Multiscale Modeling and Simulation of Limb Chondrogenesis

Mathematical and computational models are playing an increasingly prominent role in developmental biology. Many biological phenomena have interactions and behaviors that operate across multiple spatial and temporal scales, so accurate simulation of the phenomena requires those scales to be explicitly modeled. Agent-based modeling is a paradigm, typically discrete and stochastic, whereby entities or agents interact locally with other entities and their environment, and global patterns can emerge from the local interactions of many agents. In this thesis we describe a discrete, multiscale agent-based stochastic model for the behavior of limb bud precartilage mesenchymal cells in high-density cell culture. The model employs a biologically motivated reaction-diffusion process, and cell-matrix adhesion (haptotaxis), as the bases of chondrogenic pattern formation, whereby multicellular condensations are generated in a self-organizing fashion. The cells are extended, multipixel objects that can change shape in the plane and 'round up' by moving pixels into a virtual third dimension. Chemical reactions, molecular diffusion, and diffusion of cells operate on different physical and temporal scales. We calibrated the model using experimental data and study sensitivity to changes in key parameters. We have found that not only does this model reproduce the experimental data, but that additional morphogenetic features of the micromass culture system are simulated as well. Simulations show that spot and stripe patterns (which also correspond to the nodules and bars of the developing limb skeleton in vivo), are close in parameter space and can be generated in multiple ways with single parameter variations. Our simulations have disclosed two distinct dynamical regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. An important implication is that some developmental processes do not require a strict progression from one stable dynamical regime to another, but can occur by a succession of transient dynamical regimes tuned (e.g., by natural selection) to achieve a particular morphological outcome. We discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.