SBML import: MAPK signaling

Introduction

This model has been imported and automatically converted from SBML format by Morpheus. It shows oscillations in the MAPK signaling cascade (Kholodenko, 2000).

Time plots of oscillations in MAPK signaling Kholodenko, 2000)
Time plots of oscillations in MAPK signaling (Kholodenko, 2000)

Model description

Upon importing an SBML file, a Morpheus model is automatically created. A System of DiffEqns is generated, based on the function and reactions defined in the SBML file and defined as part of a CellType. Additionally, a Logger is generated to record and visualize the output.

Simulation details, such as StartTime and StopTime, as well as the time-step of System, need to be specified manually.

Things to try

Model

In Morpheus GUI: Examples 🠒 ODE 🠒 MAPK_SBML.xml.

<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="3">
    <Description>
        <Title>BIOMD0000000010</Title>
        <Details>Imported SBML model: http://www.ebi.ac.uk/biomodels-main/BIOMD0000000010
        
Kholodenko BN, Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.</Details>
    </Description>
    <Global/>
    <Space>
        <Lattice class="linear">
            <Size symbol="size" value="1 0 0"/>
            <Neighborhood>
                <Order>1</Order>
            </Neighborhood>
        </Lattice>
        <SpaceSymbol symbol="space"/>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime symbol="stop" value="1.0"/>
        <TimeSymbol symbol="time" name="time"/>
    </Time>
    <CellTypes>
        <CellType class="biological" name="sbml_ct">
            <System solver="runge-kutta-adaptive" time-scaling="4000" time-step="stop">
                <Constant symbol="V1" value="2.5"/>
                <Constant symbol="Ki" value="9"/>
                <Constant symbol="n" value="1"/>
                <Constant symbol="K1" value="10"/>
                <DiffEqn symbol-ref="MKKK" name="gained from reactions">
                    <Expression> - V1 * MKKK / ((1 + pow(MAPK_PP / Ki, n)) * (K1 + MKKK)) + V2 * MKKK_P / (KK2 + MKKK_P)</Expression>
                </DiffEqn>
                <DiffEqn symbol-ref="MKKK_P" name="gained from reactions">
                    <Expression>V1 * MKKK / ((1 + pow(MAPK_PP / Ki, n)) * (K1 + MKKK)) - V2 * MKKK_P / (KK2 + MKKK_P)</Expression>
                </DiffEqn>
                <Constant symbol="V2" value="0.25"/>
                <Constant symbol="KK2" value="8"/>
                <Constant symbol="k3" value="0.025"/>
                <Constant symbol="KK3" value="15"/>
                <DiffEqn symbol-ref="MKK" name="gained from reactions">
                    <Expression> - k3 * MKKK_P * MKK / (KK3 + MKK) + V6 * MKK_P / (KK6 + MKK_P)</Expression>
                </DiffEqn>
                <DiffEqn symbol-ref="MKK_P" name="gained from reactions">
                    <Expression>k3 * MKKK_P * MKK / (KK3 + MKK) - uVol * k4 * MKKK_P * MKK_P / (KK4 + MKK_P) + uVol * V5 * MKK_PP / (KK5 + MKK_PP) - V6 * MKK_P / (KK6 + MKK_P)</Expression>
                </DiffEqn>
                <Constant symbol="k4" value="0.025"/>
                <Constant symbol="KK4" value="15"/>
                <DiffEqn symbol-ref="MKK_PP" name="gained from reactions">
                    <Expression>k4 * MKKK_P * MKK_P / (KK4 + MKK_P) - V5 * MKK_PP / (KK5 + MKK_PP)</Expression>
                </DiffEqn>
                <Constant symbol="V5" value="0.75"/>
                <Constant symbol="KK5" value="15"/>
                <Constant symbol="V6" value="0.75"/>
                <Constant symbol="KK6" value="15"/>
                <Constant symbol="k7" value="0.025"/>
                <Constant symbol="KK7" value="15"/>
                <DiffEqn symbol-ref="MAPK" name="gained from reactions">
                    <Expression> - k7 * MKK_PP * MAPK / (KK7 + MAPK) + V10 * MAPK_P / (KK10 + MAPK_P)</Expression>
                </DiffEqn>
                <DiffEqn symbol-ref="MAPK_P" name="gained from reactions">
                    <Expression> k7 * MKK_PP * MAPK / (KK7 + MAPK) - k8 * MKK_PP * MAPK_P / (KK8 + MAPK_P) + uVol * V9 * MAPK_PP / (KK9 + MAPK_PP) - V10 * MAPK_P / (KK10 + MAPK_P)</Expression>
                </DiffEqn>
                <Constant symbol="k8" value="0.025"/>
                <Constant symbol="KK8" value="15"/>
                <DiffEqn symbol-ref="MAPK_PP" name="gained from reactions">
                    <Expression>k8 * MKK_PP * MAPK_P / (KK8 + MAPK_P) - V9 * MAPK_PP / (KK9 + MAPK_PP)</Expression>
                </DiffEqn>
                <Constant symbol="V9" value="0.5"/>
                <Constant symbol="KK9" value="15"/>
                <Constant symbol="V10" value="0.5"/>
                <Constant symbol="KK10" value="15"/>
            </System>
            <Constant symbol="uVol" value="1" name="compartment size"/>
            <Property symbol="MKKK" value="90" name="Mos"/>
            <Property symbol="MKKK_P" value="10" name="Mos-P"/>
            <Property symbol="MKK" value="280" name="Mek1"/>
            <Property symbol="MKK_P" value="10" name="Mek1-P"/>
            <Property symbol="MKK_PP" value="10" name="Mek1-PP"/>
            <Property symbol="MAPK" value="280" name="Erk2"/>
            <Property symbol="MAPK_P" value="10" name="Erk2-P"/>
            <Property symbol="MAPK_PP" value="10" name="Erk2-PP"/>
        </CellType>
    </CellTypes>
    <CellPopulations>
        <Population size="1" type="sbml_ct"/>
    </CellPopulations>
    <Analysis>
        <Logger time-step="stop/200">
            <Restriction>
                <Celltype celltype="sbml_ct"/>
            </Restriction>
            <Input>
                <Symbol symbol-ref="MAPK"/>
                <Symbol symbol-ref="MAPK_P"/>
                <Symbol symbol-ref="MAPK_PP"/>
                <Symbol symbol-ref="MKK"/>
                <Symbol symbol-ref="MKK_P"/>
                <Symbol symbol-ref="MKK_PP"/>
                <Symbol symbol-ref="MKKK"/>
                <Symbol symbol-ref="MKKK_P"/>
            </Input>
            <Output>
                <TextOutput/>
            </Output>
            <Plots>
                <Plot time-step="-1">
                    <Style grid="true" style="lines" line-width="3.0"/>
                    <Terminal terminal="png"/>
                    <X-axis>
                        <Symbol symbol-ref="time"/>
                    </X-axis>
                    <Y-axis>
                        <Symbol symbol-ref="MAPK"/>
                        <Symbol symbol-ref="MAPK_P"/>
                        <Symbol symbol-ref="MAPK_PP"/>
                        <Symbol symbol-ref="MKK"/>
                        <Symbol symbol-ref="MKK_P"/>
                        <Symbol symbol-ref="MKK_PP"/>
                        <Symbol symbol-ref="MKKK"/>
                        <Symbol symbol-ref="MKKK_P"/>
                    </Y-axis>
                </Plot>
            </Plots>
        </Logger>
    </Analysis>
</MorpheusModel>

Reference

Kholodenko BN. Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur. J. Biochem. 2000 Mar; 267(6): 1583-1588

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