Complexity And Selforganization In

BIOLOGICAL DEVELOPMENT AND EVOLUTION 49 Stuart A. Newman and Gabor Forgacs

1. Introduction: Complex Chemical Systems in Biological Development and Evolution 49

2. Dynamic, Multistability and Cell Differentiation 51

2.1. Cell states and dynamics 53

2.2. Epigenetic multistability: the Keller autoregulatory transcription factor network model 55

2.3. Dependence of differentiation on cell-cell interaction: the Kaneko-Yomo "isologous Ddiversification" model 59

3. Biochemical Oscillations and Segmentation 65

3.1. Oscillatory dynamic oscillations and somitogenesis . . 65

3.2. The Lewis model of the somitogenesis oscillator 66

4. Reaction-Diffusion Mechanisms and Embryonic

Pattern Formation 70

4.1. Reaction-diffusion systems 71

4.2. Axis formation and left-right asymmetry 71

4.3. Meinhardt's models for axis formation and symmetry breaking 72

5. Evolution of Developmental Mechanisms 76

5.1. Segmentation in insects 77

5.2. Chemical dynamics and the evolution of insect segmentation 80

5.3. Evolution of developmental robustness 83

6. Conclusions 89

References 91

3. THE CIRCLE THAT NEVER ENDS:

CAN COMPLEXITY BE MADE SIMPLE? 97

Donald C. Mikulecky

1. Introduction: The Nature of the Problem and Why it

Has No Clear Solution 97

1.1. The human mind and the external world 99

1.2. Science and the myth of objectivity 100

1.3. Context dependence and self reference 102

2. An Introduction to Relational Systems Theory 103

2.1. Relational block diagrams 103

2.2. Information as an interrogative.

The answer to "why?" 104

2.3. Functional components and their central role in complex systems 106

2.4. The answer to "why is the whole more than the sum of its parts?" 106

2.5. Reductionism and relational systems theory compared 107

2.6. The functional component is not computable 108

2.7. An example: the [M,R] system and the organism/machine distinction 108

2.8. Relational models of mechanisms 112

2.9. Newtonian dynamics is not unique; there are alternatives that yield equivalent results 112

2.10. Topology, thermodynamics and relational modeling 114

2.11. The mathematics of science or is all mathematics scientific? 117

2.12. The parallels between vector calculus and topology . . 118

3. The Structure of Network Thermodynamics as Formalism . . 118

3.1. Network thermodynamic modeling is analogous to modeling electric circuits 119

3.2. The network thermodynamic model of a system . . . 120

3.3. Characterizing the networks using an abstraction of the network elements 120

3.4. The nature of the analog models that constitute network thermodynamics 121

3.5. The constitutive laws for all physical systems are analogous to the constitutive laws for electrical networks or can be constructed as the models for electronic elements 122

3.6. The resistance as a general systems element 123

3.7. The capacitance as a general systems element 124

3.8. The topology of a network 126

3.9. The formal description of a network 126

3.10. The formal solution of a linear resistive network ... 128

3.11. The use of multiports for coupled processes:

the entry to biological applications 130

3.12. Linear multiports are based on non-equilibrium thermodynamics 130

4. Simulation of Non-Linear Networks on Spice 133

4.1. Simulation of chemical reaction networks 134

4.2. Simulation of mass transport in compartamental systems and bulk flow 134

4.3. Network thermodynamics contributions to theory:

some fundamentals 135

4.4. The canonical representation of linear non-equilibrium systems, the metric structure of thermodynamics, and the energetic analysis of coupled systems 135

4.5. Tellegen's theorem and the onsager reciprocal relations (ORR) 136

5. Relational Networks and Beyond 138

5.1. A message from network theory 138

5.2. An "emergent" property of the 2-port current divider 139

5.3. The use of relational systems theory in chemistry and biology: past, present, and future ... 141

5.4. Conclusion: there is no conclusion 144

References 148

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