Supplementary MaterialsS1 Text: Supplementary information including Tables A and B as well as Figs A, B and C. on VC results from sheep and pig ventricular trabeculae.[30] Obviously, there is a need to update rabbit AP models to incorporate an model based on rabbit data, but this is not a simple task. To date, activation parameters have been derived exclusively from VC protocols; however, since the current in the adult myocyte is usually too large to allow adequate voltage control under physiological conditions,[31] these VC protocols are carried out at low temperatures with low extracellular sodium concentrations or in HEK cells or oocyctes transfected with the SCN5A gene which encodes the cardiac channel (Nav 1.5). The first aim of this paper is usually to develop a parsimonious model for the rabbit myocyte AP based on data recorded from the rabbit under physiological conditions. A model is considered parsimonious if it accomplishes a desired level of explanation or prediction with as few parameters as possible (although, as far as we are aware, there is no definitive and scientifically rigorous definition GW788388 distributor of parsimonious). For this paper, the desired level of prediction is the following well-known and important electro-physiological phenomena, measured GW788388 distributor from rabbit ventricular myocytes/tissue under nearly identical and physiological conditions: 1) steady-state inactivation as decided from voltage clamp experiments [31]; 2) action potential depolarization in single cells; 3) recovery of AP excitability in single cells[32]; and 4) action potential depolarization dynamics during propagation in the whole heart. [33] For calibration and evaluation of the model we coupled this model with various models of Sub-model Formulization The equations of are of the form pioneered by Hodgkin-Huxley (HH) [1] is the transmembrane potential, is GW788388 distributor the maximal conductance of (fast activation) are gating variables, and (fast inactivation), and is the Nernst equilibrium potential for sodium. Beeler and Reuter [34] introduced a slow inactivation gate (models.[24C27]. The HH equations for the gating variables are of the form: represents each gating variable, equations contain 31 parameters. Since 1952 there has been significant advancement in the derivation of gating equations based on first principles.[35, 36] The simplest functional form for the rate equations of voltage dependent gating based on thermodynamics and chemical reaction rates are:[37] 1 are positive, while 0 for activation and 0 for inactivation. Using Eq 3 we can derive the equations for which is not realistic, because gating transformations cannot be instantaneous. For example, the LR1 equations predict and at 37 C, however these values Cd55 are below the resolution of voltage clamp measurements. We address this problem by removing the dependence of (making it a constant, thus eliminating parameter submodel using Eqs 1 and 3, with given by Eq 6, and equal to a constant. Parsimonious Rabbit (PR) Sub-model Calibration All model parameters are provided in Table 1. Values for and where taken directly from Table 1 in [31]. We set = 65and were computed via inverting Eq 6 given the two value pairs and with dt = 0.001 ms which is actually a very conservative choice made because of the low computational cost. The fact that is constant provides for a well-defined minimum time constant of the model which allows for the use of larger values of dt and computational efficiency compared to other models. [38] Cable simulations were performed using a central difference approximation of the Laplacian in a 4 cm long cable using = + (in order to establish a steady-state resting membrane potential) with diffusion.