ࡱ> 3 jbjb^^ \h<h<lNNNNNb4N1L>>>>>>>1111111,2 4t1>>>>>1,1>>,1,1,1>~ >>1,12>1,1z,111\QNNp!11111g5,1g51,1Gordon, R. (1999). The Hierarchical Genome and Differentiation Waves: Novel Unification of Development, Genetics and Evolution. Singapore: World Scientific and London: Imperial College Press, 2 vols., 1836p., 6943 references, list US$172 / ?108. ISBN: 981-02-2268-8 (Set)students and people in developing countries, there are discounts of 20% and 25%. Order form:  HYPERLINK "http://www.wspc.com.sg/books/lifesci/2755.html" http://www.wspc.com.sg/books/lifesci/2755.html Reviewed in: Dellaire, G. (2001).. Heredity 87, 254-255.  HYPERLINK "http://www.umanitoba.ca/faculties/medicine/radiology/stafflist/staffitems/Dellaire.pdf" http://www.umanitoba.ca/faculties/medicine/radiology/stafflist/staffitems/Dellaire.pdf (1.5 MB) Papageorgiou, S. (2001). BioEssays 23(6), 559.  HYPERLINK "http://www.umanitoba.ca/faculties/medicine/radiology/stafflist/staffitems/Dellaire.pdf" http://www.umanitoba.ca/faculties/medicine/radiology/stafflist/staffitems/Papageor.pdf (852 KB) Desnitski, A.G. (2002a). [Russian]. Ontogenez 33(3), in press.  HYPERLINK "http://www.umanitoba.ca/faculties/medicine/radiology/Dick_Gordon_papers/Desnitski_(2002a)" http://www.umanitoba.ca/faculties/medicine/radiology/Dick_Gordon_papers/Desnitski_(2002a) (1.5 MB) CONTENTS Foreword vii Figure 1. Pieter D. Nieuwkoop with Richard Gordon... viii Figure 2. Pieter D. Nieuwkoop with Natalie K. Bj?klund... xii Preface xiii Flip Animation of the Ectoderm Contraction Wave xxi Proposition Page Numbers lviii 1.00 Introduction 1 1.01 Consider a Spherical Cow 1 Figure 3. A scanning electron micrograph (SEM) of a fertilized human egg... 3 1.02 The Epigenetic Problem 7 1.03 Wholeness and the Symmetry of the Early Embryo 10 1.04 Wholeness through the Ruse of Organicism 12 1.05 The Grip of Vitalism 16 1.06 The Rise and Fall of Physics in Embryology 20 1.07 Can We Restore the Physics of the Youth of Embryology? 24 1.08 Avoiding the Spatial Component of Embryogenesis 26 1.09 Wholeness, the Environment, and Symmetry Breaking 30 1.10 Wholeness through Surface Tension 34 1.11 Nonmaterial Physics as the Entelechy of Vitalism 36 1.12 Towards a New Physics of Embryos 38 1.13 New Tools of the Trade 40 1.14 Are We Headed for Reductionism? 46 1.15 Chemical or Mechanochemical Instabilities? 49 1.16 Critique of the Theory of Self-Organizing Systems 53 1.17 Protein Folding as a Deluding Paradigm 56 1.18 A Word on Language 59 1.19 The Embryology/Psychology Merry-go-round (Carrousel) 64 1.20 The Cosmic Context 66 2.00 Neural Induction and the Organizer 69 2.01 A Moment of Discovery 69 Figure 4. The stages of embryonic development of a urodele salamander... 70 2.02 Origins of the Idea of Induction 71 2.03 Preformationism versus Epigenesis: To Be or To Become? That is the Question 75 2.04 The Hunting of the Snark (The Inducer Molecule) 80 2.05 A Cornucopia of Inducers 83 2.06 The Snark Was a Boojum 88 2.07 Limb Induction: A Parallel Case? 93 2.08 Mesoderm and Other Inductions 95 2.09 Regional Induction 99 2.10 The Cell State Splitter 101 2.11 Meet the Axolotl 105 Table 1: Timing of early stages of the axolotl embryo... 106 2.12 A History of Sexism in Science Whodunit: Hilde Mangold or Hans Spemann? 112 3.00 Theory of the Cell State Splitter 120 3.01 Overview 120 Figure 5. Classical model of differentiation... 121 Figure 6. Alternative classical model for differentiation 122 Figure 7. Our new view of differentiation... 122 Figure 8. State of determination... 123 Figure 9. Determination tree... 125 Figure 10. A differentiation tree... 126 3.02 How to Stop a Wave on a Sphere 128 Figure 11. The contraction wave... in the simple 'shell' model.... 129 Figure 12. The spherical ectoderm of a urodele embryo... in the 'shell' model... 129 Figure 13. In the 'shell' model... when... a full hemisphere... 130 3.03 How the Ectoderm Contraction Wave Actually Stops: the Lens Model 133 3.04 Internal Pressure May Synchronize Preparation of the Cell State Splitters 136 3.05 The Right Place, at the Right Time, into the Right Kinds 139 3.06 The Intracellular Mechanics of the Cell State Splitter Yields Ectodermal Differentiation 140 Figure 14. A pressure P inside an embryo... 147 3.07 Force Generating and Load Bearing Cytoskeletal Components: Microtubules (MT) 149 3.08 Force Generating and Load Bearing Cytoskeletal Components: Microfilaments (MF) 152 3.09 Force Generating and Load Bearing Cytoskeletal Components: Intermediate filaments (IF) 155 3.10 Combinations of Cytoskeletal Components 158 4.00 Development and Genetics 164 4.01 The General Cell State Splitter (Propositions 1-9) 164 4.02 Differentiation Trees (Propositions 10-20) 183 Figure 15. A few simple differentiation trees... 184 Figure 16. Terminology for parts of a differentiation tree... 189 Figure 17. When the cell state splitter mechanically resolves... 208 Figure 18. Smooth propagation of a contraction differentiation wave... 214 Figure 19. Propagation of a 'bull's-eye' wave... 214 Figure 20. Propagation of a spacing pattern wave... 215 Figure 21. The epigenetic landscape... 217 4.03 Genetics and Differentiation Trees (Propositions 21-29) 221 4.04 A New Definition of 'Tissue' (Propositions 30-39) 241 Table 2: Positional information and induction vs differentiation waves... 252 4.05 The Relationship Between Cells and Tissues in Regulating Embryos (Propositions 40-54) 263 4.06 The Relationship Between Cells and Tissues in Mosaic Embryos (Propositions 55-66) 301 Figure 22. Four dimensional geometry of the development of a mosaic organism... 313 Figure 23. Four dimensional geometry of the development of a regulating organism... 314 5.00 Development and Evolution 354 5.01 Evolution of Cell State and Tissue Splitting (Propositions 67-73) 354 Figure 24. DNA basis for a differentiation tree branch duplication... 361 Figure 25. State of the DNA after a duplication... 362 Figure 26. Coevolution of DNA after a duplication... 363 5.02 The Secondary Importance of Embryonic Induction (Propositions 74-92) 368 Figure 27. Hierarchical differentiation cascade... 374 Figure 28. Differentiation cascade as a web... 375 Figure 29. Induction is secondary... 376 Figure 30. Unbreakable inductions... 378 5.03 Dedifferentiation and Redifferentiation (Propositions 93-107) 412 Figure 31. Two models for transdifferentiation... 414 5.04 The Selfish Differentiation Tree (Propositions 108-112) 436 5.05 The Ciliate Origin of Multicellular Organisms (Propositions 113-127) 447 6.00 Macroevolution 505 6.01 Redefining Microevolution and Macroevolution (Propositions 128-133) 505 Figure 32. Nematode macroevolution... 509 Figure 33. How to delete a middle subtree of a differentiation tree... 518 Figure 34. Simplification of a differentiation tree by fusion... 519 6.02 Possible DNA Mechanisms for Macroevolutionary Change of Differentiation Trees (Propositions 134-157) 520 Figure 35. Reducing developmental time discrepancies... 528 Figure 36 Genes per cascade vs number of kinds of cells... 550 Table 3: Estimated numbers of genes per differentiation cascade... 551 Table 4: Isochore correlations... 552 Figure 37. A differentiation tree showing a terminal branch and a subtree... 557 6.03 Differentiation Trees in Punctuated Equilibrium (Propositions 158-170) 573 Figure 38. The lineage tree of the nematode... 606 6.04 The Grand Sweep of Evolution (Propositions 171-194) 609 Figure 39. Bonner's Law... 629 Figure 40. Computer simulation of a... phylogenetic tree... 633 Figure 41. Evolution of brain size in mammals... 642 6.05 Neutralist Theory (Propositions 195-197) 658 6.06 A Universe Aware of Itself: Differentiation Waves and the Brain (Propositions 198-205) 668 7.00 The Biogenetic Law 701 7.01 'Ontogeny Recapitulates Phylogeny' Revisited via Differentiation Trees (Propositions 206-218) 701 Figure 42. Differentiation tree of a common ancestor... 708 Figure 43. Differentiation tree of an archetype... 709 Figure 44. Heterotropy... 720 Figure 45. Heterochrony and differentiation trees... 725 7.02 Organisms with Two Differentiation Trees (Propositions 219-229) 726 Figure 46. In continuing differentiation metamorphosis... 733 Figure 47. In pulsatile metamorphosis... 733 Figure 48. In single tissue metamorphosis... 734 Figure 49. In dedifferentiation metamorphosis... 735 Figure 50. Deferred metamorphosis 736 7.03 Winding up Evolution (Propositions 230-240) 747 8.00 The Homeobox 764 8.01 Why Insects and Vertebrates Share Homeobox Domains (Propositions 241-250) 764 Figure 51. The Drosophila morphogenetic furrow... 794 Figure 52. a) Variogram analysis... 795 8.02 The Development of Bilateral Asymmetry (Propositions 251-258) 803 Figure 53. Microtubule/wave colored symmetry... 818 Figure 54. Bilaterally symmetric shear couples... 823 Figure 55. Torque applied to a cell on the left side... 824 Figure 56. Torque applied to a cell on the right side... 824 8.03 Facets of Embryogenesis (Propositions 259-272) 830 9.00 A Cornucopia of Differentiation Waves 865 9.01 Activation Wave 865 9.02 Cleavage Waves 867 9.03 The Compaction Wave 874 9.04 Mitotic Waves 875 9.05 Quantal Mitoses and a Model for Limb Morphogenesis 881 9.06 Head and Tail Duplications 884 9.07 First Sitings of the Differentiation Waves of the Axolotl 893 9.08 Differentiation Waves of the Neural Plate 895 9.09 A Possible Pair of Differentiation Waves in the Later Epidermis 898 9.10 Neural Crest 901 9.11 Differentiation Waves in Plant Meristems 902 9.12 Differentiation Waves in Fly and Fish Eyes 908 9.13 Single Cell versus Multiple Cell Differentiation Waves 914 9.14 Repetitive Waves 917 9.15 Drosophila Bristles: A Wave/Mechanical Reinterpretation 920 9.16 The American Shorthair Tabby Domestic Cat and Pigment Patterns 925 9.17 Butterfly Eye Spots 928 9.18 The Milk Line 936 9.19 Waves in Assorted Tissues 938 9.20 Waves on Anuran Embryos 943 Figure 57. A nearly sagittal section of a Stage 10 1/2 axolotl embryo... 951 Figure 58. Enlargement of one wave profile of the ectoderm contraction wave... 952 9.21 Hints of Other Differentiation Waves 953 9.22 Uninvited Waves 956 Figure 59. First observations of what may be waves on explants of axolotl ectoderm... 963 9.23 Are Others' Waves Our Waves? 967 Table 5: Classes of calcium waves... 977 9.24 Are Differentiation Waves Merely Epiphenomena? 980 9.25 Mutant Waves 984 9.26 Wave Parallels between Mosaic and Regulating Organisms 988 9.27 Launching Domains May Have Specific Electrical, Mechanical and Molecular Properties 990 10.00 Conclusion 993 10.01 The Logic of Evolution 993 10.02 Is Evolution Progressive? 995 10.03 Were We Inevitable? 1002 10.04 The Living Ghost of Orthogenesis 1012 10.05 On Purpose and Progress 1017 10.06 The Beads-on-a-String 'New Synthesis' 1022 10.07 Gene Duplication as the Essence of Macroevolution 1026 10.08 The Blessings of Ever Increasing Dimensionality 1030 Figure 60. Differentiation tree space... 1030 10.09 The Fractal Tree of Life 1035 Figure 61. Darwin's schematic tree of life... 1038 Figure 62. A tissue lineage tree... 1040 10.10 The Novel Unification of Development, Genetics and Evolution 1042 10.11 Exploring the Higher Order Structure of the Genome 1047 10.12 How to Find a GEM 1055 10.13 A Clockwork Universe Within: Nuclear Tensegrity Mechanics (Wurfels) as a Foundation for the Nuclear State Splitter 1058 Figure 63. Wurfel model for chromosomes... 1062 10.14 The Top Ten Questions 1070 10.15 Paradigms for Developmental Biology 1078 10.16 A New Curriculum for Biologists 1083 Appendix I 1085 Gordon, R. & G.W. Brodland (1987). The cytoskeletal mechanics of brain morphogenesis: cell state splitters cause primary neural induction. Cell Biophysics 11, 177-238. Appendix II 1147 Brodland, G. W., R. Gordon, M. J. Scott, N. K. Bj?klund, K. B. Luchka, C. C. Martin, C. Matuga, M. Globus, S. Vethamany-Globus & D. Shu (1994). Furrowing surface contraction wave coincident with primary neural induction in amphibian embryos. J. Morph. 219 (2), 131-142. Appendix III 1159 Pursued by the Differentiation Wave Appendix IV 1168 Bj?klund, N. K. & R. Gordon (1993b). Nuclear state splitting: a working model for the mechanochemical coupling of differentiation waves to master genes (with an Addendum). Russian J. Dev. Biol. 24 (2), 79-95. Appendix V 1185 Gordon, R., N. K. Bj?klund & P. D. Nieuwkoop (1994). Dialogue on embryonic induction and differentiation waves. Int. Rev. Cytol. 150, 373-420. Appendix VI 1233 Bj?klund, N.K. & R. Gordon (1994). Surface contraction and expansion waves correlated with differentiation in axolotl embryos. I. Prolegomenon and differentiation during invagination through the blastopore, as shown by the fate map. Computers & Chemistry 18 (3), 333-345. Appendix VII 1246 Gordon, R. & N.K. Bj?klund (1996). How to observe surface contraction waves on axolotls. Int. J. Dev. Biol. 40 (4), 913-914. Appendix VIII 1248 Gordon, R. (1992d). Physicist to biologist: A first order phase transition. Bulletin of the Canadian Society for Theoretical Biology (10), 4-5. Index of Propositions 1252 References 1266 Glossary and Abbreviations 1584 Citation and Subject Index 1643 Permissions and Note Added in Proof INDEX OF PROPOSITIONS Page 165 Proposition 1: every step of determination in eukaryotic cells starts with the action of a cell state splitter. 168 Proposition 2: cell state splitters come in a variety of forms. 171 Proposition 3: all cell state splitters are bistable. 172 Proposition 4: every step of differentiation results in one of two new states for the differentiating cell. 176 Proposition 5: for some steps of differentiation, all the cells in the tissue resolve towards the same new state. 177 Proposition 6: the state of embryonic tissue competence coincides with a state of mechanical metastability of the cell state splitter. 180 Proposition 7: competence is maintained until a cell resolves the mechanical instability of its cell state splitter, or disassembles it. 181 Proposition 8: the classical multistep theories of early embryogenesis may be reinterpreted in terms of multiple differentiation waves. 182 Proposition 9: cell state splitters are evolutionarily conserved. 183 Proposition 10: every organism developing from a single cell has a differentiation tree whose nodes (arranged along a time axis) correspond to events of cell state splitting. 190 Proposition 11: differentiation and morphogenesis occur between acts of cell state splitting, i.e., along the edges of the differentiation tree, during each differentiation cascade. Determination is the act of cell state splitting, and occurs at the nodes of the differentiation tree. 194 Proposition 12: during primary neural induction, in particular, all neural plate specific genes are turned on in the wake of the ectoderm contraction wave, which leaves them arrayed as gradients in and/or behind the wave. 197 Proposition 13: each act of cell state splitting triggers a differentiation cascade of changes in gene activity and its consequences at transcriptional, translational, and posttranslational levels. 199 Proposition 14: the genetic program for development is the differentiation tree, which consists of alternations between genetic and mechanical events. 203 Proposition 15: genetic determinism cannot explain the spatial component of embryogenesis. 207 Proposition 16: consideration of the spatial component of the genetic program is essential for progress in artificial life (ALife) and embryonics research. 211 Proposition 17: the nongenetic component of the generic paradigm for morphogenesis is the differentiation wave. 212 Proposition 18: propagation of a contraction differentiation wave from one cell to the next (homoiogenetic induction) involves stretch activated contraction of the microfilament ring in the cell state splitter. 213 Proposition 19: morphological histories of tissues or tissue lineages should be replaced by precisely observed differentiation trees. 215 Proposition 20: the epigenetic landscape for an organism is its differentiation tree. 222 Proposition 21: the differentiation cascade for each step of differentiation is set off by a differentiation trigger inside the cell nucleus. 222 Proposition 22: differentiation triggers, each of which starts off one of a pair of differentiation cascades, have two states. 223 Proposition 23: a commitment signal travels directly or indirectly from the cell state splitter to the nucleus and selects the differentiation trigger. The set of mechanochemical and chemical reactions transmitting this information we call the differentiation pathway. 232 Proposition 24: there exists a state of nuclear competence in which the nucleus is prepared to receive the appropriate commitment signal. 237 Proposition 25: embryological competence of a cell to go through a step of differentiation requires the presence of a cell state splitter, a commitment signal, a differentiation trigger, and a corresponding state of nuclear competence. 237 Proposition 26: a means must be available for ensuring that only the appropriate pair of differentiation triggers reacts to the commitment signal. 238 Proposition 27: each differentiation cascade released by a cell state splitter includes means of setting up the next cell state splitter, preparation of a pair of differentiation triggers, and the preparation of the next commitment signal. 238 Proposition 28: all gene subsets that are activated in a given cell at a given stage of differentiation are accessed via the strictly hierarchical organization of the differentiation tree. 239 Proposition 29: there is a distinction between activation of a differentiation cascade and activity of genes within that differentiation cascade. 241 Proposition 30: a tissue consists of the equivalence class of all cells that have followed the same path through the differentiation tree. 243 Proposition 31: tissue synchronizing mechanisms initiate the next act of cell state splitting in a tissue consisting of contiguous cells. 244 Proposition 32: if the cells in a tissue lack a synchronizing mechanism, then the precise positioning of some of the nodes of the differentiation tree along the time axis would have to be replaced by a statistical ensemble of paths of its cells along the tree. 244 Proposition 33: the community effect is caused by differentiation waves. 247 Proposition 34: at each event of cell state splitting, the so-called positional information for a cell is increased by precisely one bit, namely, which side of the future boundary between the two new tissues the cell happens to be on. 250 Proposition 35: positional information does not exist. 256 Proposition 36: the basis of a cell's 'memory' of the path it took along it's genome's differentiation tree may be a subset of the accumulation of activated genes or gene products generated at each stage of differentiation ('memoron set'). 259 Proposition 37: the memorons in a cell are triggered in response to a sequence of contraction and expansion waves, which therefore forms the differentiation code. 260 Proposition 38: the initial distinction between animal and vegetal hemispheres in amphibian fertilized eggs is due to the hydrodynamics of the yolk. 262 Proposition 39: the position of a cell is important, because that determines which kind of differentiation wave it will participate in next. 263 Proposition 40: the spatial component of differentiation, i.e., the splitting of a tissue into two new tissues, is accomplished by robust mechanical means that impart some independence from cell and embryo size. This is the essence of embryonic regulation, attributable to the properties of differentiation waves. 266 Proposition 41: cell state splitters may form the basis for fractal morphogenetic processes. 267 Proposition 42: all morphogenetic movements are secondary to differentiation waves. 270 Proposition 43: secondary morphogenetic events are robust. 271 Proposition 44: the shape of a tissue is determined by: a) the location and shape of the launching domain of the differentiation wave that creates it, b) the trajectory of its differentiation wave, including possible refraction effects; and c) the manner of termination of that wave: self-annihilation, physical barriers (absorption), annihilation upon meeting another wave, and/or propagation into another tissue (transmission). 277 Proposition 45: morphogenesis via tissue splitting explains compartmentalization of a tissue into two sharply demarcated new tissues. 280 Proposition 46: whether a wave is launched as an expansion wave or a contraction wave depends on two thresholds of mechanical tension. 284 Proposition 47: natural 'inducers' are involved in the location and type of differentiation waves launched. 286 Proposition 48: an embryonic field corresponds to the trajectory of an expansion or contraction wave. 289 Proposition 49: each change in a component of the differentiation pathway, and each gene product specific to the state of cell differentiation being triggered, will occur in the wake of the differentiation wave that initiates it, and track that wave over the embryo. 292 Proposition 50: the differentiation pathway, and the sequence of syntheses of the specific gene products, can be partially worked out from the delays between the physically observable differentiation wave and the fluorescence waves for those products. 292 Proposition 51: some morphogenetic movements, and their aberrations, may be directly caused by differentiation waves. 294 Proposition 52: in amphibians, the first cell state splitter is the apparatus for cortical rotation and gray crescent formation. 298 Proposition 53: the sex of an individual is determined by triggering of an expansion or a contraction differentiation wave, corresponding to female and male (or vice versa). 300 Proposition 54: differentiation in tissue and organ culture proceeds via differentiation waves. 301 Proposition 55: the fundamental difference between mosaic embryos and regulating embryos is that tissues in strictly mosaic embryos consist of one cell while tissues in regulating embryos consist of many cells. 304 Proposition 56: a cell state splitter is set up at every step of cell division in a strictly mosaic embryo, so that its cell lineage is identical to its differentiation tree. 308 Proposition 57: asymmetric cell divisions in mosaic organisms may correspond to a pair of contraction and expansion differentiation 'waves' that propagate across complementary portions of the dividing cell. 313 Proposition 58: so-called determinants are positioned by the cytoskeleton during asymmetric cell divisions by single cell differentiation waves. 317 Proposition 59: the spatial separation of so-called 'cytoplasmic determinants' of mosaic and regulating eggs may be caused by cell state splitters. 320 Proposition 60: cytoplasmic determinants may not exist. 324 Proposition 61: compaction is a phenomenon occurring in both regulating and mosaic embryos, at early, few cell stages, that uses both a contraction and an expansion wave to separate blastomeres into external and internal cells. 326 Proposition 62: in mosaic organisms a differentiation wave travels only over a single cell, along its cortex. 331 Proposition 63: the cell state splitter in asymmetric divisions also causes the intracellular morphogenesis that segregates components to the two distinct daughter cells. 336 Proposition 64: asymmetries in the cortical cytoskeleton in cells undergoing asymmetric division are passed on in some manner to the daughter cells, through 'orientation scars', which may be the launching sites for the next set of single cell differentiation waves. 343 Proposition 65: orientation scars are directly related to the cortical attachment site of the asymmetric spindle in unequal cleavage. 351 Proposition 66: stem cells in regulating organisms are similar to asymmetrically dividing cells in mosaic organisms. They are also members of stem tissues which have some means of postponing setup of the next cell state splitter, pair of differentiation triggers, and/or commitment signals. 354 Proposition 67: synchronization mechanisms for coordinating the appearance of cell state splitters in all of the cells of a tissue developed in the course of evolution in response to selective pressures for larger tissue sizes. 356 Proposition 68: the need for cell state splitter synchronizing mechanisms explains why regulating embryos are a later evolutionary development than mosaic embryos. 358 Proposition 69: a major step in the evolution of multicellular organisms was the ability to generate the next cell state splitter and accompanying differentiation triggers and commitment signal, i.e., the invention of continuing differentiation with postponed terminal differentiation. 359 Proposition 70: the evolution of continuing differentiation coincided with the ability to duplicate terminal branches of the differentiation tree. 360 Proposition 71: the evolution of continuing differentiation coincided with the origin of imprinting. 365 Proposition 72: continuing differentiation required the evolutionary invention of the genetic program. 366 Proposition 73: the diversity of potential differentiation trees exceeds the number of individual organisms that have ever existed. 368 Proposition 74: embryonic induction is an evolutionarily opportunistic and thus secondary interaction between two tissues. Its function may be to help coordinate the timing of their development. 371 Proposition 75: high rates of speciation via heterochronic changes may not only disrupt inductive relationships between tissues, but also tend to keep the differentiation tree from establishing crosstalk or webbing between edges. Reduced webbing permits a higher rate of species radiation. 373 Proposition 76: the regulatory levels of the differentiation tree and the differentiation cascades forming the edges of the tree might be distinguishable on the basis of the amount of web formation. 374 Proposition 77: developmentally earlier edges of the differentiation tree represent differentiation cascades that tend to be simpler. 376 Proposition 78: on an evolutionary time scale, it may be that heterochrony forces the breaking and making of new inductive relationships. 379 Proposition 79: organisms whose differentiation trees evolve into differentiation webs cease to radiate. 380 Proposition 80: organisms whose differentiation trees have largely converted to differentiation webs either have persisted with little apparent change over long geological times (exhibiting evolutionary 'stasis') or become extinct. 380 Proposition 81: homeothermic (warm-blooded) organisms may rely less on induction mechanisms to synchronize embryonic development. This may allow heterochronic mutations to be successful more often, and thus provides a basis for faster evolutionary radiation. 381 Proposition 82: the launching of one differentiation wave may have a mechanical dependence on the completion of the previous differentiation wave. This provides a new lockstep wave-wave inductive mechanism, and may explain the broad temperature independence of development in poikilothermic organisms. 385 Proposition 83: some major birth defects, partial inductions by so-called regional inducers, and incomplete or disorganized embryos (embryoids), could be due to a failure of the proper sequence of wave-wave inductions. 388 Proposition 84: induction helps break spatial symmetries in a tissue in a way that is consistent with previously broken symmetries, again assuring greater success of embryonic development. 389 Proposition 85: while a process of induction may require mere physical adhesion between two tissues, establishment of that adhesion may involve specific interactions at the interface between their cells. 391 Proposition 86: 'regional' inductions are actually multiple steps of differentiation. 395 Proposition 87: regional induction of the eye placodes may be caused by a single differentiation wave in the neural plate that splits in two waves. 401 Proposition 88: regional 'predetermination' does not occur. 403 Proposition 89: the relationships between the ectoderm and the underlying mesoderm may be mutual, and affect the trajectories of differentiation waves in these tissues. 406 Proposition 90: induction of the neural plate may not require the mesoderm at all. 408 Proposition 91: regional inductions are often caused by launching of differentiation waves by mechanisms not requiring an underlying, adjacent tissue. 409 Proposition 92: hierarchically organized homeobox genes correspond to regional differentiations by being activated by corresponding differentiation waves. 412 Proposition 93: dedifferentiation and redifferentiation may occur by cells traversing down the differentiation tree and then back up via another route. 415 Proposition 94: differentiated cells capable of dedifferentiation may have sequential back pointers to earlier cell state splitter differentiation cascades, making the differentiation tree at least partly a doubly linked structure. 417 Proposition 95: the success of nuclear transplantation between two differentiated cells is inversely dependent on the differences between their differentiation codes. 419 Proposition 96: the success of natural dedifferentiation and redifferentiation (i.e., regeneration) depends inversely on the number of backtracking steps needed to get to the node of the differentiation tree from which redifferentiation has to start. 420 Proposition 97: transdetermination occurs via dedifferentiation followed by redifferentiation. 423 Proposition 98: transdetermination in imaginal discs could be a process of revertible, somatic mutation. 424 Proposition 99: transdifferentiation or transdetermination involves differentiation tree edge jumping at the level of the nuclear state splitter. 425 Proposition 100: dedifferentiation and transdifferentiation occur via two dimensional dedifferentiation waves and transdifferentiation waves. 426 Proposition 101: all cells involved in a given homeotic transformation or transdetermination have experienced the same sequence of expansion and contraction differentiation waves. 428 Proposition 102: some cancers can be controlled via dedifferentiation. 428 Proposition 103: cancer may involve differentiation and/or dedifferentiation waves. 430 Proposition 104: the ability to deactivate single differentiation cascades is an evolutionary advancement comparable to that of continuing differentiation, and made dedifferentiation and regeneration of complex morphology possible. 430 Proposition 105: activation and deactivation of differentiation cascades during differentiation and dedifferentiation involves not only master genes, but also a physical mechanism. 431 Proposition 106: the contradiction between atavistic development and the decay to background of unused genes can be resolved via the (nongenetic) persistence of the physics of differentiation waves. 436 Proposition 107: germ cells are set aside early in development so that they avoid participation in most differentiation waves, which keeps their DNA accessible (exposed?) for the next generation. 437 Proposition 108: the differentiation tree, seen as a hierarchically organized set of differentiation cascades, is the fundamental germ-line replicator on which adaptation and thus evolution proceed. 440 Proposition 109: the differentiation tree is a logical, rather than physical, organization of the DNA, which is, for the most part, undisturbed by chromosomal rearrangements. 441 Proposition 110: chromosomal repatterning is subject to the constraint that a viable differentiation tree is preserved. 444 Proposition 111: the high correlation of chromosomal repatterning with speciation suggests that reorganization of the differentiation tree is a common basis for speciation. 446 Proposition 112: chromosome segments involved in repatterning are probably split from one another at nodes of the differentiation tree or at lower level pointers within differentiation cascades. 447 Proposition 113: ciliates pattern their surfaces via cortical waves. 453 Proposition 114: the cortical waves of ciliates may involve changes in protein expression, which may also be changes in cortical gene expression. 458 Proposition 115: centrosomes may be symbiotic organelles. 464 Proposition 116: maternal determinants may be related to centrosomes. 467 Proposition 117: bacterial colonies capable of pattern formation are homologous to the cortex of multicellular organisms. 472 Proposition 118: coordinated beating of cilia (metachronic waves) in ciliates and in multicellular organisms are homologous, perhaps evolving from surface colonies of primitive spirochetes. 476 Proposition 119: phenomena such as twinning and regeneration appear to have a universal cortical basis. 478 Proposition 120: there is an evolutionary continuity in the cortex as the seat of differentiation waves. 480 Proposition 121: during eukaryotic evolution, cortical differentiation via differentiation waves preceded cellular differentiation. 482 Proposition 122: cortical inheritance and differentiation waves preceded nuclear inheritance in the origin of eukaryotes. 483 Proposition 123: multicellular organisms are descended from ciliates via recellularization of their cortical bacterial symbionts. 493 Proposition 124: control of the nuclear genome by differentiation waves came relatively late in evolution. 497 Proposition 125: some of the Ediacaran organisms were ciliates. 498 Proposition 126: gastrulation started with the ciliates. 501 Proposition 127: the physics of the cortex may be the key to morphogenesis. 506 Proposition 128: microevolution consists of any change to any differentiation cascade that does not change the topology of the differentiation tree. Heterochrony is an example of microevolution. 507 Proposition 129: macroevolution, the evolution of major taxonomic groups, corresponds to topological change of the differentiation tree. 512 Proposition 130: microevolution results in movements across an adaptive landscape whose fixed dimensions correspond to the genes in the differentiation tree, while macroevolution produces a change in the number of dimensions of that adaptive landscape. 514 Proposition 131: macroevolution can be a nonequilibrium process when there is an expanding dimensionality of the differentiation tree. 517 Proposition 132: macroevolution by nonterminal deletions within the differentiation tree, leaving a dangling terminal branch, would in general prune the tree. 519 Proposition 133: macroevolutionary simplification of a differentiation tree could occur by the fusion of two consecutive edges or differentiation cascades. 520 Proposition 134: duplication of a terminal branch of a differentiation tree, consisting of two terminal edges with a common node, is a simple macroevolutionary change for a differentiation tree, easily explained in terms of copy and paste operations on DNA. 525 Proposition 135: edges of differentiation trees may be distinguishable from lower levels of genetic regulation by the degree of web formation. Web formation constrains duplication to units or multiples of edges of the differentiation tree (i.e., terminal branches). 527 Proposition 136: the viability of a duplication of a terminal branch of a differentiation tree is inversely related to the size of the terminal branch. 530 Proposition 137: the hopeful monster can be reconsidered, if we distinguish the 'hopeful genotype' from the 'hopeful phenotype'. 534 Proposition 138: transfer of a terminal branch of a differentiation tree is less likely to be viable than its duplication. 535 Proposition 139: the probability of gene duplication splitting essential segments of DNA, such as those used for differentiation trees, is reduced when there is a large background of functionless DNA, and may indicate an evolutionary advantage for such 'junk' DNA. 538 Proposition 140: the requirement that the differentiation tree be a linked structure implies that a duplicated or transferred terminal branch will rarely be inserted into the middle of a differentiation tree. 538 Proposition 141: multigene families are created in the course of duplication of branches of the differentiation tree. 542 Proposition 142: the cell state splitter is often amongst those elements in a copied edge. Thus the cell state splitter's sensitivity to mechanical forces can vary, permitting, for example, tissue specific variations in the conditions needed to launch expansion versus contraction waves. 543 Proposition 143: low levels of expression of genes in multigene families, outside their tissues of primary expression, may represent 'leakage' rather than 'deliberate' control. 544 Proposition 144: in many cases, differentiation cascades of the differentiation tree may share the very same 'gene modules', which may be thought of as gene cascades that are accessed by, but logically separate from, the differentiation tree. Such developmental gene modules may contain most housekeeping genes. 549 Proposition 145: gene modules are stable over evolutionary time in proportion to the number of differentiated cell types that address them. 550 Proposition 146: GC-poor isochores may correspond to edges of the differentiation tree, i.e., they may individually contain the bulk of the genes activated in the differentiation cascade for a single step of differentiation. 553 Proposition 147: conserved autosomal segments approximately correspond to the edges of the differentiation tree. 554 Proposition 148: gene modules are addressed by diffusible trans-acting molecules. 555 Proposition 149: differentiation trees and gene modules may provide a mechanistic basis for biological homology. 556 Proposition 150: a gene in a differentiation cascade will be activated as a subtree of the differentiation tree. It will be expressed as a subgraph of the subtree. 559 Proposition 151: the expression patterns of assorted genes, and mutated genes, insofar as they occur as subtrees, could be used to work out the differentiation tree. 561 Proposition 152: viruses attack tissues related as subtrees of the differentiation tree. 561 Proposition 153: virus attacks on developing organisms are, in general, more devastating than attacks on adults, because more tissues of the target subtree become available in the embryo, fetus or larva. 561 Proposition 154: birth defects and congenital mental anomalies not involving housekeeping genes may be traced back to differentiation wave defects, i.e., defective launching, propagation, or transduction of a differentiation wave. 567 Proposition 155: childhood neuroectodermal tumors may be aberrant offshoots of the brain's subtree of the differentiation tree. 569 Proposition 156: some genes and products on duplicated terminal branches may become vestigial, because they are not needed on the new copy of the terminal branch. 570 Proposition 157: transfer of a whole terminal branch of a differentiation tree, involved in formation of a specific organ or structure, from one part of the tree to another, may explain the homology between structures in different taxa that have different embryological origins in terms of cell lineage. 573 Proposition 158: matings between organisms with topologically different differentiation trees (attempts at hybridization) have incompatibilities between the differentiation trees that may usually prevent development from the stage at which the incompatibility would unfold. 576 Proposition 159: the degree of viability of hybrids is on average inversely proportional to the magnitude of the differences between the differentiation trees of the parent species. 581 Proposition 160: hybrid inviability is due most often to incompatibilities between two differentiation trees at the level of intranuclear and/or intracellular interactions. 582 Proposition 161: large topological changes in a differentiation tree may account for punctuated equilibrium. 587 Proposition 162: differentiation trees provide a basis for speciation. 588 Proposition 163: evolutionary stasis may be brought about through the high frequency of reproductive isolation of an individual from its parent population when its mutation creates a topologically different differentiation tree. 591 Proposition 164: differentiation trees explain mosaic evolution. 592 Proposition 165: during a speciation event, the partial incompatibilities between topologically different differentiation trees may produce developmental instabilities. 593 Proposition 166: 'developmental homeostasis' ('canalization') does not exist, and so does not form a basis for stasis. 598 Proposition 167: embryonic regulation does not exist. 599 Proposition 168: development consists primarily of positive feedbacks. 600 Proposition 169: the magnitude of the accumulation of developmental errors is different for mosaic and regulating organisms. 604 Proposition 170: differentiation trees may allow us to 'compute' at least mosaic organisms, and their developmental constraints. 609 Proposition 171: evolution has had four major stages, namely quasispecies evolution, single celled species, species with limited cell type differentiation, and species with continuing differentiation. 610 Proposition 172: the number of terminal edges of the differentiation tree per gram is a monotonically increasing function of the mass of an organism. 611 Proposition 173: there is a minimum size to the trajectory of a differentiation wave. In particular, this factor places a limit on the complexity of the brain, and perhaps on intelligence. It may be for this reason that 'external' food supplies (nutritive endoderm, extraembryonic yolk or placenta) for the embryo evolved. 618 Proposition 174: the average number of genes per differentiation cascade has increased during eukaryotic evolution. 621 Proposition 175: the average number of genes per differentiation cascade decreases inversely with branch order. 622 Proposition 176: the generation time of an organism with regulating embryos is a monotonic function of the maximum number of cell state splittings through which any cell could go as it traverses the differentiation tree. 622 Proposition 177: polymacroevolution requires either an increase in the size of an organism, permitting major growth to the differentiation tree, or substantial pruning of the differentiation tree, followed by regrowth. 625 Proposition 178: a general correlation will be found between body size and cell size in a Cope's law series of organisms. 626 Proposition 179: the basis of progressive evolution may be that there is in general a greater benefit to increasing the size of the differentiation tree than pruning it as a response to a given evolutionary opportunity. 628 Proposition 180: polymacroevolution proceeds by general increases of both the sizes of the differentiation trees and the physical sizes of lines of organisms, alternating with geologically sudden prunings to both smaller differentiation trees and organisms. 629 Proposition 181: some terminal branches of the differentiation tree at a given stage of macroevolution are more expendable than others, so that the ratcheting mechanism of polymacroevolution consists in the development of more effective (higher fitness value) terminal branches and the elimination of less effective terminal branches through Cope's cycles of taxon size increase followed by pruning (Bonner's law). 630 Proposition 182: the main difference between small organisms that start off consecutive Cope's cycles is that the later ones have a higher proportion of evolutionarily more effective terminal branches in their differentiation trees. 631 Proposition 183: more effective edges of differentiation trees account for the phenomenon of condensation or shortening of developmental stages, which in turn allows more terminal branches to be added. 632 Proposition 184: the fractal dimension of a differentiation tree may be related to its potential for evolutionary radiation. 634 Proposition 185: the evolution of communities during evolutionary radiation may in part be explicable as discrete selections from the space of all differentiation trees derivable from the differentiation tree of the common ancestor. This may occur in similar ways in different radiations, explaining evolutionary parallelism between unrelated groups. 635 Proposition 186: the winner in the collision of two radiations is the radiation that has previously had the most prunings of its differentiation trees. 637 Proposition 187: ratcheting mechanisms based on differentiation trees are consistent with physics and thermodynamics. 640 Proposition 188: differentiation trees may provide a basis for an irreversible thermodynamics of evolution. 645 Proposition 189: the growth of differentiation trees over evolutionary time corresponds to an increase in the maximal entropy and information available in living organisms. 646 Proposition 190: genome doubling, a major, repetitive event in evolutionary history, does not fundamentally alter the differentiation tree. 647 Proposition 191: growth and pruning of differentiation trees broadens the sharp peaks of frequency of DNA per genome due to genome doublings. 647 Proposition 192: survival of a differentiation tree depends on its compatibility at all hierarchical levels. 648 Proposition 193: there may be a rough correlation between the magnitudes of topological changes to differentiation trees in the course of evolution and proposed hierarchies in the process of evolution. 649 Proposition 194: we need an intellectual linking discipline to connect each hierarchical level to the next. 658 Proposition 195: the neutral theory of molecular evolution should be extended to encompass DNA changes of all magnitudes. Neutral changes, including morphologically neutral changes to the topology of the differentiation tree, can form the basis for speciation. 659 Proposition 196: an expanded neutral theory of evolution leads to the concept of fractal evolution, in which each individual is an incipient species. From the point of view of the individual, its problem becomes to find a reproductively compatible mate. 664 Proposition 197: the concept of fractal evolution, in which numerous differences between differentiation trees are arising frequently, may help solve some outstanding problems in evolution, such as the definition of species, cryptic species, and the advantages of sex. 668 Proposition 198: evolution of the central nervous system is primarily a matter of growth via bifurcation of its portion of the differentiation tree, which may be greater than 50% of the whole. 671 Proposition 199: pathfinding by developing neurons is secondary to the hierarchically nested placodal structure of the brain based on differentiation trees and differentiation waves. 675 Proposition 200: explanations for components of behavior, and mental phenomena such as mental rotation, could be approached in terms of differentiation waves. 677 Proposition 201: cerebral hemispheric specialization involves an asymmetric unfolding of the differentiation trees between the two hemispheres. The hierarchical nesting of the differentiation waves amplifies small left-right differences. 682 Proposition 202: learning is primarily a matter of extension of the differentiation tree beyond its inherited components. 687 Proposition 203: instinct is genetic assimilation of an extension of the differentiation tree corresponding to a learned behavior. 691 Proposition 204: instinctual behavior is evolutionarily more advanced than learned behavior. 695 Proposition 205: sleep, an evolutionarily primitive feature of animals, lasts for hours because that is how long differentiation waves involved in learning take to complete their trajectories. 701 Proposition 206: terminal topological additions to differentiation trees consisting of duplicates of terminal branches are more often compatible with reproductive success than other topological changes to the differentiation tree, because they are relatively frequently evolutionarily neutral or of selective advantage. 704 Proposition 207: except for genetic drift, the differentiation tree will preserve the history of its production by duplications of previous terminal branches. 705 Proposition 208: macroevolution proceeds primarily by addition and deletion of terminal edges of the differentiation tree. 707 Proposition 209: the differentiation tree is in effect the Bauplan of an organism. 707 Proposition 210: recapitulation is fundamentally a matter of degree of correspondence of the topologies of the differentiation trees of the organisms being compared. Given two differentiation trees, when we compare them by matching roots, either: one tree is a subtree of the other, or there is a common subtree of both. 709 Proposition 211: closely related organisms that have morphologically distinct pathways of morphogenesis nevertheless can have similar differentiation trees. 714 Proposition 212: direct and indirect development use the same differentiation tree. 717 Proposition 213: in regulating embryos, so long as a cell sheet is reconstituted which can support the next pair of differentiation waves, it does not matter what kind of morphogenetic movements occur in between, including dissociation and reassociation of its cells. 717 Proposition 214: the differentiation tree and morphogenetic movements can evolve independently of one another. 718 Proposition 215: juvenile adaptation and heterotopy can be explained in terms of macroevolutionary changes to the differentiation tree. 719 Proposition 216: phylogeny reconstruction or taxonomy should be based on the differentiation trees of organisms. 724 Proposition 217: because of the possibility of heterochrony, recapitulation need not occur in a strict chronological order. 725 Proposition 218: more conserved terminal cell types differentiate via fewer differentiation waves. 726 Proposition 219: the haploid and diploid phases probably use exactly the same differentiation tree in plants with isomorphic generations. 727 Proposition 220: the first step in an evolutionary shift from an isomorphic to a diplontic life cycle was a DNA duplication involving the whole differentiation tree. 728 Proposition 221: diploidy and polyploidy may often allow mutant differentiation trees to become established much faster than differentiation trees of haploid organisms or generations, thus permitting faster evolutionary radiation. 729 Proposition 222: organisms that undergo metamorphosis may use separate differentiation trees for each part of the life cycle. 730 Proposition 223: cataclysmic metamorphosis occurs from either a single tissue within a larva or from tissues that dedifferentiate back to a single tissue. 732 Proposition 224: different forms of metamorphosis can be distinguished on the basis of the organisms' differentiation trees. 737 Proposition 225: there are many examples of the five categories of metamorphosis. 742 Proposition 226: concatenation of distinct phyla occurs in two steps: hybridization followed by a recombination event that grafts one differentiation tree to the other. 744 Proposition 227: after the grafting of one tree onto another, subsequent transpositions of terminal branches of the adult differentiation tree could occur over evolutionary time, dispersing the adult tree over some of the terminal branches of the concatenated larva. This could be the origin of the pattern of deferred metamorphosis from a few tissues without their dedifferentiation, as in holometabolous insects. 744 Proposition 228: grafting of one whole differentiation tree onto another is more likely between distantly related phyla, providing a mechanism for one step macroevolution. 746 Proposition 229: the phylogenetic tree is, in part, a web. 748 Proposition 230: since there is a finite set of topological changes of a given magnitude that can be made to a given differentiation tree, we may be able to predict the species that are immediately derivable from an existing species, i.e., to compute the developmental constraints on a given species. 752 Proposition 231: some of the major events in evolution have been those that permitted larger size without decreasing the interface surface to volume ratio of the organisms' living cells. 752 Proposition 232: the evolution of perception can be approached via the biogenetic law. 753 Proposition 233: genetic recombination in sexually reproducing organisms causing topological changes to the differentiation tree provides a basis for more rapid speciation than in species with asexual reproduction. 755 Proposition 234: if the genetic recombination rate increases, each differentiation cascade of the differentiation tree becomes more likely to be disbursed across the genome, and radiation slows down or ceases. 756 Proposition 235: there is an inverse relationship between the number of chromosomes and the rate of evolution of differentiation trees. 757 Proposition 236: the ability of a population of organisms to undergo evolutionary radiation may depend mostly on the topology of its differentiation tree. 758 Proposition 237: if we could relink detached terminal branches of differentiation trees, we could recover organisms similar to some extinct forms. 759 Proposition 238: genetic manipulations at the pointers may be one of the quickest ways for us to design new organisms. 759 Proposition 239: defragmentation of the genome would permit a new bout of radiation. 761 Proposition 240: artificial life should be based on differentiation trees. 764 Proposition 241: insects and vertebrates have a common ancestor whose tissues differentiated by the use of differentiation waves. 769 Proposition 242: gradients of morphogens are irrelevant to differentiation. 772 Proposition 243: the earliest 'morphogen' gradients in the syncytial blastoderm stage of Drosophila are secondary phenomena. 776 Proposition 244: differentiation waves can proceed along single file rows of cells. 778 Proposition 245: gene expression boundaries are determined by the trajectories of differentiation waves. 783 Proposition 246: segmentation involves a sequence of differentiation waves. 785 Proposition 247: the genes involved in the mechanism of continuing differentiation, particularly those of the cell state splitter and the differentiation pathway, are highly conserved and pleiotropic. 788 Proposition 248: some mutations can be classified as to whether they interfere with the propagation of a differentiation wave or with the differentiation pathway it sets off. 793 Proposition 249: in the formation of spacing patterns, a differentiation wave can consist of both contracting and expanding cells. 797 Proposition 250: many spacing patterns could be due to contraction/expansion differentiation waves. 803 Proposition 251: the breaking of bilateral symmetry, as in the formation of the heart, is due to cumulative deviations, from perpendicularity of their wave fronts, of spacing pattern differentiation waves. 809 Proposition 252: asymmetric penetrance is due to failure of launching of one of a pair of differentiation waves on one side of a bilateral organism. 811 Proposition 253: incomplete penetrance of morphological features is due to a differentiation wave whose launching sometimes fails. 812 Proposition 254: left-right asymmetry is encoded in the lateral membrane cortices of ectoderm cells as left or right pitched macromolecular helices during propagation of the ectoderm contraction wave. 817 Proposition 255: the angle between the advancing wave front of the ectoderm contraction wave and the microtubule orientation remaining from cortical rotation prior to first cleavage divides the bilaterally symmetric neural plate into 8 regions related by colored symmetry. 822 Proposition 256: the coupling between the shear gradient along the midline and the apical microtubules oriented at cortical rotation is the major mechanism for left-right asymmetrization. 823 Proposition 257: paraxial microtubules and their interactions with the nucleus may be involved in bilateral asymmetry. 825 Proposition 258: left-right asymmetry develops in bottle cells at the blastopore. 830 Proposition 259: the differentiation pathway may be similar or identical for all steps of differentiation. 831 Proposition 260: critical periods in embryonic development correspond to periods when differentiation waves are moving. 832 Proposition 261: differentiation waves, being slow moving, generate long lasting gradients (i.e., gradients are epiphenomena). 833 Proposition 262: the homeobox 'code' and regional differentiation can be explained in terms of consecutive differentiation waves with nested, overlapping trajectories. 836 Proposition 263: the boundaries (grooves) for each level of segmentation in a segmenting or compartmentalizing organism are launching domains for differentiation waves. 840 Proposition 264: differentiation waves provide the common morphogenetic mechanism between cellular and syncytial organisms. 844 Proposition 265: the hierarchy of segmentation genes is reflected in and triggered by the hierarchy of segmentation differentiation waves. 844 Proposition 266: launching domains may represent the fundamental homologies in animals. 846 Proposition 267: the only 'morphogenetic' gradient not set up by differentiation waves is the original gradient of the oocyte, represented by bicoid mRNA in Drosophila and the animal/vegetal hemisphere difference in amphibians. 847 Proposition 268: cell alignment in epithelia is correlated with the direction of propagation of differentiation waves. 852 Proposition 269: alignment and perhaps single cell polarity can be better related to the propagation of a wave than to a gradient. 855 Proposition 270: a set of higher order, key-like 'homeokey' memoron molecules may exist, each of which stabilizes the state of determination of a particular cell type, and may explain the colinear organization of homeobox genes in a given homeobox gene complex, and the mechanism of dedifferentiation. 860 Proposition 271: there are a few candidates for homeokey molecules. 863 Proposition 272: the on state for a homeobox gene corresponds to a contraction wave, while the off state corresponds to an expansion wave (or vice versa ). ~lm  {|}     s t u  ȿȶȿȪțȍȿȶȿȪ~tȿȶ5>*B*CJ phjB*CJ Uph5B*CJ ph0JCJ jB*CJ UphjB*CJ Uph6B*CJ ph5B*CJ ph B*CJ ph56B*CJ 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