An Elementary Bond Graph Approach to Structured Biological Modeling

Abstract

In many cases, modern large biological models snare the following properties:

• They are “system models” i. e. “reticulations” or interconnections of elementary boxes representing structural and/or functional entities or basic mechanisms.

• Various submodels use different formalisms: Dependent on our goals, some parts need physical modeling (electrical , mechanical or hydraulical networks, network thermodynamics); others have only black box models (compartments, chemical kinetics block diagrams.

• They are “lumped models”: time is the only independent variable. In each box, the spatial variations of internal quantities are ignored and signal exchange between boxes is instantaneous. These models are defined by only two sets of equations:

  • (i) “constitutive a lgebraic or ordinary differential equations” define each elementary box by relating constant parameters , variables and inputs ;

  • (ii) “topological algebraic equations” define the constraint s imposed on the variables by the model topology (i. e. blocks interconnection).

• They can be simulated with “state oriented simulation packages” which use an user supplied subroutine (called here MODEL) i. e. a procedural sequence of statements expressing the time derivatives of all state variables as functions of parameters, values of inputs and state variables.