Predicting embryonic patterning using mutual entropy fitness and in silico evolution

During vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms. For patterning during growth (paradigm I), which is appropriate for vertebrates and short germ-band insects, the algorithm creates gene expression patterns reminiscent of Hox gene expression. The networks operate through a timer gene, the level of which measures developmental progression (a candidate is the widely conserved posterior morphogen Caudal). The timer gene provides a simple mechanism to coordinate patterning with growth rate. The timer, when expressed as a static spatial gradient, functions as a classical morphogen (paradigm II), providing a natural way to derive the AP patterning, as seen in long germ-band insects that express their Hox genes simultaneously, from the ancestral short germ-band system. Although the biochemistry of Hox regulation in higher vertebrates is complex, the actual spatiotemporal expression phenotype is not, and simple activation and repression by Hill functions suffices in our model. In silico evolution provides a quantitative demonstration that continuous positive selection can generate complex phenotypes from simple components by incremental evolution, as Darwin proposed.

[1]  E. Lewis Genes and Developmental Pathways , 1963 .

[2]  F. Crick,et al.  Compartments and polyclones in insect development. , 1975, Science.

[3]  E. Lewis A gene complex controlling segmentation in Drosophila , 1978, Nature.

[4]  P Gruss,et al.  A mouse gene homologous to the Drosophila gene caudal is expressed in epithelial cells from the embryonic intestine. , 1988, Genes & development.

[5]  G. Gibson,et al.  Head and thoracic transformations caused by ectopic expression of Antennapedia during Drosophila development , 1988 .

[6]  R. Balling,et al.  Variations of cervical vertebrate after expression of a Hox-1.1 transgene in mice , 1990, Cell.

[7]  G. Morata,et al.  The developmental effect of overexpressing a Ubx product in Drosophila embryos is dependent on its interactions with other homeotic products , 1990, Cell.

[8]  Robert K. Davis,et al.  The myoD gene family: nodal point during specification of the muscle cell lineage. , 1991, Science.

[9]  William McGinnis,et al.  Homeobox genes and axial patterning , 1992, Cell.

[10]  Lewis Eb The 1991 Albert Lasker Medical Awards. Clusters of master control genes regulate the development of higher organisms. , 1992 .

[11]  E. Lewis,et al.  The 1991 Albert Lasker Medical Awards. Clusters of master control genes regulate the development of higher organisms. , 1992, JAMA.

[12]  C. P. Hart,et al.  Homeotic transformation of the occipital bones of the skull by ectopic expression of a homeobox gene , 1992, Nature.

[13]  G. Morata Homeotic genes of Drosophila. , 1993, Current opinion in genetics & development.

[14]  R. Behringer,et al.  Homeotic transformation of cervical vertebrae in Hoxa-4 mutant mice. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[15]  D. Nilsson,et al.  A pessimistic estimate of the time required for an eye to evolve , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[16]  S. Gaunt,et al.  Forward spreading in the establishment of a vertebrate Hox expression boundary: The expression domain separates into anterior and posterior zones, and the spread occurs across implanted glass barriers , 1994, Developmental dynamics : an official publication of the American Association of Anatomists.

[17]  G. Morata,et al.  Colinearity and functional hierarchy among genes of the homeotic complexes. , 1994, Trends in genetics : TIG.

[18]  Craig Nelson,et al.  Hox genes and the evolution of vertebrate axial morphology. , 1995, Development.

[19]  D. Duboule Vertebrate Hox genes and proliferation: an alternative pathway to homeosis? , 1995, Current opinion in genetics & development.

[20]  C. Tabin,et al.  Analysis of Hox gene expression in the chick limb bud. , 1996, Development.

[21]  J. Slack,et al.  eFGF, Xcad3 and Hox genes form a molecular pathway that establishes the anteroposterior axis in Xenopus. , 1996, Development.

[22]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[23]  J. Slack,et al.  Regulation of Hox gene expression and posterior development by the Xenopus caudal homologue Xcad3 , 1998, The EMBO journal.

[24]  K Ikeo,et al.  Pax 6: mastering eye morphogenesis and eye evolution. , 1999, Trends in genetics : TIG.

[25]  R. Mann,et al.  The developmental and molecular biology of genes that subdivide the body of Drosophila. , 2000, Annual review of cell and developmental biology.

[26]  Olivier Pourquié,et al.  FGF Signaling Controls Somite Boundary Position and Regulates Segmentation Clock Control of Spatiotemporal Hox Gene Activation , 2001, Cell.

[27]  Jeremy B. A. Green,et al.  Morphogen gradients, positional information, and Xenopus: Interplay of theory and experiment , 2002, Developmental dynamics : an official publication of the American Association of Anatomists.

[28]  R. Mann,et al.  Specificity of Distalless repression and limb primordia development by abdominal Hox proteins. , 2002, Developmental cell.

[29]  L. Hood,et al.  A Genomic Regulatory Network for Development , 2002, Science.

[30]  S. Forlani,et al.  Cdx1 and Cdx2 have overlapping functions in anteroposterior patterning and posterior axis elongation. , 2002, Development.

[31]  Giuseppina Barsacchi,et al.  Specification of the vertebrate eye by a network of eye field transcription factors , 2003, Development.

[32]  D. Ferrier,et al.  Evolution of the Hox/ParaHox gene clusters. , 2003, The International journal of developmental biology.

[33]  M. Capecchi,et al.  Materials and Methods Som Text Figs. S1 to S4 Tables S1 and S2 References and Notes Hox10 and Hox11 Genes Are Required to Globally Pattern the Mammalian Skeleton , 2022 .

[34]  D. Duboule,et al.  Organizing Axes in Time and Space; 25 Years of Colinear Tinkering , 2003, Science.

[35]  A. Durston,et al.  The initiation of Hox gene expression in Xenopus laevis is controlled by Brachyury and BMP-4. , 2004, Developmental biology.

[36]  Hans Lehrach,et al.  Hox cluster disintegration with persistent anteroposterior order of expression in Oikopleura dioica , 2004, Nature.

[37]  V. Hakim,et al.  Design of genetic networks with specified functions by evolution in silico. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Julian Lewis,et al.  The vertebrate segmentation clock. , 2004, Current opinion in genetics & development.

[39]  M. Averof,et al.  Ancestral role of caudal genes in axis elongation and segmentation. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Ariel D. Chipman,et al.  Arthropod Segmentation: beyond the Drosophila paradigm , 2005, Nature Reviews Genetics.

[41]  Z. Kozmík Pax genes in eye development and evolution. , 2005, Current opinion in genetics & development.

[42]  A. Holder,et al.  Antibody-based therapies for malaria , 2005, Nature Reviews Microbiology.

[43]  Ekat Kritikou,et al.  Cell signalling: Divided divisions , 2005, Nature Reviews Molecular Cell Biology.

[44]  Joseph C. Pearson,et al.  Modulating Hox gene functions during animal body patterning , 2005, Nature Reviews Genetics.

[45]  Thomas C Kaufman,et al.  Short and long germ segmentation: unanswered questions in the evolution of a developmental mode , 2005, Evolution & development.

[46]  Claude Desplan,et al.  Localized maternal orthodenticle patterns anterior and posterior in the long germ wasp Nasonia , 2006, Nature.

[47]  Claude Desplan,et al.  A caudal mRNA gradient controls posterior development in the wasp Nasonia , 2006, Development.

[48]  O. Pourquié,et al.  Collinear activation of Hoxb genes during gastrulation is linked to mesoderm cell ingression , 2006, Nature.

[49]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[50]  V. Hakim,et al.  Deriving structure from evolution: metazoan segmentation , 2007, Molecular systems biology.

[51]  M. Capecchi,et al.  Hox patterning of the vertebrate rib cage , 2007, Development.

[52]  I. Nemenman,et al.  Optimal Signal Processing in Small Stochastic Biochemical Networks , 2006, PloS one.

[53]  David Q. Matus,et al.  Pre-Bilaterian Origins of the Hox Cluster and the Hox Code: Evidence from the Sea Anemone, Nematostella vectensis , 2007, PloS one.

[54]  O. Pourquié,et al.  Hox genes in time and space during vertebrate body formation , 2007, Development, growth & differentiation.

[55]  D. Wellik Hox patterning of the vertebrate axial skeleton , 2007, Developmental dynamics : an official publication of the American Association of Anatomists.

[56]  O. Hobert From the Cover: Gene Networks in Development and Evolution Special Feature Sackler Colloquium: Regulatory logic of neuronal diversity: Terminal selector genes and selector motifs , 2008 .

[57]  W. Bialek,et al.  Information flow and optimization in transcriptional regulation , 2007, Proceedings of the National Academy of Sciences.

[58]  Paul François,et al.  A case study of evolutionary computation of biochemical adaptation , 2008, Physical biology.

[59]  Albert Goldbeter,et al.  Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways. , 2008, Journal of theoretical biology.

[60]  S. Gaunt,et al.  Increased Cdx protein dose effects upon axial patterning in transgenic lines of mice , 2008, Development.

[61]  E. Davidson,et al.  Global regulatory logic for specification of an embryonic cell lineage , 2008, Proceedings of the National Academy of Sciences.

[62]  Andrew D. Peel The evolution of developmental gene networks: lessons from comparative studies on holometabolous insects , 2008, Philosophical Transactions of the Royal Society B: Biological Sciences.

[63]  Susan J. Brown,et al.  Analysis of the Tribolium homeotic complex: insights into mechanisms constraining insect Hox clusters , 2008, Development Genes and Evolution.

[64]  Tadahiro Iimura,et al.  Establishment of Hox vertebral identities in the embryonic spine precursors. , 2009, Current topics in developmental biology.

[65]  Gasper Tkacik,et al.  Optimizing information flow in small genetic networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  V. Wilson,et al.  Redefining the progression of lineage segregations during mammalian embryogenesis by clonal analysis. , 2009, Developmental cell.

[67]  Jacqueline Deschamps,et al.  Cdx and Hox genes differentially regulate posterior axial growth in mammalian embryos. , 2009, Developmental cell.

[68]  C. Desplan,et al.  Heads and tails: evolution of antero-posterior patterning in insects. , 2009, Biochimica et biophysica acta.

[69]  Denis Duboule,et al.  Uncoupling Time and Space in the Collinear Regulation of Hox Genes , 2009, PLoS genetics.

[70]  Olivier Pourquié,et al.  Signaling gradients during paraxial mesoderm development. , 2010, Cold Spring Harbor perspectives in biology.

[71]  A J Durston,et al.  Review: Time-space translation regulates trunk axial patterning in the early vertebrate embryo. , 2010, Genomics.