Preface Introduction to modelling 1.1 WHAT IS MODELLING? 1.1.1 What are models? 1.2 WHYBUILD MODELS? 1.2.1 Why model biological systems? 1.2.2 Why systems biology? 1.3 CHALLENGES IN MODELLING BIOLOGICAL SYSTEMS 1.4 THE PRACTICE OF MODELLING 1.4.1 Scope of the model 1.4.2 Making assumptions 1.4.3 Modelling paradigms 1.4.4 Building the model 1.4.5 Model analysis, debugging and (in)validation 1.4.6 Simulating the model 1.5 EXAMPLES OF MODELS 1.5.1 Lotka-Volterra predator-prey model 1.5.2 SIR model: a classic example 1.6 TROUBLESHOOTING 1.6.1 Clarity of scope and objectives 1.6.2 The breakdown of assumptions 1.6.3 Ismy model fit for purpose? 1.6.4 Handling uncertainties EXERCISES REFERENCES FURTHER READING Introduction to graph theory 2.1 BASICS 2.1.1 History of graph theory 2.1.2 Examples of graphs 2.2 WHYGRAPHS? 2.3 TYPES OF GRAPHS 2.3.1 Simple vs. non-simple graphs 2.3.2 Directed vs. undirected graphs 2.3.3 Weighted vs. unweighted graphs 2.3.4 Other graph types 2.3.5 Hypergraphs 2.4 COMPUTATIONAL REPRESENTATIONS OF GRAPHS 2.4.1 Data structures 2.4.2 Adjacency matrix 2.4.3 The laplacian matrix 2.5 GRAPH REPRESENTATIONS OF BIOLOGICAL NETWORKS 2.5.1 Networks of protein interactions and functional associations 2.5.2 Signalling networks 2.5.3 Protein structure networks 2.5.4 Gene regulatory networks 2.5.5 Metabolic networks 2.6 COMMONCHALLENGES&TROUBLESHOOTING 2.6.1 Choosing a representation 2.6.2 Loading and creating graphs 2.7 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Structure of networks 3.1 NETWORK PARAMETERS 3.1.1 Fundamental parameters 3.1.2 Measures of centrality 3.1.3 Mixing patterns: assortativity 3.2 CANONICAL NETWORK MODELS 3.2.1 Erdos-Renyi (ER) network model 3.2.2 Small-world networks 3.2.3 Scale-free networks 3.2.4 Other models of network generation 3.3 COMMUNITY DETECTION 3.3.1 Modularity maximisation 3.3.2 Similarity-based clustering 3.3.3 Girvan-Newman algorithm 3.3.4 Other methods 3.3.5 Community detection in biological networks 3.4 NETWORKMOTIFS 3.4.1 Randomising networks 3.5 PERTURBATIONS TO NETWORKS 3.5.1 Quantifying efects of perturbation 3.5.2 Network structure and attack strategies 3.6 TROUBLESHOOTING 3.6.1 Is your network really scale-free? 3.7 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Applications of network biology 4.1 THE CENTRALITY-LETHALITY HYPOTHESIS 4.1.1 Predicting essential genes fromnetworks 4.2 NETWORKS AND MODULES IN DISEASE 4.2.1 Disease networks 4.2.2 Identification of disease modules 4.2.3 Edgetic perturbation models 4.3 DIFFERENTIAL NETWORK ANALYSIS 4.4 DISEASE SPREADING ON NETWORKS 4.4.1 Percolation-based models 4.4.2 Agent-based simulations 4.5 MOLECULAR GRAPHS AND THEIR APPLICATIONS 4.5.1 Retrosynthesis 4.6 PROTEIN STRUCTURE, ENERGY & CONFORMATIONAL NETWORKS 4.6.1 Protein folding pathways 4.7 LINK PREDICTION EXERCISES REFERENCES FURTHER READING Introduction to dynamic modelling 5.1 CONSTRUCTING DYNAMIC MODELS 5.1.1 Modelling a generic biochemical system 5.2 MASS-ACTION KINETIC MODELS 5.3 MODELLING ENZYME KINETICS 5.3.1 The Michaelis-Menten model 5.3.2 Extending the Michaelis-Menten model 5.3.3 Limitations of Michaelis-Menten models 5.3.4 Co-operativity: Hill kinetics 5.3.5 An illustrative example: a three-node oscillator 5.4 GENERALISED RATE EQUATIONS 5.4.1 Biochemical systems theory 5.5 SOLVING ODES 5.6 TROUBLESHOOTING 5.6.1 Handing stif equations 5.6.2 Handling uncertainty 5.7 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Parameter estimation 6.1 DATA-DRIVEN MECHANISTIC MODELLING: AN OVERVIEW 6.1.1 Pre-processing the data 6.1.2 Model identification 6.2 SETTING UP AN OPTIMISATION PROBLEM 6.2.1 Linear regression 6.2.2 Least squares 6.2.3 Maximumlikelihood estimation 6.3 ALGORITHMS FOR OPTIMISATION 6.3.1 Desiderata 6.3.2 Gradient-based methods 6.3.3 Direct search methods 6.3.4 Evolutionary algorithms 6.4 POST-REGRESSION DIAGNOSTICS 6.4.1 Model selection 6.4.2 Sensitivity and robustness of biological models 6.5 TROUBLESHOOTING 6.5.1 Regularisation 6.5.2 Sloppiness 6.5.3 Choosing a search algorithm 6.5.4 Model reduction 6.5.5 The curse of dimensionality 6.6 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Discrete dynamic models: Boolean networks 7.1 INTRODUCTION 7.2 BOOLEAN NETWORKS: TRANSFER FUNCTIONS 7.2.1 Characterising Boolean network dynamics 7.2.2 Synchronous vs. asynchronous updates 7.3 OTHER PARADIGMS 7.3.1 Probabilistic Boolean networks 7.3.2 Logical interaction hypergraphs 7.3.3 Generalised logical networks 7.3.4 Petri nets 7.4 APPLICATIONS 7.5 TROUBLESHOOTING 7.6 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Introduction to constraint-based modelling 8.1 WHAT ARE CONSTRAINTS? 8.1.1 Types of constraints 8.1.2 Mathematical representation of constraints 8.1.3 Why are constraints useful? 8.2 THE STOICHIOMETRICMATRIX 8.3 STEADY-STATEMASSBALANCE:FLUXBALANCEANALYSIS (FBA) 8.4 THE OBJECTIVE FUNCTION 8.4.1 The biomass objective function 8.5 OPTIMISATION TO COMPUTE FLUX DISTRIBUTION 8.6 AN ILLUSTRATION 8.7 FLUX VARIABILITY ANALYSIS (FVA) 8.8 UNDERSTANDING FBA 8.8.1 Blocked reactions and dead-end metabolites 8.8.2 Gaps in metabolic networks 8.8.3 Multiple solutions 8.8.4 Loops 8.8.5 Parsimonious FBA (pFBA) 8.8.6 ATP maintenance fluxes 8.9 TROUBLESHOOTING 8.9.1 Zero growth rate 8.9.2 Objective values vs. flux values 8.10 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Extending constraint-based approaches 9.1 MINIMISATION OF METABOLIC ADJUSTMENT (MOMA) 9.1.1 Fitting experimentally measured fluxes 9.2 REGULATORY ON-OFF MINIMISATION (ROOM) 9.2.1 ROOMvs.MoMA 9.3 BI-LEVEL OPTIMISATIONS 9.3.1 OptKnock 9.4 INTEGRATING REGULATORY INFORMATION 9.4.1 Embedding regulatory logic: regulatory FBA (rFBA) 9.4.2 Informing metabolic models with omic data 9.4.3 Tissue-specific models 9.5 COMPARTMENTALISED MODELS 9.6 DYNAMIC FLUX BALANCE ANALYSIS (dFBA) 9.7 13C-MFA 9.8 ELEMENTARY FLUX MODES AND EXTREME PATHWAYS 9.8.1 Computing EFMs and EPs 9.8.2 Applications EXERCISES REFERENCES FURTHER READING Perturbations to metabolic networks 10.1 KNOCK-OUTS 10.1.1 Gene deletions vs. reaction deletions 10.2 SYNTHETIC LETHALS 10.2.1 Exhaustive enumeration 10.2.2 Bi-level optimisation 10.2.3 Fast-SL: massively pruning the search space 10.3 OVER-EXPRESSION 10.3.1 Flux Scanning based on Enforced Objective Flux (FSEOF) 10.4 OTHER PERTURBATIONS 10.5 EVALUATING AND RANKING PERTURBATIONS 10.6 APPLICATIONS OF CONSTRAINT-BASED MODELS 10.6.1 Metabolic engineering 10.6.2 Drug target identification 10.7 LIMITATIONS OF CONSTRAINT-BASED APPROACHES 10.7.1 Scope of genome-scale metabolic models 10.7.2 Incorrect predictions 10.8 TROUBLESHOOTING 10.8.1 Interpreting gene deletion simulations 10.9 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Modelling cellular interactions 11.1 MICROBIAL COMMUNITIES 11.1.1 Network-based approaches 11.1.2 Population-based and agent-based approaches 11.1.3 Constraint-based approaches 11.2 HOST-PATHOGEN INTERACTIONS (HPIs) 11.2.1 Network models 11.2.2 Dynamic models 11.2.3 Constraint-based models 11.3 SUMMARY 11.4 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Designing biological circuits 12.1 WHAT IS SYNTHETIC BIOLOGY? 12.2 FROMLEGO BRICKS TO BIOBRICKS 12.3 CLASSIC CIRCUIT DESIGN EXPERIMENTS 12.3.1 Designing an oscillator: the repressilator 12.3.2 Toggle switch 12.4 DESIGNING MODULES 12.4.1 Exploring the design space 12.4.2 Systems-theoretic approaches 12.4.3 Automating circuit design 12.5 DESIGN PRINCIPLES OF BIOLOGICAL NETWORKS 12.5.1 Redundancy 12.5.2 Modularity 12.5.3 Exaptation 12.5.4 Robustness 12.6 COMPUTING WITH CELLS 12.6.1 Adleman’s classic experiment 12.6.2 Examples of circuits that can compute 12.6.3 DNA data storage 12.7 CHALLENGES 12.8 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Robustness and evolvability of biological systems 13.1 ROBUSTNESS IN BIOLOGICAL SYSTEMS 13.1.1 Key mechanisms 13.1.2 Hierarchies and protocols 13.1.3 Organising principles 13.2 GENOTYPE SPACES AND GENOTYPE NETWORKS 13.2.1 Genotype spaces 13.2.2 Genotype-phenotype mapping 13.3 QUANTIFYING ROBUSTNESS AND EVOLVABILITY 13.4 SOFTWARE TOOLS EXERCISES REFERENCES FURTHER READING Epilogue: The Road Ahead Index 325

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