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.
--------------------

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.

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