\chapter{Conclusion}
This final chapter first summarises and discusses the research contributions of this thesis. Following this, future work that has been identified to extend the work reported in this thesis is outlined.

\section{Research contributions}
The research contributions of this thesis are summarised and discussed as follows:
\begin{itemize}
	\item \textit{Modelling chemical reaction networks:} A state of the art review on computational techniques applied to the modelling of chemical networks was proposed. Several families of modelling techniques were distinguished: deterministic, stochastic, probabilistic, algebraic and agent-based techniques. For each of these modelling approaches, specific techniques were individually presented and evaluated. A comparison table was provided to highlight the strengths and weaknesses of the different approaches. This evaluation showed that algebraic and agent-based techniques, both families originating from the field of computer science, are the most flexible modelling techniques. This flexibility is essentially due to the high descriptive power of these techniques which allows one to model the hierarchical and intricate nature of chemical networks and molecular species. Moreover, transformation techniques and standardised formats (i.e., SBML, CellML) permit the partial translation of algebraic/agent-based models into deterministic ones. The latter complements the range of analysis that can be conducted given an original algebraic/agent-based model.	Although deterministic and stochastic approaches remain the most employed techniques within the modelling community, the rapidly growing field of algebraic/agent-based modelling suggests the limitations of \textit{traditional} techniques and the need for flexible and more accurate modelling tools. 

	\item \textit{Evolving Cellular Information Processing Networks:} A review on evolutionary techniques applied to the evolution of organisationally closed Cellular Information Processing Networks (CIPNs) was presented. Although no methods directly applied to evolving closed CIPNs were identified, two complementary and indirectly related families of evolutionary methods were distinguished: top-down/Evolutionary Computation (EC) techniques and bottom-up/Artificial Chemistry (AC) approaches. Individual techniques from both evolutionary approaches were selected, presented and evaluated. In terms of realising and evolving computational functions using reaction networks, this evaluation showed that EC techniques have successfully demonstrated the feasibility of evolving chemical networks to perform computational functions. Nevertheless no EC techniques have to date addressed closure and self-organisation dynamics in chemical networks. On the other hand, we showed that ACs have extensively been used to examine the emergence, self-maintenance and evolution of closed reaction networks with little focus on signal-processing capabilities. 
	
A comparison of both complementary evolutionary approaches was conducted. This comparison identified the explicit definition of fitness functions as the major drawback of EC techniques. Explicit fitness functions constrain the evolutionary process and prevent, by design, an open-ended evolution from occurring. Moreover such explicit fitness functions determine the genotype/phenotype mapping which ultimately defines the complexity/hardness of the EC algorithm. As a result the quality of evolved solutions is dependent on the specific design of the employed EC algorithm. 

Our evaluation suggested that AC approaches are adequate to evolve CIPNs as these methods rely on implicit fitness functions. In ACs, agents determine by themselves their own fitness and collectively determine the system's fitness as a whole. Although no ACs have so far demonstrated an open-ended evolutionary growth of complexity, as occurring in the biosphere, we concluded that agent-based AC methods are a suitable technique to study the evolution of organisationally closed CIPNs.


	\item \textit{Evolutionary simulation platform:} A novel simulation platform capable of evolving organisationally closed reaction networks was implemented. This stochastic agent-based system termed the \MCS~employs the Holland broadcast language to specify the molecular reaction and species. The novelty of this string-based Artificial Chemistry relies on the use of the broadcast language which addresses the reflexive nature of molecular species regarded here as condition/action rules. Since Holland's original proposal in the 1970s, no studies on the broadcast language formalism have been reported in the literature. The work presented in this thesis and related publications constitute the first published evaluation of the broadcast language. 
	
Prior to the development of the \MCS, an implementation of the original broadcast language was also conducted. This system is the first publicly available implementation of the broadcast language and may assist in the evaluation of the broadcast language in allied fields (e.g., Genetic Programming and Genetic Algorithms).

	\item \textit{Emergence and self-maintenance of closed reaction networks:} A first series of experiments was conducted focusing on the spontaneous emergence and self-maintenance of closed reaction networks in the \MCS.  These experiments first demonstrated the role of binding specificity in the dynamics of replicase species. This binding specificity affected the capability of the replicases to displace other molecular species. Although this property may have been previously implicated in the dynamics of a variety of ACs, it has not been explicitly exposed in the manner presented in these experiments. 
	
Additional evolutionary experiments suggested that the spontaneous emergence of autocatalytic species/organisations, being able to self-maintain in the \MCS, was unlikely to occur. We suggested a number of factors which may have contributed to this phenomenon which has also been reported in other ACs such as Tierra. These experiments provided supplementary insights on the potential conditions necessary for the spontaneous emergence and self-maintenance of closed reaction networks in ACs. 

Following the Tierra system, further evolutionary experiments were conducted in which an ancestor species was employed. These experiments presented unexpected evolutionary dynamics in which a degenerative elongation catastrophe phenomenon was identified. This phenomenon was due to a form of parasitism which prevented replicase species from self-maintaining over time. These results indicated counter-intuitive outcomes when compared with the evolutionary dynamics reported in other ACs. 

These results are potentially artefacts of the broadcast language which could have been avoided by utilising a different AC. Nevertheless this remains hypothetical as these degenerative evolutionary dynamics may be due to specific system properties which were desired in this project (e.g., variable molecular length, reflexive structure, pattern matching based reaction scheme).

	\item \textit{Evolutionary capability in multi-level selectional models:} A parallel implementation of the \MCS~ using distributed computing facilities was conducted. This extended \MCS~addressed the concurrent nature of chemical processes and introduced compartmentalisation and multi-level selection. Using this novel version of the \MCS, two model variants were evaluated to improve the system's evolutionary capability and prevent the degenerative evolutionary phenomena from occurring. 
	
The first model explored the effects of molecular diffusion between static reactors. This model was inspired by the analytical study conducted by McCaskill et al. which demonstrated that such a model, according to a range of parameters, can stabilise the self-maintenance of closed reaction networks when subjected to disruptive parasitic effects. A series of evolutionary simulations was conducted using a limited range of parameters where the molecular diffusion coefficient was varied. Our results indicated that the elongation catastrophe phenomenon could not be averted in any of these simulations. Although these results suggest that molecular diffusion cannot control the degenerative effects due to parasitism, we cannot infer that there exists (or not) a range of parameters that could provide the autocatalytic species with resistance against parasites in the \MCS. These results highlighted the limitations of agent-based systems that are not analytically tractable. 

Following this, a cellular model where compartments/cells can grow and divide was evaluated. Similarly to previous experiments, only a limited range of parameters was examined in which the mutation rate was varied. These evolutionary experiments demonstrated that a mutation rate threshold exists where the parasitic effects can be controlled. Moreover, the introduction of chemical kinetics (due to the parallel nature of the model) improved the system's robustness and evolutionary capability in particular cases. 

Both experimental investigations provide complementary insights on the potential effects of compartmentalisation over evolutionary capability in Artificial Chemistries. As no analytically tractable method is currently available for the examination of complex ACs, such empirical investigations are necessary and may provide guidance on the construction and analysis of future evolutionary systems.

	\item \textit{Evolution of closed reaction networks:} Using the cellular model of the \MCS, further evolutionary experiments were conducted. To drive the evolution of the closed reaction networks, a novel and simple cellular division criterion was introduced. A series of evolutionary experiments was performed in which self-replication reactions were disabled. The target objective of the reaction networks was to promote/amplify a designated molecular species/signal. The modification of the cellular division criterion affected the fitness landscape which became multi-dimensional. The reaction networks' fitness was determined by their ability to both maintain closure and to amplify the production of target species.	In these experiments, we observed the evolution of reaction networks in which the ability to grow the target molecular species was enhanced whilst maintaining closure. These results indicated the feasibility of evolving closed reaction network to perform pre-specified information processing tasks. To our knowledge, this work is the first attempt to evolve closed reaction networks capable of distinct information processing functions to be reported in the literature.

	\item \textit{Crosstalk and the evolution of complexity:} The role of crosstalk in closed reaction networks was investigated. Inspired by the symbiogenesis theory and preliminary experiments conducted by Fontana and Buss, three series of evolutionary experiments were conducted to explore the effects of crosstalk on the evolutionary growth of complexity in closed reaction networks. In these evolutionary experiments, the cellular division criterion was modified to account for the pre-specified functions of both seed reaction networks. These experiments thus aimed at evolving multitasking reaction networks. In the first two series of experiments, only cell-level mutations occurred. 

We first examined the dynamics of non-crosstalking closed reaction networks when mixed in the same reaction space. Although significant differences between the \MCS~and Alchemy were identified, a common phenomenon was observed: Non-crosstalking closed reaction networks cannot cooperate and would quasi-deterministically displace each other. 

In the second experiment, crosstalking closed reaction networks were examined. First observed was a phenomenon which also occurred in the analogous Alchemy experiments. A meta-reaction network emerged which contained both seed closed-reaction networks. This cellular species was able to self-maintain for a sustained period of time. However a second phenomenon occurred (which was not reported in any Alchemy-based studies), in which a selective displacement took place. A mutant cell emerged and displaced the meta-reaction network species. This mutant cellular species was no longer maintaining both seed reaction networks but was in fact fitter at performing the pre-specified tasks. The emergence of this mutant cell was due to variations introduced by cell-level mutations. 

Finally, the third experiment extended the previous one by introducing mutations at the molecular level. A common selective displacement reported in the previous experiment was observed. However additional cellular species displacements were also observed and presented evolutionary dynamics which have not been fully understood. We discussed some of the possible pitfalls of our analysis and outlined potential explanations which may be addressed in future work. 

These experiments demonstrated that crosstalk was necessary in enabling cooperation to occur between distinct closed reaction networks. The evolutionary process was also able to optimise the reaction networks and their crosstalk properties to carry out the objective multitask function. These evolved reaction networks presented a higher level of functional and structural complexity. These experiments suggest the constructive role of crosstalk to contribute to the evolutionary growth of complexity in CIPNs.

\item \textit{The open-ended evolutionary growth of complexity:} Our evolutionary experiments demonstrated the feasibility to evolve organisationally closed CIPNs to achieve pre-specified information processing tasks. Through this evolutionary process, we observed a relative growth of complexity in CIPNs. More particularly, the crosstalk based experiments suggested an interesting avenue of research in investigating the evolutionary growth of complexity in biochemical networks. 

Nevertheless, when compared with the evolutionary dynamics reported in other ACs such as Tierra or Avida, a significant difference exists in terms of the evolutionary growth of complexity. Where Tierra exhibited numerous complex emerging phenomena (Section \ref{subsec:tierra}), our \MCS~based experiments hardly presented any comparable evolutionary dynamics at both the molecular and population/system levels.

As discussed earlier, a potential reason for this limitation is the specification of the broadcast language which may not provide a robust method to support evolvability. Future work may illuminate on these system properties which are critical to the realisation of an open-ended evolutionary system.

\end{itemize}

In the following section, we outline and discuss future research directions that may further develop some of the above contributions.

\section{Future work}
To extend the work reported in this thesis, two axes of research have been identified and are developed as follows:
\begin{enumerate}
	\item \textbf{Building a better analytical and theoretical framework}: The experimental work conducted in this thesis presented unexpected and complex evolutionary dynamics that have not been fully understood (e.g., Section \ref{riseFall} and \ref{subsecCrossMolMut}). These observations highlight the lack of appropriate analytical and theoretical tools which limits the study of Artificial Chemistries and, more generally, Complex Adaptive Systems (CAS). Several directions are suggested to address these limitations.
		\begin{enumerate}
			
			\item \textit{A formal Artificial Life:} Future work would benefit from further theoretical research such as the development of a formal method for the study of ACs. Employing a common/unified formal framework may enable one to compare differing ACs or to map a given AC into another one. Exposing the common properties or differences may suggest potential research directions for examining and understanding the effects of specific AC features (e.g., molecular folding, space, etc.) upon the system's evolutionary dynamics. Such a formal approach could be addressed by extending the AC formalism to account for further molecular and environmental properties.  
			
			\item \textit{Developing analytical frameworks:} Developing and extending analytically tractable models such as McCaskill et al.'s may provide a valuable tool for evaluating ACs. As discussed in Section \ref{sec:McCaskillsModel}, major differences existed between the \MCS~ and McCaskill et al.'s model. Extending the latter with a richer repertoire of molecular species and reactions may offer a critical tool for predicting evolutionary dynamics in ACs. Although this extension may constitute an intricate and tedious enterprise, such a mathematical approach remains a key tool to examine complex chemical systems. Chemical organisation theory is another promising research avenue which was initiated by \cite{fontana1994aft} and later enriched by \cite{dittich2007}. This algebraic approach proposes a theoretical foundation to describe closed chemical organisations and their dynamics. Organisation theory could thus be naturally employed to examine the \MCS's evolutionary dynamics. Such ``conventional'' mathematical techniques may assist in the analysis and understanding of complex chemical organisations using ACs.
		\end{enumerate}

	\item \textbf{Examining the conditions for the evolutionary growth of complexity in CIPNs:} We propose a number of system modifications that could lead to the emergence and evolution of CIPNs of higher complexity. This proposed research direction aims at understanding the conditions for the evolutionary growth of complexity in CIPNs.
		\begin{enumerate}
		
			\item \textit{Cellular division criteria:} In Chapter \ref{chap:evolClosReacNet}, two simple cellular division criteria were devised in which the objective was to promote the production of specific molecular species. Further cellular division criteria could be designed to investigate the emergence of more complex information processing functions. For example, the conditions to trigger the cellular division  could be dynamic. In this proposal, the cellular division criterion may vary according to the states of several molecular species. Similarly to experiments conducted in Chapter \ref{chap:evolClosReacNet}, a cell divides if $n_{target}$ molecules of species $s_T$ are produced. However this condition is here modulated by the presence of an additional species $s_{sw}$ acting as a switch operator. An additional target species $s_{U}$ is identified. When $s_{sw}$ is present in a given cell, the latter has to generate $n_{target}$ $s_{U}$ molecules to trigger the cellular division. If $s_{sw}$ is not present, the cellular division criterion remains the production of $n_{target}$ molecules $s_{T}$. The insertion and removal of $s_{sw}$ species are carried out manually over time. The evolutionary process may encourage the emergence of cellular species which are able to rapidly process this switching condition and promote the growth of appropriate target species. A cellular division probability can also be introduced to specify further constraints, e.g., to penalise cellular species which simultaneously promote the growth of both target species $s_T$ and $s_U$ regardless of $s_{sw}$ being present or not.
			
 			\item \textit{Detectors and effectors:} Following Holland's LCS/agent-based approach (Section \ref{subsec:ABLCS}), introducing a set of detectors and effectors is proposed to encourage the emergence of a chemotactic behaviour. In this extended \MCS~model, cells are situated in a two-dimensional space in which detectors may probe the cell's surrounding environment for chemicals. Detectors and effectors are implemented as broadcast devices that, similarly to molecular species, may be subjected to evolution. The environment is populated with gradients of food molecules (again specified as broadcast devices) that are necessary for the cells to grow and divide; this growth condition is addressed by the cellular division criterion. Upon detecting the required food species, detectors generate signalling molecular species within the cell. In contrast to detectors, effectors do not produce further molecular species upon binding to signalling species. In this chemotactic model, effectors may activate ``flagella'' which affect the cell's movement in space. The flagella's actions vary according to the nature of the effectors's action statement (a coding scheme is devised to specify this function). Such an extended \MCS~ model may potentially give rise to the emergence of regulatory/control feedback which is distinctive of the bacterial chemotaxis signalling pathway. In this approach, a clear input/output signal demarcation is introduced by the detectors and effectors. 		
 		\end{enumerate}
\end{enumerate}

Additional more ``realistic'' properties such as mass conservation, molecular folding, a genetic subsystem or advanced chemical kinetics could be introduced. These complementary properties would certainly broaden the complexity of an already difficult investigation. However there would be no guarantee of improved results, i.e., exhibiting 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 \citep{Gershenson2008}. 
	
Moreover, developing a unified theoretical framework may simply not be feasible using mathematical methods that are currently available. As a result we believe that further empirical investigations need to be performed to assemble a set of key observations. By integrating these observations we may be able to formulate further theories with regards to the evolution of complexity in CAS. Nevertheless this development will only be feasible if the employed models are not burdened with \textit{unnecessary} complex features which may distract and prevent the thorough analysis of CAS. 

Therefore we suggest that minimalist approaches to CAS, where the system is still analytically tractable and examined using available mathematical methods, should be adopted. In keeping with this final suggestion, our thesis contributed, to some extent, to the understanding of the evolutionary growth of complexity of CAS using ACs. 

\section{Summary}
In this concluding chapter, we summarised and discussed the main research contributions of this thesis with regards to autocatalytic closure and the evolution of CIPNs. Following this, we enumerated a number of future directions that may directly extend the work presented in this thesis. A series of system modifications was proposed to encourage the evolutionary growth of complexity in the \MCS. Additional proposed research investigations advocated the development of further analytical and theoretical frameworks to study Complex Adaptive Systems. However we also mentioned that the development of such a theoretical foundation may not be feasible given the mathematical methods currently available and the complexity of studied systems. We consequently and finally argued that supplementary empirical investigations should be conducted using minimalist and analytically tractable approaches to examine CAS. Such minimalist CAS approaches, as the one presented in this thesis, may facilitate the comparison and analysis of differing systems and lead to the formulation of critical theories in the field of complex systems.