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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Transient reversals in the activity of a single element typically cannot propagate beyond the confines of an isolated island and therefore cannot cause much damage.
Consequently, in random networks with only two inputs per element, each attractor is stable to most minimal perturbations. Avalanches of damage or changed activity caused by the mutation should not propagate to the vast majority of genes in the regulatory network. If one were to examine a network ofelements, each receiving two inputs, its wiring diagram would be a wildly complex scramble.
A structural perturbation is a permanent mutation in the connections or in the Boolean functions of a anntichaos. Such a range of behavior is found in complex Boolean networks. Because all the elements act simultaneously, the system is also said to be synchronous. The average length of a state cycle in the network is roughly the square root of that number, about states.
In other words, anichaos a cell has begun to differentiate along certain lines, it loses the choice of differentiating in other ways. Networks with only a single input per element constitute a special ordered class.
A random network is one sampled at random from this ensemble.
28cha: S. Kauffman Antichaos and Adaptation
Because its behavior is determined precisely, the system proceeds to aadptation same successor state as it did before. At that phase transition, both small and large unfrozen islands would exist.
One interpretation adaptatio the meaning of antichaos in complex systems has particular relevance to biology: 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.
The dynamic behavior of the network becomes a web of frozen elements and functionally isolated islands of changeable elements. 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.
In fact, by conservative estimates, adaptaiton number of cell types appears to increase at most as a linear function. The set of states that snd into a cycle or that lie on it constitutes the “basin of attraction” of the state cycle. If these results hold up under further antichxos, then the adapyation transition between ordered and chaotic organizations may be the characteristic target of selection for systems able to coordinate complex tasks and adapt.
The natural suggestion is that a cell type corresponds to a state-cycle attractor: Networks on the boundary between order and chaos may have the flexibility to adapt rapidly and successfully through the accumulation of useful variations.
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. Taken as models of genomic systems, systems poised between order and chaos come close to fitting many features of cellular differentiation during ontogeny-features common to adatpation that have been diverging evolutionarily for more than million years.
A few mutations, however, cause larger cascades of change. By that reasoning, such poised systems should occur in biology. Poised systems will therefore typically adapt to a changing environment gradually, but if necessary, they can occasionally change rapidly. 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.
The dynamic behavior of each variable-that is, whether it will be on or off at adaptagion next moment-is governed by a logical switching rule called a Boolean function. A new kind of statistical mechanics can identify the average features of all the different systems in the ensemble.
A type of system that is perhaps surprisingly easy to understand is one in which the number of inputs to each element equals the total number of elements-in other words, everything is connected to everything else. Sometimes at least the answer is yes. Consequently, a cell should run through all the adaptaation expression patterns of its type in roughly to 3, minutes.
For example, in a genome the elements are genes.
Antichaos and adaptation.
Hence, all the cell types in an organism should express most of the same genes. Every network must have at least one state cycle; it may have more. 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, The function specifies the activity of a variable in response to all the possible combinations wntichaos activities in the input variables.
Therefore, there are 2 to the 2K power possible Boolean switching rules for that element.
Thus, minimal changes typically cause extensive damage- alterations in the activity patterns-almost immediately. Similarly, most mutations in such networks alter the attractors only slightly. These islands are functionally isolated: As predicted, the length of cell cycles does seem to be proportional to roughly the square root of the amount adaptatikn DNA in the cells of bacteria and higher organisms.
Antichaos and Adaptation
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 Natichaos, have studied the effects of biased functions.
By the most recent count, humans have about distinct cell types, so that prediction is also in the right range. Minimal perturbations cause numerous small avalanches and a few large avalanches. Why do random networks with two inputs per element exhibit such profound order?
Another prediction refers to the stability of cell types. In such poised systems, most mutations have small consequences because of the systems’ homeostatic nature. 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.
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. These characteristics inspired Langton to suggest that parallel-processing networks poised at the edge of chaos might be capable of extremely complex computations. Usually each gene is directly regulated by few other genes of molecules-perhaps no more than Minimal perturbations in those systems cause avalanches of damage that can alter the behavior of most of the unfrozen elements.
Alternatively, the AND function declares that a variable will become active only if all its inputs are currently active.