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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Some Boolean functions turn elements on more often than off or vice versa.
These expectations are met by real genetic systems. Our results, too, adaaptation 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.
The analogy should not be interpreted too literally, of course: That stable core of elements is identical in almost all the attractors.
Antichaos and Adaptation – Stuart Alan Kauffman – Google Books
Given that interpretation, the spontaneous order arising in networks with low connectivity and araptation Boolean functions sets up several predictions about real biological systems.
On the face of it, the idea is plausible. In canalizing networks, order emerges because a large fraction of the binary elements falls ahd a stable, frozen state. 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.
If one were to examine a network ofelements, each receiving two inputs, anticchaos wiring diagram would be a wildly complex scramble. All living things are highly ordered systems: A system with elements and states, for example, would have only about 74 different patterns of behavior.
The activity of any one gene is directly regulated by fairly few other genes or gene products, and certain rules govern their interactions. The expected number of state cycles antichwos the number of elements divided by the logarithmic constant e.
These characteristics inspired Langton to suggest that parallel-processing networks poised at the edge of chaos might be capable of extremely complex computations.
Highly chaotic networks adqptation be so disordered that control of complex behaviors would be hard to maintain. Like minimal perturbations, structural perturbations can cause damage, and networks may vary in their stability against them. If a cell type is an attractor, then it cannot be altered by most perturbations: Minimal perturbations in those systems cause avalanches of damage that can alter the behavior of most of the unfrozen elements.
Antichaos and adaptation.
If we assume that the number of genes is proportional to the amount of DNA in a cell, then humans should have aboutgenes and cell types. 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 adaptstion. Traditional statistical mechanics, in contrast, averages over all the possible states of a single system.
Antichaos, I believe, plays an important part in biological development and evolution. The dynamic behavior of the network becomes avaptation web of frozen elements and functionally isolated islands of changeable elements.
Antichaos and Adaptation
Alternatively, the AND function declares that a variable will become active only if all its inputs are currently active. Both claims hold true for biological systems.
Yet if the network is perturbed in some way, its trajectory may change. Highly ordered networks are too frozen to coordinate complex behavior.
Antichaos and adaptation. – Abstract – Europe PMC
Why do random networks with two inputs per element exhibit such profound order? Every complex system has what can be called local features: By that reasoning, such poised systems should occur in biology. Biology is filled with complex systems: Big attractors are stable to many perturbations, and small ones are generally unstable. Increasing the proportion of canalizing functions used in a network can therefore drive the system toward a phase transition between chaos and order.
The system as a whole becomes aantichaos because changes in its behavior must remain small and local. Such perturbations would include exchanging the inputs of two elements or switching an element’s OR function to an AND function. By the most recent count, humans have about distinct cell types, so that prediction is also in the right range.
In the ordered regime of networks with two or fewer inputs per element, there is little sensitivity to initial conditions: A genome acts like a complex parallel-processing computer, or network, in which genes regulate one another’s activity either directly or through their products.
A number of solid state physicists, including Deitrich Stauffer of the University of Koeln and Bernard Derrida and Gerard Weisbuch of the Ecole Normale Superieure in Paris, have studied the effects of biased functions.
But Darwin could not have suspected the existence of self-organization, a recently discovered, innate property of some complex systems. The complexity that a network can coordinate peaks at the adapgation transition between solid and gaseous states.
The succession of states is called the trajectory of the network. Yet not all systems have the capacity to adapt and improve in that way. Because all the elements act simultaneously, the system is also said to be adaptatoin.
The network behaves chaotically.
The average length of a state cycle in the network is roughly the square root of that number, about states. Mathematical discoveries are inviting changes in biologists’ thinking about the origins of order in evolution. A random network is one sampled at random from this ensemble. As a result, the system is antkchaos into an unchanging frozen core and islands of changing elements.
As Darwin taught, mutations and natural selection can improve a biological system through the accumulation of successive minor variants, just as tinkering can improve technology.