Location: Potter, Greller, Cho, Nuttall, Stroup, Suva, Tobin, 2005 @ 5a3fc2158228 / potter_greller_cho_nuttall_stroup_suva_tobin_2005_b.cellml

Author:

pmr2.import <nobody@models.cellml.org>

Date:

2009-06-17 15:37:02+12:00

Desc:

committing version01 of potter_greller_cho_nuttall_stroup_suva_tobin_2005

Permanent Source URI:

https://models.physiomeproject.org/workspace/potter_greller_cho_nuttall_stroup_suva_tobin_2005/rawfile/5a3fc2158228b0dcb1cf4bfc0b791a1088a363c0/potter_greller_cho_nuttall_stroup_suva_tobin_2005_b.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  potter_model_2005.xml

CREATED :  23rd July 2007

LAST MODIFIED : 23rd July 2007

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.1 Specification.

DESCRIPTION :  This file contains a CellML description of Potter et al's 2005 mathematical model for parathyroid hormone receptor kinetics.

CHANGES:  
  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="potter_model_2005" name="heinze_keener_midgley_model_1998_version01">

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <sect1 id="sec_structure">
  <title>Model Structure</title>

<para>
Pulsatile administration of the parathyroid hormone (PTH) has been shown to stimulate bone formation in both animals and humans, and the PTH signalling pathway is considered as a potential target for the development of new therapeutic treatments for post-menopausal osteoporosis.  The binding of PTH to its specific receptor, the PTH Type 1 receptor (PTH1R) initiates signal transduction cascades that result in bone turnover and, as such, PTH has recently been approved as a treatment for post-menopausal osteoporosis.  However, while pulsatile PTH exposure results in bone formation, paradoxically, continuous PTH administration causes net bone loss.  
</para>

<para>
To date, the mechanisms underlying these two phenomena remain poorly understood.  To add further complexity to the conundrum, the PTH-mediated signalling pathway in osteoblasts is a complicated network that stems from the interaction of the PTH-PTH1R complex and two distinct G proteins.  The identities of the various components of this signalling network remain relatively elusive,To effectively utilise PTH as a therapeutic treatment for osteoporosis it is essential to improve our understanding of the dynamics of PTH-PTH1R binding and signal transduction.  To this end, Potter <emphasis>et al.</emphasis> have developed a mathematical model which simulates the PTH1R kinetics (summarised in the figure below).  They use this model to explore the hypothesis that the dynamics of the receptor are critical to the bone growth or loss responses to pulsatile or continuous PTH dosing patterns respectively.  Conversely, if the receptor kinetics are not crucial to the differential response, an alternative hypothesis is that downstream signal transduction events are more influential.   
</para>

<para> 
Simulation results suggest the model is biologically relevant and is capable of discriminating between pulsatile and continuous PTH dosing.  Furthermore, the simulation results were considered to be consistent with the hypothesis that PTH1R kinetics are important in mediating the PTH effects on the skeleton.
</para>  

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="potter_2005.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the two-state model for PTHR1 binding kinetics  PTH is secreted and/or dosed at a rate D and binds to the active (Ra) and inactive (Ri) forms of the receptor.  PTH-PTHR1 binding results in the formation of the active (Ca) and inactive (Ci) complexes.  In addition, there is a conversion between the active and inactive forms of the receptor and complexes, while unbound PTH is cleared from the system.</caption>
</informalfigure>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6T4Y-4G7X9V0-4&amp;_user=140507&amp;_coverDate=08%2F31%2F2005&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_cdi=4987&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=68d85a10b3ff0404024423bad9ab3f78">Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics</ulink>, Laura K. Potter, Larry D. Greller, Carolyn R. Cho, Mark E. Nuttall, George B. Stroup, Larry J. Suva, and Frank L. Tobin, 2005, <ulink url="http://www.sciencedirect.com/science/journal/87563282">
            <emphasis>Bone</emphasis>
          </ulink>, 37, 159-169.  (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6T4Y-4G7X9V0-4&amp;_user=140507&amp;_coverDate=08%2F31%2F2005&amp;_rdoc=1&amp;_fmt=full&amp;_orig=search&amp;_cdi=4987&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=8899bfa78ec32054e3174eedf5c0ef38">Full text</ulink> and PDF versions of the article are available to journal subscribers on the <emphasis>Bone</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=15921971&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 15921971</ulink>
</para>

<para> 
This model has been translated into two variant CellML models; the first CellML model considers the effects of continuous PTH administration while the second describes the consequences of pulsatile PTH dosing.
</para>

</sect1>
</article>
</documentation> 




  <units name="hour">
    <unit units="second" multiplier="3600.0"/>
  </units>

  <units name="picomolar">
    <unit units="mole" prefix="pico"/>
    <unit units="litre" exponent="-1"/>
  </units>

  <units name="flux">
    <unit units="picomolar"/>
    <unit units="second" exponent="-1"/>
  </units>

  <units name="first_order_rate_constant">
    <unit units="second" exponent="-1"/>
  </units>

  <units name="second_order_rate_constant">
    <unit units="picomolar" exponent="-1"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>

  <component cmeta:id="P" name="P">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="P">
        <dc:title>P</dc:title>
        <dcterms:alternative>PTH</dcterms:alternative>
        <dcterms:alternative>parathyroid hormone</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="picomolar" public_interface="out" name="P" initial_value="3.0"/>
    
    <variable units="second_order_rate_constant" public_interface="in" name="k1"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k1_"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k2_"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kcl"/>
    <variable units="flux" public_interface="in" name="D"/>
    <variable units="picomolar" public_interface="in" name="Ca"/>
    <variable units="picomolar" public_interface="in" name="Ci"/>
    <variable units="picomolar" public_interface="in" name="Ra"/>
    <variable units="picomolar" public_interface="in" name="Ri"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> P </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1_ </ci>
              <ci> Ca </ci>
            </apply>
            <apply>
              <times/>
              <ci> k2_ </ci>
              <ci> Ci </ci>
            </apply>
            <ci> D </ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> Ra </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> Ri </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> kcl </ci>
              <ci> P </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component cmeta:id="Ra" name="Ra">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ra">
        <dc:title>Ra</dc:title>
        <dcterms:alternative>active PTH1R</dcterms:alternative>
        <dcterms:alternative>active parathyroid hormone Type 1 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="picomolar" public_interface="out" name="Ra" initial_value="16.9"/>
    
    <variable units="second_order_rate_constant" public_interface="in" name="k1"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k1_"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3_"/>
    <variable units="picomolar" public_interface="in" name="Ca"/>
    <variable units="picomolar" public_interface="in" name="P"/>
    <variable units="picomolar" public_interface="in" name="Ri"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> Ra </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1_ </ci>
              <ci> Ca </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> Ri </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> Ra </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3_ </ci>
              <ci> Ra </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component cmeta:id="Ri" name="Ri">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ri">
        <dc:title>Ri</dc:title>
        <dcterms:alternative>inactive PTH1R</dcterms:alternative>
        <dcterms:alternative>inactive parathyroid hormone Type 1 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="picomolar" public_interface="out" name="Ri" initial_value="1.7"/>
    
    <variable units="second_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k2_"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3_"/>
    <variable units="picomolar" public_interface="in" name="Ci"/>
    <variable units="picomolar" public_interface="in" name="P"/>
    <variable units="picomolar" public_interface="in" name="Ra"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> Ri </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2_ </ci>
              <ci> Ci </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3_ </ci>
              <ci> Ra </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> Ri </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> Ri </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component cmeta:id="Ca" name="Ca">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ca">
        <dc:title>Ca</dc:title>
        <dcterms:alternative>active PTH-PTH1R complex</dcterms:alternative>
        <dcterms:alternative>active parathyroid hormone-parathyroid hormone Type 1 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="picomolar" public_interface="out" name="Ca" initial_value="4E-4"/>
    
    <variable units="second_order_rate_constant" public_interface="in" name="k1"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k1_"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k4"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k4_"/>
    <variable units="picomolar" public_interface="in" name="Ci"/>
    <variable units="picomolar" public_interface="in" name="P"/>
    <variable units="picomolar" public_interface="in" name="Ra"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> Ca </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> Ra </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> k4 </ci>
              <ci> Ci </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k1_ </ci>
              <ci> Ca </ci>
            </apply>
            <apply>
              <times/>
              <ci> k4_ </ci>
              <ci> Ca </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component cmeta:id="Ci" name="Ci">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ci">
        <dc:title>Ci</dc:title>
        <dcterms:alternative>inactive PTH-PTH1R complex</dcterms:alternative>
        <dcterms:alternative>inactive parathyroid hormone-parathyroid hormone Type 1 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="picomolar" public_interface="out" name="Ci" initial_value="0.05"/>
    
    <variable units="second_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k2_"/>
    <variable units="second_order_rate_constant" public_interface="in" name="k4"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k4_"/>
    <variable units="picomolar" public_interface="in" name="Ca"/>
    <variable units="picomolar" public_interface="in" name="P"/>
    <variable units="picomolar" public_interface="in" name="Ri"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> Ci </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> Ri </ci>
              <ci> P </ci>
            </apply>
            <apply>
              <times/>
              <ci> k4_ </ci>
              <ci> Ca </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2_ </ci>
              <ci> Ci </ci>
            </apply>
            <apply>
              <times/>
              <ci> k4 </ci>
              <ci> Ci </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component cmeta:id="rho" name="rho">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="rho">
        <dc:title>rho</dc:title>
        <dcterms:alternative>fraction of PTH1R in the active state</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable units="dimensionless" name="rho"/>
    
    <variable units="picomolar" public_interface="in" name="Ca"/>
    <variable units="picomolar" public_interface="in" name="Ci"/>
    <variable units="picomolar" public_interface="in" name="P"/>
    <variable units="picomolar" public_interface="in" name="Ra"/>
    <variable units="picomolar" public_interface="in" name="Ri"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci> rho </ci> 
        <apply>
          <divide/>
          <apply>
            <plus/>
            <ci> Ra </ci>
            <ci> Ca </ci>
          </apply>
          <apply>
            <plus/>
            <ci> Ra </ci>
            <ci> Ca </ci>
            <ci> Ri </ci>
            <ci> Ci </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>

  <component name="model_parameters"> 
    <variable units="second_order_rate_constant" public_interface="out" name="k1" initial_value="1.0E-6"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k1_" initial_value="1.0E-3"/>
    <variable units="second_order_rate_constant" public_interface="out" name="k2" initial_value="1.0E-7"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k2_" initial_value="1.0E-3"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k3" initial_value="1.0E-3"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k3_" initial_value="1.0E-4"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k4" initial_value="2.0E-3"/>
    <variable units="first_order_rate_constant" public_interface="out" name="k4_" initial_value="0.4"/>
    <variable units="first_order_rate_constant" public_interface="out" name="kcl" initial_value="5.0E-3"/>
    <variable units="flux" public_interface="out" name="D"/>

    <variable units="flux" name="De" initial_value="0.0"/>
    <variable units="flux" name="Dd"/>
    <variable units="flux" name="dmax" initial_value="0.015"/>
    <variable units="flux" name="dmin" initial_value="0.0"/>
    <variable units="hour" name="tau_on" initial_value="0.5"/>
    <variable units="hour" name="tau_off" initial_value="0.5"/>
    <variable units="dimensionless" name="j" initial_value="9.0"/>

    <variable units="hour" public_interface="in" name="time"/>

    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci> D </ci> 
        <apply>
          <plus/>
          <ci> De </ci>
          <ci> Dd </ci>
        </apply>
      </apply>

      <apply>
        <eq/> 
        <ci> Dd </ci>   
        <piecewise>
          <piece>
            <ci> dmax </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 0.0 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 0.5 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmin </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 0.5 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 1.0 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmax </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 1.0 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 1.5 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmin </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 1.5 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 2.0 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmax </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 2.0 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 2.5 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmin </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 2.5 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 3.0 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmax </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 3.0 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 3.5 </cn>
              </apply>
            </apply>
          </piece>
          <piece>
            <ci> dmin </ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci> time </ci>
                <cn cellml:units="hour"> 3.5 </cn>
              </apply>
              <apply>
                <lt/>
                <ci> time </ci>
                <cn cellml:units="hour"> 4.0 </cn>
              </apply>
            </apply>
          </piece>
        </piecewise>
      </apply>
    </math>
  </component>

  <connection>
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