226 6.4 Magnetic Force Methods
tapping beads, the probability Pteth(n) for forming n tethers is given by
( 〈〉
−〈〉
[
]
n n
n
n
exp
/ ! , thus at n = 0,
P
n
n
tech
top
0
1 1
( ) =
−〈〉
[
] =
−
(
)
exp
/
Thus,
〈〉=
−
(
)
(
)
n
n
n
tap
tap
In
/
1
d
Fraction of binding events in which >1 tether is formed:
α =
= −
−
−
p
p
p
p
p
p
tech
tech
tech
tech
tech
tech
(>1)
(1)
(>1)
1
(0)
(1)
1
(0)
= −
−〈〉−〈〉
−〈〉
−
−〈〉
1 exp[
]
exp[
]
1 exp[
]
n
n
n
n
e
No more than 0.1% tethers due to multiple tether events implies 1 in 103 or less
multiple tethers. At this threshold value, a = 0.001, indicating (after, e.g., plotting
the dependence of a on ntap from [d] and interpolating) ntap ~ 600 cycles. At 1 Hz,
this is equivalent to ~600 s, or ~10 min for a tether to be formed on average.
6.4 MAGNETIC FORCE METHODS
Magnetism has already been discussed as a useful force in biophysical investigations in the
context of structural biology determination in NMR spectroscopy as well as for the gener
ation of x-rays in cyclotrons and synchrotrons for probing biological matter (Chapter 5).
But magnetic forces can also be utilized to identify different biomolecules from a mixed
sample and to isolate and purify them; for example, using magnetic beads bound to bio
logical material to separate different molecular and cellular components, or using a mag
netic field to deflect electrically charged fragments of biomolecules with the workhorse
analytical technique of biophysics, which is mass spectrometry. Also, magnetic fields can
be manipulated to generate exquisitely stable magnetic tweezers. Magnetic tweezers can
trap a suitable magnetic particle, imposing both force and torque, which can be used to
investigate the mechanical properties of single biomolecules if tethered to the magnetic
particle.
6.4.1 MAGNETIC BEAD–MEDIATED PURIFICATION METHODS
Magnetic beads are typically manufactured using a latex matrix embedded with iron oxide
nanoscale particulates, or other similar ferromagnetic materials such as chromium dioxide. If
the concentration of ferromagnetic material in a bead is sufficiently small, then in the absence
of an external B-field such beads possess no net magnetic moment. In the presence of an
external B-field, the whole resultant bead is magnetized by induction of a magnetic moment
aligned with the B-field, but which is lost once the external B-field is removed. This is a prop
erty of paramagnetic materials, distinct from ferromagnetic materials, which can retain a net
magnetic moment after the external B-field is removed. This is a particularly useful feature
of beads used for biological purification/isolation methods, since removal of an imposed B-
field can then permit separation of components after being isolated from a mixture using a