Multiscale Modeling of Primary Cilia - Multiscale Modeling in Biomechanics and Mechanobiology - page 100

Fig. 5.13 a Bending of a primary cilium with a variable length. The thick solid line is the equilibrium
profile for the cilium with a fixed length of unity. b The corresponding cilium length over time

mesenchymal cells) increased two-fold in 3 h [ 32 ]. After the application of fluid shear,
which is known to increase intracellular Ca 2 + and decrease intracellular cAMP, the
average cilia length decreased by 20-35 %. Furthermore, it has been demonstrated
that overloading of chondrocytes results in a decrease in cilia length and conversely
stress deprivation in tendon cells results in an immediate and significant increase in
length [ 93 , 94 ].
The slender-body model can incorporate the change of length due to the molecular
alterations that are part of the cilium dynamics under load. From the molecular
description we first have an empirical model for the cilium length [ 95 ]

d L
d t =

a
L −

b , (5.9)

d L

and the fluid velocity U in Eq. 5.5 should be replaced with U

d t x s . Coefficients
a and b are related to the assembly rate and disassociation rate at the cilium tip,
respectively. If we assume that a increases with the stress at the cilium base and b
remains constant, we find that (1) the cilium deflected more and (2) the cilium length
can increase almost 16 % before an equilibrium profile is reached, see Fig. 5.13 .
Another phenomenon that requires more experimental observations for accurate
multiscale modeling is the varying circumferential arrangement of the microtubule
doublets along the axoneme [ 96 , 97 ]. Although the cause of this nonhomogeneous
organization is unclear, it is most likely due to the lack of interconnecting attachments
such as nexin links between axonemal doublets. The mechanical consequence of
the disrupted circumferential organization may give rise to inhomogeneous bending
rigidity along the length of the cilium.

+

Acknowledgments YNY acknowledges helpful discussion with Jung-Chi Liao, and partial support
of NSF from grants CBET-0853673, DMS-0708977, and DMS-0420590 for the computing cluster
at NJIT. AMN acknowledges support from NIH through grant AR59038. CRJ is supported by
NIAM/NIH through grants AR45989, AR54156 and AR62177 and New York State Stem Cell
Research Grant N08G-210.