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

Abstract

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.

The Nonlinearity of Regulation in Biological Networks

“…In contrast, a cell defecting from the collective and reverting to a more unicellular lifestyle (Metastasis) should exhibit a less predictable, controllable network due to pressures from parasites and competitors that independent unicellular organisms face. Methods for calculating controllability (e.g., linearity) are an important addition to recent efforts to solve the conundrum of interpretability of information structures in contexts ranging from machine learning to evolutionary developmental biology [24,25,26].…”

Cell Responsiveness to Physical Energies: Paving the Way to Decipher a Morphogenetic Code

“…Cells are, therefore, embedding, self-organizing chemical structures, such as microtubuli and other cytoskeletal elements, that now appear to be “written” by a software encompassing physical energies of an electromagnetic and mechanical nature. In this frame, we may refer to the genome, the proteome, and other omics (such as the kinome) as the hardware of our biological systems [ 89 , 90 ].…”

Counting with Cilia: The Role of Morphological Computation in Basal Cognition Research

“…Importantly, quite early attempts have already cast morphogenesis in terms of computation. One of the earliest explicit statements of this perspective comes from Wolpert and Lewis [ 45 ], p. 21, which attributes the following question to Sydney Brenner: “Is the adult (organism) computable from an egg?” This line of research has been expanded by, among others, Paulien Hogeweg (e.g., [ 46 ]), and more recently by Michael Levin and his collaborators (e.g., [ 47 ]), whose work is analyzed in more detail below. However, the computational nature of this process was already implicit in the reaction–diffusion system proposed by Turing, as it has been shown since that such systems can constitute analogue computers [ 48 ].…”

“…Levin and collaborators’ work (e.g., [ 47 , 51 , 52 , 53 ]) introduces a major shift in this regard. Although he states that his work on morphogenesis follows the tradition discussed in the previous paragraph, he does not merely use the computational language for explanation but rather claims that the processes of morphogenesis are literally computational and process information.…”

“…Although he states that his work on morphogenesis follows the tradition discussed in the previous paragraph, he does not merely use the computational language for explanation but rather claims that the processes of morphogenesis are literally computational and process information. This is clearly visible in the way they update the aforementioned quote originally due Brenner: instead of asking how can we, scientists, compute an organism from an egg, Manicka and Levin ask “How does an embryo compute its own pattern?” [ 47 ], (p. 1; emphasis added). They further strengthen this perspective by exploring the possibility of using insights from the study of morphogenesis in the development of artificial computational platforms.…”