CLOSURE IN ARTIFICIAL CELL SIGNALLING NETWORKS

Investigating the Emergence of Cognition in Collectively

Autocatalytic Reaction Networks

James Decraene

Artiﬁcial Life Laboratory, Research Institute for Networks and Communications Engineering

Dublin City University, Glasnevin, Dublin, Ireland

Keywords:

Cell Signalling Networks, Closure, Evolutionary Dynamics, Minimal Cognition.

Abstract:

Cell Signalling Networks (CSNs) are complex biochemical networks responsible for the coordination of cellu-

lar activities in response to internal and external stimuli. We hypothesize that CSNs are subsets of collectively

autocatalytic reaction networks. The signal processing or cognitive abilities of CSNs would originate from

the closure properties of these systems. We investigate how Artiﬁcial CSNs, regarded as minimal cognitive

systems, could emerge and evolve under this condition where closure may interact with evolution. To as-

sist this research, we employ a multi-level concurrent Artiﬁcial Chemistry based on the Molecular Classiﬁer

Systems and the Holland broadcast language. A critical issue for the evolvability of such undirected and au-

tonomous evolutionary systems is to identify the conditions that would ensure evolutionary stability. In this

paper we present some key features of our system which permitted stable cooperation to occur between the

different molecular species through evolution. Following this, we present an experiment in which we evolved

a simple closed reaction network to accomplish a pre-speciﬁed task. In this experiment we show that the

signal-processing ability (signal ampliﬁcation) directly resulted from the evolved systems closure properties.

1 INTRODUCTION

Cell Signalling Networks (CSNs) are biochemical

networks of interacting molecules (proteins, ions, sec-

ondary messengers, etc) occurring in living cells.

Through complex molecular interactions (e.g., sig-

nal transduction), CSNs are able to coordinate critical

cellular activities (e.g., cell differentiation, apoptosis)

in response to internal and external stimuli.

In the presence of a genetic subsystem, the pro-

duction of CSN components may result from the

translation of the genetic code. However to coordi-

nate this decoding process, a newborn cell still re-

quires a minimal CSN which would be inherited from

the parent cell during cellular division. In a prebiotic

world, in which genetic material may potentially not

be present, “primitive” CSNs would need an alterna-

tive mechanism to ensure their production and main-

tenance.

We may argue that both of these mini-

mal/primitive CSNs from the post/prebiotic world

may have to replicate themselves prior to the cellular

division. This would allow the replicated CSNs to be

“distributed” to the offspring cells. Errors may occur

during the replication process, e.g., an offspring

cell may inherit only a partial or mutant CSN. Thus

resulting in potentially defective cells which would

lead to a variety of undesired effects (e.g., premature

cell death).

As a result, the “ﬁtness” of a cell is implicitly rep-

resented by the survival and performance of a cell in

achieving self-maintenance and cell-level replication.

Based on the above assumption, we hypothesize that

CSNs may be regarded as subsets of collectively au-

tocatalytic (closed) reaction networks. In these closed

and synergetic reaction networks, self-maintenance is

achieved through the systems ability to produce the

catalysts and substrates for all its reactions. This cat-

alytic closure property originates from the autocat-

alytic set theory, which is one of the current candi-

date theories explaining the origins of life (Kauffman,

1997).

These closed reaction networks would have the

additional ability to replicate themselves as a whole

(during cellular division). Through the evolutionary

process, we suggest that these systems may develop

signal processing abilities which are typical of real

CSNs. However these Artiﬁcial CSNs (ACSNs) must

preserve closure to self-maintain and survive. Thus

the systems signal-processing abilities may originate

107

Decraene J. (2009).

CLOSURE IN ARTIFICIAL CELL SIGNALLING NETWORKS - Investigating the Emergence of Cognition in Collectively Autocatalytic Reaction Networks.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 107-114

DOI: 10.5220/0001545301070114

 SciTePress

from the closure properties where inputs (internal or

external stimuli) are perturbations to the system. The

system outputs would result in a modiﬁcation of the

systems state and of its closure properties.

Following (van Duijn et al., 2006) we regard the

coupling of these ACSNs signal-processing abilities

and closure properties as minimal principles for life

and cognition. By examining the conditions for the

emergence of distinctive ACSNs signal-processing

abilities, we investigate the emergence and origins of

minimal cognition. These ACSNs may thus be re-

garded as Artiﬁcial CognitiveSystems which may po-

tentially provide a range of applications in computing

and engineering. Thus the goals of this research are

twofold and can be summarized as follows:

• From a theoretical point of view: to study the ori-

gins and complexity evolution of cognition in bi-

ological systems.

• From a practical perspective: to provide a new

computational paradigm inspired by nature.

To assist this research we developed the MCS.bl,

a string-based Artiﬁcial Chemistry (AC) based on

the Molecular Classiﬁer Systems (MCS) (McMullin

et al., ) and the Holland broadcast language (Hol-

land, 1992). This technique examines the evolution

of biochemical networks from an undirected, self-

engineered and autonomous perspective. In this ap-

proach no explicit ﬁtness function is deﬁned, the evo-

lutionary process is driven by the capacity of CSNs

to self-maintain and perform the necessary signal-

processing operations or “computation” to achieve

cell-level replication.

A key step of this research is to identity the

conditions which provide evolutionary stability to

the closed reaction networks when simulated in the

MCS.bl. Examining such phenomena relates closely

to other studies which have been conducted on Hol-

land’s Alpha-Universes (Holland, 1976), Tierra (Ray,

1991) and Alchemy (Fontana and Buss, 1994b). In

this paper we ﬁrst describe the MCS.bl. We then

discuss how a multi-level and concurrent model en-

hanced the evolutionary stability of the system. Fi-

nally we present an experiment in which we evolved

a minimal closed ACNS to accomplish a pre-speciﬁed

task (signal ampliﬁcation).

2 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 re-

ﬂexive (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 com-

plexity of the chemical reactions that may be mod-

elled and simulated. In this AC, all reactants are cat-

alytic in the sense that they are not consumed dur-

ing 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 (Decraene et al., 2007) which is

used as the MCS chemical language resulting in the

MCS.bl system. The MCS.bl differs from the original

MCS (McMullin et al., ) by introducing more com-

plex chemical reactions (only replications may occur

in the MCS). A molecule may contain several condi-

tion/action rules which deﬁne the binding and enzy-

matic properties. A reaction between molecules oc-

curs if at least one conditional part from any rules in

a molecule A matches a target molecule B. A is re-

garded as an enzyme whereas B is regarded as a sub-

strate molecule. When a reaction occurs, the action

part from the satisﬁed rule in A is 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 A

are 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 sim-

pliﬁed 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 Λ called 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 broad-

cast units within a broadcast device. The symbol :

separates a condition from an action within a sin-

gle 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. Figure 1 depicts an

example broadcast device which may bind and react

with a copy of itself, this reaction is presented in Fig-

ure 2 .

A detailed description is omitted in this paper, see

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

108

Figure 1: An example broadcast device.

Figure 2: Example reaction.

Table 1: Example operations realized with the MCS.bl.

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 : ▽0 self-replication

∗▽1 : ▽10 ∗0 : 1 ∗0 : 10 concatenation

∗▽1 : ▽ ∗0 : 1 ∗0 : cleavage

(J.Decraene, 2006) for full speciﬁcation of our BL im-

plementation. Table 1 presents a number of example

operations that can be realized with the MCS.bl.

3 EXAMINING EVOLUTIONARY

STABILITY

As this evolutionary system is an undirected ap-

proach, the ﬁrst key step was to obtain catalytic net-

works that are able to self-sustain over time. In order

to achieve such evolutionary robustness, it is neces-

sary for these networks to possess mechanisms which

provide some protection from parasites that may be

formed. In this section we examine the system evolu-

tionary stability ﬁrstly when implemented as a single

level selectional model, secondly when the MCS.bl is

implemented as a multi-level concurrent system.

3.1 Single-level Selectional Model

In a single-level selectional model, all molecules are

contained in a single reactor in which they are com-

peting with each other. This molecular competition is

referred to as the ﬁrst level of selection. Each time a

successful reaction occurs, a product molecule is in-

serted into the reactor, if the latter is saturated then an-

other molecule (selected at random) is removed from

the reactor space (designating the system outﬂow),

see Figure 3.1.

A formal explanation of this outcome is given by

modelling the system with the (approximate, continu-

ous) catalytic network equation (Stadler et al., 1993).

The state of the system is described by the concentra-

tion vector x = (x

, . . . , x

) with x

+ . . . + x

= 1 and

> 0, where x

refers to the concentrationof a molec-

ular species (or collection of “chemically equivalent”

species) s

. The general dynamic behaviour is then

given by:

˙x

∑

i=1

∑

j=1

− x

∑

i, j,l=1

(1)

with k = 1, . . . , n

are the rate constants for each reaction s

→ s

+ s

. In here, these simplify to:



1 if s

+ s

→ s

+ s

0 otherwise

(2)

Previous studies (Decraene et al., 2008) demon-

strated that the spontaneous emergence and self-

maintenance of replicases in the MCS.bl was unlikely

to occur. Consequently experiments were conducted

in which, as in the Tierra system, a hand-designed

molecule called the ancestor was introduced into

the population. This replicase molecule was hand-

designed so as to possess a high binding speciﬁcity,

thus preventing exploitation from other molecules.

This speciﬁcity ensures a rapid dominance over a ran-

domly generated molecular population (which would

not be possible if a universal replicase, having no

binding speciﬁcity, was employed instead; see (De-

craene et al., 2008)). Various molecular mutations

through successful reactions were possible and a con-

straint over the molecular complexity was set due to

computational limitations (experimental details and

mathematical analysis may be found in (Decraene

et al., 2008)). Although this MCS.bl implementation

CLOSURE IN ARTIFICIAL CELL SIGNALLING NETWORKS - Investigating the Emergence of Cognition in

Collectively Autocatalytic Reaction Networks

109

Figure 3: Flowchart of the single-level selectional model.

was to some extent similar to the Tierra system, we

did not observe the emergence of collectively auto-

catalytic networks. Instead we observed a degenerate

outcome characterized by an “elongation catastrophe”

phenomenon:

During evolution, a series of parasitic displace-

ments was observed leading to ever longer molecules.

However, as the mutation effect increases (with the

length of a molecule), disruptive structural changes

may also occur more frequently. We observed

that consequences of these structural changes were

twofold:

• Molecules may become inactive, thus being con-

sidered as substrate or waste molecules. These

waste molecules would then accumulate and pre-

vent any further enzymatic activities. A potential

consequence of the BL syntax is that a mutation

may disrupt dramatically the behaviour of an en-

zymatic molecule. This degenerative effect may

be regarded as the consequence of the BL “brittle-

ness” (asymmetric mutation effects (Ray, 1992)).

• The binding speciﬁcity may be increased. Mu-

tations leading to the insertion of informational

symbols such as 0s and 1s may also increase sig-

niﬁcantly the binding speciﬁcity of molecules. As

a result, although these molecules may still pos-

sess an active site capable of some enzymatic

function, they could not catalyse any molecules

in the reactor.

Both of these phenomena result in a continual de-

crease in the overall reaction rate until reactions cease

completely (i.e., the system decays and ultimately

reaches a state of stasis). These results obtained with

this single-level AC exhibited unexpected evolution-

ary dynamics which resulted in various degenerate

cases: No stable cooperation between the molecular

species could be observed in the evolutionary simula-

tions. Thus this ﬁrst implementation of our evolution-

ary system suffered from a critical lack of “robust-

ness”.

3.2 Multi-level Selectional and

Concurrent Model

In the multi-level selectional model, we introduce

multiple reactors where each of them contains a pop-

ulation of molecules. These reactors or cells may be

subjected to cellular division, which results in the re-

placement of the parent cell and creation of two off-

spring cells. However, the number of cells in the uni-

verse is ﬁxed. As a result such a cellular division also

triggers the removal of another cell selected at ran-

dom. In a similar manner to molecules, cells are com-

peting with each other which is regarded as the second

level of selection.

In contrast to the single level model, successful

reactions do not lead to the removal of a random

molecule in the reaction space. Thus the number m

of molecules contained in a cell may increase until

the cell is full (i.e., when m is equal to the cell max-

imum capacity c). When a cell is full, a division oc-

curs 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

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110

Figure 4: Flowchart of the multi-level and concurrent

model.

random (other than the offspring and parent cell) and

removed from the cell population, see Figure 3.2.

Furthermore this multi-level model was imple-

mented 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 to-

tal number of molecular collisions), but also cells that

contain molecules that are fast to compute. For exam-

ple let us consider two cells containing complete re-

action 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 selective advantage. This

computational complexity introduces in our model a

notion of chemical kinetics and may alter the cellular

growth rate (i.e., the cells ﬁtness).s

We extended the MCS.bl with the multi-level con-

current model described above, our results indicated

that none of the evolved cells resulting from the sim-

ulations suffered from elongation catastrophe. The

nature of the evolved populations resulting from the

simulation runs were equivalent to those expected

from systems such as Alchemy: We observed the

rapid domination of molecular organizations which

involved a limited number of replicases capable to

self-sustain over time.

Moreover, in traditional multi-level selectional

models infected cells would usually be displaced only

when these have decayed (Cronhjort and Blomberg,

1997; Hogeweg and Takeuchi, 2003). Whereas in

our multi-level concurrent AC, infected cells (having

a smaller growth rate) would rapidly be displaced by

healthier cells (having a higher growth rate) due to

the concurrentnature of the system. This concurrency

property increased the system’s ability to control par-

asitism.

4 EVOLVING CLOSED

REACTION NETWORKS

The previous examination on evolutionary stabil-

ity provided us with the necessary understanding to

evolve closed reaction networks that are able to self-

sustain over time. These closed reaction networks

are regarded as primitive ACNS. Preliminary experi-

ments suggested that when self-replication is enabled,

evolved networks would present only limited interest.

As these networks would converge toward molecu-

lar organizations involving a small number of altru-

ist replicases. In the following experiment we dis-

able self-replication, and employ a minimalist (hand-

designed) collectively autocatalytic reaction network,

see Figure 5.A. Let S1 = ∗▽0 : ▽1, S2 = ∗▽0 : ▽0,

S3 = ∗▽1 : ▽1, S4 = ∗▽1 : ▽1, S5 = ∗▽⋄ : ▽1 and

S6 = ∗▽⋄ : ▽0.

In section 3.2, a cell would divide only when sat-

CLOSURE IN ARTIFICIAL CELL SIGNALLING NETWORKS - Investigating the Emergence of Cognition in

Collectively Autocatalytic Reaction Networks

111

Figure 5: A: Seed closed reaction network. B: Evolved

closed reaction network promoting growth of molecular

species S1.

100

150

200

0 0.01 0.02 0.03 0.04 0.05

Number of molecules

Time

Figure 6: Dynamics of seed closed reaction network, the

species S1 and S4 overlapping (top line) and S2 and S3 also

overlapping.

urated. We deﬁne a new cellular division criterion:

Here a cell would divide when the amount of molec-

ular species S1 reaches 200. The cellular growth rate

now depends on the molecular growth rate of S1. The

ability of the closed reaction network to promote the

growth of S1 deﬁnes the cells ﬁtness (i.e., a cell would

increase its ﬁtness by exhibiting a higher S1 growth

rate ). Thus the pre-speciﬁed task assigned to these

simple closed ACSNs is to amplify the “signal” S1.

We may also regard S1 as a necessary molecule such

as a membrane molecule to allow the cellular division

to occur. We ﬁrst present the dynamics of the seed

closed reaction network when the initial amount of

each molecular species is equal to 10, see Figure 6.

This graph was obtained by solving the ODE system

generated by the reaction network (in SBML format)

using the SBML ODE solver (Machn´e et al., 2006).

An evolutionary simulation was conducted in

which 31 concurrent cells were employed. These

100

150

200

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Number of molecules

Time

Figure 7: Dynamics of evolved closed reaction network,

the species S5 and S6 overlapping (middle line), S1 is the

top line and S4 is the bottom line. Each molecular species

amount is initialized to 10.

cells were seeded with the molecular species (with

initial amount of molecules 1) depicted in Figure 5.A.

This experiment was run for one hour, on average

the number of interactions per cell per hour was over

4.10

. The resulting dominant molecular organiza-

tion is depicted in Figure 5.B. We ﬁrst observed that

this evolved network successfully maintained closure.

We note that both species S2 and S3 have been re-

placed by new molecular species S5 and S6. These

new molecular species increased the overall number

of reactions from 6 to 9. We compare the dynamics of

this evolved closed reaction network against the seed

closed reaction network, see Figure 7.

In Figure 7, it can be seen that S1 reaches the di-

vision threshold at t ≈ 0.0422 whereas in the seed

closed reaction network S1 would reach this threshold

at t ≈ 0.0588. By reaching this threshold at an earlier

stage, the evolved network gained a selective advan-

tage over the seed network. We observed the emer-

gence of molecular species S5 and S6 which had for

effect to promote the growth of S1 whilst maintaining

closure. The network closure properties evolved and

allowed the network to promote the growth of species

S1.

Moreover results indicated that when a cellular

division occurs, the amount of the different molecu-

lar species would be optimized, see Figure 8. This

optimization resulted in the ability to encourage the

growth of S1 while limiting the growth of species S4,

S5 and S6. However this amount distribution would

not lead to the displacement of S4, S5 and S6 as these

species are necessary to maintain closure.

In Figure 8, it can be observed that S1 would reach

the division threshold when t ≈ 0.00973. This op-

timized amount distribution provided this network a

selective advantage over networks having differing

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112

100

150

200

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Number of molecules

Time

Figure 8: Typical dynamics of an evolved closed reaction

network with optimized initial molecular amounts resulting

from a cellular division

100

150

200

0 0.01 0.02 0.03 0.04 0.05

Number of molecules

Time

Figure 9: Comparison of S1 dynamics with differing net-

works and initial molecular amount distributions. S1

and

depicts the dynamics of S1 with initial molecular 10, us-

ing the seed reaction network and evolved reaction respec-

tively. S1

represents the dynamics of S1 using the evolved

reaction network and optimal initial molecular amount dis-

tribution.

amount distributions (as shown in Figure 7).

Finally Figure 9 compares the different dynamics

of S1 using the different networks and initial number

of molecules. This comparison highlights the succes-

sive improvements in the networks ﬁtness (i.e., has-

tened the production of molecules A).

5 DISCUSSION

We now discuss the current limitations of our pro-

posed evolutionary system and how future work may

address these issues. In section 4, we presented a

closed reaction network which was evolved to carry

out a pre-speciﬁed task. We examined a second

set of identical evolutionary simulations to examine

whether alternativeevolutionary trajectories could oc-

cur. In all of these experiments, we observed the con-

vergence(from a phenotypic point of view) of the sys-

tem towards reaction networks similar to Fig. 5.B.

Moreover the evolutionary process would only in-

volve a limited number of incremental steps in ﬁtness.

Based on these observations we may express that our

proposed AC still lacks some evolvability and failed

to display a “remarkable” evolution of complexity.

Some may argue that the current system is sim-

ply not complex enough and should incorporate more

realistic features such as mass conservation, multi-

dimensional space, a genetic code or advanced chem-

ical kinetics. These complementary properties would

certainly broaden the complexity of an already dif-

ﬁcult and incomplete investigation. However there

would be no guarantee of improved results, i.e., ex-

hibiting a more interesting evolutionary growth of

complexity: A ﬁrst reason for this assertion is that the

impact of environmental constraints on the evolution

of complexity still remains to date an open question

(Gershenson and Lenaerts, 2008). Secondly there is

currently no theoretical framework that would lead to

desired evolutionary growth of complexity with con-

ﬁdence.

We hypothesise that as long there is no such the-

oretical frameworks for the study of ACs, the lat-

ter would remain a black art approach where unex-

pected results are observed. Therefore a minimal-

ist/simpliﬁed approach to ACs, where the system is

still analytically tractable and examined using current

mathematical methods, should be adopted. In keeping

with this, our proposed AC contributed, to some ex-

tent, to the understanding of minimalist ACs and their

evolutionary dynamics.

Future work would beneﬁt from further theoreti-

cal research, it could involve the development of For-

mal Methods for Artiﬁcial Life (AL), this would fa-

cilitate the comparison of differing ACs. Such a for-

mal approach to AL had already been initiated but

was discontinuated (Grogono et al., 2003), an alterna-

tive could be to extend the AC formalism. Moreover

the development of further analytical tools such as the

Organization Theory, which was initiated by (Fontana

and Buss, 1994a) and later enriched by (Dittrich and

Speroni, 2007), would as well assist and contribute

to the understanding and ultimately engineering of

Complex Adaptive Systems using ACs.

Finally, although our approach may present some

limitations in terms of evolutionary growth of com-

plexity, it still demonstrated the successful evolu-

tion of closed reaction networks to accomplish a pre-

speciﬁed task. This may be regarded as an initial

CLOSURE IN ARTIFICIAL CELL SIGNALLING NETWORKS - Investigating the Emergence of Cognition in

Collectively Autocatalytic Reaction Networks

113

promising result demonstrating closure in CSNs and

may suggest a novel method to engineer autonomous

Complex Adaptive Systems for real-world applica-

tions.

6 CONCLUSIONS

We discussed how CSNs could be considered as sub-

sets of closed reaction networks and the potential role

of closure on CSNs evolution. We presented our evo-

lutionary system: a multi-level concurrent Artiﬁcial

Chemistry based on the Molecular Classiﬁer Systems

and the Holland broadcast language. The develop-

ment of this multi-level and concurrent model was

motivated to improve evolutionary stability, which

was a key missing feature of the single-level MCS.bl.

We then presented these different properties which

permitted the systems robustness to be ameliorated.

We ﬁnally presented an experiment in which a sim-

ple closed reaction network was successfully evolved

and optimized to carry out a pre-speciﬁed task (signal

ampliﬁcation) whilst maintaining closure. This opti-

mized signal-processing ability directly resulted from

the evolved closure properties. We ﬁnally discussed

the contributions and future directions of this work.

ACKNOWLEDGEMENTS

We acknowledge the ESIGNET (Evolving Cell Sig-

nalling Networks in Silico) Project funding (contract

no. 12789).

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