The Smith-Crampin Cardiac Sodium-Potassium Pump |  PDF |
Alice Boit (Bioengineering Institute, University of Auckland)
Table of Contents
The sodium-potassium pump is an essential component of cardiac myocyte electrophysiology and metabolism. This ATP-consuming transporter maintains the sodium and potassium electrochemical gradients across the cell membrane, e.g. maintaining the resting potential following an action potential. This mathematical model reduces the 15-state biophysically-based kinetic model of Läuger and Apell, Eur. Biophys. J. 13 (1986) 309, to a 4-state scheme. The simplification takes advantage of the fact that molecular processes in the kinetic scheme occur on greatly different timescales. Rapid transitions can be modeled assuming rapid equilibrium conditions.
The transition rates between the four states are associated with the transduction of free energy due to ATP cleavage during each cycle. In this way, a reduced computational effort is required to describe the kinetics of the system while the thermodynamic properties of the detailed model remain unchanged. Initial parameters for transition rates and equilibrium constants have been fitted to experimental data using an iterative minimisation algorithm. The reduced model has been used to investigate the dependency of the forward cycle rate of the pump on varying sodium and ADP concentrations, thereby contributing to modelling of metabolic disturbances associated with ischaemic disease.
The model is described here in CellML (the raw CellML description of the Smith-Crampin Sodium-Potassium Pump model can be downloaded in various formats as described in the section “Download This Model”). Figure 1 and Figure 2 show the detailed 15-state state diagram and the derived 4-state lumping scheme, respectively.
The complete original paper reference is cited below:
Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study, N. P. Smith, E. J. Crampin, 2004, Progress in Biophysics & Molecular Biology. (Full text (HTML) and PDF versions of the article are available on the Progress in Biophysics and Molecular Biology website.) PubMed ID: 15142754
smith_crampin_Na_K_pump_2004.xml — the raw XML.
smith_crampin_Na_K_pump_2004.html — an HTML version for browsing online.
smith_crampin_Na_K_pump_2004.pdf — a PDF version suitable for printing.
cellml_smith_crampin_Na_K_pump_2004.tar.gz — a gzipped tarball with the XML and this documentation.
smith_crampin_Na_K_pump_2004_maths.pdf — a PDF of the equations described in the model generated directly from the CellML description using the MathML Renderer.
