Box 5.11Levels 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 submillimeter 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, homogenization 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 orientations.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 stochastic state-transition models of macromolecular function through subcellular compartment models of representative 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 modeled. 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 simulation 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 computed 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.

SOURCE: Adapted from A.D. McCulloch and G. Huber, “Integrative Biological Modelling in Silico,” pp. 4-25 in ‘In Silico' Simulation of Biological Processes No. 247, Novartis Foundation Symposium, G. Bock and J.A. Goode, eds., John Wiley & Sons Ltd., Chichester, UK, 2002.

1

F.J. Vetterand A.D. McCulloch, “Three-dimensional Analysis of Regional Cardiac Function: A Model of Rabbit Ventricular Anatomy,” Progress in Biophysics and Molecular Biology 69(2-3):157-183, 1998.

2

K. May-Newman and A.D. McCulloch, “Homogenization Modelling for the Mechanics of Perfused Myocardium,” Progress in Biophysics and Molecular Biology 69(2-3):463-481, 1998.

3

T.P. Usyk, J.H. Omens, and A.D. McCulloch, “Regional Septal Dysfunction in a Three-dimensional Computational Model of Focal Myofiber Disarray,” American Journal of Physiology 281(2):H506-H514, 2001.

4

L.J. Leon and F.A. Roberge, “Directional Characteristics of Action Potential Propagation in Cardiac Muscle: A Model Study,” Circulation Research 69: 378-395, 1991.

F.J. Vetterand A.D. McCulloch, “Three-dimensional Analysis of Regional Cardiac Function: A Model of Rabbit Ventricular Anatomy,” Progress in Biophysics and Molecular Biology 69(2-3):157-183, 1998.

K. May-Newman and A.D. McCulloch, “Homogenization Modelling for the Mechanics of Perfused Myocardium,” Progress in Biophysics and Molecular Biology 69(2-3):463-481, 1998.

T.P. Usyk, J.H. Omens, and A.D. McCulloch, “Regional Septal Dysfunction in a Three-dimensional Computational Model of Focal Myofiber Disarray,” American Journal of Physiology 281(2):H506-H514, 2001.

L.J. Leon and F.A. Roberge, “Directional Characteristics of Action Potential Propagation in Cardiac Muscle: A Model Study,” Circulation Research 69: 378-395, 1991.

From: 5, Computational Modeling and Simulation as Enablers for Biological Discovery

Cover of Catalyzing Inquiry at the Interface of Computing and Biology
Catalyzing Inquiry at the Interface of Computing and Biology.
National Research Council (US) Committee on Frontiers at the Interface of Computing and Biology; Wooley JC, Lin HS, editors.
Washington (DC): National Academies Press (US); 2005.
Copyright © 2005, National Academy of Sciences.

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