Emergent Collective Properties, Networks and Information in Biology (eBook)

Cover 
1 
Preface 5
Contents 9
Other volumes in the series 15
Chapter 1 Molecular Stereospecific Recognition and Reduction in Cell Biology 19
1. The concepts of reduction, integration, and emergence 20
2. Stereospecific recognition under thermodynamic equilibrium conditions as the logical basis for reduction in biology 21
3. Most biological systems are not in thermodynamic equilibrium conditions 23
3.1. Simple enzyme reactions cannot be considered equilibrium systems 23
3.2. Complex enzyme reactions cannot be described by equilibrium models 26
3.2.1. Steady-state rate and induced fit 26
3.2.2. Steady state and pre-equilibrium 29
3.2.3. Pauling's principle and the constancy of catalytic rate constant along the reaction coordinate 30
4. Coupled scalar-vectorial processes in the cell occur under nonequilibrium conditions 31
4.1. Affinity of a diffusion process 31
4.2. Carriers and scalar-vectorial couplings 32
5. Actin filaments and microtubules are nonequilibrium structures 37
6. The mitotic spindle is a dissipative structure 40
7. Interactions with the environment, nonequilibrium, and emergence in biological systems 41
References 42
Chapter 2 Mathematical Prelude: Elementary Set and Probability Theory 45
1 Set theory 45
1.1. Definition of sets 45
1.2. Operations on sets 46
1.3. Relations and graphs 48
1.4. Mapping 50
2 Probabilities 50
2.1. Axiomatic definition of probability and fundamental theorems 50
2.2. Properties of the distribution function and the Stieltjes integral 54
3 Probability distributions 57
3.1. Binomial distribution 57
3.2. The Poisson distribution 60
3.3. The Laplace-Gauss distribution 62
4 Moments and cumulants 63
4.1. Moments 63
4.1.1. Monovariate moments 64
4.1.2. Bivariate moments 66
4.2. Cumulants and characteristic functions 69
5 Markov processes 70
6 Mathematics as a tool for studying the principles that govern network organization, information, and emergence 72
References 72
Chapter 3 Biological Networks 75
1. The concept of network 76
2. Random networks 77
3. Percolation as a model for the emergence of organization in a network 81
4. Small-world and scale-free networks 88
4.1. Metabolic networks are fundamentally different from random graphs 88
4.2. Properties of small-world networks 90
4.3. Scale-free networks 92
5. Attack tolerance of networks 93
6. Towards a general science of networks 95
References 97
Chapter 4 Information and Communication in Living Systems 101
1. Components of a communication system 102
2. Entropy and information 103
3. Communication and mapping 110
4. The subadditivity principle 111
5. Nonextensive entropies 114
6. Coding 115
6.1. Code words of identical length 115
6.2. Code words of variable length 116
7. The genetic code and the Central Dogma 120
8. Accuracy of the communication channel between DNA and proteins 123
References 125
Chapter 5 Statistical Mechanics of Network Information, Integration, and Emergence 127
1 Information and organization of a protein network 129
1.1. Subsets of the protein network 129
1.2. Definition of self- and mutual information of integration 132
2 Subadditivity and lack of subadditivity in protein networks 135
3 Emergence and information of integration of a network 137
4 The physical nature of emergence in protein networks 142
5 Reduction and lack of reduction of biological systems 143
6 Information, communication, and organization 147
References 149
Chapter 6 On the Mechanistic Causes of Network Information, Integration, and Emergence 151
1. Information and physical interaction between two events 151
2. Emergence and topological information 154
3. Organization and the different types of mutual information 158
3.1. Mutual information and negative correlation 159
3.2. Mutual information and physical interaction between two binding processes 159
3.3. Mutual information and network topology 159
4. Organization and negative mutual information 160
References 162
Chapter 7 Information and Organization of Metabolic Networks 163
1. Mutual information of individual enzyme reactions 164
2. Relationships between enzyme network organization and catalytic efficiency 166
3. Mutual information of integration and departure from pseudo-equilibrium 169
4. Mutual information of integration of multienzyme networks 172
4.1. Metabolic networks as networks of networks 172
4.2. Robustness of multienzyme networks 173
4.3. Regular multienzyme networks 175
4.4. Fuzzy-organized multienzyme networks 179
4.5. Topological information of regular and fuzzy-organized networks 180
5. Enzyme networks and Shannon communication-information theory 181
References 183
Chapter 8 Functional Connections in Multienzyme Complexes: Information and Generalized Microscopic Reversibility 185
1. Network connections and mutual information of integration in multienzyme complexes 186
1.1. Linear networks 186
1.2. Functions of connection 189
2. Generalized microscopic reversibility 194
3. Connections in a network displaying generalized microscopic reversibility 196
4. Mutual information of integration and reaction rate 196
5. Possible functional advantages of physically associated enzymes 198
References 199
Chapter 9 Conformation changes and information flow in protein edifices 203
1. Phenomenological description of equilibrium ligand binding and nonequilibrium catalytic processes 204
2. Thermodynamic bases of long-range site-site interactions in proteins and enzymes 206
2.1. General principles 206
2.2. Energy contribution of subunit arrangement 208
2.3. Quaternary constraint energy contribution 211
2.4. Fundamental axioms 216
3. Conformational changes and mutual information of integration in protein lattices 217
3.1. Conformation change and mutual information of integration of the elementary protein unit 219
3.2. Ligand binding, conformation changes, and mutual information of integration of protein lattices 222
3.2.1. A simple protein lattice 223
3.2.2. Mutual information of integration and conformational constraints in the lattice 225
3.2.3. Integration and emergence in a protein lattice 228
3.3. Conformational changes in quasi-linear lattices 233
3.3.1. The basic unit of conformation change 233
3.3.2. Thermodynamics of spontaneous conformational transitions in a simple quasi-—linear protein lattice 234
3.3.3. Mutual information of integration and conformation changes 236
4. Conformational spread and information landscape 241
References 242
Chapter 10 Gene networks 245
1 An overview of the archetype of gene networks: the bacterial operons 245
1.1. The operon as a coordinated unit of gene expression 246
1.2. Repressor and induction 248
1.3. Positive versus negative control 250
2 The role of positive and negative feedbacks in the expression of gene networks 251
2.1. Multiple dynamic states and differential activity of a gene 251
2.2. Formal expression of multiple dynamic states of a gene 252
2.3. Full-circuits 254
3 Gene networks and the principles of binary logic 260
4 Engineered gene circuits 263
4.1. The role of feedback loops in gene circuits 263
4.2. Periodic oscillations of gene networks 267
4.3. The logic of gene networks 268
References 242
Chapter 11 Stochastic Fluctuations and Network Dynamics 273
1. The physics of intracellular noise 274
1.1. Random walk and master equation 274
1.2. Detailed balance 276
1.3. Intracellular noise and the Langevin equation 279
1.3.1. The Langevin equation of a macromolecule subjected to random collisions 280
1.3.2. The function F(t) as the expression of the noise-driven properties 282
1.4. Intracellular noise and the Fokker-Planck equation 284
1.4.1. The Fokker-Planck equation for one-dimensional motion 284
1.4.2. Generalized Fokker-Planck equation 288
2. Control and role of intracellular molecular noise 288
References 292
Subject Index 293