Page 22 - Mathematical Techniques of Fractional Order Systems

12 Mathematical Techniques of Fractional Order Systems

Osteoclasts are multinucleated cells, that result from mononucleated
hematopoietic stem fused with progenitors cells. As they both express
RANK (Receptor Activator of Nuclear Factor kB) and c-fms (Macrophage
Colony-stimulating Factor Receptor), by biding to RANKL (RANK-ligand)
and CSF-1 (Colony-stimulating Factor 1), respectively, these cells differenti-
ate into active osteoclasts capable of bone resorption. OPG
(Osteoprotegerin), a soluble decoy receptor for RANKL and a physiological
negative regulator of osteoclastogenesis, also plays an important role in
osteoclasts performance (Boyce, 2012; Raggatt and Partridge, 2010). It is
their generation rate that dictates the BMU extension, whereas their life span
determines the depth of the resorption (Bellido et al., 2014).
Osteoblasts are mononucleated cells that differentiate from MSC (mesen-
chymal stem cells). They are controlled by BMP (bone morphogenetic protein),
Wnt-signaling, vitamin D, among other factors. PTH (parathyroid hormone)
receptors in the osteoblasts upregulate the expression of RANKL, in the pres-
ence of the hormone, which binds to RANK expressed in osteoclasts precursors.
Thus, PTH promotes their activation and bone resorption. These cells also pro-
duce OPG, which inhibits osteoclastogenesis by binding to RANKL. The secre-
tion of OPG is reduced in response to PTH, which contributes further to
osteoclastogenesis. Osteoblasts can undergo apoptosis, differentiate into osteo-
cytes or into bone lining cells (Crockett et al., 2011; Roodman, 2004).
Bone resorption and formation is mainly regulated by the RANK/
RANKL/OPG pathway and PTH. It is activated by either mechanical stimuli
on the bone, or due to systemic changes in homeostasis which result in the
production of estrogen or PTH (Raggatt and Partridge, 2010). The latter is
triggered in response to a reduced calcium concentration, which leads to cal-
cium release from the bone matrix, and is inhibited when an elevated cal-
cium concentration is sensed (Silva and Bilezikian, 2015). The remodeling
process begins when PTH triggers two mechanisms in the osteoblasts: (1)
the existing PTH reduces the osteoblasts secretion of OPG that, by being a
soluble decoy receptor for RANKL and allowing it to consequently bind to
RANK, promotes osteoclastogenesis; (2) PTH receptors also upregulate the
expression of RANKL, which again binds to RANK, further promoting oste-
oclast activation and bone resorption (Raggatt and Partridge, 2010). The ini-
tiation of the formation phase is coupled to the resorption phase in a process
not yet fully understood, as factors released from the bone matrix during
resorption (Insulin Growth Factors I and II (IGF-I, IGF-II), and
Transforming Growth Factor-β (TGF-β)) may be involved in this coupling.
Bone formation takes place even in the presence of malfunctioning osteo-
clasts, which has led to the hypothesis that osteoclasts produce the coupling
factors responsible for attracting and regulating osteoblasts to the sites of
bone resorption (Boyce, 2012). At the resorpted site, osteoblasts commence
bone formation and replace the resorpted bone by the same amount, ending
the bone remodeling cycle.