Biophysical Models of the Cardiovascular System - Systems Biology: Networks, Models, and Applications - page 269

rather than as a function of Ca 2+ concentration in the common pool.
Models of this type can exhibit graded JSR Ca 2+ release; however, such
phenomenological formulations lack mechanistic descriptions of the
processes that are the underlying basis of CICR. Accordingly, in the
following presentation, we focus on properties of common pool
models and their extensions.

Modeling Ion Channels and Currents in Cardiac Myocytes
For many years, Hodgkin-Huxley models have been the standard for
describing membrane current kinetics [21,22]. However, data obtained
using new experimental approaches, in particular those for producing
recombinant channels by coexpression of genes encoding pore-forming
and accessory channel subunits in host cells, have shown that these
models have significant limitations. First, while these models can be
expanded to an equivalent Markov chain representation having multi-
ple closed and inactivated states [23], many single-channel behaviors
such as mean open time, first latency, and a broad range of other kinet-
ics behaviors cannot be described using these equivalent Markov
models [24,25]. Second, where it has been studied in detail,
Hodgkin-Huxley models are insufficient for reproducing behaviors
that may be critically state-dependent, such as how ionic channels
interact with drugs and toxins [26,27]. Accordingly, much recent effort
in modeling of cardiac ionic currents has focused on development of
biophysically detailed Markov chain models of channel gating. We will
therefore illustrate fundamental concepts involved in modeling of ion
channel function and membrane current properties using the example
of the cardiac LCC. Examples of the application of these modeling
methods to other sarcolemmal membrane currents abound (see I Na [28],
I to1 [29], and I Kr [30]).
The structure of the cardiac LCC model, adapted from Jafri et al. [11],
is shown in figure 9.3. The channel is assumed to occupy any of
11 states. The top row of closed states corresponds to zero to four
voltage sensors being activated (C 0 through C 4 ) plus an additional
conformational change required for opening (C 4 →

O). The bottom row
of closed-inactivated states corresponds to channel inactivation pro-
duced by local increases of Ca 2+ concentration within the subspace—a
mode of inactivation known as Ca 2+ -dependent inactivation.
Horizontal state transitions are assumed to be voltage-dependent
(with the exception of the C 4 → O transition) and closed to closed-

inactivated transitions (vertical transitions) are voltage-independent,
with rate dependent on Ca 2+ concentration in the subspace. Voltage-
dependence of transition rates is given by Eyring rate theory [23]:

kT
h

− ∆ H

RT

∆ S

R

zFV
RT

λ λ λ

(1)

λ = exp + +