Common Extremalities in Biology and Physics (eBook)

Front Cover 1
The Common Extremalities in Biology and Physics 4
Copyright Page 5
Contents 6
Preface 12
1 Extreme Energy Dissipation 16
1.1 Hierarchy of the Energy Transformation 16
1.1.1 Thermodynamics—A Science That Connects Physics and Biology 16
1.1.2 Hierarchy of the Processes and Parameters in Thermodynamics 17
1.1.3 Macroparameters: Energy and the Forms of Its Exchange 18
1.1.4 Macroparameters: Heat as a Nonmechanical Method to Change the Macrostate of Thermodynamic Systems 19
1.1.5 Macroparameters: Physical Work as a Pure Mechanical Way to Change Macroparameters 19
1.1.6 Macroparameters: The Energy Conservation Law 20
1.1.7 Macroparameters: Free Energy—Macroscopic Measure of Nonequilibrium 20
1.1.8 Macroparameters: Universal Fatality of the Processes—The Second Law of Thermodynamics and the Hierarchy of Energy 21
1.1.9 Macroparameters: Helmholtz Free Energy 22
1.1.10 Macroparameters: Enthalpy 22
1.1.11 Link from Macro- to Microparameters: Physical Entropy 23
1.1.12 Microparameters: Statistical Interpretation of Free Energy and Entropy 25
1.1.13 The Removal of Energetical Nonequilibrium and the Entropy Production 26
1.1.14 Dissipation in Chemical Transformations 27
1.1.15 Dissipation of Nonequilibrium in Open Systems 28
1.1.16 Energy Dissipation or Entropy Production—The Energy Picture Can Play a Role 29
1.1.17 Biological Hierarchy and Its Complexity 30
1.1.18 Some Conclusions 32
1.2 Extreme Properties of Energy Dissipation 33
1.2.1 Comparing Extreme Approaches 33
1.2.2 How Is the Elementary Variational Problem Solved? 38
1.2.3 Other Necessary Conditions for Local Minimum 39
1.2.4 Canonical Equations or Hamiltonian Formulation 40
1.2.5 Conclusions 41
1.3 Optimal-Control-Based Framework for Dissipative Chemical Kinetics 42
1.3.1 Optimal Control and Mechanics 42
1.3.2 Dynamic Optimal Control Formulation 44
1.3.3 More General Case 48
1.3.4 Optimal Control Interpretations 50
1.3.5 Pure Physical Example—Relaxation in an Ideal Resistor-Capacitor Circuit 53
1.4 Conclusions 54
References 55
2 Some General Optimal Control Problems Useful for Biokinetics 58
2.1 Extreme Dissipation, Optimal Control, and the Least Action Principle 58
2.1.1 Conservative Mechanics: Variational Formulation 58
2.1.2 On Optimal Control Formulation of Mechanics 61
2.1.3 Dissipation in Classical Mechanics 62
2.1.4 On an Alternative Way to Describe Biological and Chemical Dissipation 64
2.1.5 Comparing Closely the Linear Dissipative and Conservative Models 69
2.1.6 A More Biological Approximation of Penalty Potential 71
2.1.7 Simple Biological/Biochemical Example in Terms of Logarithmic Penalty 72
2.1.8 Penalty and Dissipative and Conservative Motion 75
2.2 Some One-Dimensional Examples of Biokinetics and Optimal Control 77
2.2.1 General One-Dimensional Optimal Control Model 77
2.2.2 “Additive” Control—Relevant to the Control by the Rate 79
2.2.3 “Multiplicative” Control—Relevant to the Control by the Rate Constant 85
2.2.4 General Case of the Cooperative Model 88
2.2.5 General Case of Cooperative Model: Partial Case h(x)=0, Variational Formulation 90
2.2.6 Multiplicative Control Model 91
2.2.7 Logistical Cooperative Model—Pure Variational Formulation 93
2.2.8 Some Other Cooperative Functions 96
2.2.9 On the Introduction of Control into the Logistic Model 100
2.2.10 On Dynamic Optimal Control Interpretations 104
2.3 General Multidimensional Examples of the Introduction of Optimal Control into Biokinetics 106
2.3.1 “Additive” Control 106
2.3.2 On Vector Formulation of Additive Control 112
2.3.3 Variational Formulation of Additive Control 114
2.3.4 “Multiplicative” Control 115
2.3.5 General Linear “Multiplicative” Control Case 117
2.3.6 An Interesting Two-Dimensional Case: “Cross-Penalty” 119
2.4 Conclusions 124
References 124
3 Variational and the Optimal Control Models in Biokinetics 126
3.1 Optimal Control Model of Binding Cooperativity 126
3.1.1 Importance of Low Molecular Binding and Its Cooperativity 126
3.1.2 Binding Kinetics, Cooperativity, and Its Representation 128
3.1.3 Dynamical Optimal Control Outline 131
3.1.4 Optimal Control Lagrange Method 135
3.1.5 Pure Variational Formulation 135
3.1.6 Some Conclusions 137
3.2 Enzyme Kinetics and Optimal Control 138
3.2.1 The Michaelis–Menten Model 138
3.2.2 General Optimal Control Approach to Michaelis–Menten Kinetics 140
3.2.3 Control by Means of Maximal Reaction Velocity Vmax 142
3.2.3.1 Optimal Control Outline 142
3.2.3.2 Pure Variational Formulation 143
3.2.4 Hamiltonian Formulation 145
3.2.4.1 Back to the Optimal Control Formulation in Terms of State and Control Variables 147
3.2.5 Control by the Michaelis Constant KM 153
3.2.5.1 Pure Variational Outline 155
3.2.5.2 Hamiltonian Framework 157
3.2.5.3 Optimal Control Outline 159
3.2.6 Simultaneous Optimal Control by the Vmax and the Michaelis Constant KM 164
3.2.7 The Link to Biochemical Mechanisms 166
3.3 Optimal Control, Variational Methods, and Multienzymatic Kinetics 170
3.3.1 Optimal Control Method in Modeling of Multienzymatic Chains 170
3.3.2 Optimal Control Introduction into the Bier-Teusink- Kholodenko- Westerhoff–Volkenstain Model of Glycolysis 171
3.3.3 Direct Optimal Control Outline 172
3.3.4 Variational Formulation 176
3.3.5 Statistical Method to Study the Robustness 179
3.3.5.1 Optimal Control by KM in the BTKW Model of Glycolysis 181
3.3.6 Optimal Control and Multienzyme Kinetics 185
3.4 Optimal Control in Hierarchical Biological Systems: Organism and Metabolic Hierarchy 188
References 193
4 Extreme Character of Evolution in Trophic Pyramid of Biological Systems and the Maximum Energy Dissipation/Least Action Principle 202
4.1 Acceleration of Dissipation in Molecular Processes is the Cause of Emergence of Trophic Pyramid of Biological Systems 202
4.1.1 Autocatalysis and Self-Reproduction 203
4.1.2 Competition: Result of Relationships Between Various Types of Autocatalysis in the System of Chemical Reactions 205
4.1.3 Molecular Symbiosis 207
4.1.4 Advanced Symbiosis: Autocatalytic Hypercycles 208
4.1.5 Effect of Feedback Extent 210
4.1.6 Role of Information Mapping: Hypercycles with the Translation 213
4.1.7 Phase Separation 218
4.1.8 Some Conclusions 219
4.2 Maximum Energy Dissipation Principle and Evolution of Biological Systems 222
4.2.1 Role of Energetical Perspective of Biological Evolution 222
4.2.2 General Characteristic of the Energy Dissipation in the Global Biological Trophic Pyramid 225
4.2.3 Biological Evolution and the Maximum Energy Dissipation Principle 228
4.2.4 Cooperations of Macromolecules—From Molecular Hypercycles to Protobiocells 228
4.2.5 Bacterial Social Behavior 233
4.2.6 Eukaryotic Cells and Collective/Social Behavior 234
4.2.7 Organismic Level—From Acellular to Multicellular Biosystems 234
4.2.8 Symbiosis Is Fundamental for Developing Essentially New Dissipative Manners of Metabolism, Which Use Qualitatively New Free Energy Resources 236
4.2.9 Organizational Levels of the Global Biological Dissipative Pyramid 237
4.2.10 Limitations in the Scale of Free Energy Dissipation at Every Level of Bioorganization 241
4.2.11 Limitation in the Informational Mapping/Cognition 243
4.2.11.1 Informational Processing at the Level of Biosocial Species 247
4.2.11.2 Communication Languages in Social Multicellular Organisms: Dance Communications 247
4.2.12 Conclusions 253
4.3 The Pinnacle of Trophic Pyramid of Biological Systems—Symbiosis of Biological and Nonbiological Accelerating Loops: Technological Accelerating Loop 255
4.3.1 General Approach 255
4.3.2 Biological Component: Data on the Population Growth 258
4.3.3 Self-Reproductive-Like Growth of the Industrial (Nonbiological) Component 258
4.3.4 Symbiotic Accelerative Cycle of Biological and Nonbiological Things 263
4.3.5 More “Economic” Model: Four-Level Scheme of Level Interaction 267
4.3.6 Economic Interpretation of Optimal Control and the Biological Analogies 275
4.3.7 On the Interpretation of Static Optimization 276
4.3.8 Economic Interpretation of Dynamic Optimization 280
4.3.9 The Limitations in Purely Biological and Biosocial Parts of the Global Trophic Pyramid 283
4.3.10 Limitation in the Sociobiological Form of Information Mapping 288
4.3.11 Possible Postsocial Stage of Development of Dissipative Systems 292
4.3.12 Conclusions 293
References 295
5 Phenomenological Cost and Penalty Interpretation of the Lagrange Formalism in Physics 302
5.1 Fusing Mechanics and Optimal Control 302
5.1.1 Introduction 302
5.1.2 Mechanical Degrees of Freedom 302
5.1.3 Measurement Differences 303
5.1.4 The Penalty Example for a One-Dimensional Harmonic Oscillator 314
5.1.5 Dissipative, More Biological Analogue 315
5.1.6 Conclusions 317
5.2 Finiteness of the Propagation Velocity of Physical Interactions and Physical Penalty 318
5.3 Phenomenology of the Nonmechanical Penalty for Free Fields 324
5.3.1 Scalar Field 327
5.3.2 Complex Scalar Field: Charged Scalar Particles 328
5.3.3 Vector Field 330
5.3.4 Electromagnetic Field 331
5.3.5 Spinor Field 332
5.3.6 Massless Spinor Field 335
5.3.7 Penalty and Gravity 337
5.3.8 Einstein Equations 339
5.3.9 Some Final Remarks 340
5.4 Internal Symmetry of the Physical Penalty 342
5.4.1 Symmetry Breaking 349
5.4.2 Standard Model Illustrating the Physical Penalty 355
5.4.3 Grand Symmetry of the Physical Penalty 357
5.4.4 Supersymmetry of the Physical Penalty 358
5.4.5 Noncompensation of the Internal Penalty 359
5.5 Physical Interactions and Penalty 361
5.6 Physical Evolution in Light of Maximum Energy Dissipation Principle 369
5.6.1 Before the Epoch of Space-Time and Substance–Energy Separation 372
5.6.2 First Epoch: Epoch of the Barions Origin, 10-15GeV–2000GeV 372
5.6.3 Second Epoch: Epoch of Intermediate Vector Bosons, Temperature Drops from 2000 down to 50GeV 373
5.6.4 Third Epoch: Hadron Epoch 373
5.6.5 Fourth Epoch: Photon–Lepton Epoch 373
5.7 Conclusion: Physical Phenomena from the Point of View of Biological Ones 376
References 378
6 Conceptual Aspects of the Common Extrema in Biology and Physics 380
6.1 Self-Sufficiency of Extreme Transformations 380
6.1.1 Nonequilibrium/Instability 380
6.1.2 Motion Is a Striving Toward Stability 381
6.1.3 Extremeness 381
6.1.4 Ordered Way/Regularity 381
6.1.5 New Instability—The Result of the Ordered, Structured Process of the Elimination of Extreme Instability 382
6.2 Intensive and Extensive Property of Displaying of Material Instability 383
6.2.1 Energy in the Penalty Sense 385
6.2.2 Time in the Penalty Sense 385
6.3 Natural and Biotic Things—Lethal Gap or Irrational Compromise 387
6.3.1 “Continuous” Model—The Irrational Compromise 387
6.3.2 “Alternative” Model 389
Main Conclusions and Remaining Questions 392