This white paper was written with substantial contributions and serious help from the following members of our group: Stephen Adams, Natalya Cohen, Daniel Coore, Sola Grantham, Chris Hanson, Kevin Lin, Nick Papadakis, Sofya Raskhodnikova, Thanos Siapas, and Jack Wisdom.

The Science article describes the complete genome of Haemophilus influenzae Rd [3]. Mycoplasm is another organism that is almost fully sequenced; it has a mere 470 genes and almost no transcription factors. Apparently, Mycoplasm has almost no genetic control; once you turn it on, it just runs! Another organism whose workings are almost completely understood is E.coli [1]. People at Harvard have concentration data on the top 400 or so proteins in E.coli. This is essential for simulating reactions involving these chemicals. The concentrations, are extremely high -- the cell is 30 protein. Some more good numbers: an E.coli cell is 200 nm across; a typical protein is 1 nm long; so the cell is 200 ``protein lengths'' across (personal communication from Nat Goodman of the Whitehead Institute).

Languages such as *Lisp and *C developed for the connection machine encapsulate paradigms for handling aggregate data. These build on older ideas such as were found in APL.

Nobel laureate Ilya Prigogine and his associates have studied these phenomena and shown that they are important in physical and chemical as well as biological systems [8].

For example, the dilation and erosion method used in morphological image processing is accomplishing the same sort of processing, although this generally is done in the context of an underlying grid or other regular spatial arrangement of the elements. (See, for example, [5].)

The experiments with angelfish stripes described in [6] are highly suggestive that reaction-diffusion mechanisms really are at work here.

The Gray-Scott model describes the evolution of the concentrations of two morphogens according to the system of nonlinear equations:


Simulations of this system are described by Pearson [7]. Results of such simulations (done by R. Williams at Caltech) can be seen on the World-Wide Web at www.ccsf.caltech.edu/ismap/image.html. The simulation shown in figure 2 is similar to some of the ones done by Pearson and Williams, except that that we start from a random distribution of 15#15 and 16#16, do not impose periodic boundary conditions, and use a random packing of computational particles rather than a regular grid.

Gerald Jay Sussman
Thu Jun 27 16:56:19 EDT 1996