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This CellML file was generated on 24/07/2008 at 1:08:46 at p.m. using:
COR (0.9.31.979)
Copyright 2002-2008 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.CellML.org/
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<article>
<articleinfo>
<title>Hyperpolarization-Activated Graded Persistent Activity in the Prefrontal Cortex</title>
<author>
<firstname>Geoffrey</firstname>
<surname>Nunns</surname>
<affiliation>
<shortaffil>Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model runs in PCEnv and is based off the NEURON code for this paper. The units are continuous throughout but the model does not recreate the published results. It utilizes DAE solving techniques and advances in these could result in better output.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Abstract: We describe a phenomenon of hyperpolarization-activated graded persistent activity (HAGPA) in prefrontal cortex neurons. Successive hyperpolarizing pulses induced increasingly higher rates of tonic firing that remained stable for tens of seconds, allowing the neuron to retain a memory of the previous history of stimulation. This phenomenon occurred at the cellular level and in the absence of neuromodulators. Neurons with HAGPA had a sag during hyperpolarization, and blocking h-current eliminated the sag and prevented HAGPA, suggesting that the activation of this hyperpolarization-activated cationic current was necessary for the occurrence of the phenomenon. A single-neuron biophysical model including h-current modulation by intracellular calcium was able to display HAGPA. This form of neuronal memory not only allows the transformation of inhibition into an increase of firing rate, but also endows neurons with a mechanism to compute the properties of successive inputs into persistent activity, thus solving a difficult computational problem.
</para>
<para>
The original paper reference is cited below:
</para>
<para>Hyperpolarization-Activated Graded Persistent Activity in the Prefrontal Cortex, Milena Winograd, Alain Destexhe, Maria V. Sanchez-Vives, 2008, <emphasis>Proceedings of the National Academy of the Sciences of the United States of America</emphasis>, 105, 7298-7303. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=18474856&dopt=Abstract">PubMed ID: 18474856 </ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
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<caption>Schematic diagram of the neuron model.</caption>
</informalfigure>
</sect1>
</article>
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<ci>V_T</ci>
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<cn cellml:units="millivolt">15</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_n</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_second_per_millivolt">0.5</cn>
<cn cellml:units="millivolt">40</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_T</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_T</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1e-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second_per_millivolt">0.5</cn>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_T</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_T</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_n</ci>
<ci>beta_n</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>n_inf</ci>
<apply>
<divide/>
<ci>alpha_n</ci>
<apply>
<plus/>
<ci>alpha_n</ci>
<ci>beta_n</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>n_inf</ci>
<ci>n</ci>
</apply>
<ci>tau_n</ci>
</apply>
</apply>
</math>
</component>
<component name="I_KM">
<variable units="milliampere_per_cm_squared" public_interface="out" name="I_KM"/>
<variable units="millisiemens_per_cm_squared" name="g_KM" initial_value="0.004"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="dimensionless" private_interface="in" name="p"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_KM</ci>
<apply>
<times/>
<cn cellml:units="milliampere_per_millisiemens_per_millivolt">1000</cn>
<ci>g_KM</ci>
<ci>p</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="KM_p_gate">
<variable units="dimensionless" public_interface="out" name="p" initial_value="0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="dimensionless" name="p_inf"/>
<variable units="second" name="tau_p"/>
<variable units="second" name="tau_max" initial_value="4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>p_inf</ci>
<piecewise>
<piece>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<lt/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
<cn cellml:units="dimensionless">25</cn>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">25</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">1</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_p</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>tau_max</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">3.3</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<lt/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="dimensionless">25</cn>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">25</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="second">1</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>p</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>p_inf</ci>
<ci>p</ci>
</apply>
<ci>tau_p</ci>
</apply>
</apply>
</math>
</component>
<component name="I_CaL">
<variable units="milliampere_per_cm_squared" public_interface="out" name="I_CaL"/>
<variable units="cm_per_second" name="P_Ca" initial_value="2.76e-4"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="coulomb_per_cm_cubed" public_interface="in" name="G"/>
<variable units="dimensionless" private_interface="in" name="q"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_CaL</ci>
<apply>
<times/>
<cn cellml:units="millicoulomb_per_coulomb">1000</cn>
<ci>P_Ca</ci>
<apply>
<power/>
<ci>q</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>G</ci>
</apply>
</apply>
</math>
</component>
<component name="CaL_q_gate">
<variable units="dimensionless" public_interface="out" name="q" initial_value="0.00247262"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="per_second" name="alpha_q"/>
<variable units="per_second" name="beta_q"/>
<variable units="second" name="tau_q"/>
<variable units="dimensionless" name="q_inf"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_q</ci>
<apply>
<divide/>
<cn cellml:units="per_second">6.32</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
<cn cellml:units="millivolt">13.89</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_q</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_second">0.02</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">5.36</cn>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">1.31</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">2</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<apply>
<abs/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">1.31</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.36</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1e-6</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_second_per_millivolt">0.02</cn>
<apply>
<minus/>
<cn cellml:units="millivolt">1.31</cn>
<ci>V</ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">1.31</cn>
</apply>
<cn cellml:units="millivolt">5.36</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_q</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_q</ci>
<ci>beta_q</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>q_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>q_inf</ci>
<ci>q</ci>
</apply>
<ci>tau_q</ci>
</apply>
</apply>
</math>
</component>
<component name="G_nonlin">
<variable units="coulomb_per_cm_cubed" public_interface="out" name="G"/>
<variable units="dimensionless" name="Z" initial_value="2"/>
<variable units="mM" name="Ca_o" initial_value="2"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" private_interface="out" name="F"/>
<variable units="joule_per_mole_per_kelvin" public_interface="in" private_interface="out" name="R"/>
<variable units="kelvin" public_interface="in" private_interface="out" name="T"/>
<variable units="milliampere_per_cm_squared" public_interface="in" private_interface="out" name="I_CaL"/>
<variable units="mM" public_interface="out" private_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>G</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>Z</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="volt_per_millivolt">1e-3</cn>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<cn cellml:units="mole_liter_per_millimole_per_cm3">1e-6</cn>
<apply>
<minus/>
<ci>Ca_i</ci>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>Z</ci>
<ci>F</ci>
<cn cellml:units="volt_per_millivolt">1e-3</cn>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="volt_per_millivolt">1e-3</cn>
<ci>Z</ci>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="dCa_i_dt">
<variable units="mM" public_interface="out" name="Ca_i" initial_value="100e-6"/>
<variable units="mM" name="Ca_inf" initial_value="100e-6"/>
<variable units="second" name="tau_r" initial_value="17e-3"/>
<variable units="centimeter" name="d" initial_value="1e-4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="mM_per_second" name="drive_channel"/>
<variable units="fixer" name="k" initial_value="0.1"/>
<variable units="milliampere_per_cm_squared" public_interface="in" name="I_CaL"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="joule_per_mole_per_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>drive_channel</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k</ci>
<ci>I_CaL</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_inf</ci>
<ci>Ca_i</ci>
</apply>
<ci>tau_r</ci>
</apply>
<apply>
<leq/>
<ci>drive_channel</ci>
<cn cellml:units="mM_per_second">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<ci>drive_channel</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_inf</ci>
<ci>Ca_i</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="I_h">
<variable units="milliampere_per_cm_squared" public_interface="out" name="I_h"/>
<variable units="dimensionless" name="m"/>
<variable units="millivolt" name="E_h" initial_value="-20"/>
<variable units="millisiemens_per_cm_squared" name="g_hbar" initial_value="0.02"/>
<variable units="mM" name="cac" initial_value="0.006"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" private_interface="out" name="V_S" initial_value="0"/>
<variable units="mM" public_interface="in" private_interface="out" name="Ca_i"/>
<variable units="dimensionless" private_interface="in" name="o_1"/>
<variable units="dimensionless" private_interface="in" name="o_2"/>
<variable units="dimensionless" name="g_inc" initial_value="2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>m</ci>
<apply>
<plus/>
<ci>o_1</ci>
<ci>g_inc</ci>
<ci>o_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_h</ci>
<apply>
<times/>
<cn cellml:units="milliampere_per_millisiemens_per_millivolt">1000</cn>
<ci>g_hbar</ci>
<ci>m</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_h</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="kinetic">
<variable units="dimensionless" name="p_0"/>
<variable units="dimensionless" public_interface="out" name="p_1"/>
<variable units="dimensionless" name="c_1"/>
<variable units="dimensionless" public_interface="out" name="o_1"/>
<variable units="dimensionless" public_interface="out" name="o_2"/>
<variable units="dimensionless" public_interface="in" name="alpha"/>
<variable units="dimensionless" public_interface="in" name="beta"/>
<variable units="per_second" public_interface="in" name="k_1Ca"/>
<variable units="per_second" public_interface="in" name="k_2"/>
<variable units="per_second" public_interface="in" name="k_3p"/>
<variable units="per_second" public_interface="in" name="k_4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>p_0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>p_1</ci>
<ci>k_2</ci>
</apply>
<ci>k_1Ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>p_1</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>p_0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_1</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>beta</ci>
<ci>alpha</ci>
</apply>
<ci>o_1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>o_1</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>k_4</ci>
<ci>k_3p</ci>
</apply>
<ci>o_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>o_2</ci>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>c_1</ci>
</apply>
<ci>o_1</ci>
</apply>
</apply>
</math>
</component>
<component name="rate_constants">
<variable units="second" name="h_inf"/>
<variable units="second" name="tau_s"/>
<variable units="dimensionless" public_interface="out" name="alpha"/>
<variable units="dimensionless" public_interface="out" name="beta"/>
<variable units="per_second" public_interface="out" name="k_1Ca"/>
<variable units="per_second" public_interface="out" name="k_3p"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_S"/>
<variable units="dimensionless" public_interface="in" name="p_1"/>
<variable units="per_second" public_interface="out" name="k_2" initial_value="0.1"/>
<variable units="dimensionless" name="P_c" initial_value="0.01"/>
<variable units="per_second" public_interface="out" name="k_4" initial_value="1"/>
<variable units="dimensionless" name="n_Ca" initial_value="4"/>
<variable units="dimensionless" name="n_exp" initial_value="1"/>
<variable units="dimensionless" name="p_C" initial_value="0.01"/>
<variable units="mM" name="Ca_c" initial_value="0.006"/>
<variable units="mM" public_interface="in" name="Ca_i"/>
<variable units="second" name="tau_m" initial_value="20e-3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h_inf</ci>
<apply>
<divide/>
<cn cellml:units="second">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">75</cn>
</apply>
<ci>V_S</ci>
</apply>
<cn cellml:units="millivolt">5.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<ci>tau_m</ci>
<apply>
<divide/>
<cn cellml:units="second">1000</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<ci>V_S</ci>
</apply>
<cn cellml:units="millivolt">14.2</cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">89</cn>
</apply>
<ci>V_S</ci>
</apply>
</apply>
<cn cellml:units="millivolt">11.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<divide/>
<ci>h_inf</ci>
<ci>tau_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="second">1</cn>
<ci>h_inf</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_1Ca</ci>
<apply>
<times/>
<ci>k_2</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Ca_c</ci>
</apply>
<ci>n_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_3p</ci>
<apply>
<times/>
<ci>k_4</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>p_1</ci>
<ci>p_C</ci>
</apply>
<ci>n_exp</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="I_Na">
<component_ref component="Na_m_gate"/>
<component_ref component="Na_h_gate"/>
</component_ref>
<component_ref component="I_KD">
<component_ref component="KD_n_gate"/>
</component_ref>
<component_ref component="I_KM">
<component_ref component="KM_p_gate"/>
</component_ref>
<component_ref component="I_CaL">
<component_ref component="CaL_q_gate"/>
</component_ref>
<component_ref component="G_nonlin">
<component_ref component="dCa_i_dt"/>
</component_ref>
<component_ref component="I_h">
<component_ref component="kinetic"/>
<component_ref component="rate_constants"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="I_Na"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_Na"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_Na" variable_1="I_Na"/>
<map_variables variable_2="V_T" variable_1="V_T"/>
<map_variables variable_2="V_S" variable_1="V_S"/>
</connection>
<connection>
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<map_variables variable_2="V_T" variable_1="V_T"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="m" variable_1="m"/>
</connection>
<connection>
<map_components component_2="Na_h_gate" component_1="I_Na"/>
<map_variables variable_2="V_S" variable_1="V_S"/>
<map_variables variable_2="V_T" variable_1="V_T"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="h" variable_1="h"/>
</connection>
<connection>
<map_components component_2="environment" component_1="I_KD"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_KD"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_KD" variable_1="I_KD"/>
<map_variables variable_2="V_T" variable_1="V_T"/>
</connection>
<connection>
<map_components component_2="KD_n_gate" component_1="I_KD"/>
<map_variables variable_2="V_T" variable_1="V_T"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="n" variable_1="n"/>
</connection>
<connection>
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<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_KM"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_KM" variable_1="I_KM"/>
</connection>
<connection>
<map_components component_2="KM_p_gate" component_1="I_KM"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="p" variable_1="p"/>
</connection>
<connection>
<map_components component_2="I_KM" component_1="I_KD"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="environment" component_1="I_CaL"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_CaL"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_CaL" variable_1="I_CaL"/>
</connection>
<connection>
<map_components component_2="CaL_q_gate" component_1="I_CaL"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="q" variable_1="q"/>
</connection>
<connection>
<map_components component_2="environment" component_1="G_nonlin"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="G_nonlin"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="dCa_i_dt" component_1="G_nonlin"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="I_CaL" variable_1="I_CaL"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="I_CaL" component_1="G_nonlin"/>
<map_variables variable_2="G" variable_1="G"/>
<map_variables variable_2="I_CaL" variable_1="I_CaL"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_leak"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_leak" variable_1="I_leak"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="I_h"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="I_h" variable_1="I_h"/>
</connection>
<connection>
<map_components component_2="rate_constants" component_1="kinetic"/>
<map_variables variable_2="p_1" variable_1="p_1"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
<map_variables variable_2="beta" variable_1="beta"/>
<map_variables variable_2="k_1Ca" variable_1="k_1Ca"/>
<map_variables variable_2="k_2" variable_1="k_2"/>
<map_variables variable_2="k_3p" variable_1="k_3p"/>
<map_variables variable_2="k_4" variable_1="k_4"/>
</connection>
<connection>
<map_components component_2="kinetic" component_1="I_h"/>
<map_variables variable_2="o_1" variable_1="o_1"/>
<map_variables variable_2="o_2" variable_1="o_2"/>
</connection>
<connection>
<map_components component_2="rate_constants" component_1="I_h"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="V_S" variable_1="V_S"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="G_nonlin" component_1="I_h"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="stimulus_protocol" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="stimulus_protocol"/>
<map_variables variable_2="I_app" variable_1="I_app"/>
</connection>
<rdf:RDF>
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<vCard:FN>Geoff Nunns</vCard:FN>
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<vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname>
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<rdf:value>This model runs in PCEnv and is based off the NEURON code for this paper. The units are continuous throughout but the model does not recreate the published results. It utilizes DAE solving techniques and advances in these could result in better output.</rdf:value>
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<dc:title>Hyperpolarization-activated graded persistent activity in the prefrontal cortex</dc:title>
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<dcterms:W3CDTF>2008-05-20 00:00</dcterms:W3CDTF>
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<vCard:Given>Geoffrey</vCard:Given>
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<vCard:FN>Geoff Nunns</vCard:FN>
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<dc:title>Proceedings of the National Academy of Sciences</dc:title>
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<vCard:Given>Maria</vCard:Given>
<vCard:Family>Sanchez-Vives</vCard:Family>
<vCard:Other>V</vCard:Other>
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<vCard:Given>Alain</vCard:Given>
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<vCard:Given>Milena</vCard:Given>
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</model>
