Immobilization and Interaction Strategies in DFS of Biomolecular Partners - Dynamic Force Spectroscopy and Biomolecular Recognition - page 155

(a) (b)

x
β

0.45 nm
k 0 0.5 s -1

1 bond

p 1

2 bonds

F Σ

Δ L c [nm]

0.05
1
2
4

α 26 k B T

v 1

p 2

m/s
L c ,1 25 nm
a 0.7 nm

μ

AFM tip

0.02

k c 50 pN/nm
T 300 K

F 2
L c ,2

F 1
L c ,1

0.01

Bound
molecules

0 0

Substrate

50 100 150 200

Rupture force (pN)

FIGURE 4.9 Panel (a) shows two-bond rupture geometry. Panel (b) shows corresponding
probability of rupture forces for one- and two-bond ruptures for tethers of different lengths.
Significant shift in position of peak for two-bond ruptures can be noticed even for less than
10% difference in contour lengths of two linkers. In calculations, parabolic potential with
the cusp barrier was used in the kinetic model and the freely-jointed chain model extended
to fit stretching of PEG linkers in water was used for calculating dynamics of loading. The
legend and calculation parameters are shown in the graph. Here, x β is the distance from the
potential minimum to the transition state along the pulling direction, k 0 is the zero-force rate of
transition from the bound state, αis the depth of potential from the minimum to the transition
state in units of thermal energy k B T , v is the probe velocity, L c,1 is the contour length of a
shorter linker, a is the Kuhn length of polymeric linker, k c is the spring constant of the AFM
cantilever, T is the absolute temperature, and Δ L c is the difference between length of longer
and shorter linkers. (Reproduced from Guo, S. L. et al. 2010a. Journal of Physical Chemistry
C 114 (19):8755-8765.)

probe. Therefore, performing experiments by varying attachment density on the
probe might reveal contribution of multiple bonds to the data. Maximum number
of possible bonds obtained from Equation 4.1 can be used as a molar dilution factor
of biomolecules on the probe. Using this factor implies that dilution is performed
with polymers of approximately the same length. If dilution is performed with
shorter polymers, then the molar dilution factor should be higher. Assuming that
polymer attached to the surface occupies area that is approximately equal to π l rms ,

then by using Equation 4.1, the dilution factor of the back-filling polymer to the
polymeric linkers that hold recognition partner can be estimated by

C b
C 1 =

2 l rms , 1 R
l rms

(4.4)

, b