Abstract
While the primary function of the heart is a pump, ironically, the
development of myofilament models that predict developed force have
generally lagged behind the modeling of the electrophysiological
and Ca$^2+$-handling aspects of heart cells. A major impediment
is that the basic events in force generating actin-myosin interactions
are still not well understood and quantified despite advanced techniques
that can probe molecular levels events and identify numerous energetic
states. As a result, the modeler must decide how to best abstract
the many identified states into useful models with an essential tradeoff
in the level of complexity. Namely, complex models map more directly
to biophysical states but experimental data does not yet exist to
well constrain the rate constants and parameters. In contrast, parameters
can be better constrained in simpler, lumped models, but the simplicity
may preclude versatility and extensibility to other applications.
Other controversies exist as to why the activation of the actin-myosin
is so steeply dependent on activator Ca$^2+$. More specifically
steady-state force-Ca$^2+$ (F-Ca) relationships are similar
to Hill functions, presumably as the result of cooperative interactions
between neighboring crossbridges and/or regulatory proteins. We postulate
that mathematical models must contain explicit representation of
nearest-neighbor cooperative interactions to reproduce F-Ca relationships
similar to experimental measures, whereas spatially compressing,
mean-field approximation used in most models cannot. Finally, a related
controversy is why F-Ca relationships show increased Ca$^2+$
sensitivity as sarcomere length (SL) increases. We propose a model
that suggests that the length-dependent effects can result from an
interaction of explicit nearest-neighbor cooperative mechanisms and
the number of recruitable crossbridges as a function of SL.
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