Noise and Randomness in Living System

This book illustrates the role of randomness and noise in living organisms. Traditionally, the randomness and noise have been used in understanding signal processing in communications. This book is divided into two sections, the first of which introduces readers to the various types and sources of noise and the constructive role of noise in non-linear dynamics. It also analyses the importance of randomness and noise in a variety of science and engineering applications. In turn, the second section discusses in detail the functional role of noise in biological processes for example, in case of brain function at the level of ion channel, synaptic level and even at cognitive level. These are described in various chapters. One of the challenging issue finding the neuronal correlates of various meditative states is to understand how brain controls various types of noise so as to reach a state of synchronized oscillatory state of the brain corresponding to the state of Samadhi. This is described in details in one chapter called Noise, Coherence and meditation. The concept of noise and the role of randomness in living organism raise lot of controversy for last few decades. This is discussed in a separate chapter. Finally, the epistemic and ontic nature of randomness as discussed in physical science are investigated in the context of living organism. Preface 5 Acknowledgements 10 Contents 11 About the Authors 15 1 Introduction 16 1.1 Noise and Randomness in Science and Engineering 17 1.2 Stochastic Resonance and Sensory Biology 18 1.3 Developmental Noise 19 1.4 Noise in Cellular Communication 20 1.5 Ion Channel Noise in Biological Systems 21 1.6 Noise and Coherence in Meditation 22 1.7 Synthetic Biology and Noise 23 1.8 Chance, Determinism and Laws of Nature 24 References 24 Part I Science and Engineering 26 2 Noise and Randomness in Science and Engineering 27 2.1 Introduction 27 2.2 Representation of Noise 29 2.3 Different Types of Noise 30 2.4 Difference Between Classical and Quantum Noise 31 2.5 Noise Benefit in Quantum Systems 32 2.6 Discussions 33 References 33 3 Various Types of Noise and Their Sources 34 3.1 Basic Concepts of Noise in Physics 34 3.1.1 Properties of Noise 35 3.1.2 Thermal Noise 35 3.1.3 Short Noise 37 3.1.4 Excess Noise 37 3.1.5 Low Frequency Noise 37 3.2 Quantum Noise 38 References 38 4 Constructive Role of Noise and Nonlinear Dynamics 40 4.1 Introduction to Nonlinear Dynamics 40 4.2 Linear Systems 41 4.2.1 Linear Systems in 2 43 4.2.2 Stability Theory 45 4.2.3 Nonhomogeneous Linear Systems 46 4.3 Local Theory of Nonlinear Systems 46 4.3.1 Linearization 47 4.3.2 Lyapunov Function and Stability 48 4.4 Global Theory of Nonlinear Systems 50 4.5 Examples of Nonlinear Systems 52 4.5.1 Bifurcation of Nonlinear System in 2 56 4.5.2 Chaotic Systems 57 4.5.3 Fractals 58 4.6 Constructive Role of Noise 59 4.6.1 Noise Benefits in the Context of Living Organisms 60 References 61 5 Noise and Synchronization of Oscillatory Networks 63 5.1 Noise Induced Synchronization 63 5.2 Stochastic Kuramoto Model 67 References 69 Part II Living Systems 70 6 Stochastic Fluctuations at Cellular and Molecular Level 71 6.1 Introduction 71 6.2 Stochastic Partitioning at Cell Division 72 6.3 Remarks 74 References 74 7 Various Types of Noise and Their Sources in Living Organisms 76 7.1 Introduction 76 7.2 Cellular Noise 77 7.2.1 Stochastic Gene Expression Model 77 7.2.1.1 Mathematical Frameworks 78 7.2.1.2 Transcription Burst Frequency Fluctuations 80 7.2.1.3 Transcriptional Burst Size Fluctuations 82 7.2.1.4 Transcriptional Rate Fluctuations 84 7.3 Neuronal Noise 86 References 87 8 Ion Channel Noise in Biological Systems 89 8.1 Introduction 89 8.2 Structure and Function of Ion Channel 90 8.2.1 Some Basic Concepts of Noise Analysis 92 8.2.2 Channel Noise 93 8.3 Single Channel Recordings and Channel Noise 94 8.4 Role of Noise and Cooperativity in Hodgkin–Huxley (HH) Formalism 96 8.4.1 Clinical Implications of Channel Noise 98 References 98 9 Noise in Cellular Communication 100 9.1 Effect of Noises on Cell Communication 100 9.1.1 Mathematical Framework 102 9.1.2 Model Predictions 104 References 105 10 The Role of Noise in Brain Function 106 10.1 Introduction 107 10.2 Stochastic Resonance and Sensory Biology 108 10.3 Principle of Least Time and Sum over Histories 110 10.3.1 40Hz Oscillations and the Concept of Simultaneity 111 10.3.2 Principle of Least Time 113 10.3.3 Sum over Histories 113 10.3.3.1 Phase-Response Properties of Neurons 114 10.3.3.2 Fisher Information and Noise in Brain 114 10.4 Possible Implications 115 References 116 11 Noise and Gene Oscillators 118 11.1 Introduction 118 11.2 Synthetic Gene Oscillators 119 11.3 Noise Resistance in Genetic Oscillators 119 11.4 Theory: Time Delayed Genetic Oscillation with Noise 120 11.4.1 Statistical Analysis 122 References 124 12 Developmental Noise and Stability 125 12.1 Introduction 125 12.2 Source of Developmental Noise 126 12.2.1 At the Molecular Level 126 12.2.2 At the Developmental Systems Level 127 12.2.3 At the Organismal Level 127 12.3 Mechanisms of Developmental Stability 128 References 129 13 Noise and Coherence in Meditation 131 13.1 Introduction 131 13.2 Various Issues and Limitations in the Current Meditation Research 133 13.3 Cognitive Process and Oscillatory Rhythm 136 13.4 States of Meditation and Their Characterization 138 13.5 Coherence: Spatial and Temporal 139 13.5.1 Degree of Spatial Coherence 140 13.5.2 Degree of Temporal Coherence 140 13.5.3 Sources of Noise 141 13.5.3.1 Brain Function and Mental Features 142 13.5.4 Role of Noise in Meditation 146 13.6 Future Directions 147 References 147 14 Chaos, Stochasticity and Noise 151 14.1 Introduction 151 14.2 Stochastic Hodgkin–Huxley Equations 152 14.2.1 Mathematical Framework of Noiseless Hodgkin–Huxley Equation 153 14.2.2 Langevin Description 154 14.2.3 Noise Term and Spatial Dependence in the Hodgkin–Huxley Model 158 14.3 Evidence of Chaos in Hodgkin–Huxley Model 159 References 160 15 Chance, Determinism and Laws of Nature 161 15.1 Introduction 161 15.2 Chance and Randomness 163 15.3 Laws of Nature 164 References 166