164 CATALYZING INQUIRY
Box 5.11
Levels of Biological Organization
One helpful approach is to consider a set of different, but interrelated, levels of biological organization:
- Organ system, in which the entire organ can be represented by a lumped-parameter systems model that
can be used to predict the gross behavior of the organ. In the case of the heart, one model can be based on the
notion of arterial impedance, which can be used to generate the dynamic pressure boundary conditions acting
on the cardiac chambers.
- Whole organ continuum, in which the physical behavior and dynamical responses of the organ can be
calculated from finite element methods that solve the continuum equations for the mechanics of the organ. In
the case of the heart, boundary conditions such as ventricular cavity pressures are computed from the lumped
parameter model in the top level. Detailed parametric models of three-dimensional cardiac geometry and
muscle fiber orientations have been used to represent the detailed structure of the whole organ with submil-
limeter resolution.^1
- Tissue, in which constitutive laws for the continuum models are evaluated at each point in the whole organ
continuum model and obtained by homogenizing the results of multicellular network models. That is, homog-
enization theory can be used to re-parameterize the results of a micromechanical analysis into a form suitable
for continuum-scale stress analysis. In the case of tissue mechanics for the heart, the basic functional units of
tissue are represented, such as laminar myocardial sheets as ensembles of cell and matrix micromechanics
models and, in some cases, the microvascular blood vessels as well.^2 A variety of approaches for these models
have been used, including stochastic models based on measured statistical distributions of myofiber orienta-
tions.^3 In cardiac electrophysiology, the tissue level is typically modeled as resistively coupled networks of
discrete cellular models interconnected in three dimensions.^4
- Single cell, in which different types of cells are represented. As a rule, single-cell models bridge to stochas-
tic state-transition models of macromolecular function through subcellular compartment models of represen-
tative tissue structures (e.g., the sarcomere in the case of the heart). Heart cells of different types to be modeled
are representative cells from different regions of the heart, such as epicardial cells, midventricular M-cells, and
endocardial cells. For mechanical models, individual myofibrils and cytoskeletal structures are modeled by
lattices and networks of rods, springs, and dashpots in one, two, or three dimensions.
- Macromolecular complex, in which representative populations of cross-bridges or ion channels are mod-
eled. Such complexes are typically described by Markov models of stochastic transitions between discrete
states of, for example, channel gating, actin-myosin binding, or nucleotide bound to myosin.
- Molecular model, in which single cross-bridges and ion channels are represented. Cross-bridges move
according to Brownian dynamics, and it is necessary to use weighted-ensemble dynamics to allow the simu-
lation to clear the energy barriers. (For example, a weighted-ensemble Brownian dynamics simulation of ion
transport through a single channel can be used to compute channel gating properties from the results of a
hierarchical collective motion (HCM) simulation of the channel complex.) The flexibility of the cross-bridges
themselves can be derived from the HCM method, and the interactions with other molecules can be comput-
ed using continuum solvent approximations.
- Atomic model, in which molecules are represented in terms of the positions of their constituent atoms in
crystallographic structures. (Such data can be found in public repositories such as the Protein Data Bank.)
Such data feed molecular dynamics simulations in order to build the HCM model.
The approach described above—of integrating models across structural and functional lines—is generally
adaptable to other tissues and organs, especially those with physical functions, such as lung and cartilage.
