The Universal Vision of Organismal Forms through NKS’s Eyes

Luca Zammataro

University of Torino


Up to now, automata theory has put in evidence interesting aspects in the study of biologically inspired algorithms. Among these aspects the concepts of autopoiesis and cognition proposed by Varela and Maturana and subsequently introduced by Randall Beer in cellular automata, deserve consideration. An autoplectic (i.e., self-reproducing) system is a network of components constituting a distinct “entity” in the space, in which it exists (Maturana & Varela 1973), (Beer 2004). Observing cellular automata clustering in term of autopoeisis and cognition, we should distinguish an entity for each automata cluster, and this entity should be able to define distinctions through its selective response to environmental perturbations (Beer 2004). For these reasons Beer suggests that the realization of a cognitive domain inside cellular automata clusters always occurs. The concept of “unity” is the same as “body.” But in what way, and with what measuring instruments can we distinguish a cellular automata body from its environment? And what kind of biological ideas as humans could we share to consider this body as a whole cognitive process? The aim of this work is to shed light on the autopoietical and organizational aspects of geometric compartmentalizations of automata signals by means of the use of NKS, in order to demonstrate in what way, starting from random initial conditions, a body identity with its cognitive domain could develop. Browsing a universe of rules, I will describe a wide number of morphological patterns, which are spontaneously codified. The cognitive domain of each body identity rising from this universe allows the automata compartment to receive a perturbation from the surrounding environment, and to undergo transitory losses of identity, without body identity destruction. This work also puts in evidence the importance of defining more identity levels, some of which are obtained from the fusion of minor organizational level identities.

Another NKS biological application field in life geometry is represented by embryo development. Similarly to membrane compartmentalizations, we should consider an embryo body as a compartmentalized shape in development. Life functions depend on the development in space and time of basic shapes evolving into complex structures. Since Charles Darwin formulated the natural selection theory, naturalists have studied in what way developmental processes such as pattern formation, morphogenesis, and molecular evolution can spontaneously emerge, being determined only by genetic factors and environmental restrictions. The basic principle of NKS is that a simple rule can evolve with a complex overall behavior. Indeed, we can imagine that cells and multicellular organisms are nothing but the end result of a computational process running many simple and interacting rules. Here, we show that the NKS approach allows the discovery of a hierarchy of simple rules that gives rise to a composite function governing spindle pole orientation of two dividing cells and embryonic cleavage patterning. This observation provides support to a computational view of nature, in which biological systems could result from simple programs that evolve into complex patterns. In order to explain how it is possible to use the NKS’s vision of life geometry in morphogenesis, my collaborators and I provide the first evidence that an NKS approach could prove useful in shedding new light on old biological issues, such as embryonic cleavage (Zammataro, Serini et al. 2007). Embryonic cleavage depends on the distribution in the cytosol of molecular signals that influence mitotic spindle positioning (Gilbert 2000), (Zernicka-Goetz 2005), (Ahringer 2003). The computational methods used to model embryonic cleavage are represented by three-dimensional substitution systems, which is an evolution of the classic two-dimensional substitution system described by Wolfram (Wolfram 2002). I will propose a theoretical approach that is capable of modeling the mechanisms of early embryonic cleavage dynamics in metazoans. The model shows that the same spindle pole orientation rule governs the first five embryonic cleavages, which progressively allow the transition from one to thirty-two daughter cells (Zammataro, Serini, et al. 2007), (Zammataro 2004).

The entire work is focused on the universal vision of organismal forms through NKS and its computational instruments.

Ahringer, J. (2003). "Control of cell polarity and mitotic spindle positioning in animal cells." Curr Opin Cell Biol. 15(1): 73–81.
Beer, R. D. (2004). "Autopoiesis and cognition in the Game of Life." Artificial Life 103: 309–326.
Gilbert, S. F. (2000). Developmental Biology, 6th ed. Sinauer Associates, Inc.
Maturana, H. R. and Varela, F. J. (1991). "Autopoiesis: The organization of the living." In H.R. Maturana and F.J. Varela (eds.), Autopoiesis and Cognition, Boston: Reidel.
Wolfram, S. (2002). A New Kind of Science, Wolfram Media, Inc.
Zammataro, L. (2004). "Using 3D Substitution Systems to Model Compartmentalizations and Clusters Architectures in Nature: An NKS Approach.",
Zammataro, L., Serini, G., et al. (2007). "Embryonic cleavage modeling as a computational approach to sphere packing problem." J Theor Biol 245(1): 77–82.
Zernicka-Goetz, M. (2005). "Developmental cell biology: Cleavage pattern and emerging asymmetry of the mouse embryo." Nat Rev Mol Cell Biol 6(12): 919–28.