184 CATALYZING INQUIRY
Box 5.18
The MCell Simulator
MCell is a general Monte Carlo simulator of cellular microphysiology. MCell simulations provide insights into
the behavior and variability of real systems comprising finite numbers of molecules interacting in spatially
complex environments. MCell incorporates high-resolution physical structure into models of ligand diffusion
and signaling, and thus can take into account the large complexity and diversity of neural tissue at the subcel-
lular level.
MCell is based on the use of rigorously validated Monte Carlo algorithms to track the evolution of biochemical
events in time and three-dimensional space for individual ligand and effector molecules. That is, the Monte
Carlo approach is based on the use of random numbers and probabilities to effect the simulation of individual
cases of the system’s behavior.
In the MCell models used in neural signaling employing a Brownian dynamics random walk algorithm, indi-
vidual ligand molecules move according to a three-dimensional Brownian dynamics random walk and en-
counter membrane boundaries and effector molecules as they diffuse. Bulk solution rate constants are con-
verted into Monte Carlo probabilities so that the diffusing ligands can undergo stochastic chemical interactions
with individual binding sites such as receptor proteins, enzymes, and transporters. These interactions are
governed by user-specified reaction mechanisms.
The diffusion algorithms are grid-free, and the reaction algorithms are at the level of interactions between
individual molecules and thus do not involve solving systems of differential equations. Membrane boundaries
are represented as triangle meshes and may be of arbitrary complexity.
The Monte Carlo approach has certain important advantages over the finite element (FE) approach often used
to include spatial information in kinetic modeling. The FE approach divides three-dimensional space into a
regular grid of contiguous subcompartments, or voxels. It assumes well-mixed conditions within each voxel
and uses differential equations to compute fluxes between, and reactions within, each voxel. Mass action
equations are based on continuum processes and predict average concentrations. In large, simple volumes
with great numbers of a few types of molecules (e.g., reactions in a test tube), fluctuations are relatively small,
and knowledge of average concentrations accounts most of the interesting phenomena. However, synaptic
signaling is inherently discrete and stochastic because the number of molecules involved is small; hence, the
FE method will fail to describe accurately the biochemistry of synaptic signaling because these methods
provide only averaged data. Furthermore, complex cellular structures—such as the structures that characterize
the synapse—require that the voxel grid be very fine and irregular in shape, making an FE approach both
computationally expensive and difficult to implement.
MCell is very general because it includes a high-level model description language (MDL), which allows the
user to build subcellular structures and signaling pathways of virtually any configuration. MCell’s algorithms
scale smoothly from typical workstations to shared-memory multiprocessor machines to massively parallel
supercomputers.
SOURCE: For more information, see http://www.mcell.cnl.salk.edu; J.R. Stiles and T.M. Bartol, Jr., “Monte Carlo Methods for Simulating
Realistic Synaptic Microphysiology Using MCell,” pp. 87-127 in Computational Neuroscience: Realistic Modeling for Experimentalists, E. de
Schutter, ed., CRC Press, Boca Raton, FL, 2000; J.R. Stiles, T.M. Bartol, Jr., E.E. Salpeter, M.M. Salpeter, and T.J. Sejnowski, “Synaptic
Variability: New Insights from Reconstructions and Monte Carlo Simulations with MCell,” pp. 681-731 in Synapses, W. Cowan, T.C. Sudhof,
and C.F. Stevens, eds., Johns Hopkins University Press, Baltimore, MD, 2001. Discussion of the pros and cons of FE versus MC is from K.M.
Franks and T.J. Sejnowski, “Complexity of Calcium Signaling in Synaptic Spines,” BioEssays 24(12):1130-1144, 2002.
