Location: The cardiac Na+ /K+ ATPase: An updated, thermodynamically consistent model @ 9a50ca6b7625 / Terkildsen_NaK_pump_update.aux

Author:
AnandR <a.rampadarath@auckland.ac.nz>
Date:
2019-02-15 15:17:13+13:00
Desc:
Added a note on curation and annotation at the end of the paper.
Permanent Source URI:
https://models.physiomeproject.org/workspace/578/rawfile/9a50ca6b76253e9dd80fdbd00c457887ff7a7839/Terkildsen_NaK_pump_update.aux

\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\citation{terkildsen_balance_2007}
\citation{terkildsen_balance_2007}
\citation{terkildsen_balance_2007,terkildsen_modelling_2006}
\citation{terkildsen_balance_2007}
\citation{terkildsen_balance_2007}
\citation{smith_development_2004}
\citation{nakao_[na]_1989}
\citation{nakao_[na]_1989}
\citation{hansen_dependence_2002}
\citation{nakao_[na]_1989}
\citation{friedrich_na+k+-atpase_1996}
\citation{terkildsen_balance_2007}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent }
\citation{lloyd_cellml:_2004}
\citation{oster_network_1971,gawthrop_energy-based_2014}
\citation{gawthrop_metamodelling:_1996}
\citation{borutzky_bond_2010}
\citation{gawthrop_bond-graph_2007}
\citation{apell_electrogenic_1989}
\citation{smith_development_2004}
\citation{keener_mathematical_2009}
\citation{terkildsen_balance_2007}
\citation{terkildsen_balance_2007}
\citation{tran_thermodynamic_2009,guynn_equilibrium_1973}
\@writefile{toc}{\contentsline {section}{\numberline {2}Modifications}{2}{section.2}\protected@file@percent }
\newlabel{sec:modifications}{{2}{2}{Modifications}{section.2}{}}
\newlabel{eq:detailed_balance}{{1}{2}{Modifications}{equation.2.1}{}}
\citation{smith_development_2004}
\citation{terkildsen_balance_2007}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \textbf  {Reaction scheme of the cardiac Na$^+$/K$^+$ ATPase model.} Numbers for each pump state (\textit  {blue boxes}) and reaction names (\textit  {green}) are labelled, with corrected parameters shown in red.\relax }}{3}{figure.caption.1}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:NaK_scheme}{{1}{3}{\textbf {Reaction scheme of the cardiac Na$^+$/K$^+$ ATPase model.} Numbers for each pump state (\textit {blue boxes}) and reaction names (\textit {green}) are labelled, with corrected parameters shown in red.\relax }{figure.caption.1}{}}
\citation{terkildsen_balance_2007}
\citation{terkildsen_balance_2007,terkildsen_modelling_2006}
\citation{terkildsen_modelling_2006}
\citation{nakao_[na]_1989}
\citation{nakao_[na]_1989}
\citation{kennedy_particle_1995}
\citation{terkildsen_modelling_2006}
\citation{nakao_[na]_1989}
\@writefile{toc}{\contentsline {section}{\numberline {3}Reparameterisation of the model}{4}{section.3}\protected@file@percent }
\newlabel{sec:raparameterisation}{{3}{4}{Reparameterisation of the model}{section.3}{}}
\citation{nakao_[na]_1989}
\citation{nakao_[na]_1989}
\citation{nakao_[na]_1989}
\citation{nakao_[na]_1989}
\citation{hansen_dependence_2002}
\citation{nakao_[na]_1989}
\citation{friedrich_na+k+-atpase_1996}
\citation{hansen_dependence_2002}
\citation{nakao_[na]_1989}
\citation{friedrich_na+k+-atpase_1996}
\citation{faber_action_2000,luo_dynamic_1994}
\citation{terkildsen_modelling_2006}
\citation{faber_action_2000,luo_dynamic_1994}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \textbf  {Model fit of the updated cardiac Na$^+$/K$^+$ ATPase model to current-voltage measurements.} \textbf  {(a)} Comparison of the model to extracellular sodium and voltage data \citep  [Fig. 3]{nakao_[na]_1989}, with cycling velocities scaled to a value of $55\si {s^{-1}}$ at $V = 40\si {mV}$. \textbf  {(b)} Comparison of the model to whole-cell current measurements \citep  [Fig. 2(a)]{nakao_[na]_1989}.\relax }}{5}{figure.caption.2}\protected@file@percent }
\newlabel{fig:fitting}{{2}{5}{\textbf {Model fit of the updated cardiac Na$^+$/K$^+$ ATPase model to current-voltage measurements.} \textbf {(a)} Comparison of the model to extracellular sodium and voltage data \citep [Fig. 3]{nakao_[na]_1989}, with cycling velocities scaled to a value of $55\si {s^{-1}}$ at $V = 40\si {mV}$. \textbf {(b)} Comparison of the model to whole-cell current measurements \citep [Fig. 2(a)]{nakao_[na]_1989}.\relax }{figure.caption.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \textbf  {Model fit of the updated cardiac Na$^+$/K$^+$ ATPase model to metabolite dependence data.} Simulation conditions are displayed on the right of each figure. \textbf  {(a)} Comparison of the model to data with varying intracellular sodium concentrations \citep  [Fig. 7(a)]{hansen_dependence_2002}, normalised to the cycling velocity at $\mathrm  {[Na]_i = 50\si {mM}}$. \textbf  {(b)} Comparison of the model to data with varying extracellular potassium \citep  [Fig. 11(a)]{nakao_[na]_1989}, normalised to the cycling velocity at $\mathrm  {[K]_e = 5.4\si {mM}}$. \textbf  {(c) } Comparison of the model to data with varying ATP \citep  [Fig. 3(b)]{friedrich_na+k+-atpase_1996}, normalised to the cycling velocity at $\mathrm  {[MgATP] = 0.6\si {mM}}$.\relax }}{6}{figure.caption.3}\protected@file@percent }
\newlabel{fig:metabolite_dependence}{{3}{6}{\textbf {Model fit of the updated cardiac Na$^+$/K$^+$ ATPase model to metabolite dependence data.} Simulation conditions are displayed on the right of each figure. \textbf {(a)} Comparison of the model to data with varying intracellular sodium concentrations \citep [Fig. 7(a)]{hansen_dependence_2002}, normalised to the cycling velocity at $\mathrm {[Na]_i = 50\si {mM}}$. \textbf {(b)} Comparison of the model to data with varying extracellular potassium \citep [Fig. 11(a)]{nakao_[na]_1989}, normalised to the cycling velocity at $\mathrm {[K]_e = 5.4\si {mM}}$. \textbf {(c) } Comparison of the model to data with varying ATP \citep [Fig. 3(b)]{friedrich_na+k+-atpase_1996}, normalised to the cycling velocity at $\mathrm {[MgATP] = 0.6\si {mM}}$.\relax }{figure.caption.3}{}}
\citation{faber_action_2000}
\citation{faber_action_2000}
\citation{faber_action_2000}
\citation{faber_action_2000}
\citation{gawthrop_energy-based_2014}
\citation{liebermeister_modular_2010}
\citation{gawthrop_energy-based_2014}
\citation{gawthrop_hierarchical_2015}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \textbf  {A comparison of the updated cardiac Na$^+$/K$^+$ ATPase model to existing models.} (a) The action potential waveform used for pump simulation \citep  {faber_action_2000}; (b) The Na$^+$/K$^+$ ATPase currents of the original and updated models; (c) A comparison of scaled versions of the updated and original models against the Na$^+$/K$^+$ ATPase model in \citet  {faber_action_2000}. The pump density was increased by a factor of 3.4 in the updated model, and by a factor of 3.9 in the original model. $\mathrm  {[Na^+]_i} = 10\si {mM}$, $\mathrm  {[Na^+]_e} = 140\si {mM}$, $\mathrm  {[K^+]_i} = 145\si {mM}$, $\mathrm  {[K^+]_e} = 5.4\si {mM}$, $\mathrm  {pH} = 7.095$, $\mathrm  {[Pi]_{tot}} = 0.8\si {mM}$, $\mathrm  {[MgATP]} = 6.95\si {mM}$, $\mathrm  {[MgADP]} = 0.035\si {mM}$, $T = 310\si {K}$.\relax }}{7}{figure.caption.4}\protected@file@percent }
\newlabel{fig:updated_original_comp}{{4}{7}{\textbf {A comparison of the updated cardiac Na$^+$/K$^+$ ATPase model to existing models.} (a) The action potential waveform used for pump simulation \citep {faber_action_2000}; (b) The Na$^+$/K$^+$ ATPase currents of the original and updated models; (c) A comparison of scaled versions of the updated and original models against the Na$^+$/K$^+$ ATPase model in \citet {faber_action_2000}. The pump density was increased by a factor of 3.4 in the updated model, and by a factor of 3.9 in the original model. $\mathrm {[Na^+]_i} = 10\si {mM}$, $\mathrm {[Na^+]_e} = 140\si {mM}$, $\mathrm {[K^+]_i} = 145\si {mM}$, $\mathrm {[K^+]_e} = 5.4\si {mM}$, $\mathrm {pH} = 7.095$, $\mathrm {[Pi]_{tot}} = 0.8\si {mM}$, $\mathrm {[MgATP]} = 6.95\si {mM}$, $\mathrm {[MgADP]} = 0.035\si {mM}$, $T = 310\si {K}$.\relax }{figure.caption.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Bond graph model}{7}{section.4}\protected@file@percent }
\newlabel{eq:bg_general}{{10}{7}{Bond graph model}{equation.4.10}{}}
\citation{terkildsen_balance_2007}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \textbf  {A comparison of the kinetic and bond graph cardiac Na$^+$/K$^+$ models.} $\mathrm  {[Na^+]_i} = 50\si {mM}$, $\mathrm  {[Na^+]_e} = 150\si {mM}$, $\mathrm  {[K^+]_i} = 0\si {mM}$, $\mathrm  {[K^+]_e} = 5.4\si {mM}$, $\mathrm  {pH} = 7.4$, $\mathrm  {[Pi]_{tot}} = 0\si {mM}$, $\mathrm  {[MgATP]} = 10\si {mM}$, $\mathrm  {[MgADP]} = 0\si {mM}$, $T = 310\si {K}$. The bond graph model is formulated using concentration ratios thus zero concentrations were approximated by a concentration of 0.001mM to avoid numerical errors.\relax }}{8}{figure.caption.5}\protected@file@percent }
\newlabel{fig:kinetic_BG_comp}{{5}{8}{\textbf {A comparison of the kinetic and bond graph cardiac Na$^+$/K$^+$ models.} $\mathrm {[Na^+]_i} = 50\si {mM}$, $\mathrm {[Na^+]_e} = 150\si {mM}$, $\mathrm {[K^+]_i} = 0\si {mM}$, $\mathrm {[K^+]_e} = 5.4\si {mM}$, $\mathrm {pH} = 7.4$, $\mathrm {[Pi]_{tot}} = 0\si {mM}$, $\mathrm {[MgATP]} = 10\si {mM}$, $\mathrm {[MgADP]} = 0\si {mM}$, $T = 310\si {K}$. The bond graph model is formulated using concentration ratios thus zero concentrations were approximated by a concentration of 0.001mM to avoid numerical errors.\relax }{figure.caption.5}{}}
\newlabel{eq:standard}{{11}{8}{Bond graph model}{equation.4.11}{}}
\citation{terkildsen_balance_2007}
\bibstyle{model2-names_edit}
\bibdata{bibliography}
\bibcite{apell_electrogenic_1989}{{1}{1989}{{Apell}}{{}}}
\bibcite{borutzky_bond_2010}{{2}{2010}{{Borutzky}}{{}}}
\bibcite{faber_action_2000}{{3}{2000}{{Faber and Rudy}}{{}}}
\bibcite{friedrich_na+k+-atpase_1996}{{4}{1996}{{Friedrich et~al.}}{{Friedrich, Bamberg and Nagel}}}
\bibcite{gawthrop_bond-graph_2007}{{5}{2007}{{Gawthrop and Bevan}}{{}}}
\bibcite{gawthrop_metamodelling:_1996}{{6}{1996}{{Gawthrop and Smith}}{{}}}
\bibcite{gawthrop_energy-based_2014}{{7}{2014}{{Gawthrop and Crampin}}{{}}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusion}{9}{section.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {6}Acknowledgements}{9}{section.6}\protected@file@percent }
\bibcite{gawthrop_hierarchical_2015}{{8}{2015}{{Gawthrop et~al.}}{{Gawthrop, Cursons and Crampin}}}
\bibcite{guynn_equilibrium_1973}{{9}{1973}{{Guynn and Veech}}{{}}}
\bibcite{hansen_dependence_2002}{{10}{2002}{{Hansen et~al.}}{{Hansen, Buhagiar, Kong, Clarke, Gray and Rasmussen}}}
\bibcite{keener_mathematical_2009}{{11}{2009}{{Keener and Sneyd}}{{}}}
\bibcite{kennedy_particle_1995}{{12}{1995}{{Kennedy and Eberhart}}{{}}}
\bibcite{liebermeister_modular_2010}{{13}{2010}{{Liebermeister et~al.}}{{Liebermeister, Uhlendorf and Klipp}}}
\bibcite{lloyd_cellml:_2004}{{14}{2004}{{Lloyd et~al.}}{{Lloyd, Halstead and Nielsen}}}
\bibcite{luo_dynamic_1994}{{15}{1994}{{Luo and Rudy}}{{}}}
\bibcite{nakao_[na]_1989}{{16}{1989}{{Nakao and Gadsby}}{{}}}
\bibcite{oster_network_1971}{{17}{1971}{{Oster et~al.}}{{Oster, Perelson and Katchalsky}}}
\bibcite{smith_development_2004}{{18}{2004}{{Smith and Crampin}}{{}}}
\bibcite{terkildsen_modelling_2006}{{19}{2006}{{Terkildsen}}{{}}}
\bibcite{terkildsen_balance_2007}{{20}{2007}{{Terkildsen et~al.}}{{Terkildsen, Crampin and Smith}}}
\bibcite{tran_thermodynamic_2009}{{21}{2009}{{Tran et~al.}}{{Tran, Smith, Loiselle and Crampin}}}
\@writefile{toc}{\contentsline {section}{\numberline {A}Parameters}{11}{appendix.A}\protected@file@percent }
\newlabel{sec:parameters}{{A}{11}{Parameters}{appendix.A}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces \textbf  {Kinetic parameters for the updated cardiac Na$^+$/K$^+$ ATPase model.} Refer to \autoref  {fig:NaK_scheme} for a schematic.\relax }}{11}{table.caption.6}\protected@file@percent }
\newlabel{tab:Terkildsen_parameters}{{1}{11}{\textbf {Kinetic parameters for the updated cardiac Na$^+$/K$^+$ ATPase model.} Refer to \autoref {fig:NaK_scheme} for a schematic.\relax }{table.caption.6}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces \textbf  {Parameters for the bond graph version of the updated cardiac Na$^+$/K$^+$ ATPase model.} Parameters were derived by using an intracellular volume of 38pL and an extracellular volume of 5.182pL. Refer to \autoref  {fig:Terkildsen_NaK} for the bond graph schematic.\relax }}{12}{table.caption.7}\protected@file@percent }
\newlabel{tab:bg_parameters}{{2}{12}{\textbf {Parameters for the bond graph version of the updated cardiac Na$^+$/K$^+$ ATPase model.} Parameters were derived by using an intracellular volume of 38pL and an extracellular volume of 5.182pL. Refer to \autoref {fig:Terkildsen_NaK} for the bond graph schematic.\relax }{table.caption.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {B}Bond graph model structure}{13}{appendix.B}\protected@file@percent }
\newlabel{sec:BG_structure}{{B}{13}{Bond graph model structure}{appendix.B}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \textbf  {Bond graph structure of the cardiac Na$^+$/K$^+$ ATPase model.} Pump states are coloured in blue, and reactions are coloured in green. The names for these components are consistent with their labels in \autoref  {fig:NaK_scheme}.\relax }}{13}{figure.caption.8}\protected@file@percent }
\newlabel{fig:Terkildsen_NaK}{{6}{13}{\textbf {Bond graph structure of the cardiac Na$^+$/K$^+$ ATPase model.} Pump states are coloured in blue, and reactions are coloured in green. The names for these components are consistent with their labels in \autoref {fig:NaK_scheme}.\relax }{figure.caption.8}{}}