Diffusion model of gap genes in Drosophila melanogaster
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This model is used in the publication by Regueira et al. under review.
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<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
<Description>
<Title>Modelo difusion de los GAP genes en Drosophila Melanogaster</Title>
<Details> Este modelo muestra la acción de los maternal effect genes y los Gap genes sobre la expresión del gen Even-skipped (Eve) </Details>
</Description>
<Global>
<System solver="Euler [fixed, O(1)]" time-step="1.0">
<DiffEqn symbol-ref="BICOID">
<Expression>p_bicoid-deg_bicoid*BICOID</Expression>
</DiffEqn>
<DiffEqn symbol-ref="M_NANOS">
<Expression>p_nanos-deg_nanos*M_NANOS</Expression>
</DiffEqn>
<DiffEqn symbol-ref="HUNCHBACK">
<Expression>p_hunchback-deg_hunchback*HUNCHBACK</Expression>
</DiffEqn>
<DiffEqn symbol-ref="CAUDAL">
<Expression>p_caudal-deg_caudal*CAUDAL</Expression>
</DiffEqn>
<DiffEqn symbol-ref="GIANT">
<Expression>p_giant-deg_giant*GIANT</Expression>
</DiffEqn>
<DiffEqn symbol-ref="KRUPPEL">
<Expression>p_kruppel-deg_kruppel*KRUPPEL</Expression>
</DiffEqn>
<DiffEqn symbol-ref="KNIRPS">
<Expression>p_knirps-deg_knirps*KNIRPS</Expression>
</DiffEqn>
<DiffEqn symbol-ref="TAILLESS">
<Expression>p_tailless-deg_tailless*TAILLESS </Expression>
</DiffEqn>
<DiffEqn symbol-ref="EVE_REP">
<Expression>p_eve_rep-deg_eve_rep*EVE_REP</Expression>
</DiffEqn>
<DiffEqn symbol-ref="EVE_REP_CONS">
<Expression>p_eve_rep_cons-deg_eve_rep_cons*EVE_REP_CONS</Expression>
</DiffEqn>
<Constant value="0.000" symbol="deg_bicoid"/>
<Constant value="0.000" symbol="deg_nanos"/>
<Constant value="0.146" symbol="deg_hunchback"/>
<Constant value="0.00243" symbol="deg_caudal"/>
<Constant value="0.067" symbol="deg_kruppel"/>
<Constant value="0.087" symbol="deg_giant"/>
<Constant value="0.065" symbol="deg_knirps"/>
<Constant value="0.000" symbol="deg_tailless"/>
<Constant value="1" symbol="deg_eve_rep_cons"/>
<Constant value="0.03" symbol="deg_eve_rep"/>
<DiffEqn symbol-ref="REP_EVE_REP_CONS">
<Expression>p_rep_eve_rep_cons-deg_rep_eve_rep_cons*REP_EVE_REP_CONS</Expression>
</DiffEqn>
<Constant value="0.001" symbol="deg_rep_eve_rep_cons"/>
<DiffEqn symbol-ref="EVE">
<Expression>p_eve-deg_eve*EVE</Expression>
</DiffEqn>
<Constant value="0" symbol="deg_eve"/>
<!-- <Disabled>
<Rule symbol-ref="BICOID">
<Expression>0.0</Expression>
</Rule>
</Disabled>
-->
</System>
<Field name="Morphogen_Bicoid" value="0.0294*((l.x/10)^2)-4.789*(l.x/10)+191.88" symbol="BICOID">
<Diffusion rate="0.16"/>
</Field>
<Field name="Morphogen_Nanos" value="0.031*((l.x/10)^2)-1.81*(l.x/10)+16.92" symbol="M_NANOS">
<Diffusion rate="0.16"/>
</Field>
<Field name="Morphogen_Hunchback" value="-1.189e-05*(l.x/10)^4 +0.002885 * (l.x/10)^3 -0.2223 *(l.x/10)^2 + 4.661 * (l.x/10) + 61" symbol="HUNCHBACK">
<Diffusion rate="2.16"/>
</Field>
<Field name="Morphogen_Caudal" value="-0.0008175 *(l.x/10)^3 + 0.09382 *(l.x/10)^2 -0.5582 *(l.x/10) + 1" symbol="CAUDAL">
<Diffusion rate="2.25"/>
</Field>
<Field name="Morphogen" value="0" symbol="KRUPPEL">
<Diffusion rate="0.67"/>
</Field>
<Field name="Morphogen" value="0" symbol="GIANT">
<Diffusion rate="0.4"/>
</Field>
<Field name="Morphogen" value="0" symbol="KNIRPS">
<Diffusion rate="0.9"/>
</Field>
<Field name="Morphogen" value="37.81*exp(-1*(((l.x/10)-15)/4.48)^2)+143.2*exp(-1*(((l.x/10)-93.72)/8.137)^2)" symbol="TAILLESS">
<Diffusion rate="0"/>
</Field>
<Field value="0" symbol="EVE_REP">
<Diffusion rate="5"/>
</Field>
<Field value="0" symbol="EVE_REP_CONS">
<Diffusion rate="0.0"/>
</Field>
<Field value="0" symbol="REP_EVE_REP_CONS">
<Diffusion rate="4"/>
</Field>
<Field value="0" symbol="EVE">
<Diffusion rate="0"/>
</Field>
</Global>
<Space>
<Lattice class="square">
<Size value="1000, 1000, 0" symbol="size"/>
<BoundaryConditions>
<Condition type="noflux" boundary="x"/>
<Condition type="noflux" boundary="y"/>
<Condition type="noflux" boundary="-x"/>
<Condition type="noflux" boundary="-y"/>
</BoundaryConditions>
<Neighborhood>
<!-- <Disabled>
<Order>2</Order>
</Disabled>
-->
<Distance>2.5</Distance>
</Neighborhood>
<Domain boundary-type="noflux">
<Image path="domain.tif"/>
</Domain>
</Lattice>
<SpaceSymbol symbol="l"/>
</Space>
<Time>
<StartTime value="0"/>
<StopTime value="500"/>
<TimeSymbol symbol="time"/>
</Time>
<CellTypes>
<CellType name="medium" class="medium">
<Property value="0.0" symbol="clone"/>
<Variable value="0" symbol="p_bicoid"/>
<Variable value="0" symbol="p_caudal"/>
<Variable value="0" symbol="p_giant"/>
<Variable value="0" symbol="p_kruppel"/>
<Variable value="0" symbol="p_nanos"/>
<Variable value="0" symbol="p_hunchback"/>
<Variable value="0" symbol="p_knirps"/>
<Variable value="0" symbol="p_tailless"/>
<Property value="0" symbol="p_eve_rep_cons"/>
<Property value="0" symbol="p_eve_rep"/>
<Property value="0" symbol="p_rep_eve_rep_cons"/>
<Property value="0" symbol="p_eve"/>
</CellType>
<CellType name="White_cells_true" class="biological">
<VolumeConstraint target="300" strength="1"/>
<SurfaceConstraint target="1" mode="aspherity" strength="1"/>
<Property value="1.0" symbol="clone"/>
<Property value="0" symbol="p_bicoid"/>
<Property value="0" symbol="p_nanos"/>
<Property value="0" symbol="p_hunchback"/>
<Property value="0" symbol="p_caudal"/>
<Property value="0" symbol="p_kruppel"/>
<Property value="0" symbol="p_giant"/>
<Property value="0" symbol="p_knirps"/>
<Property value="0" symbol="p_tailless"/>
<Property value="1" symbol="p_eve_rep_cons"/>
<Property value="0" symbol="p_eve_rep"/>
<Property value="0" symbol="p_rep_eve_rep_cons"/>
<Property value="0" symbol="p_eve"/>
<Mapper name="Map_Bicoid">
<Input value="BICOID"/>
<Output mapping="average" symbol-ref="con_bicoid"/>
</Mapper>
<Property value="0" symbol="con_bicoid"/>
<Mapper name="Map_Nanos">
<Input value="M_NANOS"/>
<Output mapping="average" symbol-ref="con_nanos"/>
</Mapper>
<Property value="0" symbol="con_nanos"/>
<Mapper name="Map_Caudal">
<Input value="CAUDAL"/>
<Output mapping="average" symbol-ref="con_caudal"/>
</Mapper>
<Property value="0" symbol="con_caudal"/>
<Mapper name="Map_Hunchback">
<Input value="HUNCHBACK"/>
<Output mapping="average" symbol-ref="con_hunchback"/>
</Mapper>
<Property value="0" symbol="con_hunchback"/>
<Mapper name="Map_Kruppel">
<Input value="KRUPPEL"/>
<Output mapping="average" symbol-ref="con_kruppel"/>
</Mapper>
<Property value="0" symbol="con_kruppel"/>
<Mapper name="Map_Giant">
<Input value="GIANT"/>
<Output mapping="average" symbol-ref="con_giant"/>
</Mapper>
<Property value="0" symbol="con_giant"/>
<Mapper name="Map_Knirps">
<Input value="KNIRPS"/>
<Output mapping="average" symbol-ref="con_knirps"/>
</Mapper>
<Property value="0" symbol="con_knirps"/>
<Mapper name="Map_Tailless">
<Input value="TAILLESS"/>
<Output mapping="average" symbol-ref="con_tailless"/>
</Mapper>
<Property value="0" symbol="con_tailless"/>
<Mapper name="Map_Eve_Rep">
<Input value="EVE_REP"/>
<Output mapping="average" symbol-ref="con_eve_rep"/>
</Mapper>
<Property value="0" symbol="con_eve_rep"/>
<Mapper name="Map_Eve_Rep_Cons">
<Input value="EVE_REP_CONS"/>
<Output mapping="average" symbol-ref="con_eve_rep_cons"/>
</Mapper>
<Property value="0" symbol="con_eve_rep_cons"/>
<Mapper name="Map_Rep_Eve_Rep_Cons">
<Input value="REP_EVE_REP_CONS"/>
<Output mapping="average" symbol-ref="con_rep_eve_rep_cons"/>
</Mapper>
<Property value="0" symbol="con_rep_eve_rep_cons"/>
<Mapper name="Map_Rep_Eve_Rep_Cons">
<Input value="EVE"/>
<Output mapping="average" symbol-ref="con_eve"/>
</Mapper>
<Property value="0" symbol="con_eve"/>
<System name="Morphogenes" solver="Euler [fixed, O(1)]" time-step="1.0">
<Rule symbol-ref="p_hunchback">
<Expression>if((con_bicoid>19 or con_hunchback>49 or con_tailless>101) and con_caudal<122 and con_kruppel<139 and con_knirps<4 and con_nanos<110, 31.3, 0)
</Expression>
</Rule>
<Rule symbol-ref="p_caudal">
<Expression>if((con_nanos>125) and con_hunchback<61, 7.65, 0)</Expression>
</Rule>
<Rule symbol-ref="p_kruppel">
<Expression>if((con_bicoid>9 or con_kruppel>103 or con_caudal>151) and con_hunchback<176.98 and con_giant<4 and con_knirps<115 and con_tailless<20 and time>4, 16.3, 0)</Expression>
</Rule>
<Rule symbol-ref="p_giant">
<Expression>if((con_bicoid>40 or con_caudal>133 or con_giant>85) and con_kruppel<15 and con_tailless<102 and time>4, 16.1, 0)</Expression>
</Rule>
<Rule symbol-ref="p_knirps">
<Expression>if((con_bicoid>5 or con_caudal>152 or con_knirps>94) and con_hunchback<7 and con_kruppel<141 and con_giant<220 and con_tailless<18 and time>4, 17, 0)</Expression>
</Rule>
<Rule symbol-ref="p_eve_rep">
<Expression>if(con_hunchback>40 and con_giant<30 and con_kruppel<10 and time>40, 50,
if(con_eve>14, 50, 0)
)</Expression>
</Rule>
<Rule symbol-ref="p_rep_eve_rep_cons">
<Expression>if(con_hunchback>40 and con_giant<30 and con_kruppel<10 and time>40, 50,
if(con_eve>14, 50, 0)
)</Expression>
</Rule>
<Rule symbol-ref="p_eve_rep_cons">
<Expression>if(con_rep_eve_rep_cons>0.1, 0, 1)</Expression>
</Rule>
<Rule symbol-ref="p_eve">
<Expression>if(con_hunchback>40 and con_giant<30 and con_kruppel<10 and con_nanos<105 and time>40, 2,
if(con_eve_rep<0.1 and con_eve_rep_cons<0.1 and con_bicoid<70 and con_nanos<115, 2, 0)
)</Expression>
</Rule>
<Rule symbol-ref="clone">
<Expression> if(con_eve>1, 1, 0)</Expression>
</Rule>
</System>
</CellType>
</CellTypes>
<CPM>
<Interaction>
<!-- <Disabled>
<Contact value="1" type1="amoeba" type2="medium"/>
</Disabled>
-->
</Interaction>
<MonteCarloSampler stepper="edgelist">
<MCSDuration value="1"/>
<Neighborhood>
<Order>2</Order>
</Neighborhood>
<MetropolisKinetics temperature="0.2"/>
</MonteCarloSampler>
<ShapeSurface scaling="norm">
<Neighborhood>
<Distance>2.5</Distance>
</Neighborhood>
</ShapeSurface>
</CPM>
<CellPopulations>
<Population size="0" type="White_cells_true">
<InitRectangle number-of-cells="2800" mode="regular">
<Dimensions size="960, 450, 0" origin="20,250, 0"/>
</InitRectangle>
</Population>
</CellPopulations>
<Analysis>
<Gnuplotter time-step="5" decorate="false">
<Terminal name="png" persist="true"/>
<Plot>
<!-- <Disabled>
<Field symbol-ref="GIANT">
<ColorMap>
<Color value="0.0" color="white"/>
<Color value="1.0" color="blue"/>
</ColorMap>
</Field>
</Disabled>
-->
<Cells value="clone" opacity="0.55">
<ColorMap>
<Color value="0.0" color="white"/>
<Color value="1.0" color="white"/>
<Color value="2.0" color="green"/>
<Color value="3.0" color="orange"/>
<Color value="4.0" color="light-blue"/>
<Color value="5.0" color="gold"/>
</ColorMap>
</Cells>
</Plot>
</Gnuplotter>
<!-- <Disabled>
<Logger time-step="1">
<Input>
<Symbol symbol-ref="HUNCHBACK"/>
<Symbol symbol-ref="BICOID"/>
<Symbol symbol-ref="CAUDAL"/>
<Symbol symbol-ref="NANOS"/>
<Symbol symbol-ref="TAILLESS"/>
<Disabled>
<Symbol symbol-ref="KRUPPEL"/>
</Disabled>
<Disabled>
<Symbol symbol-ref="GIANT"/>
</Disabled>
<Disabled>
<Symbol symbol-ref="KNIRPS"/>
</Disabled>
</Input>
<Output>
<TextOutput file-numbering="sequential" file-format="csv" file-name="automatic"/>
</Output>
<Plots>
<Plot file-numbering="time" time-step="5">
<Style style="points" point-size="1.0" grid="true"/>
<Terminal terminal="png"/>
<X-axis>
<Symbol symbol-ref="l.x"/>
</X-axis>
<Y-axis>
<Symbol symbol-ref="HUNCHBACK"/>
<Symbol symbol-ref="BICOID"/>
<Symbol symbol-ref="CAUDAL"/>
<Symbol symbol-ref="NANOS"/>
<Symbol symbol-ref="TAILLESS"/>
<Disabled>
<Symbol symbol-ref="KRUPPEL"/>
</Disabled>
<Disabled>
<Symbol symbol-ref="GIANT"/>
</Disabled>
<Disabled>
<Symbol symbol-ref="KNIRPS"/>
</Disabled>
</Y-axis>
</Plot>
</Plots>
</Logger>
</Disabled>
-->
<ModelGraph format="dot" reduced="false" include-tags="#untagged"/>
</Analysis>
</MorpheusModel>
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