Sci Am. Aug;(2) Antichaos and adaptation. Kauffman SA(1). Author information: (1)University of Pennsylvania, School of Medicine. Erratum in . English[edit]. Etymology[edit]. 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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Increasing the proportion of canalizing functions used in a network can therefore drive the system toward a phase transition between chaos and order.

To understand how self-organization can be a force in evolution, a brief overview of complex systems is necessary. As predicted, the length of cell cycles does seem to be proportional to roughly the square root of the amount of DNA in the cells of bacteria and higher organisms. The set of states that flow into a cycle or that lie on it constitutes the “basin of attraction” of the state cycle. Like low connectivity or biases in the Boolean rules, an abundance of canalizing functions in a network can create an extensive frozen core.

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.

In the chaotic regime, networks diverge after beginning in very similar states, but in the ordered regime, similar states tend to converge on the same successor states fairly soon.

A new kind of statistical mechanics can identify the average features of all the different systems in the ensemble. For example, a hormone called ecdysone in the fruit fly Drosophila can unleash a cascade that changes the activity of about genes out of at least 5, Packard found such evolution occurring in a population of simple Boolean networks called cellular automata, which had been selected for their ability to perform a specific simple computation.

Hence, all the cell types in an organism should express most of the same genes. The system as a whole becomes orderly because changes in its behavior must remain small and local. Highly chaotic networks would be so disordered that control of complex behaviors would be hard to maintain.

In canalizing functions, at least one input has a value that can by itself determine the activity of the regulated element.

The parallels support the hypothesis that evolution has tuned adaptive gene regulatory systems to the ordered region and perhaps to antichaoa the boundary between order and chaos.


The function specifies the activity of a variable in response to all the possible combinations of activities in the input variables.

Even if each state transition took only one microsecond, it would take billions of times longer than the age of the universe for the network to traverse its attractor completely. 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. As a result, the system is partitioned into an unchanging frozen core and islands of changing elements.

As the parameters describing a complex Boolean system change, the system’s behavior alters, too: Like minimal perturbations, structural perturbations can cause damage, and networks may vary in their stability against them. It is possible that biological order reflects in part a spontaneous order aadptation which selection has acted.

These properties are observed in organisms. Cell types differ because they have dissimilar patterns of genetic activity, not because they have different genes.

Computer models suggest that certain complex systems tend toward self-organization by Stuart A. All living things are highly ordered systems: Changes in activity xdaptation be restricted to small, isolated islands of genes.

Antichaos and Adaptation

Adatation Langton, a computer scientist at Los Alamos National Laboratory, has introduced an analogy that helps one think about the change between order and disorder in different ensembles of networks. Across many phyla, the number of cell types seems to increase with approximately the square root of the number of genes per cell that is, with the number of genes raised to a fractional power that is roughly one half.

Kauffman Antichaos and Adaptation. We have begun studying the question by making Boolean networks play a variety of games with one another [see box on opposite page]. The coordinated behavior of this system underlies cellular differentiation.

In such poised systems, most mutations have small consequences because of the systems’ homeostatic nature. It will consequently cycle repeatedly through the same states. After receiving an appropriate stimulus, a gene in a eukaryotic cell needs about one to 10 minutes to become active.

Antichaos and adaptation.

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 That order, of course, is much the same as I have described for networks with low connectivity. We may have begun to understand evolution as the marriage of selection and self-organization. Mathematical models can help researchers understand the features of such complex parallel-processing systems.


The dynamic behavior of the network becomes a web of frozen elements and functionally isolated islands of changeable elements. 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.

Because the successor to any state is essentially random, almost any perturbation that flips one element would sharply change the network’s subsequent trajectory. Networks with only a single input per element constitute a special ordered class. Antichaos and Adaptation Biological evolution may have been shaped by more than just natural selection.

Some Boolean functions turn elements on more often than off or vice versa. The stability of an attractor is proportional to its basin size, which is the number of states on trajectories that drain into the attractor. Avalanches of damage or changed activity caused by the mutation should not propagate to the vast majority of genes in the regulatory network.

Since Darwin, biologists have seen natural selection as virtually the sole source of that order. Our results, too, suggest that the transition between chaos and order may be an attractor for the evolutionary dynamics of networks performing a range of simple and complex tasks. Every network must have at least one state cycle; it may have more.

28cha: S. Kauffman Antichaos and Adaptation

If a cell type is an attractor, it should be possible to predict how many cell types could appear in an organism. Because the systems show extreme sensitivity to their initial conditions and because their state cycles increase in length exponentially, I characterize them as chaotic.

For each combination, either an active or inactive result must be specified. But Darwin could not have suspected the existence of self-organization, a recently discovered, innate property of some complex systems. Highly ordered networks are too frozen to coordinate complex behavior.

Both claims hold true for biological systems. Yet not all systems have the capacity to adapt and improve in that way.