Biomedical Engineering Reference
In-Depth Information
the concentration profiles of the different signaling molecules over time in
response to a stimulus. Mass action and Michaelis-Menten kinetics are common
ways to represent the reaction kinetics. These approaches have been used to
demonstrate how even relatively small and focused modules can exhibit emergent
behavior through feedback mechanisms [
11
]. If information about the spatial
distributions of the molecules is desired, partial differential equations (PDEs) are
used. ODEs and PDEs can then be implemented deterministically or stochastically.
Deterministic systems have no element of randomness while stochastic systems
incorporate probabilities in the evolution of the system output over time. The
choice of how the model is formulated depends upon how the modeler views the
system and the biological question being answered.
While modeling of intracellular signaling networks pertaining to blood vessels
is still a relatively young field, an increasing number of computational models are
being developed to study vascular function. To date, a few aspects of vascular
intracellular signaling have been prominently modeled. Proliferation of ECs and
the formation of vessels is one such area. For example, several intracellular sig-
naling network models have been developed to study vessel formation in the
context of vasculogenesis during embryonic development and angiogenesis in both
physiologic and pathophysiological cases [
37
,
45
,
52
]. In terms of particular sig-
naling pathways, those involving NO and calcium have received much attention in
recent computational models [
60
,
65
]. We will summarize some of the published
models of vascular signaling networks in the following paragraphs and highlight
the new understanding they produced.
As noted above, among other functions, NO is a key signaling molecule that
regulates tissue-level vasodilation by affecting cell-level (SMC) contraction. One
group modeled the NO/cGMP signaling pathway in vascular SMCs and repro-
duced NO/cGMP-induced smooth muscle relaxation effects, such as intracellular
Ca
2+
concentration reduction and Ca
2+
desensitization of myosin phosphorylation
and force generation [
65
]. The authors of this model proposed a cGMP feedback-
controlled soluble guanylate cyclase (sGC) decay from its activated to its basal
form and predicted that the intermediate form of sGC is the dominant steady-state
form of sGC under physiological NO stimulation. This model thus suggested that
the sGC desensitization by cGMP feedback may limit cGMP production over a
wide range of NO concentration, which may contribute to the robustness of the
response of vascular SMCs to small perturbations in NO. The different mathe-
matical models used to investigate the role of NO in microcirculatory physiology
have been reviewed in [
60
], and one of the overarching themes is that intracellular
signaling models can provide valuable insights into roles of NO in physiology,
especially because experimentally measuring tracer amounts and signaling events
of NO in biological tissue with the appropriate spatial and temporal resolutions is
difficult.
Calcium signaling is largely coupled to NO signaling. In the arterioles, SMCs
and ECs are coupled via the exchange of Ca
2+
along with other ions and the
paracrine diffusion of NO. The vascular response to the nonlinear interactions of
subcellular components and processes including Ca
2+
signaling have been studied
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