Location: Fields Institute , 222 College Street, Toronto

October 31, 2008- 3:30 p.m.
Stuart Kauffman
Institute for Biocomplexity and Informatics,
University of Calgary

Are Cells Dynamically Critical? (audio and slides)
The genetic regulatory network in prokaryotic and eukaryotic cells is a complex non-linear dynamical system. I will discuss mathematical models of such
networks based on Random Boolean Networks, RBN, and differential equation and chemical master equation cousins. Work on RBN has demonstrated that they
behave in two regimes, ordered and chaotic, separated by a critical phase
transition, dubbed "The edge of chaos". For RBN it has been demonstrated that
they maximize the capacity to store information, maximize pairwise mutual
information among variables, maximize power availability and minimize entropy
production based on Landauer's erasure principle, evolve readily, and appear
most able to bind the highest diversity of past discriminations with reliable
future actions in the face of noise. Current work is exploring whether these
networks also can communicate with one another optimally. Thus, study of RBN
is opening a doorway to the cell as an information processing but open
thermodynamic system. Recent work suggests that in fact cells are likely to be
dynamically critical. If so, it may be that selection has optimized genetic
regulatory networks for this property.
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We have entered the era of Systems Biology, in which a dominant question is the integrated behavior of the 23,000 human genes and their products in normal development and in disease. Since Jacob and Monod, it has been known that the protein product of one gene can “turn on” or “turn off” another gene by binding to a nearby “cis acting” regulatory site. Thus the 23,000 genes and their RNA and protein products form some complex nonlinear dynamical system. This system can be studied both experimentally and with a variety of mathematical approaches, ranging from chemical master equations and the use of the Monte Carlo Gillespie algorithm, to stochastic ordinary differential equations, to deterministic differential equations, to discrete state and time models. Among these, the simplest idealized the activity of a gene as a binary device, and its product as present or absent, hence a Boolean variable.
We do not know the detailed structure or logic of the genetic network in any cell or organism. Random Boolean Networks, RBN, are a class, or ensemble, of disordered causal networks in which diverse ensembles of networks are studied in a kind of ensemble statistical mechanics that seeks the generic behavior of typical members of an ensemble, as specified by parameters such as connectivity. A random Boolean net is constructed by defining an input and perhaps an output distribution among the genes, possible biases on the Boolean functions assigned to genes, then constructing networks by randomly assigning inputs to each gene from among all or a subset of (regulating) genes, and a Boolean function to each regulated gene. In the simplest case, time comes in discrete moments and all genes update their activities simultaneously.
Such networks behave in two broad regimes, ordered and chaotic, separated by a crisp “critical” phase transition. The ordered regime is itself astonishing: even randomly assembled networks exhibit highly ordered behavior, belying our earlier intuitions of the requirements for dynamical order, and hinting that self organization may be as important as selection in evolution. Attractors of such networks are models of cell types.
Recent evidence begins to suggest that cells are critical.. If so, it hints a “law”, the marriage of self organization and selection may afford and achieve criticality because of its powerful selective advantages.
I will describe the ordered, chaotic, and critical behavior of RBN, the variety of reasons for thinking that criticality is selectively strongly advantageous, including information storage and propagation, reliable binding of past discriminations to future reliable action, and most importantly, the growing evidence that cells are critical.
But a cell is also an open thermodyamic system displaced from equilibrium. Cells do work cycles. Maximization of energy efficiency in work cycles occurs if the cycle is performed infinitely slowly – a poor way to win the Darwinian race. Evolution may, instead, have selected for maximum power efficiency per unit fuel. Maximum power efficiency occurs at a finite displacement from equilibrium, far from the Onsager or Prigogine domains. Using Landauer erasure as a principled measure of entropy production in RBN, we have recently shown that critical RBN maximize power efficiency and minimize entropy production. Thus, very early steps are underway to create a needed field of far from equilibrium thermodynamics for life linking information and energy flow in open systems. More is needed, however. Work is the constrained release of energy into a few degrees of freedom, but it takes work to construct those very constraints; and cells do work to construct free energy gradients that store energy and release it in constrained ways to do work. We need a broad new theory.