Multiscale Computational Modeling in Vascular Biology: From Molecular Mechanisms to Tissue-Level Structure and Function - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 219

steps of biological ABMs can span a range of scales, from milliseconds to hours
[ 14 , 44 ], and simulation times can span years [ 1 ].
Outputs of ABMs include the spatial arrangements of agents within their
simulation space, their internal state, and the state of the environment. Spatial
patterns of agent organization may emerge during the simulation, and these can be
analyzed quantitatively. For example, in an ABM simulating angiogenesis, the
pattern of new microvessel growth can be assessed by measuring the new vascular
length, counting branch points of vessel trees, and quantifying the number of new
capillary sprouts that have developed over the course of the simulation time
window. Analyzing agent patterns using metrics that are also used to quantify
biological phenomena experimentally facilitates direct comparison of ABM pre-
dictions to experimental data, which enables rigorous model validation. Because
ABMs generalize intracellular processes, but are more fine-grained (discrete) than
is suitable for continuum analysis, they are uniquely suited to bridging disparate
biological scales.
3.3 Signaling Pathways and Illustrative
Vascular-Specific Models
Intracellular signaling pathways govern basic cell functions and allow cells to
adapt to their microenvironments. These signaling pathways consist of a complex
network of interacting molecules that give rise to a diverse range of cell functions
such as proliferation and differentiation. Often, an extracellular ligand binds to a
cell-surface receptor and triggers a cascade of intracellular interactions between
signaling molecules and second messengers that ultimately results in a change in
transcriptional activity, metabolism, or other regulatory function.
Because network elements of signaling pathways often overlap, the causal
relationship between input and output is not always explained by a linear series of
events. Furthermore, network motifs, such as positive and negative feedback
loops, make it difficult to deduce the relationships between the network elements
solely by intuition [ 2 ]. To better study and understand intracellular signaling
pathways and networks, a combination of experimental and mathematical
approaches have been used to disentangle the functions of the highly intercon-
nected components. Mathematical and computational Intracellular Signaling
Models (ISM) are used to contextualize experimental data and predict possible
emergent behaviors that are difficult to realize by experimentation alone. Through
cycles of model refinement and experimental validation, one can begin to
understand and probe the complexities of the signaling network and make pre-
dictions about how specific cellular functions arise.
These computational models predict dynamic behaviors of biochemical reac-
tions by using mathematical relations to describe the underlying molecular inter-
actions. Traditionally, ordinary differential equations (ODEs) are used to model