Biomedical Engineering Reference
In-Depth Information
this section, problem of multiple interactions is addressed by considering the follow-
ing questions: (1) What is the expected probability of the single-molecule interac-
tions in comparison to the multiple interactions and (2) How to distinguish effects of
multiple interactions in the measured data.
4.5.1 P
ROBABILITY OF
S
INGLE-
M
OLECULE
E
VENTS
It might be expected that if the radius of the probe curvature were so low so that only
one molecule can be attached at the apex, then there will be no problem of multiple
bond ruptures. It has been proposed that AFM probe equipped with carbon nanotube
at the apex is suitable for single-molecule measurements by covalent functionaliza-
tion with biological molecule of interest (Wong et al. 1998). However, preparation
of such probes is difficult and did not find wide spread use in DFS. Moreover, there
is still no guarantee that only one molecule will reside at the end of the nanotube
(Wong et al. 1998).
Probes with gold-coated tips usually have higher radius of curvature than the bare
probes (according to manufacturers' specification by 10-30 nm). Therefore, accord-
ing to Equation 4.1, it might be expected that such probes are more prone to the mul-
tiple bond artifacts than the uncoated probes. Thus, dilution of functionalized linkers
with chemically inert linkers is necessary to reduce number of multiple interactions
and such dilution should be more substantial for gold-coated probes. If probability of
forming bonds between multiple recognition partners on the tip and on the substrate
follows Poisson distribution, then fraction of events that involve rupture of
N
bonds
is (Tees et al. 2001)
P
tot
−
1
ln
1
1
P
tot
N
−
P
(
N
)=
(4.2)
N
!
where
P
tot
is the overall probability of detecting rupture events. Consequently, frac-
tional probability of rupturing more than one bond
P
mult
is
1
P
tot
−
1
ln
1
P
mult
=
1
−
(4.3)
1
−
P
tot
This equation indicates that multiple bond ruptures are expected to occur rather
often in DFS measurements if
P
tot
is high. For example, if
P
tot
=
.
5, then the mul-
tiple bond ruptures occur only approximately twice less as often as the single bond
ruptures. According to Equation 4.3, for multiple bond ruptures to constitute less
than 5% fraction of all bond ruptures the overall probability
P
tot
should be less than
10%.
If formation of bonds between recognition partners is not independent of each
other, then Poisson statistics does not apply and Equation 4.3 breaks down. This
might occur when recognition partners are multivalent or cluster during sample
preparation (Guo et al. 2010a). In this case, multiple interactions will occur more
often than predicted by Equation 4.3. Another assumption in estimation of fraction of
0
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