Sci Am. Aug;(2) Antichaos and adaptation. Kauffman SA(1). Author information: (1)University of Pennsylvania, School of Medicine. Erratum in . English. Etymology. anti- + chaos, coined by Stuart Kauffman in Antichaos and Adaptation (published in Scientific American, August ). Antichaos and Adaptation Biological evolution may have been shaped by more than just natural selection. Computer models suggest that.
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One of the central dogmas of developmental biology is that liver cells, neurons and other cell types differ because varied genes are active in them.
The stability of an attractor is proportional to its basin size, which is the number of states on trajectories that drain into the attractor.
antichaos – Wiktionary
Consequently, ontological development from a fertilized egg should proceed by successive branching pathways of differentiation. Moreover, about two thirds of all the possible states fall within the basins of only a few attractors-sometimes of just one.
As far as biologists know, cell differentiation in multicellular organisms has been fundamentally constrained and organized by successive branching pathways since the Cambrian period almost million years ago. A random network is one sampled at random from this ensemble. Since then, mathematicians, computer scientists and solid state physicists, among them my many colleagues at the Santa Fe Institute in New Mexico, have made substantial progress.
Recently my colleague Sonke Johnsen of the University of Pennsylvania and I have found further evidence of evolution proceeding to the edge of chaos. The genomic regulatory network orchestrates those possibilities into changing patterns of gene activity over time.
If a cell type is an attractor, it should be possible to predict how many cell types could appear in an organism. Yet antichqos would emerge spontaneously: Similarly, most mutations in such networks alter the attractors only slightly. If a binary element has K inputs, then there are 2K possible combinations of inputs it could receive.
A genome that containssnd has the potential for at leastpatterns of gene expression. In such poised systems, most mutations have small consequences because of the systems’ homeostatic nature. At that phase transition, both small and large unfrozen islands would exist. Selection has molded, but was not compelled to invent, the native coherence of ontogeny, or biological development.
It has been more than 20 years since I discovered those features of random networks, and they still surprise me. The OR function is a typical canalizing function.
If one were to examine a network ofelements, each receiving two inputs, its wiring diagram would be a wildly complex scramble. A new kind of statistical mechanics can identify the average features of all the different systems adaptayion the ensemble.
Because the systems show extreme sensitivity to their initial conditions and because their state cycles increase in length exponentially, I characterize them as chaotic. In other words, once a cell has begun to differentiate along certain lines, it loses the choice of differentiating in other ways.
When K drops to two, however, the properties of random Boolean networks change abruptly: Yet certain properties of complex systems are becoming clear.
Antichaos and adaptation.
By the most recent count, humans have about distinct cell types, so that prediction is also in the right range. A system with elements and states, for example, would have only about 74 different patterns of behavior.
The expected size of avalanches in canalizing genomes with 5, elements or in those with low connectivity and a frozen core containing roughly 80 percent of the genes is about In contrast, if the level of bias is well below the critical value-as it is in chaotically active systems-then a web of annd elements spreads across the system, leaving only small islands of frozen elements.
Because all the elements act simultaneously, the system is also said to be synchronous. As predicted, the length of cell cycles does seem to be proportional to roughly the square root of xnd amount of DNA in the cells of bacteria and higher organisms.
Transient reversals in the atnichaos of a single element typically cannot propagate beyond the confines of an isolated island and therefore cannot cause much damage. The predicted number of cell types could therefore increase according to a fractional power greater than one half the square root but less than one.
Antichaos and Adaptation
First, each cell type should correspond to a very small number of gene expression patterns through which it cycles. In a canalizing ensemble, however, each model cell can differentiate directly into only a few alternative cell types because each attractor is “near” only a few others. The length of amd attractor in a genome withgenes would be about states.