144 CATALYZING INQUIRY
a concrete system of differential and algebraic equations. This experimental geometry may assume well-
mixed compartments or a one-, two-, or three-dimensional spatial representation (e.g., experimental im-
ages from a microscope). Models are constructed from biochemical and electrophysiological data mapped
to appropriate subcellular locations in images obtained from a microscope. A variety of modeling approxi-
mations are available including pseudo-steady state in time (infinite kinetic rates) or space (infinite diffu-
sion or conductivity). In the case of spatial simulations, the results are mapped back to experimental
images and can be analyzed by applying the arsenal of image-processing tools that is familiar to a cell
biologist. Section 5.4.2.4 describes a study undertaken within the Virtual Cell framework.
Simulation models can be useful for many purposes. One important use is to facilitate an understand-
ing of what design properties of an intracellular network are necessary for its function. For example, von
Dassow et al.^53 used a simulation model of the gap and pair-rule gene network in Drosophila melanogaster
to show that the structure of the network is sufficient to explain a great deal of the observed cellular
patterning. In addition, they showed that the network behavior was robust to parameter variation upon
the addition of hypothetical (but reasonable) elements to the known network. Thus, simulations can also
be used to formally propose and justify new hypothetical mechanisms and predict new network elements.
Another use of simulation models is in exploring the nature of control in networks. An example of
exploring network control with simulation is the work of Chen et al..54 in elucidating the control of different
phases of mitosis and explaining the impact of 50 different mutants on cellular decisions related to mitosis.
Simulations have also been used to model metabolic pathways. For example, Edwards and Palsson
developed a constraint-based genome-scale simulation of Escherichia coli metabolism (Box 5.8). By ap-
plying successive constraints (stoichiometric, thermodynamic, and enzyme capacity constraints) to the
metabolic network, it is possible to impose limits on cellular, biochemical, and systemic functions,
thereby identifying all allowable solutions (i.e., those that do not violate the applicable constraints).
Compared to the detailed theory-based models, such an approach has the major advantage that it does
not require knowledge of the kinetics involved (since it is concerned only with steady-state function).
(On the other hand, it is impossible to implement without genome-scale knowledge, because only
genome-scale knowledge can bound the system in question.) Within the space of allowable solutions, a
particular solution corresponds to the maximization of some selected function, such as cellular growth
or a response to some environmental change. A more robust model accounting for a larger number of
pathways is also described in Box 5.8.
The Edwards and Palsson model has been used to predict the evolution of E. coli metabolism under
a variety of environmental conditions. In the words of Ibarra et al., “When placed under growth
selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700
generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico
model. These results open the possibility of using adaptive evolution of entire metabolic networks to
realize metabolic states that have been determined a priori based on in silico analysis.”^55
Simulation models can also be used to test design ideas for engineering networks in cells. For
example, very simple models have been used to provide insight into a genetic oscillator and a switch in
E. coli.^56 Models have also been used to test designs for the control of cellular networks, as illustrated by
(^53) G. Von Dassow, E. Meir, E.M. Munro, and G.M. Odell, “The Segment Polarity Network Is a Robust Developmental Module,”
Nature 406(6792):188-192, 2000.
(^54) K.C. Chen, A. Csikasz-Nagy, B. Gyorffy, J. Val, B. Novak, and J.J. Tyson, “Kinetic Analysis of a Molecular Model of the
Budding Yeast Cell Cycle,” Molecular Biology of the Cell 11(1):369-391, 2000.
(^55) R.U. Ibarra, J.S. Edwards, and B.O. Palsson, “Escherichia coli K-12 Undergoes Adaptive Evolution to Achieve in Silico Pre-
dicted Optimal Growth,” Nature 420(6912):186-189, 2002.
(^56) M.B. Elowitz and S. Leibler, “A Synthetic Oscillatory Network of Transcriptional Regulators,” Nature 403(6767):335-338,
2000; T.S. Gardner, C.R. Cantor, and J.J. Collins, “Construction of a Genetic Toggle Switch in Escherichia coli,” Nature
403(6767):339-342, 2000.