Complexity_ A Guided Tour - Melanie Mitchell [136]
Genetic Regulation and Kauffman’s “Origins of Order”
Stuart Kauffman is a theoretical biologist who has been thinking about genetic regulatory networks and their role in constraining evolution for over forty years, long before the ascendency of Evo-Devo. He has also thought about the implications for evolution of the “order” we see emerging from such complex networks.
Kauffman is a legendary figure in complex systems. My first encounter with him was at a conference I attended during my last year of graduate school. His talk was the very first one at the conference, and I must say that, for me at the time, it was the most inspiring talk I had ever heard. I don’t remember the exact topic; I just remember the feeling I had while listening that what he was saying was profound, the questions he was addressing were the most important ones, and I wanted to work on this stuff too.
Kauffman started his career with a short stint as a physician but soon moved to genetics research. His work was original and influential; it earned him many academic accolades, including a MacArthur “genius” award, as well as a faculty position at the Santa Fe Institute. At SFI seminars, Kauffman would sometimes chime in from the audience with, “I know I’m just a simple country doctor, but … ” and would spend a good five minutes or more fluently and eloquently giving his extemporaneous opinion on some highly technical topic that he had never thought about before. One science journalist called him a “world-class intellectual riffer,” which is an apt description that I interpret as wholly complimentary.
Stuart Kauffman (Photograph by Daryl Black, reprinted with permission.)
Stuart’s “simple country doctor” humble affect belies his personality. Kauffman is one of Complex Systems’ big thinkers, a visionary, and not what you would call a “modest” or “humble” person. A joke at SFI was that Stuart had “patented Darwinian evolution,” and indeed, he holds a patent on techniques for evolving protein sequences in the laboratory for the purpose of discovering new useful drugs.
RANDOM BOOLEAN NETWORKS
Kauffman was perhaps the first person to invent and study simplified computer models of genetic regulatory networks. His model was a structure called a Random Boolean Network (RBN), which is an extension of cellular automata. Like any network, an RBN consists of a set of nodes and links between the nodes. Like a cellular automaton, an RBN updates its nodes’ states in discrete time steps. At each time step each node can be in either state on or state off.
FIGURE 18.2. (a) A random Boolean network with five nodes. The in-degree (K) of each node is equal to 2. At time step 0, each node is in a random initial state: on (black) or off (white). (b) Time step 1 shows the network after each node has updated its state.
The property that on and off are the only allowed states is where the term Boolean comes in: a Boolean rule (or function) is one that gets some number of inputs, each equal to either 0 or 1, and from those inputs it produces an output of a 0 or 1. Such rules are named after the mathematician George Boole, who did extensive mathematical research on them.
In an RBN, links are directional: if node A links to node B, node B does not necessarily (but can possibly) link to node A. The in-degree of each node (the number of links from other nodes to that node) is the same for each node—let’s call that number K.
Here is how to