Epigenetic Regulation of the Mammalian Cell
Keith Baverstock
1
*, Mauno Ro¨ nkko¨
2
*
1 Department of Environmental Science, University of Kuopio, Kuopio, Finland, 2 Department of Computer Science, University of Kuopio, Kuopio, Finland
Abstract
Background: Understanding how mammalian cells are regulated epigenetically to express phenotype is a priority. The
cellular phenotypic transition, induced by ionising radiation, from a normal cell to the genomic instability phenotype, where
the ability to replicate the genotype accurately is compromised, illustrates important features of epigenetic regulation.
Based on this phenomenon and earlier work we propose a model to describe the mammalian cell as a self assembled open
system operating in an environment that includes its genotype, neighbouring cells and beyond. Phenotype is represented
by high dimensional attractors, evolutionarily conditioned for stability and robustness and contingent on rules of
engagement between gene products encoded in the genetic network.
Methodology/Findings: We describe how this system functions and note the indeterminacy and fluidity of its internal
workings which place it in the logical reasoning framework of predicative logic. We find that the hypothesis is supported by
evidence from cell and molecular biology.
Conclusions: Epigenetic regulation and memory are fundamentally physical, as opposed to chemical, processes and the
transition to genomic instability is an important feature of mammalian cells with probable fundamental relevance to
speciation and carcinogenesis. A source of evolutionarily selectable variation, in terms of the rules of engagement between
gene products, is seen as more likely to have greater prominence than genetic variation in an evolutionary context. As this
epigenetic variation is based on attractor states phenotypic changes are not gradual; a phenotypic transition can involve
the changed contribution of several gene products in a single step.
Citation: Baverstock K, Ro¨nkko¨ M (2008) Epigenetic Regulation of the Mammalian Cell. PLoS ONE 3(6): e2290. doi:10.1371/journal.pone.0002290
Editor: Axel Imhof, University of Munich and Center of Integrated Protein Science, Germany
Received September 30, 2007; Accepted April 22, 2008; Published June 4, 2008
Copyright:
2008 Baverstock, Ro¨nkko¨. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors have no support or funding to report.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: keith.baverstock@uku.fi (KB); mauno.ronkko@uku.fi (MR)
Introduction
Today one of the most pressing issues in biology is to
understand how the epigenetic aspects of the cell are regulated,
that is, how the appropriate gene products are brought into action
when and only when appropriate. Writing in 1958 Nanney [1]
poses, under the heading ‘‘Epigenetic Control’’, the question of
whether it is a ‘‘template replicating mechanism’’, i.e. DNA
replication, or ‘‘some other’’ unspecified mechanism, which
manifests phenotype at the cellular level. In essence Nanney was
questioning whether all the then known empirical evidence about
biological function, which he reviews, regarding the stability of
phenotype could be accounted for as a result of ‘‘genetic
regulation’’, or whether there was a need to invoke ‘‘epigenetic
regulation’’ in addition. He concludes by nominating two separate
mechanisms by which ‘‘homeostasis’’ could be achieved, namely a
replicating template mechanism or another, ‘‘perhaps self-regulating
metabolic patterns’’ as suggested by Delbru¨ck at a Congress on
Genetics in 1949. In the discussion following a paper that had
attributed a specific phenomenon to the reproduction of genes
that were favoured or inhibited by environmental conditions
Delbru¨ck noted that ‘‘many systems in flux equilibrium are capable
of several different equilibria under identical conditions. They can pass from
one state to another under the influence of transient perturbations.’’ [2]
Today we would refer to ‘‘flux equilibrium’’ as a dynamic steady
state.
In the event biology has invested heavily in the ‘‘template
replicating mechanism’’ to the almost complete exclusion of any
alternative. Prior to 1953 the concept of a gene was much more
fluid than it is today being based primarily on empirical evidence
of how it could be inherited and mutated. However, it can be
argued that the case made by Schro¨dinger in 1943 [3], on
quantum mechanical grounds, that the property ‘‘life’’ could not
be based on statistical averaging, as is for example, temperature,
and must therefore (because at that time there was no obvious
alternative) be based on a mechanism (he used the analogy of a
clock based on an aperiodic crystal) was highly influential in the
subsequent development of cell and molecular biology. The
extraordinary elegance of DNA as a semi-conservative replicating
mechanism seems to have sealed the fate of the subject up to at
least 2000.
Phenomena such as imprinting and the fact that a single
genotype gives rise to more than 200 cellular phenotypes, could
not, however, be explained without resort to some kind of ‘‘extra
genetic’’ or epigenetic phenomenon. Indeed, assuming that all the
information necessary to regulate the deployment of the code is
encoded in the genotype leads to an infinite regression. Today
there is a high degree of consensus that imprinting and other
aspects epigenetic regulation are controlled by chemical marking,
methylation and acetelylation, of DNA and the histones in
chromatin [4,5] and that these marks also constitute the epigenetic
memory [6]. These it is generally assumed serve in a complex
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manner and in conjunction with sequences in the genome
associated with coding regions, to regulate the transcription
process. The study of the role of these ‘‘epigenetic marks’’ is now a
major activity in cell and molecular biology [7].
In parallel and in recognition of the fact that separating the
genome into fragments for detailed study followed by re-synthesis
has limits as a strategy for understanding biology, approaches
under the heading of ‘‘systems biology’’ have burgeoned.
However, as is made clear by O’Malley and Dupre´ [8] it is far
from clear what exactly the term ‘‘systems biology’’ means. They
define two main approaches, namely pragmatic (labelled type 1)
and theoretic (type 2). The majority of systems biologists are of
type 1 and ‘‘for them ‘‘system’’ is a convenient but vague term that covers a
range of detailed interactions with specifiable functions.’’ [8]. Type 2
systems biologists see a fundamental aspect to the term ‘‘system’’
along the lines of that advanced by Bertalanffy [9] as general
systems theory. The essence of this approach is that the system is
thermodynamically open and that the high level properties of a
system, such as phenotype, emerge from the global interactions of its
component parts to give a result that is greater than the sum of
those parts. This leads Huang [10] to distinguish between types 1
and 2 by the terms ‘‘localist’’ and ‘‘globalist’’.
Recently uncovered features of the cell would argue strongly for
the globalist perspective as the more likely to be relevant to
understanding biology. For example, detailed study of chromatin
in the nucleus of eukaryotic cells has revealed substantial order in
respect of both the location of gene coding sequences and of
discrete chromosome territories within the ‘‘nuclear architecture’’
that are associated with gene regulation [11–15]; indeed, Fraser
and Bickmore [15] conclude that ‘‘the genome’s spatial organisation is a
key contributor to function.’’ In a comparison of the differentiation of
haemopoietic cells to neutrophils and erythroid cells it was found
that co-regulated gene sequences were clustered in chromosomes
and spatially proximal in the nucleus [16]. These results suggest
that epigenetic regulation is indeed a global genomic phenomenon
involving both spatial and conformational transitions in chromatin
among other features.
Here we propose a hypothesis/model based on recognised
features of the cell to describe the epigenetic regulation of the
mammalian cell as a system somewhat similar to the concept
Delbru¨ck advanced in 1949 [2], namely based on dynamic steady
states and thermodynamically open. We strive for realism in our
assumptions recognising that the complexity of the model may
make it computationally relatively intractable. However, we
believe that the qualitative understanding of the way the cell
operates would provide the most relaible basis for simplifying the
model. We examine the evidence that supports the model and
discuss its implications for understanding the processes that
regulate cells.
We start with the phenomenon of genomic instability as induced
by ionising radiation [17]. Previously we have drawn attention to
the implications of the chemically friable nature of DNA under
physiological conditions [18] and subsequently described genomic
instability as a stochastic epigenetic phenotypic transition between
attractors, essentially specific patterns of gene products active in
the cell, representing phenotype [19]. Subsequently, Huang et al
[20] have identified, experimentally, such attractors as represen-
tatives of phenotype in the chemically induced differentiation of
neutrophil precursors to the terminally differentiated state.
Essentially, the chemical perturbation of the precursor attractor
stimulates the transition to other attractors [21] and ultimately the
terminally differentiated state.
Attractors are components of a state space with a dimension for
each of the gene products coded for by the genotype, i.e., more
than 100,000 in the human. A typical attractor might involve
between 1000 and 10,000 active gene products. The attractors
within the system are defined by rules of engagement between
gene products and envisaged to be essentially point attractors, as
opposed to limit cycle attractors, but they should be seen as
elements of a limit cycle representing the cell cycle.
In the case of radiation induced genomic instability the physical
properties of energy deposition by ionising radiation and the low
doses required to initiate genomic instability indicate that the
transition to instability is not a genetic effect and must therefore be
epigenetic in character [22,23]. It has been proposed [19] that the
normally stable phenotype of a cell is represented by an
evolutionarily conditioned or ‘‘home’’ attractor, that is, one that
has been evolutionarily selected most importantly for two
properties, namely robustness, or resistance to perturbation and
fidelity in the replication of the genotype, or stability.
Exposure to ionising radiation, because it causes molecular
damage to the genomic DNA and therefore genotype, which, if
not repaired prior to cell division may compromise the genotype,
thus places increased demands on the on going damage detection
and repair processes in the cell, which are components of the
home attractor. If that stress exceeds a critical value an
irreversible, due to the high dimensionality of the attractor,
transition to a variant and unconditioned attractor is stimulated.
See Figure 1. If the cell can survive and divide at the variant
attractor it will accrue the genotypic damage that characterises the
instability phenotype by virtue of a lower level of fidelity in
replication. The genomic instability phenotype is thus a mutator
phenotype.
Thus, genomic instability can be seen as the loss, at the cellular
level, of the ability to replicate the genotype with the optimal level
of integrity that was gained substantially through evolutionary
conditioning subsequent to the origin of the species to which that
Figure 1. Illustration of responses of the system to genotypic
damage. Panel A: A relatively small exposure to ionising radiation
creates damage in the genomic DNA (red trace) which is detected and
repaired by the cell. The prevailing home attractor, H, is perturbed but
not irreversibly so, i.e. the basin of attraction is not exceeded and the
system stays in the H attractor. Panel B: A larger exposure to ionising
radiation but still within the capacity of the cell to repair causes the cell
to exceed the basin of attraction of the home attractor, H, and
stimulates the irreversible transition to the variant attractor V
1
.
doi:10.1371/journal.pone.0002290.g001
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cell belongs. In effect evolutionary conditioning minimises the
residual damage in the dynamic steady state between DNA
degradation and repair; the conditioning is thus a purely
epigenetic evolutionary selection process.
It is the openness of the cell to its environment that is at the root
of the instability phenomenon. Exposure to radiation, an extrinsic
agent, causes the cell to respond to detect and repair the damage
to the genotype. The consequent increased demand for the gene
products responsible for detection and repair of the damage
represents a perturbation of the attractor, which if sufficiently
severe will exceed the basin of attraction in respect of one or more
gene products and thus the adoption of the variant attractor. (See
Figure 2)
Methods
Statement of hypothesis and definition of terms
Our hypothesis is that the cellular phenotype of a mammalian
cell is represented by a complex high dimensional dynamic
attractor embedded in a state space with a dimension for each
active gene product encoded in the genotype. The state space is
therefore a proteomic state space. The active gene products are
assumed to interact selectively through rules of engagement, which
are non-deterministic to allow for interactions with the environ-
ment, including other cells in the organism (one aspect of the
openness). We further assume that the gene products are
metabolised by the system (a second aspect of openness) and we
assume there exists for each gene product a multi-compartmental
dynamic steady state originating in the transcription of the coding
sequences and terminating in the depletion of the active gene
product, either as a result of it having been incorporated into the
cellular architecture or selectively destroyed after use or being
subject to spontaneous degradation. See Figure 3. This is referred
to as the post-transcriptional dynamic steady state. Prior to use
gene products are stored or present in inactive forms, mRNA,
tRNA, unfolded peptide and inactive protein. Being an open
system driven by attractors there is no continuum of stable states in
the system; stable states are ‘‘quantised’’ at the discrete high
dimensional attractors.
The attractors available for occupation in the state space are an
emergent property of the system determined by the rules of
engagement, which also give rise to an architecture that influences
transitions between attractors. The rules of engagement can be
seen as the edges in a network, the nodes of which are the gene
products and as does the genotype, they exhibit selectable
variation. It is therefore assumed that they have been acted upon
in evolutionary terms to increase the fitness of the architecture,
including the attractor locations in the state space. Attractor
transitions are equivalent to phenotypic transitions and thus
represent biological processes at the cellular level such as
differentiation, carcinogenesis and evolution.
The system: It is important to be clear about the boundary
between the system and its environment. In this case we define the
system as the mammalian cell and all the material therein.
However, we exclude the informational content (base sequence) of
the genomic DNA but not the substance. Thus, the system is open
in the sense that coding information derives along with other non-
system ‘‘information’’ from the environment, including the
neighbouring cells in the tissue and organism as well as, where
appropriate, cohabiting organisms [24] such as bacterial flora, and
the environment beyond, for example, ionising radiation and
chemicals.
Gene products: these are the proteins and certain of the RNA
species, specifically the microRNAs, manufactured in the cell and
which either are incorporated into the cellular structure or used by
the system. We are interested in the behaviour of these gene
products with time. We denote time by t. Consider a specific gene
product, gp. Then, the activity m of the gene product at any given
time is captured as a function of time, m
gp
(t).
Attractor: Attractors are an emergent property of the system,
which occupy a ‘‘point’’ or ‘‘volume’’ of the state space and are
surrounded by a basin of attraction from which states drain into
the attractor. It thus represents a domain of stability, albeit, limited
by the boundary of the basin of attraction. Each gene product gp
is governed by an attractor a
gp
. The attractor determines a value
range, a lower and an upper bound for the activity of the gene
product. We denote the range of the attractor by [low
gp
,up
gp
].
In particular, if the activity of the gene product is within the
attractor range, it remains there. In other words, if low
gp
#
m
gp
(t1)#up
gp
holds for some t1, then also the condition
low
gp
#m
gp
(t2)#up
gp
holds for any t1,t2. Each attractor a
gp
determines a basin b
gp
. The basin of the attractor is a value range,
indicating the minimum and maximum bounds for the activity of
the gene product, such that if the activity of the gene product is
within the range, it will eventually reach a value within the
attractor range. We denote the range of the basin by [min
gp
,
max
gp
]. Thus, formally, if min
gp
#m
gp
(t1)#max
gp
holds for
some t1, then there exists also t2 such that t1,t2 and
low
gp
#m
gp
(t2)#up
gp
holds. In addition to the attractors and
their basins of attraction, there exist volumes of state space
through which the system transits during transitions and which
exert some influence over the direction of migration.
Dynamic steady state: a condition in which two or more
opposing processes are balanced to produce a stable state. Two
categories are of particular interest, namely the DNA degradation
under physiological conditions (due to, for example, hydrolysis)
opposed to the repair of that degradation by cellular repair
processes, and the metabolic process generating gene products,
commencing with their transcription opposed to their depletion
through use, the post-translational steady state. (See Figure 3)
Figure 2. Illustration of a state space. The figure illustrates a very
simplified state space for a two dimension system, the coordinates
indicating the activities of gene products x and y. The potential
attractors are represented by circles, the diameters of which are
proportional to their basins of attraction, the home attractor H being
the largest because of environmental conditioning. A perturbation P of
H beyond the basin of attraction due to an increase in gene product y
causes the adoption of variant attractor V
1
. This is the initiation step of
genomic instability. Subsequently, due to the relatively reduced
robustness of variant, i.e., unconditioned, attractors, further transitions
(dotted lines) to other variant attractors characterises the genomic
instability phenotype.
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Rule of engagement: The rules of engagement speak of the
active gene products in time. Consider, for instance gene products
gp
a
and gp
b
. Then a rule is of the generic form ‘‘IF gp
a
is active
THEN gp
b
is active’’, stating that the activity of gp
a
implies the
activity of gp
b
. Formally, the activity of a gene product is
expressed with respect to some activity ranges, r
gpa
and r
gpb
,at
points t1 and t2 in time. Then, a rule of engagement is a relation:
m
gpa
(t1)Mr
gpa
)m
gpb
(t2)Mr
gpb
. For a gene product there are
typically many rules of engagement and, thus, a gene product can
be engaged with several other gene products. Consequently, a
perturbation of any one gene product has the potential to perturb
all those with which it is engaged.
Stability: within this context stability refers to the ability of the
genome to replicate its genotype with maximum fidelity. DNA is
an unstable compound under physiological conditions and thus is
subject to ongoing repair. Degradation and repair are opposing
processes which create a dynamic steady state of minimal residual
damage in the system at any point in time [18,19]. This dynamic
steady state is crucial for the long term stability of the system.
Robustness: the property of the system to resist perturbations of
its stable states and of its transitions between stable states.
Homeostasis: is the property of an open system to regulate its
internal state and maintain a stable condition.
Evolutionary conditioning: an evolutionary process whereby
variations in the rules of engagement are selected particularly if
they improve the integrity of the replication of the genotype, i.e.
enhance stability, and/or expand the basin of attraction of the
attractor, thus enhancing robustness.
Results
Description of the operation of the system
The system comprises two primary components, namely, the
rules of engagement governing the regulation or deployment of the
gene products and the material which is regulated to ‘‘build’’ the
system. Placed in the environment, rather than the system, is the
genotypic information that codes for the gene products. The
reason for this is that the rules of engagement can be regarded as
the formal causal component of the system (the syntax). The
residue, genomic coding sequence and environmental influences,
are then regarded as the semantic component. Separating them in
this way, as does for example Rosen [25,26], allows for a clearer
logical definition [8] and treatment of the system.
Spatial distribution of gene coding sequences in the nucleus
ensures that the gene products that are required by the current
attractor are available to be drawn upon [15,16]. It is assumed that
the gene coding sequences are transcribed stochastically as and
when two conditions are met, namely that the chromatin structure
is appropriate for the transcriptional apparatus to access the
coding sequence and the sequence is activated for transcription.
The transcribed products are stored (usually) in inactive forms in
multi-compartmented dynamic steady states (one for each gene
product) as a component of the routine metabolic activity of the
cell. See Figure 3.
In general, if an attractor a
gp
is perturbed, i.e., the value for
m
gp
(t),min
gp
(t) or m
gp
(t).max
gp
(t) for one or more gene
products, the system will exit the current attractor and adopt a
variant attractor v
gp
.
Two circumstances in which the prevailing attractor can be
perturbed are now considered. One can be regarded as scheduled
within the system and its environment and thus part of its normal
operation and the other unscheduled or stochastic and ‘‘forced’’ from
the environment.
Differentiation is the most common scheduled phenotypic
transition between attractors at the cellular level. It can be initiated
through signalling from its close environment or from within the
system. It can be induced in the laboratory by specific drugs [20].
There are several ways of perturbing the existing state of the
attractor. For example, a change in the level of activity of specific
gene products can be induced by acting on the inactive protein of
a specific gene product precursor to up-regulate the gene product,
or by transfer of active gene product from the cytoplasm to the
nucleus. In effect any perturbation of the activity of a gene
product, m
gp
, up- or down-regulation, that places it outside the
range of activities of the attractor and its basin, m
gp
(t),min
gp
,
or m
gp
(t).max
gp
will lead to a transition.
An example of an unscheduled phenotypic transition is the
induction of genomic instability by ionising radiation. Here it is
envisaged that stress on the post-transcriptional steady states of
gene products dealing with the damage detection and repair of the
Figure 3. Illustration of the multi-compartmental dynamic steady state. The figure illustrates the multi-compartmental dynamic steady state
initiated by the transcription of coding sequences to mRNA, which is translated to peptide and finally yields active gene products which are depleted
(block arrow) through use. There may be additional depletion (not indicated) by spontaneous decay from the product compartments.
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genotype can cause the basin of attraction to be exceeded and the
system to be released from its ‘‘normal’’ or ‘‘home’’ attractor. In
this case the system will migrate to a variant attractor, which
because it has not been occupied before has not been
evolutionarily conditioned. It is thus likely to be less robust, i.e.,
a smaller basin of attraction and less stable, i.e., less proficient at
error free replication of the genotype, than the normal attractor. A
consequence of the loss of robustness will be that the variant
attractor will be more prone to environmental perturbation and
thus prone to migrate to other variant attractors. See Figure 2. For
this reason the instability phenotype is best referred to an incomplete
phenotype. A second consequence will be due to the loss of
stability resulting in a mutator phenotype.
Support for the hypothesis
We briefly review here the evidence that supports the idea that
cellular regulation, both in mammalian cells and their evolution-
ary precursors, micro-organisms, is essentially a physical process
involving transitions between dynamic attractors, which are a
product of self-organisation.
That randomly organised systems can exhibit self-organisation
has been conclusively demonstrated by Kauffmann [27]. Random
Boolean networks, where any node connects through rules of
engagement with two others on average, exhibit state cycle
attractors, that is, as the system is refreshed by applying the rules
sequentially and repeatedly to each node in turn, the system settles
into a relatively short cyclic sequences of states, a state cycle
attractor. Naturally evolved networks, including genetic networks,
tend to be of the scale free rather than random [28] and these also
exhibit robust self organisation [29].
Studies of micro-organisms from which it is assumed that multi-
cellular organisms evolved demonstrate the ability of cells subject
to environmental stress to adapt to previously un-encountered
conditions. Most notably the experiments of Kashiwagi et al [30]
show that a micro-organism with a synthetic bi-stable gene switch
that is able to exploit two nutritional environments but with
mutual inhibition (so that both do not operate simultaneously) can
adopt an adaptive attractor state that is able to exploit the
alternative nutrient if deprived of the prevailing nutrient. In other
words the organism switches from one state to the other according
the availability of nutrient and since the apparatus that enables the
switch is artificial there can be no existing signalling transduction
pathway for it. Bacteria, unlike mammalian cells, continuously
transcribe their gene products directly to the active state and
attractors form spontaneously.
Kashiwagi et al [30] argue that the range of potential
environmental stresses to which cells are exposed must be much
larger than the signal transduction pathways that have evolved to
meet such challenges. Thus, cells must have the ability to select
adaptive attractors in the absence of any evolved process. They
propose that this property is a general consequence of the
stochastic nature of the network dynamics. In the absence of
nutrient cellular activity falls and the stochastic process of
transcription generates transcriptional noise. If as a result an
adaptive attractor is encountered, allowing a higher cellular
activity and thus turnover of mRNA and production of
appropriate gene products, this suppresses the influence of the
noise and the new attractor is established. These observations
illustrate the fundamental nature of dynamic attractors represent-
ing phenotype in cells.
In fission yeast (S. Pombe) a model based on a Boolean network
predicts the known sequence of activities of the gene products
through the cell cycle purely on the basis of the observed
biochemical interactions (rules of engagement) [31]. The model
exhibits a stationary state (attractor) at the G1 stage (cell growth
phase) of the cell cycle. If a single randomly chosen gene product is
perturbed during the cell cycle the system reverts to the G1
attractor in the majority (81%) of the trials. Similarly in another
yeast model, S. cerevisiae, [32] it was shown that for 2048 initial
states of a network with 11 elements there were 7 fixed point
attractors with 86% of final states in the attractor associated with
the G1 stage of the cell cycle.
In single celled organisms transcription of the coding sequence
and regulation are more-or-less synonymous (although fission yeast
is an exception). For multi-celled organisms, cooperating to form a
tissue or organism, a more complex form of regulation is required.
We therefore postulate that before multi-cellular growth could be
established measures had to evolve to regulate the production of
gene products much more closely and reduce the noise at the gene
product level. This we propose is achieved through the
development of post-translational processes, which serve to partly
de-couple regulation from transcription. Transcription is stochastic
but a post transcriptional steady state in which gene products in
inactive forms are stored intervenes between transcription and
regulation. (See Figure 3)
Huang et al [20] have provided the first experimental
demonstration in mammalian cells showing that the drug induced
in vitro differentiation of a neutrophil precursor to the terminally
differentiated state involved the transition between two high
dimensional attractors representing phenotype. Human promy-
elocytic HL60 cells in vitro can be reliably stimulated to
differentiate to stable neutrophils with drugs, for example DMSO.
Serial measurements of gene profiling as a surrogate for the
genomic state during the process induced by two drugs, showed
that the differentiation pathways were dependent on the identity of
the initiating drug. Thus, the concept of a single encoded
differentiation pathway within the system was rejected. When
the differentiation process is reversed by manipulating the drug
concentration hysteresis was observed [21]. This is interpreted by
the authors as indicating the presence in the differentiation process
of attractor states intermediate between the precursor and the
terminally differentiated state. These experiments provide strong
support for the concept of cellular processes being in essence
transitions between attractors representing phenotypic states, the
actual ‘‘route’’ of the transition being dependent on the conditions
initiating the transition rather than an encoded pathway.
The proposal that the well established phenomenon of genomic
instability induced by ionising radiation can be understood in
terms of an epigenetic transition between dynamic attractors
representing phenotype was advanced in 2000 [19]. A prediction
of the proposal is that once destabilised the genome will
‘‘wander’’ in the state space adopting variant attractors,
Figure 2, and thus a destabilised clone will exhibit an increasing
diversity of gene expression with time. A study of the transcription
products of fresh human cells rendered unstable with ionising
radiation and followed over several generations demonstrated the
predicted increase in diversity of gene expression compared to
unirradiated cells [33]. Furthermore, clones expanded from a
single cell (4 irradiated and 4 controls) and cultured for between
22 and 46 days showed that about 43% of the transcripts were
common to the irradiated and unirradiated clones. Using a
variation filter the 4 clones derived from the irradiated cells
showed consistently higher variation than the clones derived from
the unirradiated cells. In a pair wise comparison of irradiated
with irradiated and unirradiated with unirradiated clones, in only
one of the 12 comparisons was the number of changed clones in
the irradiated comparison less than the highest in the unirradiated
comparison [33].
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Thus, there is clear support for the contention that dynamic
attractors represent phenotype in mammalian cells and that this
has been inherited from more primitive organisms. Attractors are
robust to disruptive environmental influences to a degree but
beyond a limit defined by the basin of attraction, which is a
product of evolutionary conditioning, the system can be
irreversibly perturbed adopting the instability phenotype. This
we argue is a fundamentally important property of the epigenetic
regulatory system that in germ cells plays a pivotal role in
evolution and in somatic cells in carcinogenesis.
Discussion
Implications of the hypothesis
We now describe the principal implications entailed by the
hypothesis/model:
N
Epigenetic regulation and epigenetic memory are fundamen-
tally physical processes deriving in part from the intrinsic rules
of engagement between active gene products and in part from
extrinsic influences. At mitosis, and fusion in germ cells, the
attractor is inherited to determine the phenotype of the
offspring.
N
Due to the influences from the environment the rules of
engagement are indeterminate. Further, due to its openness
the system operates far from equilibrium. This results in
indeterminacy in the identities of the gene products. To deal
with this inherent indeterminacy it is proposed that predicate
logic systems, such as Refinement Calculus, are the most
appropriate computational tools.
N
Epigenetic variation exists in the form of attractors that are
dormant (variant attractors) in the system but which can be
occupied if the system is subject to an unscheduled expulsion
from its normal attractor. When such a transition occurs there
is a step change in phenotype, i.e., the change is not gradual.
Epigenetic variation in germ cells could play a role in
speciation. In somatic cells the adoption of a variant attractor
could be the initiation of carcinogenesis.
Each of these implications will be addressed in outline here and
in more detail elsewhere.
Epigenetic regulation and memory
Epigenetic regulation can be seen as a physical process preceded
by the stochastic transcription of the appropriate coding
sequences, dependent on the spatial ordering of the chromatin
and the ‘‘status’’ of those sequences and contingent on the
availability of the gene product precursors contained in multi-
compartment post-translational steady states. Thus, although the
transcriptome reflects the regulatory processes of the cell it is not as
direct a reflection as the active proteome due to the buffering effect
of the post-transcriptional steady states. For example, within a
minute or two of damage being inflicted on the genotype by
ionising radiation H2AX labelling occurs at damage sites,
checkpoints are instigated to delay replication and macroscopically
discernable foci of proteins assemble around the break [34–36] but
it is not until tens of minutes later that the system responds with
transcriptional responses [37].
The epigenetic memory at mitosis involves the inheritance of
the attractor by the offspring cells and thus is again a physical
process. Following meiosis and fusion in germ cells the situation,
specifically for male cells, is more complicated [38–41]. In the final
stages of spermatogenesis the last traces of cytoplasm are expelled
from the sperm thus precluding translation of transcripts to
peptides, i.e. in effect interrupting the post translational processes.
However, in principle the attractor could be sustained by the
previously translated but inactive and stored precursors to gene
products. It would seem reasonable to assume that attractors with
low metabolic activity could thus survive the final stage of
spermiogenesis through to fusion.
There is ample evidence of epigenetic inheritance of genomic
instability along the germ line and the subject has been extensively
reviewed recently [42,43] so it will not be repeated here. It is
important to recognise that the epigenetic inheritance of the GI
phenotype is not Lamarckian in character in so far as it is wholly
without direction; the GI phenotype is a purely stochastic response
to an environmental stimulus.
The current view, namely that epigenetic regulation is based on
chromatin and DNA marking, certainly applies to, for example,
imprinting. However, marking regulates at the transcription stage
and it is evident that other more ‘‘immediate’’ processes are
involved in the second by second regulation of the system. We
therefore conclude that regulation is primarily a physical property
of the attractor of which marking may be a consequence. Much
the same argument applies to the epigenetic memory.
Indeterminacy
We predict that the operation of the system will be characterised
by indeterminacy and thus there are implications for the
computational approaches that appropriately address the system.
As the system is open in respect of mass and energy flux it is far
from equilibrium. Specific protein structures derived from a given
peptide sequence result from the folding of the peptide and the
characteristic structure is usually taken to be that with the lowest
energy, i.e., the equilibrium structure. In the open environment of
the cell such a restriction would not apply and many folded
proteins could result from a single peptide, i.e., coding sequence.
In addition many proteins have indeterminate structures [44,45]
and in some cases can adopt a binding structure under the
influence of the binding site [46].
Thus, any computational approach has to be top-down and able
to accommodate the inherent uncertainties. We suggest that
Refinement Calculus will find an application here. Refinement
Calculus [47] is a lattice-theoretic framework for reasoning. It was
originally introduced as a tool for proving properties about
specifications and computer algorithms, to be able to refine them
into executable computer programs in a provably correct, stepwise
manner. Because of this, Refinement Calculus is particularly suited
for reasoning about open and complex systems, when there is only
partial information available in the presence of non-determinism.
Because of its strong uniform formal foundation, built upon
lattice theory and higher-order logic, Refinement Calculus bridges
the gap between many popular reasoning styles, including agent
based reasoning, contract based reasoning, and use of game
theory. In other words, Refinement Calculus is at its best in
reasoning about the precondition for reaching a certain state,
when the interaction mechanisms are known only to some degree
of certainty. Such a piece of information is crucial, if we wish to
ensure that a set of specifications and claims about the system are
consistent.
When considering a dynamically based system, the rules of
engagement are seen as (partial) specifications in terms of
Refinement Calculus. By measuring some of the attractors and
the attractor ranges, we can then start proving the consistency of
the rules, and infer other potential rules of engagement governing
the system. It should be noted that due to the openness and
complexity of the underlying system, the cell dynamics, there is
very little hope of obtaining an algorithm-like, mechanical
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description of its functionality; rather, the system will most likely
be described as a network of partial specifications, or rules of
engagement, interacting in a non-deterministic manner. Then,
Refinement Calculus provides a valuable tool, fixed-point
reasoning [48], for understanding the potential outcome of those
interactions. In particular, Refinement Calculus excels at finding
out the governing state for some specific state to be reached by the
network of rules of engagement.
However, there are indications that some measure of simplifi-
cation can still result in meaningful models. For example, treating
the fission yeast cell cycle as consisting of some 15 elements (gene
products) operating in a Boolean fashion, i.e., either ‘‘on’’ or ‘‘off’’,
with rules of engagement in terms of either activation or
suppression, Davidich and Bornholdt [31] are able derive a model
that predicts the cell cycle sequence. S. pombe has some 4800 open
reading frames so their model uses only about 0.3% of the
potential dimensions of its state space. In a similar earlier study
[32] on the cell cycle of S. cerevisiae a good model of the cell cycle
was obtained using about 1.3% of the some 800 regulatory
elements known to be deployed in the cell cycle.
Another potentially simplifying feature with respect to compu-
tation might be modularity [49] of the state space. By defining the
cell as the ‘‘system’’ and all outside it as the ‘‘environment’’ we
have recognised the relative independence of the cell as a module
within the organism. Within the cell specific cell lineages consist of
chains of attractors linked by scheduled transitions (but not defined
pathways [20]) and thus it might be assumed that there are
‘‘barriers’’ that essentially isolate these ‘‘lineage domains’’ to some
degree from the rest of the state space, enabling their treatment in
relative isolation of the remainder of the cell.
We conclude that type 2 systems approaches will be productive
but that indeterminacy will frustrate type 1 approaches. Indeed,
even in a very limited and ‘‘idealised’’ network of only four genes,
the ‘‘reverse engineering’’ from data on transcription products to
infer the underlying regulatory network structure is plagued by
indeterminacy [50].
Epigenetic variation
Variant attractors are a source of evolutionarily selectable
variation in addition to genetic variation. The induction of
genomic instability, that is, the adoption of a variant attractor, is
the adoption by the cell of an epigenetic variant. If such a
transition takes place in the germ cells of an established species we
can envisage two consequences relative to the originating cell.
Firstly, the integrity of replication will be relatively impaired and
the variant will exhibit an increased mutation rate. Secondly, the
robustness of the variant attractor is likely to be reduced leading to
a greater propensity to adopt further variant attractors in response
to perturbations.
The first of these is self-evident; genomic instability is
characterised by the accretion of damage to the genotype; it is a
mutator phenotype. The reduced robustness is less obvious. In the
Boolean model of fission yeast [31] the attractor size predicted by
the specific network is compared with that predicted by randomly
connected networks with the same number of inhibiting and
activating links, self-degrading and self-activating links and the
same activation thresholds. The random networks typically had
smaller attractors indicating that the network specific to S. pombe,
i.e., the one that had been subject to evolutionary conditioning,
had been optimised for dynamical robustness. This would imply
that a variant attractor of the fission yeast, where a random change
to a rule of engagement was applied, would likely show reduced
robustness.
An important feature of the adoption of epigenetic variants is
that phenotypic change will not be gradual: the adoption of a
variant attractor could involve a change in the contribution of
several gene products in a single transition. This has implications
for the evolutionary selection of epigenetic variation. Gradualism
is universally accepted as fundamental to Darwinian theory
[51,52]. According to Gould the term is a ‘‘deductive intellectual
consequence of asserting that natural selection acts as the creative mechanism of
evolutionary change’’. It has three meanings in the theory, namely as a
means of distinguishing the theory from other so called theories
such as Lamarckianism, as a means of refuting saltationism, which
it is argued would compete with natural selection as the creative
force behind evolution and finally supporting the view that the
demonstrable micro-evolutionary process (adaptation) that is
central to Darwinism, would over geological timescales produce
the full diversity of life that is observed today and in the fossil
record. The theory of punctuated equilibrium [53] refutes this last
meaning of gradualism, requiring that the process of evolution
occurs in rapid spurts followed by long periods of ‘‘equilibrium’’
where no or very little, change takes place, as the fossil record
indicates.
It should be noted that the non-gradualism we are proposing,
saltationism, does not challenge Darwin’s ‘‘creative force’’ as the
change it produces is subject to natural selection.
Depending on the specific circumstances, that is, relative loss of
stability and robustness, and the extent of phenotypic change, such
transitions to genomic instability in germ cells could co-evolve
genetically and epigenetically, potentially resulting in evolutionary
consequences ranging from minor adaptation to the origin of a
new species. The initial stages in the case of speciation would be
characterised by increased frequency of mutation, which over
several generations would decline as integrity of replication
increased and the new home attractor increased in robustness,
both features that would be subject to selection for fitness.
Out of the two sources of variation it would seem that the
epigenetic variation would make the more important contribution
to a new species or the evolution of a new phenotypic feature, this
by virtue of the non-gradual element inherent in this process.
Consider the similarities in genotypes of mammalian species and
the concurrent diversity in phenotypes. For example, mice have
about the same number of protein coding genes as humans and
over 90% of the mouse and human genomes can be partitioned
into corresponding regions of conserved synteny, that is, the order
of genes has been conserved since the two species diverged from a
common ancestor [54]. More than 99% of the proteins in the
mouse genome are shared with other mammals and 98% with
humans. Similarly the chimpanzee has a genome that differs from
the human genome in only 4% of the bases overall and less than
1% in gene sequences coding for proteins [55].
An overwhelmingly large fraction of the phenotypic differences
between mammalian species relies on the arrangement, including
scale, of a more or less common set of cellular phenotypes. Thus,
in theory one could contemplate identical genotypes for mouse
and man with only the rules of engagement defining the
phenotypic differences.
The notion that non-gradualism underlies speciation has been
discussed since Darwin’s time. For example, as noted by Patrick
Bateson [56], Galton used the analogy of a ‘‘rough stone’’ with
many facets that could, if sufficiently perturbed, make a jerky
transition from resting on one facet to resting on another. This
analogy captures the essence of the present model.
If the transition to genomic instability takes place in a somatic
cell we suggest that the end result may be malignancy.
Carcinogenesis, like genomic instability, is characterised by a
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mutator phenotype [57]. The relative loss of stability and
robustness of the instability phenotype may result in changes in
epigenetic regulation and the acquisition of mutations that a) give
a selective growth advantage by, for example, the loss of a
checkpoint and b) preclude the complete reversal of the process by
modification of the state space due to the loss of or gain of
dimensions (active gene products). Again a co-evolution of genetic
and epigenetic variation may result in the instability phenotype
resolving into a malignant phenotype. That there is an epigenetic
component to carcinogenesis has been long recognised. Early
experiments transplanting malignant cells into blastocysts demon-
strated that the malignant phenotype could be reversed [58,59].
Later, malignant nuclei from mice transplanted into enucleated
eggs were grown into normal embryos [60]. The view of
carcinogenesis advanced here (see also [19]), while recognising
the importance of mutations in achieving the ‘‘hallmarks of
cancer’’ [61], e.g., loss of senescence, anchorage free growth, etc.
sees such mutations as the consequence of an underlying and more
fundamental epigenetic process that leads the system into a specific
domain of the state space associated with malignancy, via a series
of randomly adopted variant attractors, Figure 2. Thus, as is
observed, the malignant phenotype is not well defined either in
terms of the attractor that represents it or in terms of the mutations
that it has acquired, although both may be ‘‘characteristic’’ of the
disease.
Conclusion
In his Spinoza Lectures, the philosopher John Dupre´ [62] says
‘‘scientific modelling is not like building a scale model of a ship …..
rather scientific models are successful to the extent that they
identify the factors, or variables, that really matter’’. Regarding the
cell as a material system driven by external ‘‘forces’’ in terms of the
genotype, signals from neighbouring cells in the same organism
and influences from the wider environment, including in some
cases other organisms, is an attempt to extract those factors.
Necessarily the detail that characterises the internal working of the
cell, which is the subject of mainstream cell and molecular biology,
is ignored. Walter Elsasser in 1981 [63] sought principles,
consistent with quantum mechanics, governing biology, where
replicates at any level, organisms within a species to cells in a
tissue, were characterised by intrinsic variability, and thus at odds
with the concept of ‘‘mechanisms’’. He concluded biology relied
on selection from a vast number of states and that [hereditary]
reproduction rather than being duplication (possibly with errors)
was better represented as ‘‘creativity with constraints’’, a process
‘‘released’’ by genes as operators or predicates. It is our contention
that the evidence that can be garnered from the products of cell
and molecular biology research since 1981 fully support Elsasser’s
prognosis.
Acknowledgments
The authors gratefully acknowledge the comments of an anonymous
referee and insightful and productive discussions over a number of years
with Oleg Belyakov, Bob Cundall, Harold Hillman, Hooshang Nikjoo,
Darius Leszczynski, Mike Thorne, Dillwyn Williams and especially Alwyn
C. Scott who sadly died on 22 January 2007.
Author Contributions
Wrote the paper: KB. Other: Conceived and developed the ideas with the
exception of the relvance of Refinement Calculus to the model/hypothesis
proposed: KB. Contributed the insight that refinement Calculus was an
appropriate modality to deal with the model/hypothesis proposed by the
first author: MR.
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