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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At the next clocked moment, the elements turn on or off in accordance with their individual functions. The activity of any one gene is directly regulated by fairly few other genes or gene products, and certain rules govern their interactions.

In canalizing networks, order emerges because a large fraction of the binary elements falls into a stable, frozen state. He has related network behavior to the phases of matter: A genome that containsgenes has the potential for at leastpatterns of gene expression. Mathematical models can help researchers understand the features of such complex parallel-processing systems.

Antichaos and Adaptation

It is possible that biological order reflects in part a spontaneous order on which selection has acted. 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. Cell types differ because they have dissimilar patterns of genetic activity, not because they have different genes. Sometimes at least the answer is yes. How much order and chaos do the genomic systems of viruses, bacteria, plants and animals exhibit?

In contrast, other simple mathematical models for genomic systems predict that the number of cell types would increase exponentially with the number of genes. 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.


The ordered network regime is therefore characterized by a homeostatic quality: We have begun studying the question by making Boolean networks play a variety of games with one another [see box on opposite page]. Mathematical discoveries are inviting changes in biologists’ thinking about the origins of order in evolution.

They have found that if the degree of bias exceeds a critical value, then “homogeneity clusters” of elements that have frozen values link with one another and percolate across the network.

Such a range of behavior is found in complex Boolean networks. The analogy should not be interpreted too literally, of course: Every complex system has what can be called local features: An OR function for two inputs, for example, will turn an element on in response to three out of the four possible combinations of binary signals. 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.

First, each cell type should correspond to a very small number of gene expression patterns through which it cycles. If a cell type is an attractor, then it cannot be altered by most perturbations: Packard of the University of Illinois at Champaign-Urbana may have been the first person to ask whether selection could drive parallel-processing Boolean networks to the edge of chaos. One can therefore calculate how long such cell cycles should be. It is not a necessary condition, however. One phenomenon found in some cases has already caught the popular imagination: Given that interpretation, the spontaneous order arising in networks with low connectivity and canalizing Boolean functions sets up several predictions about real biological systems.

They persist as K the number of inputs per element decreases to about three.

Antichaos and adaptation.

Yet certain properties of complex systems are becoming clear. The discovery of antichaos in biology began more than 20 years ago with my efforts to understand mathematically how a fertilized egg differentiates into multitudes of cell types. The Boolean wiring diagram for the genome is therefore sparse, and the individual gene elements have few inputs.


It will consequently cycle repeatedly through the same states. Poised systems will therefore typically adapt to a changing environment gradually, but if necessary, they can occasionally change rapidly.

Antichaos and Adaptation – Stuart Alan Kauffman – Google Books

This figure approximates the correct range for real biological systems. The OR function is a adapyation canalizing function. Consequently, in random networks with only two inputs per element, each attractor is stable to most minimal perturbations.

Computer models suggest that certain complex systems tend toward self-organization by Stuart A. The efforts are still so new that there is not yet even a generally accepted, comprehensive definition of complexity. The complexity that a network can coordinate peaks at the liquid transition between solid and gaseous states.

In the ordered regime of networks adaptwtion two or fewer inputs per element, there is little sensitivity to initial conditions: In contrast, if the level of bias is well below the critical value-as it is in chaotically active systems-then a web of oscillating elements spreads across the system, leaving only small islands of frozen elements.

But Darwin could not have suspected the existence of self-organization, a recently discovered, innate property of some complex systems.

These systems are named after George Boole, the English inventor of an algebraic approach to mathematical logic. Therefore, there are 2 to the 2K ahd possible Boolean switching rules for that element.

Usually each gene is directly regulated by few other genes of molecules-perhaps no more than