Abstract
Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the “efficient cause” of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min–max principle). Passing from a microscopic (or cellular) level (optimal min–max solution of the simple mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application “a minima” models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first “peptidic machine,” a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish.
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References
Abbas L, Demongeot J, Glade N (2009) Synchrony in reaction-diffusion models of morphogenesis: applications to curvature-dependent proliferation and zero-diffusion front waves. Phil Trans Royal Soc A 367:4829–4862
Adhikary S, Eilers M (2005) Transcriptional regulation and transformation by Myc proteins. Nat Rev Mol Cell Biol 6:635–645
Almeida L, Bagnerini P, Habbal A, Noselli S, Serman F (2009) Tissue repair modeling, singularities in nonlinear evolution phenomena and applications. In: Novaga M, Orlandi G (eds) CRM series. Scuola Normale Superiore, Pisa, pp 27–46
Almeida L, Bagnerini P, Habbal A, Noselli S, Serman F (2011) A mathematical model for dorsal closure. J Theor Biol 268:105–119
Ben Amor L, Cadau S, Elena A, Dhouailly D, Demongeot J (2009) Regulatory networks analysis: robustness in biological regulatory networks. In: AINA’ 09 & BLSMC’ 09, IEEE Press, Piscataway, pp 224–229
Beretta CA, Brinkmann I, Carl M (2011) All four zebrafish Wnt7 genes are expressed during early brain development. Gene Expr Patterns 11:277–284
Cheng JC, Miller AL, Webb SE (2004) Organization and function of microfilaments during late epiboly in zebrafish embryos. Dev Dyn 231:313–323
Cinquin O, Demongeot J (2002) Positive and negative feedback: striking a balance between necessary antagonists. J Theor Biol 216:229–241
Demongeot J (2009) Biological boundaries and biological age. Acta Biotheor 57:397–419
Demongeot J, Moreira A (2007) A circular RNA at the origin of life. J Theor Biol 249:314–324
Demongeot J, Elena A, Weil G (2006) Potential-Hamiltonian decomposition of cellular automata. Application to degeneracy of genetic code and cyclic codes III. Comptes Rendus Biologies 329:953–962
Demongeot J, Glade N, Moreira A (2008) Evolution and RNA relics. A systems biology view. Acta Biotheoretica 56:5–25
Demongeot J, Glade N, Moreira A, Vial L (2009a) RNA relics and origin of life. Int J Mol Sci 10:3420–3441
Demongeot J, Ben Amor H, Gillois P, Noual M, Sené S (2009b) Robustness of regulatory networks. A generic approach with applications at different levels: physiologic, metabolic and genetic. Int J Mol Sci 10:4437–4473
Demongeot J, Elena A, Noual M, Sené S, Thuderoz F (2011a) “Immunetworks” I, attractors and intersecting circuits. J Theor Biol 280:19–33
Demongeot J, Elena A, Noual M, Sené S (2011b) Random boolean networks and attractors of their intersecting circuits. In: IEEE AINA’ 11 & BLSMC’ 11, IEEE Proceedings, Piscataway, pp 483–487
Demongeot J, Noual M, Sené S ( 2012) Combinatorics of boolean automata circuits dynamics. Discrete Appl Math 160:398–415
Di Giulio M (1989a) Some aspects of the organization and evolution of the genetic code. J Mol Evol 29:191–201
Di Giulio M (1989b) The extension reached by the minimization of the polarity distances during the evolution of the genetic code. J Mol Evol 29:288–293
Fjose A, Njølstad PR, Nornes S, Molven A, Krauss S (1992) Structure and early embryonic expression of the zebrafish engrailed-2 gene. Mech Dev 39:51–62
Gettings M, Serman F, Rousset FR, Bagnerini P, Almeida L, Noselli S (2010) JNK signaling controls remodelling of the segment boundary through cell reprogramming during drosophila morphogenesis. PLoS Biol 8:e1000390
Goodarzi H, Najafabadi HS, Nejad HA, Torabi N (2005) The impact of including tRNA content on the optimality of the genetic code. Bull Math Biol 67:1355–1368
Heo JS, Lee SH, Han HJ (2008) Regulation of DNA synthesis in mouse embryonic stem cells by transforming growth factor-α: involvement of the PI3-K/Akt and Notch/Wnt signaling pathways. Growth Factors 26:104–116
Hermeking H, Eick D (1994) Mediation of c-Myc-induced apoptosis by p53. Science 265:2091–2093
Higgs PG, Pudritz RE (2009) A thermodynamic basis for prebiotic amino acid synthesis and the nature of the first genetic code. Astrobiology 9:483–490
Holloway BA, de la Torre Gomez, Canny S, Ye Y, Slusarski DC, Freisinger CM, Dosch R, Chou MM, Wagner DS, Mullins MC (2009) A novel role for MAPKAPK2 in morphogenesis during zebrafish development. PLoS Genet 5:e1000413
Hutson MS, Tokutake Y, Chang MS, Bloor JW, Venakides S, Kiehart DP, Edwards GS (2003) Forces for morphogenesis investigated with laser microsurgery and quantitative modeling. Science 300:145–149
Ivanov VN, Hei TK (2005) Combined treatment with EGFR inhibitors and arsenite upregulated apoptosis in human EGFR-positive melanomas: a role of suppression of the PI3K-AKT pathway. Oncogene 24:616–626
Johnson AP, Cleaves HJ, Dworkin JP, Glavin DP, Lazcano A, Bada JL (2008) The miller volcanic spark discharge experiment. Science 322:404
Kohn KW (1999) Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol Biol Cell 10:2703–2734
Köppen M, Fernández BG, Carvalho L, Jacinto A, Heisenberg CP (2006) Coordinated cell-shape changes control epithelial movement in zebrafish and Drosophila. Development 133:2671–2681
Krauss S, Korzh V, Fjose A, Johansen T (1992) Expression of four zebrafish wnt-related genes during embryogenesis. Development 116:249–259
Lachnit M, Kur E, Driever W (2008) Alterations of the cytoskeleton in all three embryonic lineages contribute to the epiboly defect of Pou5f1/Oct4 deficient MZspg zebrafish embryos. Dev Biol 315(1):1–17
Lee WJ, Kim SH, Kim YS, Han SJ, Park KS, Ryu JH, Hur MW, Choi KY (2000) Inhibition of mitogen-activated protein kinase by a Drosophila dual-specific phosphatase. Biochem J 349:821–828
Lehmann J, Cibils M, Libchaber A (2009) Emergence of a code in the polymerization of amino acids along RNA templates. PLoS One 4:e5773
Lepage SE, Bruce AE (2010) Zebrafish epiboly: mechanics and mechanisms. Int J Dev Biol 54:1213–1228
Lewis JL, Bonner J, Modrell M, Ragland JW, Randall T, Dorsky R, Raible DW (2004) Reiterated Wnt signaling during zebrafish neural crest development. Development 131:1299–1308
Littleton JT, Ganetzky B (2000) Ion channels and synaptic organization: analysis of the Drosophila genome. Neuron 26:35–43
Logan CY, Nusse R (2004) The Wnt signaling pathway in development and disease. Annu Rev Cell Dev Biol 20:781–810
Mantrova EY, Hsu T (1998) Down-regulation of transcription factor CF2 by Drosophila Ras/MAP kinase signaling in oogenesis: cytoplasmic retention and degradation. Genes Dev 12:1166–1175
Martin AC (2010) Pulsation and stabilization: contractile forces that underlie morphogenesis. Dev Biol 341:114–125
Martin P, Parkhurst SM (2004) Parallels between tissue repair and embryo morphogenesis. Development 131:3021–3034
McEwen DG, Peifer M (2005) Puckered, a Drosophila MAPK phosphatase, ensures cell viability by antagonizing JNK-induced apoptosis. Development 132:3935–3946
Michon F, Forest L, Collomb E, Demongeot J, Dhouailly D (2008) BMP-2 and BMP-7 play antagonistic roles in feather induction. Development 135:2797–2805
Miller SL (1987) Which organic compounds could have occurred on the prebiotic earth. Cold Spring Harbor Symp Quant Biol 52:7–27
Moreau de Maupertuis PL (1746) Les lois du mouvement et du repos, déduites d’un principe de métaphysique. Königlich Preußische Sozietät der Wissenschaften 2:267–294
Nagata D, Suzuki E, Nishimatsu H, Yoshizumi M, Mano T, Walsh K, Sata M, Kakoki M, Goto A, Omata M, Hirata Y (2000) Cyclin A downregulation and p21cip1 upregulation correlate with GATA-6–induced growth arrest in glomerular mesangial cells. Circ Res 87:699–704
Noual M (2010) Dynamics in parallel of double boolean automata circuits. ArXiv, 1011.3930v2
Pelengaris S, Khan M, Evan G (2002) c-MYC: more than just a matter of life and death. Nat Rev Cancer 2:764–776
Pikkarainen S, Tokola H, Kerkelä R, Ruskoaho H (2011) GATA transcription factors in the developing and adult heart. Cardiovasc Res 63:196–207
Richard A (2011) Local negative circuits and fixed points in non-expansive Boolean networks. Discrete Appl Math 159:1085–1093
Saenz-Robles MT, Maschat F, Tabata T, Scott MP, Kornberg TB (1995) Selection and characterization of sequences with high affinity for engrailed proteins of Drosophila. Mech Dev 53:185–195
Salinas PC, Zou Y (2008) Wnt signaling in neural circuit assembly. Annu Rev Neurosci 31:339–358
Siddiqui M, Sheikh H, Tran C, Bruce AE (2010) The tight junction component Claudin E is required for zebrafish epiboly. Dev Dyn 239:715–722
Siegler MVS, Jia XX (1999) Engrailed negatively regulates the expression of cell adhesion molecules connectin and neuroglian in embryonic Drosophila nervous system. Neuron 22:265–276
Solnica-Krezel L (2006) Gastrulation in zebrafish—all just about adhesion? Curr Opin Genet Dev 16:433–441
Tonnelier A, Meignen S, Bosch H, Demongeot J (1999) Synchronization and desynchronization of neural oscillators: comparison of two models. Neural Netw 12:1213–1228
Trifonov E (2000) Consensus temporal order of amino-acids and evolution of the triplet code. Gene 261:139–151
Vickers ER, Sharrocks AD (2002) The use of inducible engrailed fusion proteins to study the cellular functions of eukaryotic transcription factors. Methods 26:270–280
Warga RM, Kimmel CB (1990) Cell movements during epiboly and gastrulation in zebrafish. Development 108:569–580
Wood W, Jacinto A, Grose R, Woolner S, Gale J, Wilson C, Martin P (2002) Wound healing recapitulates morphogenesis in Drosophila embryos. Nat Cell Biol 4:907–912
Zeng YA, Verheyen EM (2004) Nemo is an inducible antagonist of wingless signaling during Drosophila wing development. Development 131:2911–2920
Zhou FQ, Snide WD (2005) GSK-3β and microtubule assembly in axons. Science 308:211–214
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Almeida, L., Demongeot, J. Predictive Power of “A Minima” Models in Biology. Acta Biotheor 60, 3–19 (2012). https://doi.org/10.1007/s10441-012-9146-4
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DOI: https://doi.org/10.1007/s10441-012-9146-4