Morphogenetic Pattern Formation Research Articles

Minimal Developmental Computation: A Causal Network Approach to Understand Morphogenetic Pattern Formation.

What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal ‘genetic’ networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions—a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel “causal network” analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns—an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization.

Morphogenesis through elastic phase separation in a pneumatic surface

We report a phenomenon of phase separation that relates in many aspects to Yves Couder's work: an inflatable architectured elastomer plate, expected to expand homogeneously in its plane, buckles instead widely out-of-plane into very complex shape when internal pressure is applied. We show that this morphogenetic pattern formation is due to a two-dimensional elastic phase separation, which induces incompatible patchy non-Euclidean reference metric.

The Role of Criticality of Gene Regulatory Networks in Morphogenesis

Gene regulatory network (GRN)-based morphogenetic models have recently gained an increasing attention. However, the relationship between microscopic properties of intracellular GRNs and macroscopic properties of morphogenetic systems has not been fully understood yet. Here, we propose a theoretical morphogenetic model representing an aggregation of cells, and reveal the relationship between criticality of GRNs and morphogenetic pattern formation. In our model, the positions of the cells are determined by spring-mass-damper kinetics. Each cell has an identical Kauffman’s $NK$ random Boolean network (RBN) as its GRN. We varied the properties of GRNs from ordered, through critical, to chaotic by adjusting node in-degree $K$ . We randomly assigned four cell fates to the attractors of RBNs for cellular behaviors. By comparing diverse morphologies generated in our morphogenetic systems, we investigated what the role of the criticality of GRNs is in forming morphologies. We found that nontrivial spatial patterns were generated most frequently when GRNs were at criticality. Our finding indicates that the criticality of GRNs facilitates the formation of nontrivial morphologies in GRN-based morphogenetic systems.

Scaling of Morphogenetic Patterns.

Mathematical studies of morphogenetic pattern formation are commonly performed by using reaction-diffusion equations that describe the dynamics of morphogen concentration. Various features of the modeled patterns, including their ability to scale, are analyzed to justify constructed models and to understand the processes responsible for these features in nature. In this chapter, we introduce a method for evaluation of scaling for patterns arising in mathematical models and demonstrate its use by applying it to a set of different models. We introduce a quantity representing the sensitivity of a pattern to changes in the size of the domain, where it forms, and we show how to use it to perform a formal analysis of scaling for chemical patterns forming in continuous systems.

How Active Mechanics and Regulatory Biochemistry Combine to Form Patterns in Development.

The development of organisms starting from their zygotic state involves a tight integration of the myriad biochemical signaling interactions with the mechanical forces that eventually pattern and shape the resulting embryo. In the past decade, it has become increasingly evident that several important developmental processes involve mechanical forces in an essential manner. In this review, we highlight the multifaceted role of mechanics in pattern formation, from protein and cell sorting to the generation of tissue shape. We then review the ways in which the active cellular cytoskeleton self-organizes to form dynamic patterns. Finally, we focus on mechanochemical feedback, where signaling proteins can establish patterns via coupling to the activity of the cytoskeleton. Throughout the review, we focus on the generic physical principles of the establishment of active mechanochemical patterns and point toward future directions in studying how the principles of mechanics and chemistry combine to drive morphogenetic pattern formation.

Growth and Form in Biology: Generation of the Plant Morphologyby Spontaneous Symmetry Breaking Based on a Pressure Field

Considering the role of mechanical forces playing in the morphogeneticpattern formation, we propose a second-order differential equation forthe growth and form of plants based on the turgor pressure field at theorgan and cellular level. The solutions can well describe various kindsof morphological features of flowers under certain hypotheses. The plantmorphology is considered as the spontaneous symmetry breaking of acircular growing boundary, while the employed hypotheses are subjectedto further experimental confirmation.

Morphogenetic pattern formation during ascidian notochord formation is regulative and highly robust

The ascidian notochord forms through simultaneous invagination and convergent extension of a monolayer epithelial plate. Here we combine micromanipulation with time lapse and confocal microscopy to examine how notochord-intrinsic morphogenetic behaviors and interactions with surrounding tissues, determine these global patterns of movement. We show that notochord rudiments isolated at the 64-cell stage divide and become motile with normal timing; but, in the absence of interactions with non-notochordal tissues, they neither invaginate nor converge and extend. We find that notochord formation is robust in the sense that no particular neighboring tissue is required for notochord formation. Basal contact with either neural plate or anterior endoderm/lateral mesenchyme or posterior mesoderm are each alone sufficient to ensure that the notochord plate forms and extends a cylindrical rod. Surprisingly, the axis of convergent extension depends on the specific tissues that contact the notochord, as do other patterns of cell shape change, movement and tissue deformation that accompany notochord formation. We characterize one case in detail, namely, embryos lacking neural plates, in which a normal notochord forms but by an entirely different trajectory. Our results show ascidian notochord formation to be regulative in a fashion and to a degree never before appreciated. They suggest this regulative behavior depends on a complex interplay between morphogenetic tendencies intrinsic to the notochord plate and instructive and permissive interactions with surrounding tissues. We discuss mechanisms that could account for these data and what they imply about notochord morphogenesis and its evolution within the chordate phylum.

Contact response of cells can mediate morphogenetic pattern formation

Abstract Theories of morphogenetic pattern formation have included Turing's chemical prepatterns, mechanochemical interactions, cell sorting, and other mechanisms involving guided motion or signalling of cells. Many of these theories presuppose long-range cellular communication or other controls such as chemical concentration fields. However, the possibility that direct interactions between cells can lead to order and structure has not been seriously investigated in mathematical models. In this paper we consider this possibility, with emphasis on cells that reorient and align with each other when they come into contact. We show that such contact responses can account for the formation of multicellular patterns called parallel arrays. These patterns typically occur in tissue cultures of fibroblasts, and consist of clusters of cells sharing a common axis of orientation. Using predictions of a mathematical model and computer simulations of cell motion and interactions we show that contact responses alone, in the absence of other global controls, can promote the formation of these patterns. We suggest other situations in which patterns may result from direct cellular communication. Previous theories of morphogenesis are briefly reviewed and compared with this proposed mechanism.

A model of morphogenetic pattern formation

A model for the morphogenetic movement of surfaces composed of cellular monolayers is proposed. The cells are presumed joined at their lateral surfaces. An otherwise unspecified substance called a "morphogen" is introduced which is the agent of change in the individual cell (or cell-like region). The distribution of these cellular deformations define a surface (the middle surface, through the middle of the cell heights) via equations given for the Gauss and Mean curvatures of the surface defined at each point. The Gauss curvature as a function of the morphogen level determines the metric of the surface "g(u, v)" in conformal co-ordinates u, v. A unique equation for the morphogen distribution over the survace is presented which has the property of size invariance, that is, the model "regulates" without need of further arguments. The two resulting coupled equations for the metric and the morphogen, eqns (4) and (2), both non-linear equations, are to be solved self-consistently, once the individual cell deformation as a function of morphogen is given. The surface geometry determines the morphogen distribution, and the morphogen distribution in turn affects the surface geometry. Extension of the model to two or more morphogens is straightforward, and the key property of "regulation" or size invariance of the model is retained. Numerical integration of the two coupled equations is carried out in the case of axial symmetry, and the results presented by the case that individual cells deform by changing the ratio of their apical to basal areas, as well as their heights. Gastrulation in small regulating holoblastic eggs (e.g. starfish, sea urchin and amphioxus) is discussed in light of the present model.

Chemical patterns in circular morphogenetic fields

A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.