A Computational Approach of the French Flag Model to Connect Growth and Specification in Developmental Biology

The scaling of goals from cellular to anatomical homeostasis: an evolutionary simulation, experiment and analysis

Complex living agents consist of cells, which are themselves competent sub-agents navigating physiological and metabolic spaces. Behaviour science, evolutionary developmental biology and the field of machine intelligence all seek to understand the scaling of biological cognition: what enables individual cells to integrate their activities to result in the emergence of a novel, higher-level intelligence with large-scale goals and competencies that belong to it and not to its parts? Here, we report the results of simulations based on the TAME framework, which proposes that evolution pivoted the collective intelligence of cells during morphogenesis of the body into traditional behavioural intelligence by scaling up homeostatic competencies of cells in metabolic space. In this article, we created a minimal in silico system (two-dimensional neural cellular automata) and tested the hypothesis that evolutionary dynamics are sufficient for low-level setpoints of metabolic homeostasis in individual cells to scale up to tissue-level emergent behaviour. Our system showed the evolution of the much more complex setpoints of cell collectives (tissues) that solve a problem in morphospace: the organization of a body-wide positional information axis (the classic French flag problem in developmental biology). We found that these emergent morphogenetic agents exhibit a number of predicted features, including the use of stress propagation dynamics to achieve the target morphology as well as the ability to recover from perturbation (robustness) and long-term stability (even though neither of these was directly selected for). Moreover, we observed an unexpected behaviour of sudden remodelling long after the system stabilizes. We tested this prediction in a biological system-regenerating planaria-and observed a very similar phenomenon. We propose that this system is a first step towards a quantitative understanding of how evolution scales minimal goal-directed behaviour (homeostatic loops) into higher-level problem-solving agents in morphogenetic and other spaces.

French flag gradients and Turing reaction-diffusion versus differentiation waves as models of morphogenesis

The Turing reaction-diffusion model and the French Flag Model are widely accepted in the field of development as the best models for explaining embryogenesis. Virtually all current attempts to understand cell differentiation in embryos begin and end with the assumption that some combination of these two models works. The result may become a bias in embryogenesis in assuming the problem has been solved by these two-chemical substance-based models. Neither model is applied consistently. We review the differences between the French Flag, Turing reaction-diffusion model, and a mechanochemical model called the differentiation wave/cell state splitter model. The cytoskeletal cell state splitter and the embryonic differentiation waves was first proposed in 1987 as a combined physics and chemistry model for cell differentiation in embryos, based on empirical observations on urodele amphibian embryos. We hope that the development of theory can be advanced and observations relevant to distinguishing the embryonic differentiation wave model from the French Flag model and reaction-diffusion equations will be taken up by experimentalists. Experimentalists rely on mathematical biologists for theory, and therefore depend on them for what parameters they choose to measure and ignore. Therefore, mathematical biologists need to fully understand the distinctions between these three models.