Mathematical models of canine right and left atria cardiomyocytes

Abstract

The aim of this study is to build two mathematical models of canine ionic currents specific to right atria and left atria. The canine left atria mathematical model was firstly modified from the Ramirez-Nattel-Courtemanche (RNC) model using the recently available experimental data of ionic currents and was further developed based on our own experimental data. A model of right atria was then built by considering the differences between right atria and left atria. The two developed models well reproduced the experimental data on action potential morphology, the rate dependence, and action potential duration restitution. They are useful for investigating the mechanisms underlying the heterogeneity of canine regional action potentials and would help the simulation of whole heart excitation propagation and cardiac arrhythmia in the near future.

Fig. 1

I-V relationships for I _K1 of the RNC model and our LA model Corresponding experimental values are also shown. Error bar is the scale of experimental data from our group and other investigators (Table 1), and filled squares are values used in our model to fit the I-V relationship

Fig. 2

Rapid delayed rectifier K⁺ current I _Kr: (a) Simulated current traces with LA model (inset, pulse protocol); (b) Results of I-V relationships from our modified models for both LA and RA The experimental values of RA and LA were also presented. The error bars indicate their variability obtained from our group and other investigators (Table 1)

Fig. 2

Rapid delayed rectifier K⁺ current I _Kr: (a) Simulated current traces with LA model (inset, pulse protocol); (b) Results of I-V relationships from our modified models for both LA and RA The experimental values of RA and LA were also presented. The error bars indicate their variability obtained from our group and other investigators (Table 1)

Fig. 3

Slow delayed rectifier K⁺ current I _Ks: (a) Simulated current traces with LA model (inset, pulse protocol); (b) Results of I-V relationships from our modified model for LA and the RNC model The experimental values of LA were also presented. The error bars indicate the variability of the experimental data obtained by our group and other investigators (Table 1)

Fig. 3

Slow delayed rectifier K⁺ current I _Ks: (a) Simulated current traces with LA model (inset, pulse protocol); (b) Results of I-V relationships from our modified model for LA and the RNC model The experimental values of LA were also presented. The error bars indicate the variability of the experimental data obtained by our group and other investigators (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 4

Transient outward K⁺ current I _to: (a) Steady-state activation curves from the RNC model and our modified LA model; (b) Activation time constant curve, derived from the RNC model; (c) Steady-state inactivation curves from the RNC model and our modified LA model; (d) Inactivation time constant curves for the RNC model and our modified LA model; (e) Simulated current traces with LA model by using voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships of LA model and RNC model The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 5

Ultra-rapid delayed rectifier K⁺ current I _Kur,d: (a) Simulation curves of voltage-dependent maximal conductance (G _Kur,d) for RNC model and our LA model; (b) Peak I-V relationships for RNC model and our LA model The experimental data summarized from Li et al. (2000, 2001) and Feng et al. (1998) are also shown as error bar scales

Fig. 5

Ultra-rapid delayed rectifier K⁺ current I _Kur,d: (a) Simulation curves of voltage-dependent maximal conductance (G _Kur,d) for RNC model and our LA model; (b) Peak I-V relationships for RNC model and our LA model The experimental data summarized from Li et al. (2000, 2001) and Feng et al. (1998) are also shown as error bar scales

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 6

L-type Ca²⁺ current I _CaL: (a) Model curves of voltage-dependent steady-state activation for RNC model and our LA model; (b) Activation time constant curve derived from RNC model; (c) Model curves of voltage-dependent steady-state inactivation for RNC model and our LA model; (d) Inactivation time constant curves for RA model (the same with RNC model) and LA model; (e) Simulated current traces with LA model by voltage-clamp experiments (inset, pulse protocol); (f) The peak I-V relationships for I _CaL of RNC model and LA model (also for RA model) The experimental data for the relevant parameters are also included. They were summarised from our own experiments and other published studies (Table 1)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 7

Simulation results of RA model and LA model under 1-Hz pacing. (a) Model action potential; (b) Typical calcium transient; (c) Inward rectifier current (I _K1); (d) L-type calcium current (I _CaL); (e) Transient outward current (I _to); (f) Ultra-rapid delayed rectifier current (I _Kur,d); (g) Rapid delayed rectifier current (I _Kr); (h) Slow delayed rectifier current (I _Ks)

Fig. 8

Comparison of rate dependence of APD from our RA model and the experimental data obtained by Li et al. (2001)

Fig. 9

Comparison of APDR curves between the RA and LA obtained with the dynamic restitution protocol