Box 5.10Testing the Potential Relevance of the Boolean Network Model

Because of the extreme simplifications embedded in the Boolean network model, detailed predictions (e.g., genes A and B turn on gene C) are unlikely to be possible. Instead, the utility of this approach as a way of looking at genetic regulation will depend on its ability to make qualitative predictions about large-scale structure and trends. Put differently, can Boolean networks behave in biologically plausible ways?

Under certain circumstances, Boolean networks do exhibit certain regularities. Thus, the operative question is whether these features have reasonable biological interpretations that afford insight into the integrated behavior of the genomic system. Consider the following:

  1. A large fraction of the genes in Boolean networks converge to fixed states of activity, on or off, that contain the same genes on all cell-type attractors. The existence of this “stable core” predicts that most genes will be in the same state of activity on all cell types of an organism. Direct experimental testing of this prediction is possible using DNA chip technology today.
  2. Nearby states in the state space of the system typically lie on trajectories that converge on each other in state space. This might be tested by cloning exogenous promoters upstream of a modest number of randomly chosen genes to transiently activate them, or by using inhibitory RNA to transiently inactivate a gene's RNA products, and following the trajectory of gene activities in unperturbed cells over time and perturbed cells where the gene's activity is transiently altered, using DNA chips to assess whether the states of activity become more similar.
  3. The Boolean model predicts that if randomly chosen genes are transiently reversed in their activity, a downstream avalanche of gene activities will ensue. The size distribution of these avalanches is predicted to be a power law, with many small avalanches and few large ones. There is a rough maximum size avalanche that scales as about three times the square root of the number of genes, hence about 500 for human cells. This is testable, again by cloning upstream controllable promoters to transiently activate random genes, or inhibitory RNA to transiently inactivate random genes, and following the resulting avalanche of changes in gene activities over time using DNA chips.
  4. The Boolean model assumes cell types are attractors. As such, cell-type attractors are stable to about 95 percent of the single gene perturbations—the system returns to the attractor from which it was perturbed. Similarly, it is possible to test whether cell types are stable in the same homeostatic way by perturbing the activity of many choices of single genes, one at a time.
  5. The stable core leaves behind “twinkling islands” of genes that are functionally isolated from one another. These are the subcircuits that determine differentiation, since each island has its own attractors, and the attractors of the network as a whole are unique choices of attractor from each of the twinkling islands in a kind of combinatorial epigenetic code. Current techniques can test for such islands by starting avalanches from different single genes. Two genes in the same island should have overlapping downstream members of the avalanches they set off. Genes in different islands should not. The caveat here is that there may be genes downstream from more than one island, affected by avalanches started in each.

SOURCE: Stuart Kauffman, Santa Fe Institute, personal communication, September 20, 2002.

From: 5, Computational Modeling and Simulation as Enablers for Biological Discovery

Cover of Catalyzing Inquiry at the Interface of Computing and Biology
Catalyzing Inquiry at the Interface of Computing and Biology.
National Research Council (US) Committee on Frontiers at the Interface of Computing and Biology; Wooley JC, Lin HS, editors.
Washington (DC): National Academies Press (US); 2005.
Copyright © 2005, National Academy of Sciences.

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