schizophrenia.
For some genes, they state, evidence exists that a small
change in the level of DNA methylation, especially in the
lower range in an animal model, can dramatically alter gene
expression. The timing of nutritional insufficiency or other
environmental exposures may also be critical. In particular
low-level maternal care was associated with developmental
dysfunction and altered stress response in the young. Given
how widely stress is implicated in disease onset and relapse,
Foley et al. claim it is difficult to overstate the potential
implications of such findings.
Foley et al. especially note that when epigenetic status or
change in status over time is the outcome, then models for
either threshold-based dichotomies or proportional data will
be required. Threshold models, defined by a given level or
pattern of methylation or a degree of change in methylation
over time, will, in their view, benefit from relevant functional
data to identify meaningful thresholds.
A special contribution of the approach taken here is that
just such threshold behavior leads ‘naturally’ to a language-
like ‘dual information source’ constrained by the necessary
conditions imposed by information theory’s asymptotic limit
theorems, allowing development of statistical models of com-
plicated cognitive phenomena, including but not limited to
cognitive gene expression.
A recent review by Weaver (2009) focuses on the epigenetic
effects of glucocorticoids - stress hormones. In mammals,
Weaver argues, the closeness or degree of positive attach-
ment in parent-infant bonding and parental investment during
early life has long-term consequences on development of inter-
individual differences in cognitive and emotional development
in the offspring. The long-term effects of the early social ex-
perience, he continues, particularly of the mother-offspring in-
teraction, have been widely investigated. The nature of that
interaction influences gene expression and the development
of behavioral responses in the offspring that remain stable
from early development to the later stages of life. Although
enhancing the offspring’s ability to respond according to en-
vironmental clues early in life can have immediate adaptive
value, the cost, Weaver says, is that these adaptations serve as
predictors of ill health in later life. He concludes that mater-
nal influences on the development of neuroendocrine systems
that underlie hypothalamic-pituitary-adrenal (HPA) axis and
behavioral responses to stress mediate the relation between
early environment and health in the adult offspring. In par-
ticular, he argues, exposure of the mother to environmental
adversity alters the nature of mother-offspring interaction,
which, in turn, influences the development of defensive re-
sponses to threat and reproductive strategies in the progeny.
In an updated review of epigenetic epidemiology, Jablonka
(2004) claims it is now clear that the health and general phys-
iology of animals and people can be affected not only by the
interplay of their own genes and conditions of life, but also
by the inherited effects of the interplay of genes and environ-
ment in their ancestors. These ancestral influences on health,
Jablonka finds, depend neither on inheriting particular genes,
nor on the persistence of the ancestral environment.
Significantly, Bossdorf et al. (2008) invoke ‘contexts’ much
like Baars’ model of consciousness (Wallace, 2005), and infer
a need to expand the concept of variation and evolution in
natural populations, taking into account several likely inter-
acting ecologically relevant inheritance systems. Potentially,
this may result in a significant expansion, though by all means
not a negation, of the Modern Evolutionary Synthesis as well
as in more conceptual and empirical integration between ecol-
ogy and evolution.
Recently Scherrer and Jost (2007a, b) have explicitly in-
voked information theory arguments in their extension of the
definition of the gene to include the local epigenetic machin-
ery, that they characterize as the ‘genon’. Their central point
is that coding information is not simply contained in the
coded sequence, but is, in their terms, provided by the genon
that accompanies it on the expression pathway and controls
in which peptide it will end up. In their view the information
that counts is not about the identity of a nucleotide or an
amino acid derived from it, but about the relative frequency
of the transcription and generation of a particular type of
coding sequence that then contributes to the determination
of the types and numbers of functional products derived from
the DNA coding region under consideration.
From our perspective the formal tools for understanding
such phenomena involve asymptotic limit theorems affecting
information sources - active systems that generate informa-
tion - and these are respectively the Rate Distortion Theorem
and its zero error limit, the Shannon-McMillan Theorem.
We begin with a brief reconsideration of the current de-
facto standard systems biology neural network-analog model
of development that we will subsequently generalize.
2 The spinglass model
Following closely Ciliberti et al. (2007), the spinglass model
of development assumes that N transcriptional regulators, are
represented by their expression patterns
S(t) = [S1 (t),..., SN (t)]
at some time t during a developmental or cell-biological pro-
cess and in one cell or domain of an embryo. The transcrip-
tional regulators influence each other’s expression through
cross-regulatory and autoregulatory interactions described by
a matrix w = (wij). For nonzero elements, if wij > 0 the
interaction is activating, if wij < 0 it is repressing. w repre-
sents, in this model, the regulatory genotype of the system,
while the expression state S(t) is the phenotype. These regu-
latory interactions change the expression of the network S(t)
as time progresses according to a difference equation
Si(t + ∆t) = σ[XN wijSj(t)],
j=1
(1)