COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 123
give a framework for observations (as noted in Section 5.2.1) and thereby suggest what needs to be
measured experimentally and, indeed, what need not be measured—that is how to refine the set of
observations so as to extract optimal knowledge about the system. This is particularly true when models
and experiments go hand-in-hand. As a rule, several rounds of modeling and experimentation are
necessary to lead to informative results.
Carrying these general observations further, Selinger et al.^8 have developed a framework for un-
derstanding the relationship between the properties of certain kinds of models and the experimental
sampling required for “completeness” of the model. They define a model as a set of rules that maps a set
of inputs (e.g., possible descriptions of a cell’s environment) to a set of outputs (e.g., the resulting
concentrations of all of the cell’s RNAs and proteins). From these basic properties, Selinger et al. are able
to determine the order of magnitude of the number of measurements needed to populate the space of all
possible inputs (e.g., environmental conditions) with enough measured outputs (e.g., transcriptomes,
proteomes) to make prediction feasible, thereby establishing how many measurements are needed to
adequately sample input space to allow the rule parameters to be determined.
Using this framework, Salinger et al. estimate the experimental requirements for the completeness
of a discrete transcriptional network model that maps all N genes as inputs to all N genes as outputs in
which the genes can take on three levels of expression (low, medium, and high) and each gene has, at
most, K direct regulators. Applying this model to three organisms—Mycoplasma pneumoniae, Escherichia
coli, and Homo sapiens—they find that 80, 40,000, and 700,000 transcriptome experiments, respectively,
are necessary to fill out this model. They further note that the upper-bound estimate of experimental
requirements grows exponentially with the maximum number of regulatory connections K per gene,
although genes tend to have a low K, and that the upper-bound estimate grows only logarithmically
with the number of genes N, making completeness feasible even for large genetic networks.
5.2.9 Models Can Predict Variables Inaccessible to Measurement,
Technological innovation in scientific instrumentation has revolutionized experimental biology.
However, many mysteries of the cell, of physiology, of individual or collective animal behavior, and of
population-level or ecosystem-level dynamics remain unobservable. Models can help link observations
to quantities that are not experimentally accessible. At the scale of a few millimeters, Marée and
Hogeweg recently developed^9 a computational model based on a cellular automaton for the behavior of
the social amoeba Dictyostelium discoideum. Their model is based on differential adhesion between cells,
cyclic adenosine monophosphate (cAMP)^ signaling, cell differentiation, and cell motion. Using detailed
two- and three-dimensional simulations of an aggregate of thousands of cells, the authors showed how
a relatively small set of assumptions and “rules” leads to a fully accurate developmental pathway.
Using the simulation as a tool, they were able to explore which assumptions were blatantly inappropri-
ate (leading to incorrect outcomes). In its final synthesis, the Marée-Hogeweg model predicts dynamic
distributions of chemicals and of mechanical pressure in a fully dynamic simulation of the culminating
Dictyostelium slug. Some, but not all, of these variables can be measured experimentally: those that are
measurable are well reproduced by the model. Those that cannot (yet) be measured are predicted inside
the evolving shape. What is even more impressive: the model demonstrates that the system has self-
correcting properties and accounts for many experimental observations that previously could not be
explained.
(^8) D.W. Selinger, M.A. Wright, and G.M. Church, “On the Complete Determination of Biological Systems,” Trends in Biotechnol-
ogy 21(6):251-254, 2003.
(^9) A.F.M. Marée and P. Hogeweg, “How Amoeboids Self-organize into a Fruiting Body: Multicellular Coordination in
Dictyostelium discoideum,” Proceedings of the National Academy of Sciences 98(7):3879-3883, 2001.