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Marty Shankland - One of the best experts on this subject based on the ideXlab platform.
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Evolution of Developmental Control Mechanisms A member of the Six gene family promotes the specification of P cell fates in the O/P Equivalence Group of the leech Helobdella
2020Co-Authors: Ian K Quigley, Matthew Schmerer, Marty ShanklandAbstract:article i nfo The lateral ectoderm of the leech embryo arises from the o and p bandlets, two parallel columns of blast cells that collectively constitute the O/P Equivalence Group. Individual blast cells within this Equivalence Group become committed to alternative O or P developmental pathways in accordance with their respectively ventrolateral or dorsolateral position (Weisblat and Blair, 1984). We here describe a novel member of the Six gene transcription factor family, Hau-Six1/2A, which contributes to the patterning of these cell fates in the leech Helobdella sp. (Austin). During embryogenesis Hau-Six1/2A expression is restricted to the dorsolateral column of p blast cells, and thus correlates with P cell fate over most of the body's length. Experimental manipulations showed that Hau-Six1/2A expression is induced in p blast cells by the interaction with the adjoining q bandlet. In addition, misexpression of Hau-Six1/2A in the ventrolateral o blast cells by injection of an expression plasmid elicited the dorsolateral P cell fates ectopically. These data imply that Hau-Six1/2A is a component of the molecular pathway that normally distinguishes O and P cell fates within this Equivalence Group. Genomic analysis revealed that the Six1/2 subfamily has expanded to a total of six genes in Helobdella. The pattern of Hau-Six1/2A expression during later embryogenesis suggested that this gene may have lost ancestral function(s) and/or acquired novel roles in association with the gene duplications that produced this expansion.
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a member of the six gene family promotes the specification of p cell fates in the o p Equivalence Group of the leech helobdella
Developmental Biology, 2010Co-Authors: Ian K Quigley, Matthew Schmerer, Marty ShanklandAbstract:Abstract The lateral ectoderm of the leech embryo arises from the o and p bandlets, two parallel columns of blast cells that collectively constitute the O/P Equivalence Group. Individual blast cells within this Equivalence Group become committed to alternative O or P developmental pathways in accordance with their respectively ventrolateral or dorsolateral position ( Weisblat and Blair, 1984 ). We here describe a novel member of the Six gene transcription factor family, Hau-Six1/2A, which contributes to the patterning of these cell fates in the leech Helobdella sp. (Austin). During embryogenesis Hau-Six1/2A expression is restricted to the dorsolateral column of p blast cells, and thus correlates with P cell fate over most of the body's length. Experimental manipulations showed that Hau-Six1/2A expression is induced in p blast cells by the interaction with the adjoining q bandlet. In addition, misexpression of Hau-Six1/2A in the ventrolateral o blast cells by injection of an expression plasmid elicited the dorsolateral P cell fates ectopically. These data imply that Hau-Six1/2A is a component of the molecular pathway that normally distinguishes O and P cell fates within this Equivalence Group. Genomic analysis revealed that the Six1/2 subfamily has expanded to a total of six genes in Helobdella. The pattern of Hau-Six1/2A expression during later embryogenesis suggested that this gene may have lost ancestral function(s) and/or acquired novel roles in association with the gene duplications that produced this expansion.
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evolutionary diversification of specification mechanisms within the o p Equivalence Group of the leech genus helobdella
Development, 2004Co-Authors: Marty ShanklandAbstract:Developmental fates and cell lineage patterns are highly conserved in the teloblast lineages that give rise to the segmental ectoderm of clitellate annelids. But previous studies have shown that the pathways involved in specification of the ventrolateral O lineage and the dorsolateral P lineage differ to some degree in distantly related clitellate species such as the leeches Helobdella and Theromyzon , and the sludgeworm Tubifex . To examine this developmental variation at a lower taxonomic level, we have explored the specification pathways of the O and P lineages in the leech genus Helobdella . In leech, the O and P lineages arise from a developmental Equivalence Group of O/P teloblasts. In this study, we demonstrate that the cell-cell interactions involved in cell fate specification of the O/P Equivalence Group differ among three laboratory colonies of closely related species. In two populations, the Q lineage is necessary to specify the P fate in the dorsalmost O/P lineage, but in the third population the P fate can be specified by a redundant pathway involving the M lineage. We also observe interspecific variation in the role played by cell interactions within the O/P Equivalence Group, and in the apparent significance of extrinsic signals from the micromere cell lineages. Our data suggest that cell fate specification in the O/P Equivalence Group is a complex process that involves multiple cell-cell interactions, and that the developmental architecture of the O/P Equivalence Group has undergone evolutionary diversification in closely related species, despite maintaining a conserved morphology.
Ralf J Sommer - One of the best experts on this subject based on the ideXlab platform.
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hairy like transcription factors and the evolution of the nematode vulva Equivalence Group
Current Biology, 2006Co-Authors: Benjamin Schlager, Waltraud Roseler, Min Zheng, Arturo Gutierrez, Ralf J SommerAbstract:Summary Background Nematode vulva formation provides a paradigm to study the evolution of pattern formation and cell-fate specification. The Caenorhabditis elegans vulva is generated from three of six equipotent cells that form the so-called vulva Equivalence Group. During evolution, the size of the vulva Equivalence Group has changed: Panagrellus redivivus has eight, C. elegans six, and Pristionchus pacificus only three cells that are competent to form vulval tissue. In P. pacificus, programmed cell death of individual vulval precursor cells alters the size of the vulva Equivalence Group. Results We have identified the genes controlling this cell-death event and the molecular mechanism of the reduction of the vulva Equivalence Group. Mutations in Ppa-hairy , a gene that is unknown from C. elegans , result in the survival of two precursor cells, which expands the vulva Equivalence Group. Mutations in Ppa-groucho cause a similar phenotype. Ppa -HAIRY and Ppa -GROUCHO form a molecular module that represses the Hox gene Ppa-lin-39 and thereby reduces the size of the vulva Equivalence Group. The C. elegans genome does not encode a similar hairy -like gene, and no typical HAIRY/GROUCHO module exists. Conclusions We conclude that the vulva Equivalence Group in Pristionchus is patterned by a HAIRY/GROUCHO module, which is absent in Caenorhabditis . Thus, changes in the number, structure, and function of nematode hairy -like transcription factors are involved in the evolutionary alteration of this Equivalence Group.
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the pristionchus hox gene ppa lin 39 inhibits programmed cell death to specify the vulva Equivalence Group and is not required during vulval induction
Development, 1998Co-Authors: Ralf J Sommer, Andreas Eizinger, Benno Jungblut, A Bubeck, Isabel SchlakAbstract:In the two nematode species Caenorhabditis elegans and Pristionchus pacificus the vulva Equivalence Group in the central body region is specified by the Hox gene lin-39. C. elegans lin-39 mutants are vulvaless and the vulval precursor cells fuse with the surrounding hypodermis, whereas in P. pacificus lin-39 mutants the vulval precursor cells die by apoptosis. Mechanistically, LIN-39 might inhibit non-vulval fate (cell fusion in C. elegans, apoptosis in P. pacificus), promote vulval fate or do both. To study the mechanism of lin-39 function, we isolated P. pacificus cell death mutants and identified mutations in ced-3. Surprisingly, P. pacificus ced-3; lin-39 double mutants form a functional vulva in the absence of LIN-39 activity. Thus, in P. pacificus lin-39 specifies the vulva Equivalence Group by inhibiting programmed cell death. Furthermore, these data reveal an important difference in a later function of lin-39 between the two species. In C. elegans, LIN-39 specifies vulval cell fates in response to inductive RAS signaling, and in P. pacificus LIN-39 is not required for vulval induction. Thus, the comparative analysis indicates that lin-39 has distinct functions in both species although the gene is acting in a homologous developmental system.
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apoptosis and change of competence limit the size of the vulva Equivalence Group in pristionchus pacificus a genetic analysis
Current Biology, 1996Co-Authors: Ralf J Sommer, Paul W SternbergAbstract:Abstract Background: To understand how alterations in the molecular mechanisms underlying developmental processes generate a diversity of biological forms, comparative developmental biology can be combined with genetic analysis. The formation of the nematode vulva is one tractable system for such evolutionary developmental analysis, as much is understood about its development in Caenorhabditis elegans . In Caenorhabditis , six of twelve ventral epidermal cells form the ‘vulva Equivalence Group'; although all six cells are competent to adopt vulval cell fates in response to an inductive signal, only three of these cells are induced to form vulval tissue. Results In some species of the nematode families Rhabditidae, Neodiplogastridae and Panagrolaimidae, the number of cells in the vulva Equivalence Group is limited by apoptosis and decreased responsiveness to inductive signals (competence). We have initiated a genetic analysis in one of these species, Pristionchus pacificus , to understand the evolution of the specification of ventral epidermal cells that are competent to generate the vulva. A ped-4 mutation restores competence to an incompetent cell. Mutation of either of two other genes of Pristionchus cause two anterior cells that die in wild-type to survive. A ped-5 mutation causes these cells to be competent to respond to inductive signals, expanding the Equivalence Group. A ped-6 mutation causes these cells to form ectopic, anterior vulva-like invaginations. Conclusion During nematode evolution, apoptosis and change of competence alter the number and potency of ventral epidermal cells. The phenotypes of Pristionchus mutants suggest that alterations in homeotic gene control of anteroposterior patterning is involved in creating this cellular diversity.
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evolution of cell lineage and pattern formation in the vulval Equivalence Group of rhabditid nematodes
Developmental Biology, 1995Co-Authors: Ralf J Sommer, Paul W SternbergAbstract:Abstract During the formation of the vulva in many nematode hermaphrodites or females, pattern formation, induction, and cell specification can readily be studied at a single-cell level. Nematodes thus allow an evolutionary analysis of developmental processes. We have analyzed cell lineages and pattern formation in the vulva Equivalence Group of six rhabditid nematodes of the genera Oscheius, Rhabditella, Rhabditoides, Pelodera, and Protorhabditis . The comparison of these species with four previously analyzed species of this family reveals evolutionary modification at several levels. The number of vulva precursor cells (VPCs) differ among species. Of the three particular cell lineages (1°, 2°, and 3°) generated by the vulva precursor cells in Caenorhabditis, two (2° and 3°) are altered, whereas the third lineage (1°) is conserved among the analyzed species. While most vulval lineages are invariant, we observe variability of the 3° lineage in Pelodera with respect to the number of precursor cells adopting this fate and the number of progeny formed. In two species, the 3° lineage generates an asymmetrical set of cells, oriented by the gonad. In Protorhabditis we frequently find animals with an additional or altered set of VPCs forming vulval tissue.
Paul W Sternberg - One of the best experts on this subject based on the ideXlab platform.
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the roles of egf and wnt signaling during patterning of the c elegans bγ δ Equivalence Group
BMC Developmental Biology, 2009Co-Authors: Adeline Seah, Paul W SternbergAbstract:Background During development, different signaling pathways interact to specify cell fate by regulating transcription factors necessary for fate specification and morphogenesis. In Caenorhabditis elegans, the EGF-Ras and Wnt signaling pathways have been shown to interact to specify cell fate in three Equivalence Groups: the vulval precursor cells (VPCs), the hook competence Group (HCG) and P11/12. In the VPCs, HCG and P11/12 pair, EGF and Wnt signaling positively regulate different Hox genes, each of which also functions during fate specification. In the male, EGF-Ras signaling is required to specify the Bγ fate within the Bγ/δ Equivalence pair, while Notch signaling is required for Bδ fate specification. In addition, TGF-β signaling by dbl-1/dpp controls ceh-13/labial/Hox1 expression in Bγ.
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The roles of EGF and Wnt signaling during patterning of the C. elegans Bγ/δ Equivalence Group
BMC Developmental Biology, 2009Co-Authors: Adeline Seah, Paul W SternbergAbstract:Background During development, different signaling pathways interact to specify cell fate by regulating transcription factors necessary for fate specification and morphogenesis. In Caenorhabditis elegans, the EGF-Ras and Wnt signaling pathways have been shown to interact to specify cell fate in three Equivalence Groups: the vulval precursor cells (VPCs), the hook competence Group (HCG) and P11/12. In the VPCs, HCG and P11/12 pair, EGF and Wnt signaling positively regulate different Hox genes, each of which also functions during fate specification. In the male, EGF-Ras signaling is required to specify the Bγ fate within the Bγ/δ Equivalence pair, while Notch signaling is required for Bδ fate specification. In addition, TGF-β signaling by dbl-1/dpp controls ceh-13/labial/Hox1 expression in Bγ.
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apoptosis and change of competence limit the size of the vulva Equivalence Group in pristionchus pacificus a genetic analysis
Current Biology, 1996Co-Authors: Ralf J Sommer, Paul W SternbergAbstract:Abstract Background: To understand how alterations in the molecular mechanisms underlying developmental processes generate a diversity of biological forms, comparative developmental biology can be combined with genetic analysis. The formation of the nematode vulva is one tractable system for such evolutionary developmental analysis, as much is understood about its development in Caenorhabditis elegans . In Caenorhabditis , six of twelve ventral epidermal cells form the ‘vulva Equivalence Group'; although all six cells are competent to adopt vulval cell fates in response to an inductive signal, only three of these cells are induced to form vulval tissue. Results In some species of the nematode families Rhabditidae, Neodiplogastridae and Panagrolaimidae, the number of cells in the vulva Equivalence Group is limited by apoptosis and decreased responsiveness to inductive signals (competence). We have initiated a genetic analysis in one of these species, Pristionchus pacificus , to understand the evolution of the specification of ventral epidermal cells that are competent to generate the vulva. A ped-4 mutation restores competence to an incompetent cell. Mutation of either of two other genes of Pristionchus cause two anterior cells that die in wild-type to survive. A ped-5 mutation causes these cells to be competent to respond to inductive signals, expanding the Equivalence Group. A ped-6 mutation causes these cells to form ectopic, anterior vulva-like invaginations. Conclusion During nematode evolution, apoptosis and change of competence alter the number and potency of ventral epidermal cells. The phenotypes of Pristionchus mutants suggest that alterations in homeotic gene control of anteroposterior patterning is involved in creating this cellular diversity.
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evolution of cell lineage and pattern formation in the vulval Equivalence Group of rhabditid nematodes
Developmental Biology, 1995Co-Authors: Ralf J Sommer, Paul W SternbergAbstract:Abstract During the formation of the vulva in many nematode hermaphrodites or females, pattern formation, induction, and cell specification can readily be studied at a single-cell level. Nematodes thus allow an evolutionary analysis of developmental processes. We have analyzed cell lineages and pattern formation in the vulva Equivalence Group of six rhabditid nematodes of the genera Oscheius, Rhabditella, Rhabditoides, Pelodera, and Protorhabditis . The comparison of these species with four previously analyzed species of this family reveals evolutionary modification at several levels. The number of vulva precursor cells (VPCs) differ among species. Of the three particular cell lineages (1°, 2°, and 3°) generated by the vulva precursor cells in Caenorhabditis, two (2° and 3°) are altered, whereas the third lineage (1°) is conserved among the analyzed species. While most vulval lineages are invariant, we observe variability of the 3° lineage in Pelodera with respect to the number of precursor cells adopting this fate and the number of progeny formed. In two species, the 3° lineage generates an asymmetrical set of cells, oriented by the gonad. In Protorhabditis we frequently find animals with an additional or altered set of VPCs forming vulval tissue.
Roman O. Popovych - One of the best experts on this subject based on the ideXlab platform.
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Direct methods of construction of conservation laws
2020Co-Authors: Roman O. PopovychAbstract:The basic notions and statements of conservation laws of difierential equations are reviewed. The main attention is paid to constructive methods of flnding conservation laws for general systems of difierential equations, which are not Euler{Lagrange equations of a functional and, therefore, do not admit application of the symmetry approach based on the Noether theorem. Recently introduced notions of Equivalence of conservation laws with respect to Lie symmetry Groups for flxed systems of difierential equations and with respect to Equivalence Groups or sets of admissible transformations for classes of such systems are considered. To construct conservation laws, we develop and apply a modiflcation of the most direct method, which is efiective to construct both local and potential conservation laws, especially, in the case of two independent variables. Classiflcation of potential conservation laws of difiusion{convection equations with respect to the associated Equivalence Group and exhaustive list of locally inequivalent potential systems corresponding to these equations are adduced as an example on calculation of complete hierarchy of potential conservation laws. More details are presented on simpler classiflcation of local conservation laws of variable coe‐cient difiusion{reaction equations.
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Enhanced Group classification of nonlinear diffusion–reaction equations with gradient-dependent diffusivity
Journal of Mathematical Analysis and Applications, 2020Co-Authors: Stanislav Opanasenko, Vyacheslav Boyko, Roman O. PopovychAbstract:Abstract We carry out the enhanced Group classification of a class of (1+1)-dimensional nonlinear diffusion–reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously finding the Equivalence Groups of an unnormalized class of differential equations and a collection of its subclasses, we suggest an optimized version of the direct method. The optimization includes the preliminary study of admissible transformations within the entire class and the successive splitting of the corresponding determining equations with respect to arbitrary elements and their derivatives depending on auxiliary constraints associated with each of required subclasses. In the course of applying the suggested technique to subclasses of the class under consideration, we construct, for the first time, a nontrivial example of finite-dimensional effective generalized Equivalence Group. Using the method of Lie reduction and the generalized separation of variables, exact solutions of some equations under consideration are found.
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Zeroth-order conservation laws of two-dimensional shallow water equations with variable bottom topography
arXiv: Mathematical Physics, 2019Co-Authors: Alexander Bihlo, Roman O. PopovychAbstract:We classify zeroth-order conservation laws of systems from the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The classification is carried out up to Equivalence generated by the Equivalence Group of this class. We find additional point Equivalences between some of the listed cases of extensions of the space of zeroth-order conservation laws, which are inequivalent up to transformations from the Equivalence Group. Hamiltonian structures of systems of shallow water equations are used for relating the classification of zeroth-order conservation laws of these systems to the classification of their Lie symmetries. We also construct generating sets of such conservation laws under action of Lie symmetries.
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Lie symmetries of two-dimensional shallow water equations with variable bottom topography
arXiv: Exactly Solvable and Integrable Systems, 2019Co-Authors: Alexander Bihlo, Nataliia Poltavets, Roman O. PopovychAbstract:We carry out the Group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The Equivalence Group of this class is found by the algebraic method. Using algebraic techniques, we construct additional point Equivalences between some of the listed cases of Lie symmetry extensions, which are inequivalent up to transformations from the Equivalence Group.
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Differential invariants for a class of diffusion equations.
arXiv: Mathematical Physics, 2019Co-Authors: Elsa Dos Santos Cardoso-bihlo, Alexander Bihlo, Roman O. PopovychAbstract:We find the complete Equivalence Group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the normalization procedure, a moving frame for a Group related to the Equivalence Group in the context of Equivalence transformations among equations of the class under consideration. Using the moving frame constructed, we describe the algebra of differential invariants of the former Group by obtaining a minimum generating set of differential invariants and a complete set of independent operators of invariant differentiation.
J C Ndogmo - One of the best experts on this subject based on the ideXlab platform.
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Characterization of the class of canonical forms for systems of linear equations
arXiv: Classical Analysis and ODEs, 2015Co-Authors: J C NdogmoAbstract:The Equivalence Group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation. Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution.
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Equivalence transformations of the Euler–Bernoulli equation
Nonlinear Analysis-real World Applications, 2012Co-Authors: J C NdogmoAbstract:Abstract We give a determination of the Equivalence Group of the Euler–Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.
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On Dummy Variables of Structure-Preserving Transformations
Mathematical Problems in Engineering, 2012Co-Authors: J C NdogmoAbstract:A method is given for obtaining Equivalence subGroups of a family of differential equations from the Equivalence Group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on fewer variables. Examples of applications to classical equations are presented, some of which show how the method can actually be used for a much easier determination of the Equivalence Group itself.
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On structure-preserving point transformations of differential equations
Physics Letters A, 2009Co-Authors: J C NdogmoAbstract:We apply a novel method for the Equivalence Group and its infinitesimal generators to the investigation of invariants of ODEs. First, a comparative study of this method is illustrated by an example. Next, the method is used to obtain invariants of low order linear ODEs, and the Equivalence transformations for an arbitrary order of these equations. Other properties of the equations are also obtained, including the exact number of their invariants.
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Invariants associated with linear ordinary differential equations
arXiv: Analysis of PDEs, 2008Co-Authors: J C NdogmoAbstract:We apply a novel method for the Equivalence Group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next, the method is used to obtain the invariants of low order linear ordinary differential equations, and the structure invariance Group for an arbitrary order of these equations. Other properties of these equations are also discussed, including the exact number of their invariants.