COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 151
dates arbitrary geometries, explicit stochastic input, and specific small-scale events. Because the model
is built from the ground up, it can predict emergent behavior that would not be apparent from intuition
or qualitative description of the behavior of individual parts. On the other hand, the simulation requires
multiple runs of its stochastic, individual molecule-based model, and parametric relationships emerge
not from closed-form equations that demonstrate qualitative functional dependencies but from en-
sembles of many repeated simulations.
The trajectories generated by this model of L. monocytogenes motility display repeated runs and
pauses that closely resemble the actual nanoscale measurements of bacterial motion.^64 Further analysis
of the simulation state at the beginning and ends of simulated pauses indicate that there is no character-
istic step-size or pause duration in these simulated trajectories and that pauses can be caused both by
correlated Brownian motion and by synchronously strained sets of ActA-actin filament mechanical
links.
5.4.2.4.3 Morphological Control of Spatiotemporal Patterns of Intracellular SignalingFink and
Slepchenko studied calcium waves evoked by activation of the bradykinin receptor in the plasma
membrane of a neuronal cell.^65 The neuromodulator bradykinin applied to the cells produced a calcium
wave that starts in the neurite and spreads to the soma and growth cones. The calcium wave was
monitored with digital microscope imaging of a fluorescent calcium indicator. The hypothesis was that
interaction of bradykinin with its receptor on the plasma membrane activated production of inositol-
1,4,5-trisphosphate (InsP 3 ) that diffused to its receptor on the endoplasmic reticulum, leading to calcium
release.
Using the Virtual Cell software environment, they assembled a simulation model of this phenom-
enon.^66 The model contained details of the relevant receptor distributions (via immunofluorescence)
within the cell geometry, the kinetics of InsP 3 production (via biochemical analysis of InsP 3 in cell
populations and photorelease of caged InsP 3 in individual cells), the transport of calcium through the
InsP 3 receptor calcium channel and the sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA)
pump (from literature studies of single-channel kinetics and radioligand flux), and calcium buffering by
both endogenous proteins and the fluorescent indicator (from confocal measurements of indicator
concentrations).
The mathematical equations generated by this combination of molecular distributions and reaction
and membrane transport kinetics were then solved to produce a simulation of the spatiotemporal pattern
of calcium that could be directly compared to the experiment. The characteristic calcium dynamics re-
quires rapid, high-amplitude production of [InsP 3 ]cyt in the neurite. This requisite InsP 3 spatiotemporal
profile is provided, in turn, as an intrinsic consequence of the cell’s morphology, demonstrating how
geometry can locally and dramatically intensify cytosolic signals that originate at the plasma membrane.
In addition, the model predicts and experiments confirm that stimulation of just the neurite, but not the
soma or growth cone, is sufficient to generate a calcium response throughout the cell.
(^64) S.C. Kuo and J.L. McGrath, “Steps and Fluctuations of Listeria Monocytogenes During Actin-based Motility,” Nature
407(6807):1026-1029, 2000; J. McGrath, N. Eungdamrong, C. Fisher, F. Peng, L. Mahadevan, T.J. Mitchison, and S.C. Kuo, “The
Force-Velocity Relationship for the Actin-based Motility of Listeria Moncytogenes,” Current Biology 13(4):329-332, 2003. (Both
cited in Alberts and Odell, 2004.)
(^65) C.C. Fink, B. Slepchenko, I.I. Moraru, J. Schaff, J. Watras, and L.M. Loew, “Morphological Control of Inositol-1,4,5-
Trisphosphate-dependent Signals.” Journal of Cell Biology 147(5):929-935, 1999; C.C. Fink, B. Slepchenko, I.I. Moraru, J. Watras,
J.C. Schaff, and L.M. Loew, “An Image-based Model of Calcium Waves in Differentiated Neuroblastoma Cells,” Biophysical
Journal 79(1):163-183, 2000.
(^66) B.M. Slepchenko, J.C. Schaff, I. Macara, and L.M. Loew, “Quantitative Cell Biology with the Virtual Cell,” Trends in Cell
Biology 13(11):570-576, 2003.