126 CATALYZING INQUIRY
other hand, statistical influence models are not causal and may not lead to a better understanding of
underlying mechanisms.
Quantitative models make detailed statements about biological processes and hence are easier to
falsify than more qualitative models. These models are intended to be predictive and are useful for
understanding points of control in cellular networks and for designing new functions within them.
Some models are based on power law formalisms.^21 In such cases, the data are shown to fit generic
power laws, and the general theory of power law scaling (for example) is used to infer some degree of
causal structure. They do not provide detailed insight into mechanism, although power law models
form the basis for a large class of metabolic control analyses and dynamic simulations.
Computational models—simulations—represent the other end of the modeling spectrum. Simula-
tion is often necessary to explore the implications of a model, especially its dynamical behavior, because
Box 5.2
On Graphical ModelsA large fraction of today’s knowledge of biochemical or genetic regulatory networks is represented either as
text or as cartoon-like diagrams. However, text has the disadvantage of being inherently ambiguous, and
every reader must reinterpret the text of a journal article. Diagrams are usually informal, often confusing, and
thus fail to present all of the information that is available to the presenter of the research. For example, the
meanings of nodes and arcs within a diagram are inconsistent—one arrow may mean activation, but another
arrow in the same diagram may mean transition of the state or translocation of materials.To remedy this state of affairs, a system of graphical representation should be powerful enough to express
sufficient information in a clearly visible and unambiguous way and should be supported by software tools.
There are several criteria for a graphical notation system, including the following:1.Expressiveness.The notation system should be able to describe every possible relationship among the
entities in a system—for example, those between genes and proteins in a biological model.
2.Semantical unambiguity.Notation should be unambiguous. Different semantics should be assigned to
different symbols that are clearly distinguishable.
3.Visual unambiguity.Each symbol should be identified clearly and not be mistaken with other symbols.
This feature should be maintained with low-resolution displays, using only black and white.
4.Extension capability.The notation system should be flexible enough to add new symbols and relationships
in a consistent manner. This may include the use of color coding to enhance expressiveness and readability,
but information should not be lost even with black-and-white displays.
5.Mathematical translation.The notation should be able to convert itself into mathematical formalisms, such
as differential equations, so that it can be applied directly for numerical analysis.
6.Software support.The notation should be supported by software for its drawing, viewing, editing, and
translation into mathematical formalisms.No current graphical notation system satisfies all of these criteria fully, although a number of systems satisfy
some of them.^1SOURCE: Adapted by permission from H. Kitano, “A Graphical Notation for Biochemical Networks,” Biosilico 1(5):159-176. Copyright
2003 Elsevier.(^1) See, for example, K.W. Kohn, “Molecular Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems,” Molecular
Biology of the Cell 10(8):2703-2734, 1999; K. Kohn, “Molecular Interaction Maps as Information Organizers and Simulation Guides,” Chaos
11(1):84-97, 2001.
(^21) E.O. Voit and T. Radivoyevitch, “Biochemical Systems Analysis of Genomewide Expression Data,” Bioinformatics 16(11):1023-
1037, 2000. (Cited in Arkin, 2001.)