Random Boolean Networks: Disordered Dynamical Systems and the Order They Exhibit
Dr. Stuart Kauffman
University of Vermont, Complex Systems Center
October 29, 2010
4:00 - 5:00 pm
It is now some 45 years since I came to invent random Boolean networks as ensembles of disordered binary valued models of genetic regulatory networks. Recent work had just revealed that genes, which encode proteins, can turn one another on and off, or up and down. Thus the genetic network among what we know now is about 23,000 genes and their products is some vast nonlinear dynamical system within each cell, with some variables shared between cells in tissues and organs.
A deep debate in biology is whether the true genetic regulatory network is, in a still poorly defined sense, a very special network and logic system, or a relatively generic member of some ensemble of networks. I hoped then and hope now for the latter, for then self organization AND selection play a role in biological evolution. This is in full contrast to the view of most biologists that natural selection is the only source of order in biology.
It has turned out that random Boolean nets and now their continuous and piecewise cousins, show astonishing order in the first two of their three generic regimes: Order, Criticality and Chaos. I have modeled cell types as dynamical attractors of such networks, and more recently, given evidence of stochastic noise, perhaps as different ergodic sets of attractors in very new work. The scaling laws for the number of attractors in critical networks, matches roughly the scaling laws for the number of cell types in an organism as a function of the DNA per cell.
More, a growing abundance of simulation and analytic work suggests that critical networks have optimal properties with respect to information storage in basins of attractions, the capacity to simultaneously maximize the number of "worlds" the network can discriminate and act reliably in the presence of noise, maximize pairwise mutual information between dynamical variables, maximize a new measure, Set Complexity, of the diversity of organized behaviors such networks can attain, and maximize the diversity of behaviors of linked networks modeling tissues and organs for sparse coupling between the networks.
These results are now a cornerstone of the new sciences of complexity. While theorems are available in some regards, this class of disordered non-linear causal systems tells us that the requirements for ordered behavior have not yet been understood, and enough is now known about their simulated behaviors to warrant mathematical attention.
Dr. Stuart Kauffman, who holds a medical degree (M.D.) from the University of California, San Francisco, is well known for his work on models in various areas of biology, including autocatalytic sets in origin of life research, gene regulatory networks in developmental biology, and fitness landscapes in evolutionary biology. He holds the founding broad biotechnology patents in combinatorial chemistry and applied molecular evolution, and received a MacArthur Fellowship for 1987-1992.
Dr. Kauffman rose to prominence through his association with the Santa Fe Institute (a non-profit research institute dedicated to the study of complex systems), where he was faculty in residence from 1986 to 1997 and where he continues to be an external professor. In January of 2010, he joined the University of Vermont faculty where he is continuing his work with UVM's Complex Systems Center.
For more information about Dr. Kauffman, please see his UVM webpage.