  Recent advances in microscopy and 3D reconstruction methods have allowed for
characterization of cellular morphology in unprecedented detail, including the
irregular geometries of intracellular subcompartments such as membrane-bound
organelles. These geometries are now compatible with predictive modeling of
cellular function. Biological cells respond to stimuli through sequences of
chemical reactions generally referred to as cell signaling pathways. The
propagation and reaction of chemical substances in cell signaling pathways can
be represented by coupled nonlinear systems of reaction-transport equations.
These reaction pathways include numerous chemical species that react across
boundaries or interfaces (e.g., the cell membrane and membranes of organelles
within the cell) and domains (e.g., the bulk cell volume and the interior of
organelles). Such systems of multi-dimensional partial differential equations
(PDEs) are notoriously difficult to solve because of their high dimensionality,
non-linearities, strong coupling, stiffness, and potential instabilities. In
this work, we describe Spatial Modeling Algorithms for Reactions and Transport
(SMART), a high-performance finite-element-based simulation package for model
specification and numerical simulation of spatially-varying reaction-transport
processes. SMART is based on the FEniCS finite element library, provides a
symbolic representation framework for specifying reaction pathways, and
supports geometries in 2D and 3D including large and irregular cell geometries
obtained from modern ultrastructural characterization methods.
