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<a href="http://www.ucalgary.ca/oncampus/weekly/april22-05/kauffman.html" rel="nofollow">Stu Kauffman</a> just gave a fascinating talk at the <a href="http://www.almaden.ibm.com/institute" rel="nofollow">Almaden Institute on Complexity</a>.

I would bet that his discussion of cells and genetic signaling networks will also apply to the brain and synaptic networks. The evolution of evolution itself moves up a hierarchy of abstractions to act at the network topology level.

Here are my rough notes from Kauffman’s talk:

Cells are dynamically critical because being critical is the best way to coordinate complex behaviors. (critical meaning the edge between chaos and order)

We have been taught that natural selection is the only source of order. What if there was a law that governs all of biology? It would be profound and would alter our view of biology. There are organizing principles that biology “obeys” because it is selectively useful. It’s like finding one of Newton’s law of motion for cells.

Cells are very complex. Genetic regulatory nets: Transcriptome in yeast regulates 6500 genes, Humans: 25K Transcription factor -> promoter or enhancer. Protein signaling cascades. Transcriptome+protein signaling network is a parallel processing non-linear stochastic dynamical system. Huge web. Nobody knows structures and dynamics. Systems biology is trying to look for general laws 10^8000 genome state space. Percolate: order, all fixed states. Derrida deconstructionist. Mafia+deconstructionist = make you an offer you can’t understand Hamming distance. Fan-in of K=2 or less. Take a Random network. Take 60K logic gates at random. Each gate has 2 inputs. The system Behavior is simple. It spontaneously goes to ordered regime. Nearby states converge. Dt = Dt+1 is the critical line.

Being critical is very, very rare. If it exists, it must have been selected for over 3.8B years of evolution.

Why cells should be critical? Cells must bin past discriminations to future reliable actions • Order: convergence in state space forgets past distinctions. Info-lossy • Chaotic: small noise yields divergence in state space trajectories precluding reliable action • Critical: near parallel flow optimizes capacity to bind past and future Bacteria: operons for different food and different enzymes

Critical Boolean networks maximize robustness to mutations Cell types correspond to attractors Critical networks maximize the probability that such mutations leave all existing attractors intact and occasionally add new attractors. Thus, critical networks optimize robustness of cell types to mutations and the capacity to evolve new cell types.

Mutual information: correlation between 2 variables. Entropy of variable A + B – joint entropy. Between 0 and 1. 0 = no correlation. Ways to go from order and chaos. Inputs: order until K=2, peak for criticality. If k greater than 2, then put lots of 1’s in there. P-bias of .15 Model of floral development shows criticality.

E.Coli: apply random 1500 values on real network; also to Yeast medusa network, 200 regulatory genes in medusa head, rest are regulated 3500 genes (humans 2500 regulating genes in medusa head, 23K regulated). If apply random Boolean functions to the yeast network, why would it be critical? This is about the dynamics of the networks. Cells do thermodynamic work. Work is constrained release of energy in few degrees of freedom, but it takes work to create the constraints. Cells do this, but we don’t have concepts for it in physics.

Hela 48 hourly time point. Affy gene array data. Lempel-Ziv analysis. Cells clearly are not chaotic; they are either ordered or critical (data lie on top of each other) Avalanche size distribution. Deletion – see how many other genes change. Log-log straight line power law. Slope -1.5 power law (critical branching process). 250 yeast deletions, measure how many alter their activity. Ilya’s work.

NCD: normalized compression distance. Analysis of toll-like receptors on surface of macrophage. Ideal compressor. Take random length n, concatenate 2 of them. Ideal compressor will compress to n. 2 random ones, won’t be able to compress it. The more you can compress, the more similar they are. Regression gives a diagonal line, indicating it is critical. Nature, Dec 2006 Max Planck. Binary and ternary discretization leads to line that is critical. It’s breathtaking.