of an organism, sheets of epithelial cells expand, contract and bend due to forces generated within the cell sheets. These forces can be probed by laser hole-drilling -- a method borrowed from the analysis of residual stress in manufactured widgets -- in which a laser microbeam ablates a single cell surface or the edge shared by adjacent cells. We have applied this method to the embryonic epithelia of GFP-labeled fruit fly \textit{(Drosophila)} embryos. After ablation of one shared edge, we follow the recoil dynamics (strain relaxation) of adjacent cell edges (with time resolution down to 2 ms). The recoils show two distinct phases; and the initial recoil velocity can be consistently retrieved through a double-exponential fit. We observe a strong correlation between the initial recoil velocity and the orientation of the ablated cell edge. This correlation is particularly pronounced in embryos during late dorsal closure. Measuring orientation with respect to the long (anterior-posterior) axis of the embryo, both the recoil velocities and the distribution of cell edge orientations have sharp peaks near 30\r{ } and 150\r{ }. In early dorsal closure, the distribution of cell edge orientation has three much weaker peaks and the recoil velocities only show a weak maximum near 90\r{ }.   

Laser Hole-Drilling as a Probe of Morphogenetic Stresses in Embryonic Epithelia: Finite Element Models

During the development of an organism, sheets of epithelial cells expand, contract and bend due to forces generated within the cell sheets. These forces can be probed by laser hole-drilling; however, the observed recoil dynamics (or strain relaxations) depend strongly on the local cellular geometry. To better understand this dependence and help interpret our experimental observations, we have conducted a series of laser hole-drilling simulations using cell-level finite element models. Even the simplest of these simulations (i.e. homotypic cell sheets with constant cell boundary tensions) produce a wide range of initial recoil velocities. The velocities are correlated with particular aspects of the local geometry -- most notably the aspect ratio and orientation of cells adjacent to the ablated cell edge. These simulations also produce biphasic recoils; however, the two phases are not as distinct as those observed experimentally. To more closely reproduce the experimental recoils, the cell edges must include an elastic component. We will discuss using such finite element models to inversely determine local stresses in an epithelial sheet from the observed strain relaxations after laser ablation.   

Forces driven by morphogenesis modulate Twist Expression to determine Anterior Mid-gut Differentiation in \textit{ Drosophila} embryos

By combining magnetic tweezers to \textit{in vivo} laser ablation, we locally manipulate \textit{Drosophila} embryonic tissues with physiologically relevant forces. We demonstrate that high level of \textit{Twist} expression in the stomodeal primordium is mechanically induced in response to compression by the 60$\pm $20 nN force developed during germ-band extension (GBE). We find that this force triggers the junctional release and nuclear translocation of Armadillo involved in Twist mechanical induction in the stomodeum in a Src42A dependent way. Finally, stomodeal-specific RNAi-mediated silencing of Twist during compression impairs the differentiation of midgut cells, as revealed by strong defects in Dve expression and abnormal larval lethality. Thus, mechanical induction of Twist overexpression in stomodeal cells is necessary for subsequent midgut differentiation. \newline \newline In collaboration with Nicolas Desprat, Willy Supatto, and Philippe-Alexandre Pouille, MGDET, UMR168 CNRS, Institut Curie11 rue Pierre et Marie Curie, F-75005, Paris, France; and Emmanuel Beaurepaire, LOB, Ecole Polytechnique, CNRS and INSERM U 696, 91128 Palaiseau, France.   

Mechanical forces in the development of leaf venation networks

Leaf venation patterns, like leaf shapes, are extremely diverse, yet their local structure has been shown to satisfy a simple, universal property: the angles veins form at junctions are related to their diameters by a vectorial equation analogous to a force balance. This structure is the signature of a reorganization of vein networks during the development of leaves, a process we investigated numerically using a cell proliferation model. Provided that vein cells are given different mechanical properties, tensile forces develop along the veins during growth, causing the network to deform progressively. The statistics of the patterns obtained in these simulations are in good quantitative agreement with observations on leaves, supporting the notion that the local structure of leaf venation networks reflects a balance of mechanical forces.   

Pattern Formation in a Synthetic Multicellular System

Pattern formation has been studied for a long history since the Turing's proposal for a reaction-diffusion system and been found in numerous physical, chemical and biological examples. However, experimental study about pattern formation advances slowly. Here we present an artificial pattern formation system. By engineering cellular communication in bacteria \textit{E. Coli} and plating these engineered cells onto a solid-phase agarose plate, we are able to program the pattern formation of this multicellular system. The pattern changes dramatically with different levels of an external inducer IPTG. A simple model is developed to explain the experimental results.   

A Model of R8 Cell Specification in the \textit{Drosophila} Eye

R8 photoreceptors are specified in a precise hexagonal pattern behind an advancing front as it traverses the eye imaginal disc during \textit{Drosophila} development. In an attempt to better understand this patterning event, we have developed a mathematical model consisting of coupled differential equations on a lattice incorporating auto-activation, long-range activation, and short-range inhibition. The model is based on known elements of the regulatory gene network involved in patterning, and an analogy with discrete Nagumo systems is helpful in understanding its dynamics. We have developed analytic and numeric results for its behavior on a 1D lattice. Significantly, this model can reproduce patterns similar to those seen both in wild-type eye discs and in several mutant phenotypes. We argue that much of the model's behavior is a consequence of the fact that self-activation is cell-autonomous; this behavior represents a novel mode of pattern formation distinct from classical ideas such as Turing patterns or morphogen-dependent positional information.   

Emergence of hyper-hexagonal patterns in orientation map models of reduced rotation symmetry

Neurons in the primary visual cortex preferentially respond to visual stimuli of a particular orientation. These orientation preferences are arranged in aperiodic 2-D patterns, known as orientation preference maps (OPMs). Symmetry assumptions have been used successfully to derive a class of theoretical model which accounts for the emergence of aperiodic pinwheel-rich OPMs. Measurements revealed anisotropic coupling statistics in the underlying neural tissue, suggesting that the symmetry of models for the formation of orientation maps is reduced from the previously assumed E(2)xO(2) to E(2). In dynamical models for OPMs with E(2)xO(2) symmetry interactions represented by quadratic terms cannot occur but may be present in models of reduced E(2) symmetry. Here, we present a general analysis of the impact of such interactions on the formation of OPMs. We demonstrate that near the onset of pattern formation only two basic types of quadratic interaction terms exist, introduce a general parametric representation of permissible quadratic interactions near pattern formation onset, and derive the most general amplitude equations describing pattern selection in models incorporating quadratic interactions. We study the impact of such interactions on the spatial structure of OPMs, by incorporating them into a Swift-Hohenberg-model of OPM formation.   

Dynamics of Gas Exchange through the Fractal Architecture of the Human Lung, Modeled as an Exactly Solvable Hierarchical Tree

The acinar airways lie at the periphery of the human lung and are responsible for the transfer of oxygen from air to the blood during respiration. This transfer occurs by the diffusion-reaction of oxygen over the irregular surface of the alveolar membranes lining the acinar airways. We present an exactly solvable diffusion-reaction model on a hierarchically branched tree, allowing a quantitative prediction of the oxygen current over the entire system of acinar airways responsible for the gas exchange. We discuss the effect of diffusional screening, which is strongly coupled to oxygen transport in the human lung. We show that the oxygen current is insensitive to a loss of permeability of the alveolar membranes over a wide range of permeabilities, similar to a ``constant-current source'' in an electric network. Such fault tolerance has been observed in other treatments of the gas exchange in the lung and is obtained here as a fully analytical result.   

Evolution of Optimum Foraging Distributions in Two Dimensions

In the pursuit of optimally efficient foraging, preferred distributions of movement characteristics have been shown to exist for many types of animals and environments.~ Specifically, planktonic organisms such as \textit{Daphnia} use exponential distributions of turning angles, $\alpha $, in a \textit{``hop, pause, turn by angle $\alpha $, hop{\ldots}'' }random walk-type sequence of movement when traversing experimentally prepared feeding solutions consisting of freeze dried \textit{Spirolina} and water. We investigate the evolution of such random walks in a two-dimensional foraging model. In this model, agents traverse a feeding patch of finite size and for a finite amount of time using hop lengths and turning angles chosen randomly from inherited distributions. Distributions evolve as the choices made by the most efficient forager of one generation influence the distributions available to the succeeding generation. Preliminary results show that initially uniform turning angle distributions evolve to explicit exponential distributions after thousands of generations, consistent with the experimental observations described above.