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Crosstalk and the Cooperation of Collectively Autocatalytic
Reaction Networks
James Decraene, George G. Mitchell, Barry McMullin
Abstract—We examine a potential role of signalling crosstalk
in Artificial Cell Signalling Networks (ACSNs). In this research,
we regard these ACSNs or Artificial Biochemical Networks
(ABNs) as collectively autocatalytic (i.e., closed) reaction net-
works being able to both self-maintain and to carry out a
distinct signal processing function. These signalling crosstalk
phenomena occur naturally when different biochemical net-
works become mixed together where a given molecular species
may contribute simultaneously to multiple ACSNs. It has been
reported in the biological literature, that crosstalk may have
effects that are both constructive (e.g., coordinating cellu-
lar activities, multi-tasking) and destructive (e.g., premature
programmed cell death). In this paper we demonstrate how
crosstalk may enable distinct closed ACSNs to cooperate with
other. From a theoretical point of view, this work may give new
insights for the understanding of crosstalk in natural biochemi-
cal networks. From a practical point view, this investigation may
provide novel applications of crosstalk in engineered ABNs.
I. INTRODUCTION
Cell Signalling Networks (CSNs) are biochemical net-
works occurring in cells which are capable of signal pro-
cessing or cognitive abilities. These abilities coordinate the
cellular activities in response to internal and external stim-
uli. CSNs are responsible for the intricate functioning and
ultimately survival of a cell in its dynamic environment. By
taking the in silico counterparts of real CSNs - Artificial
CSNs (ACSNs) we use an evolutionary simulation platform
to identify new computational paradigms which are directly
inspired by nature [1]. This evolutionary system is built
upon Artificial Chemistries (AC) which have been shown to
provide a suitable framework to model, simulate and analyse
ABNs [2].
As CSNs are contained in cells and are randomly dis-
tributed to offspring cells during cellular division, a mecha-
nism is necessary to ensure the replication of CSNs prior to
the cellular division. This assertion applies to systems where
a genetic subsystem is present, as the latter still requires
a minimal CSNs to coordinate the translation of the ge-
netic code (which may produce further CSN’s components).
Closure is one candidate mechanism which would enable
the CSN’s self-replication or maintenance: A collectively
autocatalytic reaction network (i.e., a closed system) is able
to produce all the catalysts and substrates for its reactions,
thus achieving the self-maintenance of the system.
Based on above assumption, we conjecture that ACSNs are
subsets of collectively autocatalytic reaction networks, see
James Decraene is with the Research Institute for Networks and Com-
munications Engineering, School of Electronic Engineering, Dublin City
University, Dublin (phone: +353 1 700 7697; fax: +353 1 700 5508; email:
james.decraene@eeng.dcu.ie).
Fig. I. Closure in ACSNs is also of interest from a practical
point of view, e.g., engineering ABNs which are autonomous
self-maintaining/repairing cognitive systems.
We may identify ABNs as networks which are made up
of more than one specific ACSNs, each responsible for a
distinct signal processing function (involving an input/output
relationship) see Fig. I. Interactions between different AC-
SNs may occur and this phenomenon is called signalling
crosstalk. This arises very naturally in real CSNs due to the
fact that the molecules from all pathways may share the same
physical reaction space (the cell). Depending on the relative
specificities of the reactions there is then an automatic
potential for any given molecular species to contribute to
signal levels in multiple pathways.
Fig. 1. Cell Signalling Network Xbeing a subset of the closed reaction
network C
In traditional communication and signal processing engi-
neering, crosstalk is regarded as a defect, an unintended or
undesigned interaction between signals, that therefore has the
potential to cause system malfunction. This can also clearly
be the case of crosstalk in CSNs.
However, in the specific case of CSNs, crosstalk also has
additional potential functionalities, which may actually be
constructive:
•Even where an interfering signal is, in effect, adding
uncorrelated noise to a functional signal, this may
sometimes improve overall system behaviour. This is
well known in conventional control systems engineering
in the form of so-called dither. Compare also, [3], [4]
on constructive biological roles of noise.
•The crosstalk mechanism provides a very generic way
of creating a large space of possible modifications or in-
teractions between signalling pathways. Thus, although
many cases of crosstalk may be immediately negative
in their impact, crosstalk may still be a key mechanism
in enabling incremental evolutionary search for more
elaborate or complex cell signalling networks.
Fig. 2. Crosstalk between Cell Signalling Networks Xand Y
In this paper we present another potential constructive role
of crosstalk in ABNs: Signalling crosstalk is a key feature
allowing distinct collectively autocatalytic reaction networks
to cooperate when occurring in the same reaction space.
Our seminal inspirations to this work originate from spe-
cific experiments carried out by Fontana with the Alchemy
system [5]: When mixing two collectively autocatalytic re-
action networks (which were obtained from previous in-
dependent experiments), two outcomes could be observed
according to the level of interaction between the two reaction
networks:
1) If no molecular interactions (i.e., no crosstalk) exist
between the two networks then one would displace the
other network.
2) If, to the contrary, some molecular interactions occur
between the two crosstalking networks then a “meta”
closed reaction network emerges which contains and
maintains both seed closed reaction networks.
We extend this seminal investigation on crosstalk in ABNs
using an Artificial Chemistry (AC) called MCS.bl based
on the Molecular Classifier Systems (MCS) and Holland’s
broadcast language (BL) [6]. A number of key differences
exist between Alchemy and the MCS.bl:
•Alchemy is based on the λ−calculus formalism,
whereas the MCS.bl employs the broadcast language
(a term-rewriting system which was the precursor to
Holland’s Learning Classifier Systems).
•Similarly to Alchemy, molecules may interact and com-
pete with each other. In addition to this first level of
selection we introduced a higher level of selection:
Molecules are contained in multiple reactors (i.e., cells)
which are capable of competing with each other through
a cellular division process.
•We defined mutation operators at both the molecular and
cellular level. No evolutionary operators were specified
in Alchemy.
•We evolved the seed closed reaction networks to carry-
out pre-specified tasks. The meta reaction network hav-
ing to therefore functionally carry out both pre-specified
tasks. In Alchemy, the reaction networks were self-
organized without any target functions.
This paper is organized as follows: We first introduce
the MCS.bl, we then present a first series of experiments
involving non-crosstalking reaction networks. Following this,
we examine a second series of experiments using crosstalking
reaction networks where only cell level mutation applies.
Finally, a third series of experiments is described where we
employ crosstalking reaction networks where both cellular
and molecular mutations occur. We finally outline potential
future work and conclude this paper.
II. THE ARTIFICIAL CHEMISTRY
We first present the MCS metaphor and outline the Hol-
land broadcast language which is employed to specify the
molecular reactions. We then describe the reactor algorithm
which was implemented on a concurrent system (using a
cluster of computers).
A. The Molecular Classifier Systems
Molecular Classifier Systems are a class of string-rewriting
based AC inspired by Learning Classifier Systems (LCS). As
opposed to traditional string-rewriting systems, operations
are stochastic and reflexive (no distinction made between
operands and operators). The behaviour of the condition
(binding) properties and action events (enzymatic functions)
is defined by a language specified within the MCS. This
“chemical” language defines and constrains the complexity of
the chemical reactions that may be modelled and simulated.
In this AC, all reactants are catalytic in the sense that they are
not consumed during reactions. These reactions result from
successful molecular interactions which occur at random.
When a reaction occurs, a product molecule is inserted into
the reactor.
We proposed a simplification of the Holland broadcast
language [1] which is used as the MCS chemical language
resulting in the MCS.bl system. The MCS.bl differs from
the original MCS [7] by introducing more complex chemical
reactions (only replications may occur in the MCS). A
molecule may contain several condition/action rules which
define the binding and enzymatic properties. A reaction
between molecules occurs if at least one conditional part
from any rules in a molecule Amatches a target molecule
B.Ais regarded as an enzyme whereas Bis regarded as
a substrate molecule. When a reaction occurs, the action
part from the satisfied rule in Ais utilized to perform the
enzymatic operations upon the bound substrate molecule B.
This operation results in the production of another offspring
(product). If several rules in Aare satisfied by B, then one
of these rules is picked at random and employed to carry out
the enzymatic function.
A number of differences exist between our simplified
broadcast language (BL) and the LCS, e.g., the LCS’s
alphabet is λ={1,0,#}whereas the BL includes
additional symbols Λ = {1,0,∗,:,♦,△,′,▽}. The
basic elements of the BL are strings made from Λcalled
broadcast devices. A broadcast device is parsed into zero, one
or more broadcast units, where each unit represents a single
condition/action rule. The symbol ∗separates broadcast units
within a broadcast device. The symbol :separates a condition
from an action within a single broadcast unit. 0s and 1s are
basic informational symbols. {♦,▽,△} are single/multiple
character(s) wildcards that may also transpose matched
strings into output strings. Quoted symbols (preceded by ′)
are prevented from interpretation. Fig. 3 depicts an example
broadcast device which may bind and react with a copy of
itself, this reaction is presented in Fig. 4 .
Fig. 3. An example broadcast device
Enzyme substrate product operation
∗▽1 : ▽0 1 : 0 ∅no reaction
∗▽1 : ′∗▽0 : 1 ∗0 : 1 activation
∗′∗0▽: 0▽∗0 : 1 0 : 1 inhibition
∗▽:▽∗00 : 11 ∗00 : 11 universal replication
∗▽0 : ▽0∗▽0 : ▽0∗▽0 : ▽0self-replication
∗▽1 : ▽10 ∗0 : 1 ∗0 : 10 concatenation
∗▽1 : ▽∗0 : 1 ∗0 : cleavage
TABLE I
EXAMPLE OPERATIONS RE ALIZED WITH THE MCS.BL
A detailed description is omitted in this paper, see [8] for
full specification of our BL implementation. Table I presents
a number of example operations that can be realized with
the MCS.bl.
B. Multi-level selectional and concurrent model
We implemented the MCS.bl as a multi-level selectional
model, we introduced multiple reactors where each of them
Fig. 4. Example reaction
contains a population of molecules. These reactors or cells
may be subjected to cellular division, which results in the
replacement of the parent cell and creation of two offspring
cells. However, the number of cells in the universe is fixed.
As a result such a cellular division also triggers the removal
of another cell selected at random. In a similar manner to
molecules, cells are competing with each other which is
regarded as the second level of selection.
Successful reactions do not lead to the removal or degra-
dation of molecules in the reaction space. Thus the number
mof molecules contained in a cell may increase until the cell
is full (i.e., when mis equal to the cell maximum capacity
c). When a cell is full, a division occurs as follows: Half of
the molecules contained in the cell are selected at random,
then these molecules are removed from this cell and are
inserted into the offspring cell. This newly created cell is
then inserted into the cellular population. Finally, a cell is
picked at random (other than the offspring and parent cell)
and removed from the cell population, see Fig. 5.
1) Initialize molecular species, go to 3.
2) If simulation termination criterion is
satisfied go to 8 else go to 3.
3) Collide two molecules selected at random, go
to 4.
4) If the two selected molecules can react with
each other go to 5 else go to 2.
5) Create and insert product molecule into the
cell, go to 6.
6) If the cell contains cmolecules then go to 7
else go to 2.
7) Divide and displace another cell selected at
random, go to 2.
8) End of simulation.
Fig. 5. Multi-level reactor algorithm, each single cell/CPU runs this
algorithm simultaneously.
Furthermore this multi-level model was implemented as
a concurrent system where each cell is run on a single
CPU. In this concurrent model, the fittest cells would not
only be the cells that exhibit a high rate of successful
reactions (when compared to the total number of molecular
collisions), but also cells that contain molecules that are fast
to compute. For example let us consider two cells containing
complete reaction networks (i.e., all molecular collisions lead
to the successful production of molecules). Those cells would
moreover contain molecules having different computational
complexities. In here the cell which possesses a smaller
overall molecular computational complexity will have the se-
lective advantage. This computational complexity introduced
in our model a notion of chemical kinetics and may alter the
cellular growth rate (i.e., the cells fitness).
III. EXPERIMENTS
We present three series of experiments, in which we
explore the effects of signalling crosstalk in systems where
closed reaction networks are employed. We first define the
different reaction networks X, Y and Zwhich are utilized
throughout these series of experiments, see Table II.
X Y Z
A=∗▽00 : ▽01 E=∗▽10 : ▽11 I=∗▽10 : ▽00
B=∗▽00 : ▽00 F=∗▽10 : ▽10 J=▽1∗▽00 : ▽10
C=∗▽0⋄:▽00 G=∗▽1⋄:▽10 K=∗▽10 : ▽10
D=∗▽0⋄:▽01 H=∗▽1⋄:▽11 L=▽1∗▽00 : ▽00
TABLE II
MOLECULAR SPECIES CONTAINED IN ACSNSX,YAND Z
No molecular species from Xmay interact with any
molecular species from Yand vice versa. Xand Yare
non-crosstalking reaction networks. The species A, B, C and
Dfrom Xmay interact with species I, J, K and Lfrom
Z, whereas species Jand Lmay interact with Band C
from X.Xand Zare crosstalking reaction networks. X, Y
and Zwere obtained from previous experiments in which
they were evolved to maximize the production of molecular
species A, E and Irespectively. Fig. 6 depicts the bipartite
reaction network graphs of ACSNs X, Y and Z, note that X
and Ypossess the same network topology. A cell dominated
by a molecular species Ais denoted as CA. The number
of molecules of a given species Acontained in a cell iis
denoted as ni
A. All experiments are run for a pre-defined
amount of time tmax = 3600 (seconds). Finally, no self-
replication reactions are allowed in these experiments (as
was the case in analogous Alchemy experiences).
A. Non-crosstalking networks
In this first series of experiments, we investigate the
dynamics of a system in which the non-crosstalking closed
reaction networks Xand Yare used. 30 concurrent cells
are employed and initialized with 10 molecules from each
species from both Xand Y. A cell idivides if ni
A≥
200 ∧ni
E≥200. As previously presented in Section II-B,
during cellular division half of the molecules in the parent
cell are selected at random and transferred into the offspring
cell. During this stochastic process some molecular species
may not be transmitted to the offspring cells, resulting in a
“mutant” cell containing a different reaction network (which
may not be closed). We refer to this error prone transmission
X/Y
B/F
R1
R2
R4
R7
C/G
R3 R5
R6
R9
A/E
R8
D/H
Z
I
R1
R2
R4
R5
K
R3
J
L
R6
Fig. 6. Bipartite reaction network graphs of ACSNs X/Y and Z. The
topology of molecular interactions of Xand Yare equivalent, e.g., the
reaction R4would involve the molecular species Band Cin X, whereas
R4would involve the molecular species Fand Gin Y.
1⋅101
1⋅102
1⋅103
1⋅104
10 20 30 40 50 60 70 80 0
2
4
6
8
10
Number of molecules
Number of cellular displacements
time (s)
A
E
Cellular displacements
Fig. 7. Growth of molecular species Aand Ein a sample cell c1. The
impulses represent the number of cellular displacements (i.e., the sum of all
events where c1displaced another cell and was itself displaced by another
cell).
as mutation at the cell level. No other mutations (e.g., at the
molecular level) occur in the system at present.
In Fig. 7, we observe an early phase where molecular
species Aand Edominate each other in an alternating
fashion. In each of these alternated domination periods, nc1
A
or nc1
Eis increasing rapidly, typically 7 to 10 times higher
than the molecular amount of the other species. Moreover
this phase is associated with recurrent displacement events
which punctuate each domination phase (showing a level
of activity at the cell population level). At t≈32 a
displacement event occurs, following this we note that nc1
E
is now rapidly increasing, reaching up to 8.103whereas nc1
A
stagnates at 2.102. This cell is now saturated with molecular
species Eand will not grow and divide any further. In
addition we do not observe any further displacements that
may be due to other cells, this suggests that the growth of
the other cells is also null (which could be due to a similar
behaviour where a molecular species saturates the cell).
0
5
10
15
20
25
30
0 20 40 60 80 100
Number of cells
time (s)
CA
CE
Cellular displacements
Saturated cell
Fig. 8. Domination of molecular species Aand Eat the cell level. A cell i
is dominated by Aif ni
A> ni
Eand vice versa. The impulses represent the
total number of cellular displacements occurring in the cellular population.
Fig. 8 provides a cell population view of the simulation in
which we may observe the domination of Aand Eat the cell
level. We first note that the early phase previously shown in
a given cell can be generalized at the cell population level,
i.e., the domination of cell CAand CEswitches rapidly and
is associated with a high overall cellular activity (i.e, the
cellular growth rate which is best captured by the number of
cellular displacements). We also distinguish that the number
of saturated cells increases rapidly when t≈30 which
correlates with previous observations conducted in Fig. 7.
However we note that the number of saturated cells does
not exceed 28 throughout the simulation. A complementary
investigation (not documented here) revealed that the non-
saturated cells contained reaction networks in which no
successful reactions could occur. These reaction networks
resulted from cell level mutation.
Additional experiments were conducted to explore any
potential differing dynamics. The above phenomenon was
found to be exhibited in all of these experiments.
Although based on a different AC, these experiments
shared a key property with experiments conducted in
Alchemy: When two non-crosstalking closed reaction net-
works are mixed together, one displaces the other one.
B. Crosstalking networks
In the remaining sections, cellular species are discrimi-
nated by the specific reaction network contained in a given
cell (and not by the dominant molecular species as in previ-
ous section). We now investigate the effects of crosstalking
closed reaction networks upon the system’s dynamics. In this
experiment, the cells are seeded with molecular species from
the crosstalking reaction networks Xand Z. A cell idivides
if ni
A≥200 ∧ni
I≥200. Any other experimental conditions
are identical to those described in the previous section.
Our results showed that the interactions between molec-
ular species from Xand Yled to the production of new
molecular species M, N , O and P(which may engage in
novel reactions with existing molecular species). This new
cellular species, denoted as C1, contains both networks X
and Y, and presents an increased level of complexity (the
reaction network now contains 12 molecular species and 55
reactions, see Fig. 9). Moreover these C1cells were able
to self-maintain for a sustained period of time. This first
observation also applied in analogous experiments conducted
in Achemy, in which a meta-reaction network emerged and
had the ability to maintain both seed closed reaction networks
throughout the simulation.
However, an additional phenomenon occurred which was
not observed in Fontana’s AC. We distinguished a selective
displacement event between C1and a new cellular species. In
this series of experiments, a level of diversity was maintained
due to cell level mutation, as depicted in Fig. 10. At t≈380
we note the emergence of a new cellular species, denoted as
C2and shown in Fig. 9, which later displaced C1. During
this displacement phase, we note that the cell diversity also
increased suggesting that other cellular species may also have
contributed to the displacement of C1cells.
A
R4
R5 R13
R20
R6
R7
R27
B
R1R12
R19
R2
R3
R8
R26
R45
R48
R52
C
R14R21
R9
R15
R16
R17
R18
R28
R46
R49
R53
D
R22
R23
R24
R25
R29
J
R54
R55
R37
R44
R41
I
K
R36
R47
R10
R30
R34
R35
R50
R40
R42
R43
L
R11 R32R51
O
R31
R38R39
M
R33
N
P
Fig. 9. Reaction network of cellular species C1which contains all
molecular species from ACSNs Xand Zin addition to new molecular
species M, N , O and P.
In Fig. 11 we compare the fitness of reaction networks
C1and C2. The fitness of a given cell iis defined as the
necessary (real) time tito satisfy the condition ni
A≥200 ∧
ni
I≥200. With the present concurrent system, if a cell is
faster to satisfy the condition, then by definition it is a fitter
cell.
We note in Fig. 11 that C2cells produce molecular species
0
5
10
15
20
25
30
200 250 300 350 400 450 500 550 600
Number of cells
Time (s)
Cell type diversity
Cell type 1
Cell type 2
Fig. 10. Cellular species displacement between C1and C2. The cellular
species diversity refers to the number of different (from a qualitative point
of view) reaction networks present at a given time.
0
50
100
150
200
0⋅100 1⋅103 2⋅103 3⋅103 4⋅103 5⋅103 6⋅103 7⋅103 8⋅103
Number of molecules
Time (CPU clock ticks)
C1A
C1I
C2I
C2A
Fig. 11. Comparison of molecular growth of species Aand Iin C1and C2.
The growth of compared molecular species were obtained through solving
the Ordinary Differential Equation systems extracted from SBML models of
C1and C2. We conducted additional experiments to measure tC1and tC2
in CPU clock ticks. These measurements were then employed to rescale the
time course of the different molecular species’ growth.
Aand Iat a faster pace than C1cells (i.e., tC2> tC1).
According to our definition of fitness, C2cells are therefore
fitter than C1cells. We observed a selective displacement
in which C2evolved its qualitative properties and exploited
crosstalk to maximize the production of molecular species A
and I. We may also identify this increase in fitness in Fig. 12,
in which we distinguish a net increase in the overall cellular
growth rate following the displacement event. The “multi-
tasking” C2cells were able to self-maintain throughout the
entire simulation while cell level mutation continued to occur.
Moreover the modifications due to cell level mutations
resulted in the removal of specific molecular species from
Xand Zin C2. The evolved cellular species C2was no
longer maintaining the seed reaction networks Xand Z. As
we cannot identify Xand Zin C2, a natural open-question
follows: does C2still contain crosstalking ACSNs? Such
0
5
10
15
20
25
30
35
0 500 1000 1500 2000 2500 3000 3500
Number of cellular displacements/cellular species
Time (s)
Cellular displacements
Cellular species diversity
Fig. 12. Dynamics of cellular growth rate and diversity. The cellular
growth rate is represented by the total number of displacements (where
cells displaced other cells). A spline function was employed to approximate
the cellular displacement and cellular species diversity curves.
a question could be addressed if we employ an adequate
formalism and identify distinct ACSNs as subsystems in C2.
This issue is nevertheless beyond the scope of this paper but
the reader may find further details in [9], where an abstract
cell model is proposed to investigate such issues.
N
R1
R2
R3
R6
R9
R14
R19
C
R4
R7
R10
R11
R12
R13
R16
R21
I
R5
R8
R17
R23 R25R26
R27
A
R15
R20
D
R18R22
M
R24 R28R29
R30
O
R31
P
R32
K
Fig. 13. Reaction network present in cellular species C2in which molecular
species B, J and Lfrom ACSNs C1are absent.
C. Crosstalking networks and molecular mutation
We finally examine the effects of molecular mutation in
systems where the crosstalking reaction networks Xand
Zare used. Molecular mutations are defined and occur as
follows:
•When a new molecule is produced, a mutation with
probability psym = 0.00005 may be applied to each
of its symbols. Therefore, the longer the molecule, the
higher the probability of mutation occurring.
•Three types of mutation are distinguished and are ap-
plied with equal probabilities:
–Symbol flipping: The current symbol is replaced
with a symbol picked uniformly at random from
Λ.
–Symbol insertion: A symbol is picked uniformly
at random from Λand inserted after the current
symbol.
–Symbol deletion: The current symbol is removed.
Complementary experimental parameters are identical to
those presented in Section III-B. Using above conditions,
we conducted an experiment in which we identified the
following distinctive behaviour.
We first note in Fig. 14 that the variance of cell level
activity shares some similarities with the cellular growth rate
exhibited in the previous experiment (depicted in Fig. 12).
Indeed we observe a common early phase where the cellular
activity is approximately equal to 16 cellular displacements
per second, then at t≈250 the cellular growth rate starts
to increase. This common behaviour is due to the presence
of C1(i.e., the meta-reaction network containing both seed
reaction networks Xand Z) which was also able to self-
maintain for a period of time. Then this phase was followed
by the emergence of mutant cells which increased the level
of cellular growth rate. However due to molecular muta-
tions occurring, a significant difference exists in the cellular
species diversity. Here a high level of diversity is exhibited
(i.e., averaging at 20.3061 different cellular species compared
to 1.1991 in the previous experiment) and is maintained
throughout the evolutionary simulation.
0
5
10
15
20
25
30
35
0 500 1000 1500 2000 2500 3000 3500
Number of cellular displacements/cellular species
Time (s)
Cellular displacements
Cellular species diversity
Fig. 14. Dynamics of cellular growth rate and diversity when molecular
mutations occur. A spline function was employed to approximate the cellular
displacement and cellular species diversity curves
A cellular species displacement is defined as follows: Such
a displacement occurs when cells from a specific cellular
species continuously dominate the cellular population for
at least 50 seconds. In Fig. 15, we note that 52 cellular
species displacements occurred (compared to the unique
displacement observed in Fig. 10). In addition, it can be
observed that the cells’ domination rarely exceeded half of
the population.
30
25
20
15
10
5
1 0 500 1000 1500 2000 2500 3000 3500
Number of cells
Time (s)
Cellular species displacement events
Dominant cellular species
Fig. 15. Dynamics of dominant cellular species. A spline function was
employed to approximate the cellular species curve. The vertical lines
identify the cellular species displacement events. Only displacements which
led to the domination of a given cellular species for at least 50 seconds are
shown.
We compare the fitness of the final dominant cellular
species, denoted as C3see Fig. 16, resulting from this
evolutionary simulation. The cellular species C3shared an
equivalent level of complexity (containing 13 molecular
species and 66 reactions) with C1cells.
0
50
100
150
200
0⋅100 1⋅103 2⋅103 3⋅103 4⋅103 5⋅103 6⋅103 7⋅103 8⋅103
Number of molecules
Time (CPU clock ticks)
C1A
C1I
C2I
C2A
C3A
C3I
Fig. 16. Comparison of molecular growth of species Aand Iin C1, C2
and C3.
Since t2< t3< t1and the above definition of fitness, it
may be argued that the cellular species C3is fitter than C1
and less fit than C2. Our definition of fitness may thus not
be applicable here (otherwise we would expect the cellular
species C2to be the dominant species and not C3). In typical
evolutionary simulations it is usually expected to observe an
incremental improvement in the species’ fitness. However an
additional investigation of the different successive dominant
cellular species revealed that this incremental evolutionary
improvement (according to our definition of fitness) did not
occur.
When comparing the overall cellular growth rate depicted
in Fig. 12 and Fig. 16, we identify a roughly equivalent
level of cellular growth rate (≈22 cellular displacements per
second). This would thus indicate that although C2are fitter
(producing molecular species Aand Imore rapidly) than C3,
the latter (or potentially the cell population as a whole) may
have developed other features which maintained a similar
cellular growth rate.
At present we have not fully understood the details of this
particular evolutionary dynamic, nevertheless we formulate
a number of potential explanations:
•Our simplistic view of fitness may not be appropriate in
the current experiment. As molecular mutation is now
occurring, the cellular species or the cellular population
as a whole may have developed new features to cope
with negative mutation effects. These features may have
enabled the cellular population to maintain a competi-
tive overall cellular growth rate while mutations occur.
Such features improving the cellular growth rate should
then be accounted for in the cellular species’ fitness.
•Our classification of cellular species may not expose the
dominant cellular species properly. A different classifi-
cation scheme may be defined which would be based
on some key properties of the cell’s reaction network
(and not only on the species being present in the cell).
•The chaotic nature of the dominant cellular species
dynamics (see Fig. 15) may also suggest that the ob-
served displacements might not only be due to selection.
This chaotic behaviour may have resulted from the
relatively small cellular population size employed here.
This parameter may have increased the sensibility of the
cellular population to statistical fluctuations.
This experiment presented a range of interesting and unex-
pected issues which resulted directly from the key differences
existing between Alchemy and the MCS.bl system. Further
analytical work using adequate tools such as Organization
Theory [10] may clarify these complex issues.
IV. CONCLUSION
We introduced our work which hypothesises that CSNs are
subsest of closed reaction networks being able to both self-
maintain and to carry out a distinct signal processing func-
tion. The nature and potential roles of signalling crosstalk
were presented in real CSNs and engineered communication
systems. Inspired by specific experiments related to crosstalk
conducted with Alchemy by Fontana, we investigated a
potential constructive role of crosstalk: To allow distinct
closed reaction networks to cooperate with each other when
occurring in the same reaction space. We indicated the
similarities and key differences between the Alchemy system
and our MCS.bl, which we briefly introduced. Three series
of experiments were then detailed:
1) Two non-crosstalking closed reaction networks were
employed. Although significant differences exist be-
tween the MCS.bl and Alchemy, we essentially iden-
tified a similar behaviour: one reaction network would
displace the other.
2) Two crosstalking closed reaction networks were uti-
lized. We first noted a phenomenon (which also oc-
curred in the corresponding Alchemy experiments), in
which a meta-reaction network emerged and contained
both seed closed-reaction networks. This new cellular
species was able to self-maintain for a sustained period
of time. However a second phenomenon occurred
(which was not observed in Alchemy), in which a se-
lective displacement took place. A mutant cell emerged
and displaced the meta-reaction network. This mutant
cellular species was no longer maintaining the seed
reaction networks but was in fact fitter at performing
the pre-specified tasks.
3) Two crosstalking closed reaction networks were used
and molecular mutations were applied. Multiple suc-
cessive cellular species displacements were observed
and presented evolutionary dynamics which are not
fully understood yet. The role of crosstalk in this
particular evolutionary process remains unclear.
These experiments demonstrated the constructive role of
signalling crosstalk in enabling cooperation to occur between
closed reaction networks. The evolutionary process was also
able to optimize the reaction networks (which exhibited a
higher complexity) and their crosstalk properties to carry out
the pre-defined multi-task function. However future analyti-
cal work remains necessary as the final series of experiments
presented intriguing evolutionary dynamics.
ACKNOWLEDGEMENT
Funding and distributed computing facilities were provided
by the EU FP6 ESIGNET project (Evolving Cell Signaling
Networks in Silico).
REFERENCES
[1] J. Decraene, G. G. Mitchell, and B. McMullin, “Evolving artificial
cell signaling networks: Perspectives and methods.” in Advances in
Biologically Inspired Information Systems. Springer, 2007, vol. 69,
pp. 165–184.
[2] P. Dittrich, J. Ziegler, and W. Banzhaf, “Artificial Chemistries-A
Review,” Artificial Life, vol. 7, no. 3, pp. 225–275, 2001.
[3] A. M. Arias and P. Hayward, “Filtering transcriptional noise
during development: concepts and mechanisms,” Nature Reviews
Genetics, vol. 7, no. 1, pp. 34–44. [Online]. Available:
http://dx.doi.org/10.1038/nrg1750
[4] D. Volfson, J. Marciniak, W. J. Blake, N. Ostroff, L. S. Tsimring,
and J. Hasty, “Origins of extrinsic variability in eukaryotic
gene expression,” Nature, December 2005. [Online]. Available:
http://dx.doi.org/10.1038/nature04281
[5] W. Fontana and L. Buss, “The arrival of the fittest: Toward a theory
of biological organization,” Bulletin of Mathematical Biology, vol. 56,
no. 1, pp. 1–64, 1994.
[6] J. Holland, Adaptation in natural and artificial systems. MIT Press
Cambridge, MA, USA, 1992.
[7] B. McMullin, C. Kelly, and D. O’Brien, “Multi-level selectional
stalemate in a simple artificial chemistry.” in Proceedings of ECAL
2007, ser. LNCS. Springer.
[8] J.Decraene, “The Holland Broadcast Language,” RINCE, Dublin
City University, Tech. Rep. ALL-06-01, 2006. [Online]. Available:
http://elm.eeng.dcu.ie/˜alife/jd/ALL-06-01/
[9] O. Wolkenhauer and J. Hofmeyr, “An abstract cell model that describes
the self-organization of cell function in living systems,” Journal of
Theoretical Biology, vol. 246, no. 3, pp. 461–476, 2007.
[10] P. Dittrich and P. Speroni, “Chemical Organisation Theory,” Bulletin
of Mathematical Biology, vol. 69, no. 4, pp. 1199–1231, 2007.
