A Multiple-Mechanism Developmental Model for Defining Self-Organizing Geometric Structures

Abstract

This thesis introduces a model of multicellular development. The model combines elements of the chemical, cell lineage, and mechanical models of morphogenesis pioneered by Turing, Lindenmayer, and Odell, respectively. The internal state of each cell in the model is represented by a time-varying state vector that is updated by a differential equation. The differential equation is formulated as a sum of contributions from different sources, describing gene transcription, kinetics, and cell metabolism. Each term in the differential equation is multiplied by a conditional expression that models regulatory processes specific to the process described by that term. The resulting model has a broader range of fundamental mechanisms than other developmental models. Since gene transcription is included, the model can represent the genetic orchestration of a developmental process involving multiple mechanisms. We show that a computational implementation of the model represents a wide range of biologically relevant phenomena in two and three dimensions. This is illustrated by a diverse collection of simulation experiments exhibiting phenomena such as lateral inhibition, differentiation, segment formation, size regulation, and regeneration of damaged structures. We have explored several application areas with the model: Synthetic biology. We advocate the use of mathematical modeling and simulation for generating intuitions about complex biological systems, in addition to the usual application of mathematical biology to perform analysis on a simplified model. The breadth of our model makes it useful as a tool for exploring biological questions about pattern formation and morphogenesis. We show that simulated experiments to address a particular question can be done quickly and can generate useful biological intuitions. As an example, we document a simulation experiment exploring inhibition via surface chemicals. This experiment suggests that the final pattern depends strongly on the temporal sequence of events. This intuition was obtained quickly using the simulator as an aid to understanding the general behavior of the developmental system. Artificial evolution of neural networks. Neural networks can be represented using a developmental model. We investigate the use of artificial evolution to select equations and parameters that cause the model to create desired structures. We compare our approach to other work in evolutionary neural networks, and discuss the difficulties involved. Computer graphics modeling. We extend the model to allow cells to sense the presence of a 3D surface model, and then use the multicellular simulator to grow cells on the surface. This database amplification technique enables the creation of cellular textures to represent detailed geometry on a surface (e.g., scales, feathers, thorns). In the process of writing many developmental programs, we have gained some experience in the construction of self-organizing cellular structures. We identify some critical issues (size regulation and scalability), and suggest biologically-plausible strategies for addressing them.

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