- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-08-19 11:25:08+12:00
- Desc:
- Added image in eps format
- Permanent Source URI:
- https://models.cellml.org/workspace/elowitz_leibler_2000/rawfile/721f3816c96532ba603bd8e31ce278c4a68050b0/elowitz_leibler_2000.cellml
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COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
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<title>A synthetic oscillatory network of transcriptional regulators. </title>
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<para>
This CellML version of this model is not able to reproduce the results shown in Fig1c of the original publication, as the initial conditions for protein concentrations were not provided. The original published equations were scaled and modified with reference to the same model on the Biomodels database (<ulink url="http://biomodels.caltech.edu/BIOMD0000000012">BIOMD0000000012 - Elowitz2000_Repressilator</ulink>). Once the model comes to equilibrium (t > 400 minutes,) its output is correct.
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The units have been checked in this model and are consistent.
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<para>
ABSTRACT: Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the
functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems. Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function.
</para>
<para>
We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed
the repressilator, in Escherichia coli. The network periodically induces the synthesis of green fluorescent protein as a readout of
its state in individual cells. The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the
state of the oscillator has to be transmitted from generation to generation. This artificial clock displays noisy behaviour, possibly
because of stochastic fluctuations of its components. Such 'rational network design' may lead both to the engineering of
new cellular behaviours and to an improved understanding of naturally occurring networks.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A synthetic oscillatory network of transcriptional regulators, Michael B. Elowitz and Stanislas Leibler, 2000,<emphasis> Nature: International Weekly Journal of Science</emphasis>, 403, 335-338. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/10659856">PubMed ID: 10659856</ulink>
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<rdf:value xml:lang="en">There was an error in rescaling previously:
m in the equations in box 1 is not rescaled to the mRNA divided by the translation efficiency, M/eff, but is just M*eff/K_m, with the efficiency taken in units of rescaled protein p = P/K_m.
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<variable name="n" units="dimensionless" initial_value="2" public_interface="out"/>
<variable name="alpha_0" units="dimensionless" public_interface="out"/>
<variable name="alpha" units="dimensionless" public_interface="out"/>
<variable name="beta" units="dimensionless" public_interface="out"/>
<variable name="K_m" units="dimensionless" initial_value="40" public_interface="out"/>
<variable name="efficiency" units="dimensionless" initial_value="20" public_interface="out"/>
<variable name="mRNA_halflife" units="minute" initial_value="2" public_interface="out"/>
<variable name="t_ave" units="minute" public_interface="out"/>
<variable name="kd_prot" units="first_order_rate_constant" public_interface="out"/>
<variable name="kd_mRNA" units="first_order_rate_constant" public_interface="out"/>
<variable name="prot_halflife" units="minute" initial_value="10" public_interface="out"/>
<variable name="tps_repr" units="per_sec" initial_value="5e-4" public_interface="out"/>
<variable name="tps_active" units="per_sec" initial_value="0.5" public_interface="out"/>
<variable name="k_tl" units="first_order_rate_constant" public_interface="out"/>
<variable name="a_tr" units="first_order_rate_constant" public_interface="out"/>
<variable name="a0_tr" units="first_order_rate_constant" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>t_ave</ci>
<apply>
<divide/>
<ci>mRNA_halflife</ci>
<apply>
<ln/>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>kd_prot</ci>
<apply>
<divide/>
<apply>
<ln/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>prot_halflife</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>kd_mRNA</ci>
<apply>
<divide/>
<apply>
<ln/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>mRNA_halflife</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_tl</ci>
<apply>
<times/>
<ci>efficiency</ci>
<ci>kd_mRNA</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>a_tr</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>tps_active</ci>
<ci>tps_repr</ci>
</apply>
<cn cellml:units="second_per_minute">60</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>a0_tr</ci>
<apply>
<times/>
<ci>tps_repr</ci>
<cn cellml:units="second_per_minute">60</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>a_tr</ci>
<ci>efficiency</ci>
</apply>
<apply>
<times/>
<ci>kd_prot</ci>
<ci>K_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>a0_tr</ci>
<ci>efficiency</ci>
</apply>
<apply>
<times/>
<ci>kd_prot</ci>
<ci>K_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<divide/>
<ci>kd_prot</ci>
<ci>kd_mRNA</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="M_lacl">
<variable name="M_lacl" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="P_cl" units="dimensionless" public_interface="in"/>
<variable name="n" units="dimensionless" public_interface="in"/>
<variable name="a0_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="K_m" units="dimensionless" public_interface="in"/>
<variable name="kd_mRNA" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M_lacl</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>a0_tr</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>a_tr</ci>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>P_cl</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>kd_mRNA</ci>
<ci>M_lacl</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="M_tetR">
<variable name="M_tetR" units="dimensionless" initial_value="20" public_interface="out"/>
<variable name="a_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="P_lacl" units="dimensionless" public_interface="in"/>
<variable name="n" units="dimensionless" public_interface="in"/>
<variable name="a0_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="K_m" units="dimensionless" public_interface="in"/>
<variable name="kd_mRNA" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M_tetR</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>a_tr</ci>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>P_lacl</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
<ci>a0_tr</ci>
</apply>
<apply>
<times/>
<ci>kd_mRNA</ci>
<ci>M_tetR</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="M_cl">
<variable name="M_cl" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="P_tetR" units="dimensionless" public_interface="in"/>
<variable name="n" units="dimensionless" public_interface="in"/>
<variable name="a0_tr" units="first_order_rate_constant" public_interface="in"/>
<variable name="K_m" units="dimensionless" public_interface="in"/>
<variable name="kd_mRNA" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M_cl</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>a_tr</ci>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_m</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>P_tetR</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
<ci>a0_tr</ci>
</apply>
<apply>
<times/>
<ci>kd_mRNA</ci>
<ci>M_cl</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="P_lacl">
<variable name="P_lacl" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="k_tl" units="first_order_rate_constant" public_interface="in"/>
<variable name="M_lacl" units="dimensionless" public_interface="in"/>
<variable name="kd_prot" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_lacl</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_tl</ci>
<ci>M_lacl</ci>
</apply>
<apply>
<times/>
<ci>kd_prot</ci>
<ci>P_lacl</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="P_tetR">
<variable name="P_tetR" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="k_tl" units="first_order_rate_constant" public_interface="in"/>
<variable name="M_tetR" units="dimensionless" public_interface="in"/>
<variable name="kd_prot" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_tetR</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_tl</ci>
<ci>M_tetR</ci>
</apply>
<apply>
<times/>
<ci>kd_prot</ci>
<ci>P_tetR</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="P_cl">
<variable name="P_cl" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="k_tl" units="first_order_rate_constant" public_interface="in"/>
<variable name="M_cl" units="dimensionless" public_interface="in"/>
<variable name="kd_prot" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_cl</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_tl</ci>
<ci>M_cl</ci>
</apply>
<apply>
<times/>
<ci>kd_prot</ci>
<ci>P_cl</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_lacl" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_tetR" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_cl" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_lacl" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_tetR" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_cl" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_lacl" component_2="parameters"/>
<map_variables variable_1="a_tr" variable_2="a_tr"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="a0_tr" variable_2="a0_tr"/>
<map_variables variable_1="K_m" variable_2="K_m"/>
<map_variables variable_1="kd_mRNA" variable_2="kd_mRNA"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_lacl" component_2="P_cl"/>
<map_variables variable_1="P_cl" variable_2="P_cl"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_tetR" component_2="parameters"/>
<map_variables variable_1="a_tr" variable_2="a_tr"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="a0_tr" variable_2="a0_tr"/>
<map_variables variable_1="K_m" variable_2="K_m"/>
<map_variables variable_1="kd_mRNA" variable_2="kd_mRNA"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_tetR" component_2="P_lacl"/>
<map_variables variable_1="P_lacl" variable_2="P_lacl"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_cl" component_2="parameters"/>
<map_variables variable_1="a_tr" variable_2="a_tr"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="a0_tr" variable_2="a0_tr"/>
<map_variables variable_1="K_m" variable_2="K_m"/>
<map_variables variable_1="kd_mRNA" variable_2="kd_mRNA"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="M_cl" component_2="P_tetR"/>
<map_variables variable_1="P_tetR" variable_2="P_tetR"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_lacl" component_2="parameters"/>
<map_variables variable_1="k_tl" variable_2="k_tl"/>
<map_variables variable_1="kd_prot" variable_2="kd_prot"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_lacl" component_2="M_lacl"/>
<map_variables variable_1="M_lacl" variable_2="M_lacl"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_tetR" component_2="parameters"/>
<map_variables variable_1="k_tl" variable_2="k_tl"/>
<map_variables variable_1="kd_prot" variable_2="kd_prot"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_tetR" component_2="M_tetR"/>
<map_variables variable_1="M_tetR" variable_2="M_tetR"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_cl" component_2="parameters"/>
<map_variables variable_1="k_tl" variable_2="k_tl"/>
<map_variables variable_1="kd_prot" variable_2="kd_prot"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P_cl" component_2="M_cl"/>
<map_variables variable_1="M_cl" variable_2="M_cl"/>
</connection>
</model>
