Biomedical Engineering Reference
In-Depth Information
between voltage-gated membrane currents, membrane pumps, and exchangers
that regulate Ca
2+
, Na
+
and K
+
levels, and additional intracellular Ca
2+
cycling
processes in the cardiac myocyte—the DiFrancesco-Noble model of the Pur-
kinje fiber (8). This important model established the conceptual framework from
which all subsequent models of the myocyte have been derived (ventricular
myocytes (9-12); SA node cells (13-16), and atrial myocytes (17,18)). These
models have proven reproductive and predictive properties and have been ap-
plied to advance our understanding of myocyte function in both health and dis-
ease.
Each of the integrative models of the myocyte cited above are of a type
known as "common pool" models (19), the structure of which is shown in Figure
1B. In such models, Ca
2+
flux through both L-type Ca
2+
channels (LCCs) and
ryanodine-sensitive Ca
2+
release channels (RyRs) in the JSR membrane is di-
rected into a single common Ca
2+
compartment referred to as the subspace. The
subspace represents the total volume of the ~5,000 diadic spaces present in the
ventricular myocyte. Stern demonstrated that common pool models are structur-
ally unstable, exhibiting all-or-none Ca
2+
release except (possibly) over some
narrow range of model parameters (20). This instability occurs because Ca
2+
release from JSR produces a large, rapid increase of Ca
2+
concentration in the
subspace. This in turn results in a very strong positive feedback effect in which
increased binding of Ca
2+
to RyR induces further RyR channel opening and re-
lease of Ca
2+
. Despite this inability to reproduce experimentally measured prop-
erties of graded JSR Ca
2+
release, common pool models have been very
successful in reproducing and predicting a range of myocyte behaviors. This
includes properties of interval-force relationships that depend heavily on proper
dynamic modeling of intracellular Ca
2+
uptake and release mechanisms (21). In
the following sections we describe the components from which common pool
models are formed.
2.3. Model Components: Ion Channels and Currents
For many years Hodgkin-Huxley models have been the standard for de-
scribing membrane current kinetics (22). However, data obtained using new
experimental approaches, in particular those for producing recombinant chan-
nels by coexpression of genes encoding pore-forming and accessory channel
subunits in host cells, have shown these models to have significant limitations.
First, while these models can be expanded to an equivalent Markov chain repre-
sentation having multiple closed and inactivated states (24), many single chan-
nel behaviors such as mean open time, first latency, and a broad range of other
kinetic behaviors cannot be described using these equivalent Markov models
(6,25). Second, where it has been studied in detail, as is the case for cardiac Na
channels, Hodgkin-Huxley models are insufficient for reproducing behaviors
