Modelling Beta-adrenergic Control of Cardiac Myocyte Contractility in Silico

In 2003, Saucerman et al. published a mathematical model which describes the beta-adrenergic signalling network in cardiac myocytes. This model of the signal transduction pathway was then embedded within an extension of the Luo-Rudy Ventricular Model II (dynamic), 1994, which was modified for the rabbit ventricular myocyte (Puglisi-Bers Rabbit Ventricular Myocyte Model, 2001). The model was further adapted by including the equations for the L-type calcium channel from the Jafri-Rice-Winslow Ventricular Model (I_Ca,L), and also the steady-state potassium current (I_ss), and the calcium-independent transient outward potassium current (I_t), from the Pandit et al. Adult Rat Left Ventricular Myocyte Model, 2001.

This example is naturally illustrated by use of the import feature of CellML 1.1. Components are imported into the Saucerman et al. 2003 model from the adapted Puglisi et al. 2001 model. The imported variables (membrane potential V and intracellular calcium concentration Ca_i) from the Puglisi model are then connected up to the relevant components in the Saucerman et al. model.

Since all the models involved in this current Saucerman et al. model have been previously coded up in CellML1.0 (listed above), it was possible to use the import feature of CellML1.1 to produce the adapted Puglisi-Bers model, without having to code it up from scratch. The modified Puglisi-Bers model can be seen in the section “Download This Model” below.

In cardiac myocytes, the beta-adrenergic signalling network is triggered in response to norepinephrine and epinephrine binding to the Gs-protein coupled beta-adrenergic receptor. Receptor-ligand binding activates the coupled Gs-protein, which in turn activates adenylate cyclase. ATP is converted into the secondary messenger cyclic AMP (cAMP). cAMP promotes dissociation of the protein kinase A (PKA) holoenzyme, whose catalytic subunits go onto phosphorylate a wide range of target proteins, two of which are the L-type calcium channel and phospholamban - which both play essential roles in the regulation of calcium dynamics and transport. In healthy cardiac myocytes, the end result of this signal transduction pathway is to provide coordinated control of contractility, metabolism and gene regulation. However, altered beta-adrenergic signalling may also play a role in the progression of heart failure.

Molecular components of this signalling pathway have been studied in detail as potential therapeutic targets in heart failure. However, the situation is complex, with intracellular compartmentation and functional integration of pathways being suggested as playing an important role in the signalling outcome. Systems level mathematical modelling will help make sense of large quantities of experimental data. Since The Hodgkin-Huxley Squid Axon Model was published in 1952, many ionic models of cell electrophysiology have been developed. Recently systems modelling has been identified as a potential method for improving understanding of signaling networks and the response to genetic and pharmaceutical perturbations.

While to date, portions of the mammalian beta-adrenergic signalling network have been described by mathematical models of neuron and HEK-293 cells, no analysis has modelled and validated an entire pathway from ligand to effectors such that neuro-hormonal regulation of cell physiology can be predicted. In the publication described here, Jeffrey Saucerman et al. have developed a systems biology model to investigate the molecular mechanisms underlying the control of the beta-adrenergic signalling network over cardiac myocyte contractility (see Figure 1 below). The model was validated using a wide range of experimental data, and model simulations were used to investigate quantitatively the effects of specific molecular perturbations (with potential for pharmaceutical testing). By performing systems analysis the effects of molecular perturbations in the beta-adrenergic signalling network may be understood within the context of integrative physiology.

The complete original paper reference is cited below:

Modeling beta-adrenergic control of cardiac myocyte contractility in silico, Jeffrey J. Saucerman, Laurence L. Brunton, Anushka P. Michailova, and Andrew D. McCulloch, 2003, Journal of Biological Chemistry, 48, 47997-48003. (Full text (HTML) and PDF versions of the article are available on the Journal of Biological Chemistry website.)

Figure 1. Schematic diagram of the integrated model components, including the beta-adrenergic network, calcium handling, and the electrophysiology of the rat ventricular myocyte.