COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 127
human intuition about complex nonlinear systems is often inadequate.^22 Lander cites two examples.
The first is that “intuitive thinking about MAP [mitogen-activated protein] kinase pathways led to the
long-held view that the obligatory cascade of three sequential kinases serves to provide signal amplifi-
cation. In contrast, computational studies have suggested that the purpose of such a network is to
achieve extreme positive cooperativity, so that the pathway behaves in a switch-like, rather than a
graded, fashion.”^23 The second example is that while intuitive interpretations of experiments in the
study of morphogen gradient formation in animal development led to the conclusion that simple
diffusion is not adequate to transport most morphogens, computational analysis of the same experi-
mental data led the opposite conclusion.^24
Simulation, which traces functional biological processes through some period of time, generates
results that can be checked for consistency with existing data (“retrodiction” of data) and can also
predict new phenomena not explicitly represented in but nevertheless consistent with existing datasets.
Note also that when a simulation seeks to capture essential elements in some oversimplified and
idealized fashion, it is unrealistic to expect the simulation to make detailed predictions about specific
biological phenomena. Such simulations may instead serve to make qualitative predictions about ten-
dencies and trends that become apparent only when averaged over a large number of simulation runs.
Alternatively, they may demonstrate that certain biological behaviors or responses are robust and do
not depend on particular details of the parameters involved within a very wide range.
Simulations can also be regarded as a nontraditional form of scientific communication. Tradition-
ally, scientific communications have been carried by journal articles or conference presentations. Though
articles and presentations will continue to be important, simulations—in the form of computer pro-
grams—can be easily shared among members of the research community, and the explicit knowledge
embedded in them can become powerful points of departure for the work of other researchers.
With the availability of cheap and powerful computers, modeling and simulation have become
nearly synonymous. Yet, a number of subtle differences should be mentioned. Simulation can be used
as a tool on its own or as a companion to mathematical analysis.
In the case of relatively simple models meant to provide insight or reveal a concept, analytical
and mathematical methods are of primary utility. With simple strokes and pen-and-paper compu-
tations, the dependence of behavior on underlying parameters (such as rate constants), conditions
for specific dynamical behavior, and approximate connections between macroscopic quantities
(e.g., the velocity of a cell) and underlying microscopic quantities (such the number of actin fila-
ments causing the membrane to protrude) can be revealed. Simulations are not as easily harnessed
to making such connections.
Simulations can be used hand-in-hand with analysis for simple models: exploring slight changes in
equations, assumptions, or rates and gaining familiarity can guide the best directions to explore with
simple models as well. For example, G. Bard Ermentrout at the University of Pittsburgh developed XPP
software as an evolving and publicly available experimental modeling tool for mathematical biolo-
gists.^25 XPP has been the foundation of computational investigations in many challenging problems in
neurophysiology, coupled oscillators, and other realms.
Mathematical analysis of models, at any level of complexity, is often restricted to special cases that
have simple properties: rectangular boundaries, specific symmetries, or behavior in a special class. Simu-
lations can expand the repertoire and allow the modeler to understand how analysis of the special cases
(^22) A.D. Lander, “A Calculus of Purpose,” PLoS Biology 2 (6):e164, 2004.
(^23) C.Y. Huang and J.E. Ferrell, “Ultrasensitivity in the Mitogen Activated Protein Kinase Cascade,” Proceedings of the National
Academy of Sciences 93(19):10078-10083, 1996. (Cited in Lander, “A Calculus of Purpose,” 2004.)
(^24) A.D. Lander, Q. Nie, and F.Y. Wan, “Do Morphogen Gradients Arise by Diffusion?” Developmental Cell 2(6):785-796, 2002.
(Cited in Lander, 2004.)
(^25) See http://www.math.pitt.edu/~bard/xpp/xpp.html.