Biomedical Engineering Reference
In-Depth Information
k
int
k
int
k
int
k
int
k
int
m
k
1
k
2
k
2
k
2
k
2
k
2
B2
B1
x
1
x
1
x
1
x
1
x
2
x
2
x
2
x
2
Fig. 14.12.
A simplified linear spring model of a particle simultaneously acted upon
by optical forces from a set of twin optical tweezers and a cellular interactive force
when a cell is in contact with the particle in the equilibrium trapping position of
the tweezers on the right
k
int
is force constant of the protein-protein interaction modeled as a linear
spring; and the rest of the symbols are the same as those described earlier
in association with (14.8). In (14.9), we have assumed that the equilibrium
position of the protein-protein interaction at the cellular membrane coincides
with that of the second optical tweezers; this was accomplished experimentally
by bringing the cell to touch the particle when it was stably trapped in the
second tweezers as is illustrated schematically in Fig. 14.12.
The steady-state solution at the fundamental frequency of (14.8) and
(14.9) above can be expressed as
x
(
t
)=
D
e
i(
ωt−φ
)
(14.10)
and
x
(
t
)=
D
e
i(
ωt−φ
)
− x
0
,
(14.11)
respectively, where
D
is the amplitude,
φ
the phase lag (with respective to
that of the driving source), and
x
0
the equilibrium position of the oscillating
particle.
Solving (14.8) with an assumed solution in the form of (14.10) gives
D
(
ω
)
D
(0)
k
k
2
+(
βω
)
2
=
(14.12)
− mω
2
