The Artificial Epigenetic Network Alexander Phillip Turner Ph.D. The University of York Department of Electronics October 2013 Abstract The term epigenetics refers to typically heritable biological mechanisms which facilitate stable yet reversible modifications of gene expression or phenotype state, without alteration of the underlying genetic code. More specifically, epigenetic mechanisms allow organisms to control which genes are active at a given time. In eukaryotes, epigenetic mechanisms have essential roles in gene regulation, cellular differentiation and genetic packaging. These epigenetic mechanisms give rise to functionality which DNA alone is generally incapable of providing. This thesis takes inspiration from the fields of genetics and epigenetics, and builds a com- putational model which captures the beneficial properties of epigenetics in silico. This com- putational model is referred to as the artificial epigenetic network. The artificial epigenetic network can dynamically control which genes within the network are active at a given time, allowing certain groups of genes to become specialised towards specific aspects of a task. Hence, the artificial epigenetic network can contain many different regulatory circuits, each with specific properties. This gives the networks the ability to more readily express a wider range of dynamical behaviours, which were found to produce a number computational bene- fits. The artificial epigenetic network is applied to a diverse range of control tasks, each with varying dynamics, to ascertain how the functionality of the artificial epigenetic structures ef- fects the functionality of the network. An emergent property is that the epigenetic structures can partition the network into functional units corresponding to the logical decomposition of the tasks, and control these units with a switch like behaviour. This provides an inter- face, where a user can gain control over the complex dynamics of the target domain via the activation or deactivation of these switches. 3 Contents Acknowledgements 18 Declaration 19 Hypothesis 20 1 Introduction 21 1.1 Overview . 21 1.2 Artificial Gene Regulatory Networks . 22 1.3 Evolutionary Algorithms . 22 1.4 Epigenetics . 22 1.5 The Artificial Epigenetic Network . 23 1.6 Contributions . 23 1.7 Thesis Organisation . 23 2 The Structures and Processes Of Genetics And Epigenetics 25 2.1 Proteins . 26 2.1.1 Enzyme Catalysis . 27 2.1.2 Protein Binding . 28 2.1.3 Protein Switching . 29 2.1.4 Structural Proteins . 30 2.2 Nucleic Acids . 30 2.2.1 Nucleotides . 30 2.2.2 DNA and RNA . 30 2.3 Protein Synthesis . 32 2.3.1 Transcription . 32 2.3.2 Translation . 34 2.3.3 Posttranslational Modifications . 34 2.4 Genes . 35 2.4.1 Gene Regulation . 36 2.5 Biochemical Networks . 37 2.5.1 Gene Regulatory Networks . 38 4 Contents 5 2.5.2 Metabolic Networks . 39 2.5.3 Cell Signalling Networks . 40 2.6 Epigenetics . 40 2.6.1 Definitions of Epigenetics . 41 2.6.2 History of Epigenetics . 42 2.7 Epigenetic structures . 43 2.7.1 Histones . 43 2.7.2 Chromatin . 45 2.7.3 DNA Methylation . 46 2.7.4 MicroRNA . 46 2.8 Biological Advantages Of Epigenetic Mechanisms . 47 2.8.1 Genetic Packaging . 47 2.8.2 Cellular Differentiation . 48 2.8.3 Genetic Memory . 48 2.8.4 Higher Order Gene Regulation . 49 2.9 Summary . 50 3 Properties And Characteristics Of Biological Systems 51 3.1 Evolution . 51 3.1.1 Vertical Gene Transfer . 52 3.1.2 Horizontal Gene Transfer . 53 3.2 Evolvability . 54 3.3 Robustness . 55 3.3.1 Modularity . 55 3.3.2 Redundancy . 56 3.3.3 Decoupling . 56 3.3.4 Homoeostasis . 57 3.4 Emergence Of Complex Behaviours In Silico . 57 3.5 Complex Systems Analysis . 58 3.6 Summary . 62 4 Evolutionary Algorithms 63 4.1 Genetic Algorithms . 63 4.1.1 Non-Dominated Sorting Genetic Algorithm II . 66 4.2 Genetic Programming . 67 4.3 Evolutionary Programming . 68 4.4 Evolutionary Strategies . 70 4.5 Summary . 71 5 Artificial Gene Regulatory Networks 72 Contents 6 5.1 Random Boolean Networks . 73 5.1.1 RBN Variants . 76 5.1.2 RBN Analysis . 77 5.2 Ordinary Differential Equations . 77 5.3 Stochastic Networks . 79 5.4 Continuous Valued Discrete Time Gene Regulatory Networks . 80 5.4.1 The Canonical Gene Regulatory Network Within This Thesis . 81 5.4.2 Variants Of Continuous Valued Discrete Time Artificial Gene Regula- tory Networks . 83 5.4.3 Similarities to other Models . 83 5.5 Summary . 84 6 The Artificial Epigenetic Network 86 6.1 Introduction . 86 6.2 Background Overview And Assertions . 87 6.3 Representing Epigenetic Mechanisms In Silico . 88 6.3.1 The Reference Space . 89 6.4 Artificial Epigenetic Network Model . 92 6.4.1 The Epigenetic Analogue . 92 6.4.2 Formal Description . 93 6.5 Task Specificity . 94 6.6 Optimisation Of The Networks For Computation . 95 6.7 Previous Model . 95 6.7.1 The Artificial Epigenetic Regulatory Network Structure . 97 6.7.2 Execution Of The Artificial Epigenetic Regulatory Network . 98 6.8 Summary . 99 7 Experimental Methods 100 7.1 Chaos Targeting . 100 7.1.1 Traditional Controller Design . 101 7.2 Evolving Controllers . 101 7.2.1 Experimental Design . 102 7.2.2 Genetic Algorithms . 103 7.3 Control Tasks . 104 7.4 Summary . 105 8 Chirikov's Standard Map 106 8.1 Description of Chirikov's Standard Map . 107 8.2 The Artificial Epigenetic Regulatory Network . 108 8.2.1 Experimental Design And Parameters . 108 Contents 7 8.2.2 Results . 109 8.2.3 Analysis . 111 8.2.4 Reduced Dimensionality Controllers . 112 8.3 The Artificial Epigenetic Network . 113 8.3.1 Experimental Design And Parameters . 113 8.3.2 Results . 114 8.3.3 Analysis . ..